Eye Makeup Techniques for Different Occasions

There are a multitude of eye makeup techniques using only a mascara, a very versatile product that any woman can use to modify their appearance. Besides all the colors like black, blue, brown, there is also the mascara to lengthen lashes without much color.

When it comes to applying mascara, there are different techniques that can be used depending on if it works or not with the upper and lower lashes. For best results with the lower lashes, hold the mascara so that only the edge of the brush touches the tip of the lashes of the lower eyelids with a new sweep, forward and backward.

If you have dark circles, dark mascara on top lashes tend to emphasize those circles under the eyes making them look even darker, so you should use a lighter shade or even not to use mascara. And remember to use mascara too often can weaken the eyelashes causing severe damage.

When you apply mascara on top lashes, try to use as close to the root of the lashes as possible to make them look thicker and full. Let dry for 10 seconds mascara or so before applying another layer and then with a tissue under the eyes, blinking several times to finish the excess tissue and not in your cheeks. You should keep your old mascara cleaning brushes for use as separate tabs or apply a little Vaseline on the eyebrows to straighten or lengthen lashes without any color.

The different techniques using eye makeup eyeliner, either liquid or pencil, they can also change your appearance as much more subtle to dramatic. The eyeliner can really make eyelashes look longer and eyes look bigger, or create any effect you want. Always apply eyeliner to the outer edge of the eyelid and never in the inner edge near the eye. The eyeliner also should be used sparingly unless you're trying to be truly remarkable aspect.

Use a variety of shades can easily change your look with exotic barely visible to a few eye makeup techniques different. Today there are sets of eye shadows that are sold together for for different eye colors, so you dont need to investigate what colors you use, depending on your complexion or eye color.

With any simple technique of eye makeup you can call attention to the most intriguing to have a face look beautiful and above all be the focus of the festival or event to attend.

Seven Car Insurance Tips

Now we offer a number of useful tips for hiring a car insurance.

Increase your deductible

The deductible is the amount you pay from your pocket before making a car insurance claim. The disadvantage of raising your claim is when you do ... you'll pay more. However, if you're a safe driver, whom overtime give greater savings by increasing your insurance deductible, you'll have to look at your previous insurance claim history and make a decision based on it.

Collision Coverage

If your car is not worth much, why pay for car insurance coverage against all risks and collision? You can visit a variety of places online to find real value of your vehicle.

Use of low mileage

Some auto insurers offer discounts if you drive less than a certain number of miles you travel short distances or even your job.

Consider your insurance payments

If you consider your move will be a good idea to call your insurance agent and obtain their opinion on the insurance costs in the new city or state.

Low profile cart

Your car determines the cost of insurance in general. Some cars are favorite for thieves, then it will be difficult to find a good price. Some cars are more expensive to repair. It makes sense to do the proper amount of research before you buy your auto insurance.

Make sure your car is correctly listed by your insurance agent

Many manufacturers offer similar model names to your car, but car insurance costs vary. Also, if your car has 2 or 4 doors or model you were wrong, it can affect your car insurance quote.

Ask your insurance agent to check other insurance company discounts

Many insurers offer discounts if you and your spouse are insured with the same insurer. Also, if you're looking for home insurance or life insurance receive some discounts. Check with your auto insurance agent about the savings you can make.

Gossip of the nonsense

Zulma Lobato's career in the world of Chimento, started on a cable news channel. Because of its poor image and bad performance in the song became the pearl of almost all the programs dedicated to collecting the oddities of the TV. Last week, journalist Susan Roccasalva shows in its program of Channel 26, called Lobato to the living room of his program, which also was Mitch, another media personality, which around the time a man tried to Zulma; this response was bashed on camera. After the hidden camera show, they did last Saturday in Passion Saturday, Ricky bailantero Wonder began to beat the players who participated in this joke. Ricky beat the participants of the hidden camera when they tried to "cats" their "Rikytas." Neither the driver nor his partner Hernan Caire, Marcela Bathrooms, could believe what was happening live in America. Although no longer on the air the program Dancing for a Dream (now absent from the screen), chimenteros cycles must adapt to the changing course of ShowMatch, now 20 years old who has wagered the humor.Así, with winds of renewal, Guido reappeared Sullen, who on "The Professionals Always" featured his alleged 20 year old son, whom he met through Facebook.

Alleged false paternity was confirmed this past Saturday night in the program 70.20.10, led by Chiche Gelblung. In this television cycle, Guido Sullen confirmed that although he had just checked it was not his biological child in the future would adopt and take care as such. Log in to vote and I will vote for your fan!

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Cultural Penetration

To maintain the condition of a dependent country needed a cultural superstructure designed to prevent knowledge of their identity. This superstructure is organized on the basis of a set of organizations and practices planned and developed by the imperialist powers and their internal operations, the native oligarchies.

Arturo Jauretche in the prophets of hate and bonus, creates the concept of "Driving Educational Colonization? To define how it is organized and develops cultural dependence. The figure of "Apparatus? can display a set of organizations, acting with the same goal to create and sustain addiction. The concept of "colonization?, Allows us to understand culture as a political space whose function is directly related to the maintenance of this unit. The idea of ​​"pedagogy? to understand that this process involves a long-range educational function, which is exercised through the "Device? in order to "colonize?.

The nineteenth and twentieth centuries, showed an acceleration of events, at first glance, would mark fundamental changes in the history of mankind. In light of reality offered by the twenty-first century, it appears that no such changes, but different makeup for the same face. The inhuman face of savage capitalism, the Western world, which now takes the name of "globalization?

Until the seventeenth century, the agricultural economy of Europe was farming a double problem: on the one hand, a chronic shortage of winter feed for their livestock, forcing it to sacrifice a large part in the fall and keep your meat for winter consumption, which which produced a great demand for spices for flavoring and preservation.

The seasoning was salt cheaper, coming mostly from Portugal. But the most effective spices: pepper, cinnamon, nutmeg, ginger, occurred in the East. This market also gave him to Europe, luxury items such as silk, perfumes, velvet, porcelain, with great benefits for traders.

One of the first in the exploration of new routes in search of these markets, were the Portuguese. During 1400, around? Africa, came to the ocean? Index. Then pass the Spanish adventure with Christopher Columbus, who came to America, but never found out.

Between the fifteenth and seventeenth centuries, Europeans go hunting. Your stop is America? Africa, the invaders found civilizations that had achieved a remarkable development. In America, though, some people lived in huts and had a very simple social organization, there were also some much more advanced.

The Aztecs, in the current region of Mexico, were a powerful union of diverse peoples. Its capital Tenochtitlan was described with amazement by Hernan Cortez, in a letter to Charles V: "cities as large as Seville and Cordoba, (...) there are several places that serve the market, among them, there is a larger than the city of Salamanca, surrounded by porticoes, where more than 60,000 souls, bought and sold continuously and in large numbers, all food and goods that are in the rest of the universe?

The Aztecs used pictographic writing, on paper or animal skin. Education, very strict, was taught from childhood: music, religion, history, mathematics, interpretation of the codices, martial arts, writing, timing and knowledge of other disciplines. Men are inculcated warrior vocation.

The Maya, located in Central America, leaving signs of a phenomenal architecture, seen in the ruined cities of Palenque, Uxmal, Mayapan, Copán, Tikal, Chichen Itzzá, and others.,

They were skilled weavers, produced fine pottery, unsurpassed in the Spanish colonies. They developed a hieroglyphic writing, and recorded their mythology, history and ritual, into blocks or pillars of stone, on paper made of tree bark and animal skin parchment., Later in the sixteenth century in, Mayan language, but Latin alphabet, there are two of the most valuable texts of pre-Columbian culture, the Popol Vuh and the Books of Chilan Balan. They had advanced astronomical and mathematical knowledge. . They created a calendar of 365 days, more accurate than all known to the Gregorian calendar. Gave a value different from the figures, according to their position, and found zero, which had failed the Egyptians, Sumerians, Greeks and Romans.

The Incas in South America, structured a powerful empire that stretched from Ecuador and southern Colombia to northern Chile and northern and central Argentina stop. Headquarters (Cuzco) and major cities were in Peru and Bolivia. They built magnificent temples, fabulous palaces and mighty fortresses, such as Machu Picchu.

Built more than 16,000 kms. roads, (as well paved, which are still used) and suspension bridges, to connect and communicate to the empire. To develop agriculture on the mountain terraces and created an irrigation system which is still preserved. Metal handles very well and created an accounting system and communication through multicolored Tweety strategic nodes, called "quipus?, Meaning knot.

The different types of societies that existed in Asia,? Africa and South America, of course was not homogeneous and harmonious. There were deep differences of evolution, tribal wars and domination of some processes developed empires, like the Chinese or Mongols in Asia, the Arabs? Africa, the Aztecs or the Incas, in America.

But, not having entered the capitalist system, even those seeking to expand peoples invading neighboring territories, have maintained and cared for a harmonious relationship with its landscape and its inhabitants. Tended the ecological and social balance.

The presence of the white man, marked by the profit motive, means not only genocide, ethnocide, but also the destruction of the environment, breaking a cultural harmony, which operated from then on the future of these continents, in two levels: one, destruction of the economy. The farming and care of natural assets, in order to sustain a decent standard of living, were replaced by a system of exploitation, which displays this property, just as objects of sale. The invaders were an ecological crisis, social and cultural consequences of which we are suffering today.

The other superstructure, emphasized conceptual, ideologically. The peoples of these "new? continents, regardless of their commitment or loyalty to the ruling classes or sacred symbols, in general, had a practice of collective participation, which did not respond to a plan to benefit one sector of society, or for personal enrichment, even for overcomes transformation, but a feeling, a natural relationship with the land and with their peers. Europeans imported the concept of personal wealth, which carries the maximum use of any production, surplus production, speculation.

The white man, from his goal of domination and conquest, to make simple human capacity in goods and automate work, stripping it of any possibility of personal creation, has no choice but to destroy an ancient balance between man and nature.

Jean Paul Sartre, analyzing the situation, says: "Remember those Indians of Brazil, which are left to die quietly, when the Portuguese tried to attach them to the ground. I wonder sometimes if sadness is not working exactly the same reasons. The Indians have not been wiped out by the formal characteristics of slavery, but by changing their way of working and their way of life, which involved a different power and forced passage of nomadic to sedentary lifestyle, the advent of automation, task of plots and mass production, would not result from current workers a similar mismatch. The interest in the work decreases, fatigue increases., Structures break the working world, depersonalization, physiological deformations. Interchangeability, remove the worker eventually working his reasons?.

The concept of work and linking with the same man, is a serious, deep transformations produced by the white invader.

Thus we come to today. In our country and in Latin America, the process of cultural domination, had differences of nuance. There were native oligarchies, like Brazil, totally submissive to the imperialist, installed in power since its inception as a republic, and another, such as Paraguay, which was directly destroyed, when he had begun a process of independent development.

"The uprising of the people today without borders. The internationalization of the economy, internationalization national struggles. And these struggles, which, although formally nationals in their particular contents, are global by their ends. Such a struggle is true on two fronts, against imperialism in general, and the native oligarchies, in particular.

Native classes economically dependent and culturally corrupted by the colossal media machine of world monopolies. This imperialist policy in the colonial countries, uses the residual income system to fold into its orbit, not just the oligarchs vernacular, but to certain sectors of the middle class, especially the petty bourgeoisie commercial, industrial and intellectual property. And even at the higher layers of the working class. The anti-national consciousness of these groups, is fed with the crumbs scattered throughout the global system of power.? Hernández Arregui. "The formation of national consciousness?.

World power invariably produce two facts need to strengthen their domain: any attempt to remove people's organization, and avoid or dilute any thought to point to national autonomy.

From there, all social conflict is the product "the infiltration of foreign ideas?, And the constant and repeated discovery of international extremist plots. Curiously and sadly funny that the fiercest representatives of the extreme right, submissive servants of imperialist domination plans (Videla, Pinochet, Somoza, Stroessner, Menem), are the spokesmen and defenders of "national being?

The goal of domination becomes in turn a necessity. Continuing with Latin America, operating territory of the United States and trying to limit ourselves to each country, in every respect, so as to become adjuncts of central power, so you can not solve anything without your assistance.

It is not possible coexistence of different models, as in certain times in our country with an economy and a technique dependent on Britain, a Prussian army, and an outstanding intellectual of French ideas.

This need is due not only to the objective of strengthening its domination, but also not to allow the advancement of Europe, Japan or China, where inter-clash to conquer markets.

Everything is for these purposes, including matters within the central power are irritants or face the system, are exported to the dependent countries, some as entertainment (the hippies, rock, protest song) -.

Yet the ideological apparatus of the system is organized to accomplish a goal: the cultural alienation, education, press, cinema, theater, comics, literature, television advertising.

This is to prevent the development of popular culture, which inevitably becomes a national culture, built by the collective memory, the understanding of the triumphs and defeats, the insight to analyze the present and the intelligence to develop the furo.

National culture and political freedom are inseparable. So the system fills us with a neutral culture, away from any contamination with reality.

In Chile, achieved the victory of the Popular Unity, with Salvador Allende, as part of national liberation, in its transition to socialism, the State Publishing, began publishing a children's magazine, which sought to neutralize the ideological influence of the usual story, at that time, all of U.S. origin, in particular, any line developed by Walt Disney.

With great scandal and a critical overreaction to the right, who called demystifying attitude as extremely dangerous, alongside the Chilean Ariel Dorfman and Armand Mattelart Belgian, published a will

This book reveals how, behind a seemingly idyllic and harmonious relationship, develop a stifling world where there is no room for affection and solidarity, by contrast, conduct that reflects is an absolute authoritarianism and a ruthless competition.

All the contradictions resolved by the triumph of the values ​​"adults?. Of course, the adult world, is the world of capitalism.

With the image of cute animals and candy, presents the hardest and savage society, where the behavior is habitual cruelty, blackmail, taking advantage of the weaknesses of others, envy, fear.

The model, dressed Coya, a Hindu. of black African tribesman Brazilian or is a monotonous repetition of a savage and stupid innocent, ready to deliver

In the field of culture, the nature of capitalist development and competition among, economic and financial empires, was achieved two methodologies for determining

These giant monopolies and synergistic multimedia empires, are intended to control only the content but also of all the elements involved in the production industry and laboratories, technology, transmission facilities and cultural activity.

This means the simultaneous control in the hands of one company, dozens of television channels, radio stations, satellites, telecommunications companies, chains of newspapers and magazines, film producers, distributors of video, cable TV, record labels, amusement parks, as well as hotel chains, airlines, etc. This also avoid being hostages or victims of sabotage or blocks, by corporate rivals.

In addition to building this network of full service, are a form overactive, where communicators can shop, play, make phone calls all over the Internet.

An obvious example is the Disney company.

The Walt Disney Company (also known as Disney Enterprises Inc., or simply Disney) was founded in 1923 and is one of the largest corporations in the world devoted to communications and entretenimiento0. It is the second communications company. In 2002, had revenue of 22 billion dollars, from the acquisition of Capital Cities ABC, controls:

Film producer and distributor Disney, Touchstone, Hollywood, Miramax, The Sports Network, Arts & Entertainment, Lifetime, ABC, Disney Channel, ESPN, several television stations and networks.

Cable channels: ESPN, Disney Channel, ABC Family, Toon Disney, SoapNet and Lifetime Entertainment Services of A & E Television Network and Et Network, ABC News, also operates Walt Disney Television Animation and Kid Fox International.

Recreation parks: Disneyland (Anaheim, Florida), Disney World (Orlando, Florida), Disneyland Resort Paris and the Tokyo Disney Resort, plus a new park in Hong Kong.

Advertising companies, as well as newspaper chains and magazines.

Toy chains: Disney Stores.

Companies that produce and distribute videos: Direct-to-video, linked to its own distributor Buena Vista.

Publishing companies: Fairchild.

Companies of video programming and interactive services.

Telephone and communication companies: Baby Bella (detachment of Bell Telephone Company)

Disney Consumer Products: This division began operating in 1929, currently licensed by Disney products covers a wide range of products ranging from toys to art, to electronics and food, and is divided as follows:

Disney Consumer Products

Disney Publishing (Hyperion Books for Children, Disney Press and Disney Editions) Buena Vista Games.

The Baby Einstein Company.

Disney Disney Stores worldwide

Direct Marketing (Disney Store.com and The Disney Catalog), Disney Media Networks. Disney Cruise Line also operates, The Disney Vacation Club, Disney Regional Entertainment, ESPN Zone sports dining and entertainment locations and Anaheim Sports Inc., which operates the hockey team "The Mighty Ducks? the NHL, and had the basketball team "Anaheim Angels? sold to businessman Arturo Moreno.

The possession of money and mastery of technology, by itself, does not allow the power to influence and dominate so many people in the distance. It is imperative passibility complicity and those who do not have the courage to face it.

The cultural industry is developed covered by the neoliberal state, but also by large sections of society. Beyond the image of omnipotence and the real power of these large corporations (able to make or break political or social leaders, overthrow governments or bombing cities), its action is possible through the cooperation and selflessness of countless local accomplices: the decision makers at the national level, those who obstruct the creative initiatives, and those who "select the movies? in commercial distribution, and those who "build news, those who destroy buildings and historic towns, to make buildings" modern. Creative, intellectual, professional, radio and television broadcasters, artists, merchants.

The paradigms that sustained until the 70's the work of the social sciences into crisis, Crisis caused by the emergence of new realities result of both technological advances and changes in social reality. The debate over postmodernism is a witness to these changes. Protagnismo Parallel to this the social movements that emerged from the grassroots, contradicts the idea of ​​"folk," the "picturesque" of pure indigenous

Define what is popular culture, it is difficult nastante. For some sectors, popular culture would not exist in practice and only have spaces for the "high culture?, Manipulated by the mass media.

At the other extreme, interpret popular culture as a stronghold to retain intact the national sense, especially in countries like ours, suffer from constant invasion of foreign posts.

Accepting that the media are a key resource of imperialism to impose ideological contraband on traditional and local cultures, then "the priority task of the anthropologist, sociologist, historian, is to study traditional practices are lost, inheritance disintegrating . In short, restore and conserve memory.

Cheap Car Insurance For Young Women

Perhaps many young men may have had the same question, but the fact is that women can get cheaper car insurance than young men. While there is an effort to promote gender equality in most areas, auto insurance is a part that women have a definite advantage.

What are the reasons that young women can get a cheaper car insurance?

The first reason that men have to pay car insurance premiums are higher because men have the most road accidents. According to official statistics, the men had 92% of convictions of driving in Mexico. On the contrary, she was only 8% of convictions for driving. That's a huge difference to the auto insurance companies take into account.

According to statistics, young women have a lower rate of road accidents, so it's not hard to understand why they have auto insurance premiums cheaper. Thus, young women are less risky for insurers, as they have safer driving habits.

Young women tend to drive slower and shorter distances to travel. These habits protect them from serious accidents, but when accidents result in minor consequences. This decreases the cost for car insurance.

Young women can achieve a reduction in auto insurance premiums until the age of 45 years when premiums for men and women generally are the same. Some insurers may not provide incentives for women cheaper and use an average of all drivers of both sexes to determine a car insurance premium acceptable.

However, in some countries there are several car insurance agencies ensure that only women and to eliminate the possibility that women subsidize men accidents through your auto insurance policy. Other auto insurance companies cater to young men and women between 17 and 40, or specialize in insuring drivers first.

Young women get great deals on car insurance because they represent less risk to an insurer. Check out the car insurance brokers and determines the auto insurance policy that is right for you.

With car insurance information

Photo Of The Day: 12/05/2011 "Father Flying"

I remember years ago, I loved reading The Adventures of Tintin. I do not remember the title of the book, but one of them was a priest who levitated and the father called him flying ... to see this picture I could not help remembering. Leaving aside the irreverence, what is undeniable is the timelessness of this image. I can not see any detail that might indicate the time when the photograph was taken. Perhaps the perfection of the pavement, would reveal a certain modernity in the making, but still, could also have been taken in the seventies or a fortnight ago. However, and more succulent guessed that date, I would find out what thought crossed the brain of the brother, in that moment. ¿Analyze perhaps the loss of faith in our civilization, or hunger that plagues too many people?. Valued Perhaps a better distribution of wealth in this society, or why not, the relentless growth of AIDS? Africa?. Being honest, I think I was just watching the scenery. It is a meditation exercise like any other.

PS: FYI, if you write "father flying" in Google Image tab, not a single picture out of priests flying ... Curious no?.

You can find more articles of this series in http://fotoblogedurneiza.blogspot.com

We invite you to visit www.edurneiza.com

Photo: Edurne Iza

Text: Iza Otamendi Onintza

You can download this picture freely. The only restriction is for sale and / or profitable use of it. Do not forget that all work belongs to its author, make good use of it.

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Online Reservations

Allowing you to online booking engine is that your clients have more facilities to book a room or other services.

An Internet booking engine (IBE) is an application that helps book travel and tourism industry support over the Internet. It helps consumers to book flights, hotels, vacation packages, insurance and other online services. This is a very necessary for the aviation industry as it has become one of the fastest growing channel sales.

Today more and more bookings are made through the Internet on hotels, hostels, farmhouses ... this is very handy for both the client and the hotel establishment. The customer can book and pay for your room via the Internet, either by credit / debit card, Paypal or bank transfer. As the hotel establishment, the online booking engine allows you to manage all your rooms through the Internet in an easy and practical. It also allows you, the hotel establishment, increase sales opportunities, customer loyalty of portals and save commissions intermediaries in the marketing of their rooms or other services.

Providers of online booking engines keep adding new features to online booking engines, such as multiple search options so that a customer can book a flight or rooms in a way that suits his / her requirements. If the customer is "time sensitive" and must comply with the dates of specific travel and accommodation, online booking engine offers tickets to give priority to the travel schedule.

Allowing you to online booking engine is that your clients have more facilities to book a room or other services

One reason why ending a relationship - a lack of understanding

One of the main causes of the separation of couples is a lack of understanding of each other. When we begin to understand your partner, to put ourselves in their place, from that moment the circumstances change in our relationship. This lack of understanding we can see in our own negative comments we make against our couple, many of them do not even realize that we do. Where to tell others how we feel by customs or attitudes that do not understand.

In particular way, I'd like to give some examples. My partner would scold me because I was a mess, often the disorder is caused by my partner, but I just try to understand that if I give the opposite at the time, for something so simple would provoke discussions. But I try to understand what happens and it only helped clean up that mess. Do not deny that sometimes I get upset, but I also try to realize that we're a couple and I must also help by reducing clutter.

At first she tried to realize, he did, but not solved. I concluded that I was wasting time bothering me. What I did was put in place to realize his own disgust and what I did was try to help. This could give some examples of other situations, but more importantly, we must understand each of these situations, if exceeded, excellent! if not exceeded, helping to avoid being a nuisance.

Not understanding our partners, we generated a discussion that usually does not end well. When initiating a discussion must be calm. Any word that offends us, cause us to respond well. But if we do not hurt those who hurt us, you will feel guilty after you pass the shower and all be forgotten, if we really understand that whatever happened was crazy. But if we forget, we will keep this animosity where there are others, to expel him in a moment of anger.

If we begin to understand your partner, for example, by work stress, lack of time, the troubles of the outside world, by the pressures of payments and we, as a couple we are, looking for ways to reduce these problems with good times, will not be another problem coming home will be a blessing.

Of course it is accompanied by understanding the communication. Yes see the stress of our partner and we tell our other half is going, we inform you about all the problems arising from a bad mood, emotional instability, resentment, lack of sleep, etc.. perhaps to reduce some of the pressure. And we ought to find ways to forget some of the problems, take a vacation or a departure every week for the problems in our heads drop, it would be helpful.

Learn to escuhar our partner, start closer communication, we know what the needs are so we can have a more solid and stable. If we try to understand your partner a bit, improved communication and look for ways to distract us to forget the stress, we can go far.

If you want to improve your relationship with your partner or get your ex back, visit: as reconquered my ex. Com

Monte Gordo

Monte Gordo is a parish (administrative organization into which a municipality) of Villa Real de Santo Antonio, this division is bordered Ayamonte, Spanish town and also the Rio Guadiana. It is a residential area dedicated to tourism and has about 4500 inhabitants.

It is a hamlet (place and attached to a municipality governed by a mayor himself) who is listed as a people and is located about three kms from the town center, Villa Real de Santo Antonio, a former fishing village in the Algarve. The area was initiated by an incredible escalation in the construction of the 60 hotels currently available Monte Gordo one of the largest hotel deals in the Algarve.

Monte Gordo, a place where you can enjoy the beach, entertainment, sports, nature, as well, an important cultural offer. This is a very important tourist destination in what is Algarve, and is only an hour and a half from Seville and Faro, the nearest international airport.

To enjoy your holiday in Monte Gordo, know that in this locality enjoy restaurants, bars, the casino of Monte Gordo, apartments, houses, hotels, cottages, hostels as well as numerous religious temples and sites to visit the during your free time.

Getting there

Monte Gordo, near Ayamonte, on the border with Spain, the municipality with which bordered on the east, and Tavira, a town with which bordered on the west. We get here by road, train or plane. Road

Madrid Taking as a starting point to get to Monte Gordo, know that you must take National Highway IV or Andalusia, or National V, Extremadura road. Both have the same fate of both Sevilla.

Once in Seville, take the A-49 or E 1 to Huelva, and then to Portugal, joining the A 22 in Portugal. Exit once you arrive in Portugal to Monte Gordo and Vila Real de Santo Antonio.

By air

To arrive by plane, you should know that the two nearest airports are Monte Gordo Faro, about 45 minutes from Monte Gordo, and Seville, just over an hour and a half away.

The beach

Monte Gordo beach known for its natural environment in much of it are beaches surrounded by pine forests, dunes and golden sand. The beaches are very clean waters, where you can practice different water activities while vacationing in Portugal.

The Monte Gordo beach is another area that is more developed, and has beach bars, sunbeds, bars and numerous facilities, and other amenities.

His nature

Places to note are two Monte Gordo, Vila Real de Santo Antonio as far as nature is concerned, the channel of the Guadiana River and the forest nursery, we must not forget that the beach of Monte Gordo in its entirety is a natural paradise . We should point out his beach, as well as the vegetation that covers the entire coastline of the area, is based on pine or oak in limestone belt, oak or carob. If we are to know the area of ​​the Sierra, we highlight the oak, as well as its wide rows of cork.

It also highlights the area known as the Natural Reserve of Mata de Vila Real de Santo Antonio, an area covered by pine trees reaching to Monte Gordo.

Ritual Magic in Practice

One question that constantly do many consultants esoteric communities TarotyBrujeríaenLinea MiracleOn6thStreet + ® is the reason why that should be activated rituals conjured spells in all types of Magic, and particularly in magic at a distance. The explanation is as follows: The ritual is an expression of the manifest will of the client to achieve a goal through the Magic. The ritual helps the client to connect to the Higher or Divine Energy of the Universe that creates our reality. When a client agrees to conduct a ritual magic, should be done with formality and convinced that you will get what is called isolating any distraction of mind, they release a game of magical power always cause problems and has often caused the death of the client.

Energy Control is the most important for good results from the activation of spells and talismans. To align the way they verbalize the goals of the client and instructs the subconscious mind to achieve them. Now, it is not possible for the client to do certain things required in ritual magic acts, such as the slaughter of an animal or material offerings in Distance Magic always asked a symbolic offering of money, defined as Opening sacrificial ritual that takes place in all magical work since ancient times for the purpose of showing detachment from material goods consultant, spiritual commitment that requires the power of magic, as well as the sincerity and humility provides the universe with the goal of making a favorable magical work. <<>> © 2008 All Rights Reserved. The information content published here can be used, quoted and disseminated in whole or part by any means, non-commercial purposes provided the source is linked to our websites: www.tarotybrujeriaenlinea.com | www.miracleon6thstreet.com

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American Beauty o In Search of Lost Time

One of the most interesting films of the past 20 years is American Beauty. The story revolves around the life of Lester Burnham, a public relations tired of his life and his work. This seemingly harmless situation is turning into a tragedy when Lester falls in love with Angela, a friend of his daughter and twenty years younger than him. From that tiny and forbidden emotion, Lester begins to confront his own current situation, becoming, for the first time in years, the owner of his own destiny. Quit your job, try to win back his wife, seeks friendship with his daughter, beginning an exercise regimen and begins to consume recreational drugs.

However, the film takes poetic piping because of the past Lester showing love with his wife. This is a photograph in which Lester, his wife Carolyn and his daughter Jane, hugging enjoy a night on the rides. The time Carolyn has made an ambitious real estate broker, obsessed with self-help courses and find the perfect rose. The metaphors are repeated: When Angela Lester dreams, sees rose petals surrounded by perfect. Angela Is an attempt to recover the wife Carolyn was? Using the metaphor of the rose, suggests that it is. Meanwhile, Carolyn has an affair with Buddy Kane, a real estate broker egocentric.

When Lester learns of the infidelity of his wife, can not be bothered or depressed, is glad. When Lester lets go to Carolyn, his obsession with Angela disappears and instead the girl, played by Mena Suvari impressive, Lester decides to conquer. By the time Lester has her way with Angela, has already lost interest in it. He has already lost his wife: it was then and now.

The making of American Beauty-level plot is comparable to a Baroque cathedral, in which the symbols are repeated and are opposed to each other. The humor that runs through the work, to appreciate the symbols in the eye, as friends we've known for a while. Thus, the work accomplished in a Macdonalds Lester, contrasts with the ambitious realtors. The gay couple whose neighbors turn out to be healthier than the traditional family that moves into the block. The Lester and Ricky breaks (the son of his neighbor) remind us that even at 40 or 50 years, we remain the same, with the same ability to have fun and love. When Lester is identified with Ricky, the latter ends insulting Angela, seeing in her ugliness that Lester, with more experience, is unable to see. Lester is more mature and wise observer and yet Ricky Ricky is able to see beauties that are not of this world, but to inhabit it.

Filled symbols, humor and tragedy, American Beauty is a film for the story, which is able to portray the magic of life that sometimes seems to fade with time.

...

Where to Learn English?

Once you decide to learn English, the next step is deciding where to study. The time and money play an important role in your decision. Before you decide, you should take a look at all available options to define where you should learn English.

The most obvious answer is: in school. However, there are all kinds of schools that dictate all kinds of English courses. The traditional course of English in schools, is available only to those who are enrolled as students in those schools.

If you are beyond school age, there are public universities that offer classes to learn English. Teachers can be the same that dictate the courses in schools, are sometimes retired professors. Even can be any person who has demonstrated his knowledge of fluency in English and Spanish.

In most cities there are private institutes fees for people who want to learn English. Most focus on grammar and written work. Some English institutes are created for the entrepreneur, although their study programs are long, take between 5 and 7 years and ultimately very costly.

Having a particular English teacher is also a way to learn English. The teacher can tailor instruction to meet your particular needs. If some words are needed in your work, such as the names of tools, for example, the teacher may be able to supply. A tutor gives more personal attention, although the cost is usually very high.

There are also courses that allow you to learn to communicate orally in English (most important in a language) and written, losing their fear of losing face, removing inhibitions, phobia language, and so on. through a balanced program of grammar and oral practice. There are English classes are fast learning systems, employing the latest advances in medicine, particularly in neuroscience and psychology, developing learning systems that allow learning to achieve a natural, stress-free, stress-free, rewarding, with a deep attachment of the information, reducing class time by almost 50% and therefore costs. Another place to learn English is an English speaking country. This is called immersion learning. He surrounded himself with people who speak English. You put yourself in situations where you have to talk and communicate with people who only speak English. This is a powerful way to learn English and also reduces time.

If you're in an English speaking country, you can learn English even faster if you go to a university. You can attend courses that teach English to foreigners. These classes are taught by the country's residents. Sometimes these classes are taught in community centers and sometimes they are private universities.

You can learn English from your home through distance education. You can take English courses online or by correspondence, or you can take online courses. Some of these courses even allow you to talk to other people.

If you decide to do, it's easy to find a place to learn English, I have to do is decide how much time, effort and money you are willing to use for this learning. Then do it. If you want more information or to recommend a specific place to contact me: I send my info@ingles-ya.com.ar and recommended systems to learn English quickly and effectively

The Internet and the computer or the new myth of Education

THE INTERNET AND COMPUTER

MYTH OR NEW EDUCATION.





Gabriel Hernandez Santamaria

gsnama@prodigy.net.mx





In late twentieth century, information technology and communication (ICT) have changed radically praise production processes.

Similarly, the spread, almost instantaneous, knowledge is made available to anyone who would use it. Thus almost all professional activities adopted these tools as part of their exercise.

The education was not exempt from this global phenomenon, even the concept of educational technology - born of the current American pragmatism - gained strength and was redesigned to meet the education based on multimedia, computer and the Internet, especially to promote the model of distance education through video conferencing and online learning in the early years of this century has changed the practices and processes of education and job training.

With respect to education or classroom attendance, the actors of the educational process in general, have shown particular interest in adaptation. We must not forget the controversial Enciclomedia program, as well as the proliferation of media classrooms and even the teaching of computing. All this in the context of magical thinking where instruments [Internet and Computer] not only serve to rethink the relevance of educational activity and facilitation of learning but are unique and critical element for improving educational quality.

The myth came to forget that the genius of the learning process lies in the relationship between student and instructional design and teaching practice of teachers and not the instruments or tools to expose knowledge.

Eciclomedia Thus, the media classrooms and computer education are being, in most cases, ornamental objects.

Not that children and young people unfamiliar with the management of these tools and this is complicated to use in the classroom. No, I do not, most of them know their management. Only the use they make of the Internet and the computer is only as a center of entertainment (online games, social networking and chat sites [Chat]) hence the attraction they exert on ICT.

Why then in education have not worked as a tool to facilitate or make available quickly and appropriately with the necessary knowledge to solve problems and build meaningful learning?

First, because the teachers, the vast majority lack the training to use as a teaching resource.

Second, because the number of computers connected and Internet in schools is insufficient.

Third, because if the teacher wants to use as a reference to work outside the classroom would be exercising a measure of inequality, given that the vast majority of students do not have a computer at home or are connected to the Internet.

Thus, forgetting is not in demystifying the use of ICT in the school but to banish his presence alone gives status and quality.

It therefore required to:

a. A training process to equip the faculty teaching skills to use ICT in different subjects and levels of education básica.b. An educational planning, made by the same teachers, according to the availability of technology and educational goals for each subject or subject.

Otherwise there is a serious risk that the equipment and resources to deteriorate for lack of use or become obsolete without having educational use. For this to not happen to be teachers themselves who promote training activities, planning, teaching and above all, the relevant use of the resources that your school account, thereby making the practice of teaching to reach acceptable levels the formation of their students.

Hotels in Europe and their differences in prices

Peter Gutierrez Flickr CC

When you search for cheap hotels worldwide, Europe is a place where we can stop, as no doubt due to its proximity and social customs of Europe we have many opportunities ahead of a weekend getaway week or enjoy a fabulous vacation.

As in other articles we have read the chances of finding cheap accommodation in different countries and cities worldwide, which provide us with data and various proposals. Today in this article we want to stop a special way in Europe, as price differences found in hotels.

Although generalizations are never completely accurate, the prices of accommodation as general information is half that are not usually very far from reality.

France, UK and Italy are the most expensive countries in Europe to stay, citing them in that order as well as information, since as we have first to France, where the ranking of a high average price of accommodation per night is stipulated at about 169 euros.

On the other hand we also have three other countries, such as Bulgaria, Romania and Hungary, which have a very particular ranking, with prices cheaper means for housing, being cited in these cases a price that makes this ranking of 64 euros per night's accommodation.

The above mentioned does not mean that in Bulgaria there are no high-end hotels with prices quite high and that in France we can not find reasonably priced hotels, we do, we will definitely mark a trend that should be taken into account when planning a trip, however it is advisable to go to professionals who can offer different proposals and the traveler can choose the one that best suits your needs and enjoy a friendly welcome.

What career to follow? The Dilemma Of Young

I chose this topic because I think play is one of the starting points, which help to trace the path of success. When I was 16 years old and was about to finish school my father directed me on the race could continue, then it was fashionable economy (start of the 80s). To be honest I was not sure if it meant I could live ymenos my profession. Times have changed, now there is a test range of vocational, professional and dedicated to guiding young people to give a fuller picture of reality that will be living. Yet I decided to study economics.

Now that I'ma father of two teenagers, one of the topics of conversation with other parents is contemporary And your child knows to be studied? What college going? My son for example, school ends next year and still not sure which career to follow. I have known few young people who speak with conviction about their future and boy, I admire those who convey that assurance that I had at that age. There are probably a thousand and one reasons that influence the decision to be taken by a teenager. Some want to be doctors because, as children, always saw the father in and out of home, with the white coat in the arm, others want to be lawyers to defend the unfairness of life. My other son for example has to be clear what he likes and video productions from and helps me with my work in video production in the workshops that I do ...! Good for him

He talked recently with a lady on a journey back and I explained all the effort they had made as a mother for her daughter to follow a career in architecture, as you know is expensive for the materials they require. The problem was that her daughter wanted to leave the university, half way, to follow a fashion design school. Times have changed and how much ... In my time, go to college was a very difficult challenge, requiring preparation thoroughly, sleepless nights and constant struggle to overcome my own fears. Now there are new ways to enter the university, beginning with assessments in the final year of study and requires only a personal interview and in many cases, simply check the solvency of the parent requirement. I think that the fact of having "facilitated" the university entrance in the first place has taken the pressure I had before the applicant and has been transferred to parents who have to "stretch" their budgets to meet the payments and obligations. Secondly, I was always taught that what is achieved with effort is more valuable. Therefore, before, if they chose the wrong career, you looked in the obligation to go forward not to disappoint the "pocket" of your parents.

Today young people entering the first cycle and find that they like what they study, simply must inform parents and go ... it sounds something like, "Dad, I realized that the career I chose to take a lot of math ... Then I prefer letters "or" The university requires me a lot and I have no time to meet people ... I want to change "

Another criterion for deciding to study is to determine whether they chose the profession will meet my needs if I have the dream house, travel and so on. ie assessing the return on investment. On the other hand is choosing to study a career because I love what I do. It is true that there must be a balance between profitability and a taste for what I do, personally at this stage of "party" I am convinced that one must choose not only what you "fill the pocket", but what will "fill the spirit "that give you fulfillment. I am an economist, I repeat, but over the years I discovered my true calling. I am dedicated to training and HR consulting, I enjoy when I make dynamic, I enjoy working with people, learn from them, help them realize that they can stop doing and can incorporate into their lives. I discovered that I can help by writing about topics that seem so simple, as this article, but we filled, sometimes, anxiety and worry. I worked in a newspaper many years ago was not explained at that time ... time gave me the answer.

I can only tell you what they decide, do it with love, enjoy it, feel the adrenaline when you are facing a challenge, look to see opportunities for growth problems. If you chose the wrong race does not matter, everything you learned is used to find your way to success, and do not talk about money, we know that is only half that can help but can also complicate the lives of many. Before worrying about the outside world, look within yourself, take time to know what they like, evaluate their strengths, analyze their actions in context, to define a vision that will motivate, design your life plan, get informed on current economic and social development in which they live, to make better decisions. Perhaps this explains it better piece of poem by Antonio Machado: "Traveller your footsteps are the only way, Walk This Way is made by walking"

Until next time!

Fundamental Concept Brainstem

Brainstem



The human brain has three main structural components: the large cerebral hemispheres (part of the brain) dome-shaped (top), cerebellum, and somewhat smaller spherical shape (below right), and brainstem ( center). In the brainstem, the pons stands (the central widening) and spinal medulla oblongata (just below the previous one). The cerebral hemispheres are responsible for intelligence and reasoning. The cerebellum helps to maintain balance and posture. The brainstem is involved in maintaining involuntary functions such as breathing. The thalamus, located between the brainstem and cerebral hemispheres, acts as a relay center for electrical impulses that travel to and from the cerebral cortex.



Brain, part of the central nervous system of vertebrates contained within the skull. Is the control center of the movement, sleep, hunger, thirst, and almost all vital activities necessary for survival. All human emotions like love, hate, fear, anger, joy and sadness, are controlled by the brain. It is also responsible to receive and interpret the many signals that come from the body and the outside.

In the brain to distinguish four distinct but connected parts: the brain or telencephalon, consisting of two almost symmetrical hemispheres, the diencephalon whose main structures are the thalamus and the hypothalamus located in the midline of the brainstem and cerebellum below, the cerebellar hemispheres formed by two smaller ones that are located in the back of the brain and brain stem or trunk, a estructuracentral that gradually becomes the spinal cord and leaving the skull through an opening called the foramen magnum. The term brain stem refers generally to all structures between the brain and spinal cord, ie, the midbrain, pons or pons and medulla oblongata or spinal (medulla oblongata) .

Read the full article HERE about the brainstem ..

Do not die for love

Not always fall in love with the person that you really should, but when that happens in most cases you will find that simply, you've been idolizing someone who is not really worth it. Or maybe he did deserve it but it is preferable that you focus on your shortcomings to one hundred percent completely forget him and leave aside their virtues. At least until you feel strong enough to transform love into friendship. Although it is impossible to believe now sure with a little time you get it.

No one dies for love, that's the reality. It is also true that you can spend fatal, mourn for hours, feeling like life has lost meaning in a way, feel anxious because you think you might never know the true love ... Stop being stuck in the wheel of the negativity, for the mind and simply enjoy the magic of reality. Delete your mobile phone book the other person. Of course, avoid having you as a friend on facebook to avoid any temptation to know what you are doing.

Focus on your friends to one hundred percent. Go out with them even though you do not want. Make plans, do not be afraid to be busy because that's what suits you best. However, you must also be flexible with yourself and if one day need to be alone, take that gift. Allow yourself the privilege to mourn in private because that's also liberating.

No one dies for love, fortunately. However, sometimes we fall into a very dramatic and exaggerate all things when in reality, you may have in love with a person you do not even know. You know nothing of it and already have become the center of your world.

There are people who are particularly receptive to the idea of ​​love: that people are very amorous, moreover, can also occur in this situation people wearing too much time alone, on the other hand, in your environment certainly know people who are in love with love that is, people always have someone in mind. In this way, are people who tend to put their value in the opinion of others.

There are love songs that send a wrong message totally distorted and the listener. The right love is not one who makes you suffer, it is one in which you have to overcome obstacles to be near one hundred other (at least not so in most cases). This summer, be encouraged to find a partner and enjoy this in the best company. .

Tips For Business Travelers In Rome

Traveling for business can be fun and at the same time, a good way to see the world and make money at the same time. Traveling on business, you can enjoy the same advantages as a tourist. You can go to all the trendy restaurants to enjoy superb sightseeing dinner at night, to finish the job, perfect time to enjoy the architecture of the site without crowds and with a different highlight. Although obviously have to work: you are traveling to get a result and it means to be produced quickly and efficiently. I will highlight some of the challenges and some solutions for the business traveler in Rome. Getting around in Rome Getting around the city used to be easy for the traveler who had expenses paid. The taxis were invented for that! You take a taxi at the airport, in the office, hotel or restaurant, a nice guy you closer to your destination, and just even give you some advice about restaurants worth eating or a few bars worth a visit and a good coffee. In times of crisis, however, travel budgets are smaller and probably the thing that you should submit invoices less the absurdity of taxis.

Here are some tips for saving some eurillos of your travel expenses: Upon arrival at Rome Fiumicino Airport you can take the Leonardo Express to Rome's main station, Termini, which is also terminal of many bus routes. From Termini, you can take a taxi to your hotel or even if it's one of the leading hotels in Rome, walking. Moreover, from Fiumicino airport, another train will take you to Roma Trastevere station or Rome Ostiense. The Rome metro is not very big, but if you're lucky, you will find accommodation near metro stops one of two metro lines in Rome. Anyway, if you decide to take a taxi, they are one of the local numbers for yourself you can call a taxi: June 3570, June 6645, 068,822. If no phone call from an Italian, typing +39 and then the number (including zero). Please note that airport taxis accept credit cards, while taxis that you will call or you will take on the street usually accept only cash.

Engaging in Rome In fact, you can communicate by speaking in Spanish or in English: I usually understand Italian, but not necessarily respond to you in Spanish or English. Even if memorizáis some keywords in Italian will make your stay more enjoyable, so encouragement and learn a little Italian:

Numbers are important if you want to get directions, or product prices to tip in a restaurant. You can save just by learning the numbers from 1 to 10, and then joining them, but if you want more satisfaction, poderéis continue until 1000. The numbers from 1 to 10 in Italian are: one, due, tre, quattro, cinque, sei, sette, otto, nove, sixteen to book your hotel in Rome or make restaurant reservations, will serve you seven days a week: lunedì , martedì, mercoledì, giovedì, venerdì, Sabato, domenica. Now we have the numbers and days. To add "please? pregutas to your "per favor?. Now that we can reach the sites and shopping, to thank the taxi driver or waiter for a good meal, "grazie? and to say anything "prego?. With a vocabulary of 15-20 words, I feel much more at home in Rome. Rome business world mobile phone charges while roaming are slowly beginning to be lower in the European Union, even if you have to do a couple of conference calls from abroad will still cost a pretty penny. The easiest solution is to buy a prepaid SIM card in any phone shop.

For about 10 euros will have an Italian number and SIM card that you can use any GSM phone free. Two telephones take you on your journey, or buy one when you arrive at a cost of 30 euros. If you do not have to pay when roaming on a conference call with the headquarters of your company, you will have saved. When I buy a local number, which I always do is send an email to my colleagues and contacts you have to talk during my stay. Internet access is not so easy. You can buy a prepaid 3G Internet account, but is expensive and so are the costs per megabyte. The best option is to find a bar with wireless around your accommodation in Rome: you will recognize because they tend to have a Wifi Zone logo on the outside. A plus will be a good cappuccino or espresso aroma as much revisáis your email. Eating out in Rome There are many articles and even books that speak of eating in Rome, so I'll give you two directions so you can quickly decide where breakfast, lunch and dinner.

For breakfast, nothing easier than filling the stomach with good breakfast buffet in your hotel. If you want to get close to one of the many cafes in Rome, you can hang out with the Romans and Roman live morning atmosphere and even save a few euros. Many cafes are open from 7 in the morning. So you can enjoy an Italian croissant, which in Italy is called "cornetto? capuuccino and delicious way to start the day. My suggestion is that you enter only the sites you see Italians and tourists. While many scientists study how the Italians can be as thin with a diet of pasta, different kinds of bread and olive oil, experience tells me it's because they eat a lot. Working in Rome, I have seen many of my colleagues not only eat, but pass the cappuccino or espresso in the morning until dinner. So if you expect a meal, to acquire something lighter just in case ... Take breakfast and try to find something to eat. In Rome, as in Italy, it is easy to find a piece of pizza or a plate of taglio to survive until the pasta dinner.

The Romans often dine from eight or eight and a half: the restaurants are open until 23.00. Choose restaurant can be a daunting task, but in Rome there are hundreds. Many of these restaurants are tourists and do not necessarily care about the love of cooking, so I advise you ask among your Italian colleagues or partners. In addition, TripAdvisor will give very useful recommendations on restaurants. Anyway, if you have no chance to inquire about where to go for dinner, try the following steps: If the place has more than 5-10 tables, do not enter if the restaurant's name is named after a tourist attraction, do not enter if People see tourist hats and cameras hanging from his neck, the better to avoid If you find waiters out the door inviting you to come, do not enter if the menu is written in English, do not enter if is a small restaurant with Italian families with children or elderly people discussing animatedly in Italian, have found the ideal place to have dinner in Rome! I hope you enjoy your stay in Rome even if you are traveling for work! To get the most from your business trip, here are some of the best hotels in Rome EUR (for business): Hotel H10 Roma Città Mancini Park Hotel All Time Relais & Sport Hotel

Travel to and from Barcelona by train

Train travel to and from Barcelona is quite fast and cheaper than by plane. In addition, all cities and towns have railway stations and other places not so relevant also have at least one. Therefore, to get to Barcelona by train is a good option. If you want to go to Barcelona or Barcelona to travel from the train, you should use the long distance trains of Renfe. These trains are moving in areas of Catalonia that are further away, such as Lleida or Puigcerdà. And in other parts of Spain such as Madrid and Valencia.

There are different Renfe offering long distance service. However, there is no doubt that the most popular and most used are the Talgo, Euromed and AVE (high speed train). In addition, other trains can travel long distance, as Altaris, Altaria, Alavi, Arco, Day, Star and Trenhotel. Choose the appropriate train according to their destination, prices and times you are most interested. The Madrid-Barcelona AVE has become the most common way to travel between the two main cities of Spain, much more popular than the aircraft, especially among entrepreneurs. Your comfort is greatly appreciated. On the other hand, do not have such strict rules in terms of baggage as some airline companies, for example.

Stations of Sants and França often the last stop of all these trains from Barcelona, ​​who always make a stop at these stations in Barcelona. You can book your ticket online at Renfe website.

Useful tips on the train from Barcelona

* Purchase ticket Renfe short distance from stations either machines or over the counter (there's always more tail in the latter). * Purchase tickets to middle and long distance RENFE in Sants station, or online on the Renfe website. I recommend buying it online, as Sants station is usually crowded and you can always get to do 3 hours in line. * Purchase tickets Ferrocarrils short distance from the Catalans at the stations, either from in vending machines (you can pay card) or on the counter. Not all stations have a ticket, but there are vending machines in all. * Get a brochure on the train schedules or question in the frequency counter and the last train. * Make sure you get the right ticket for your destination and areas you need, otherwise you might be fined if it enters the conductor (not happens a lot) .. * Make sure you get the right train asking users. As there are sometimes delays, especially on trains of Renfe, you could miss it. * Pets and bicycles are allowed on trains in Barcelona. * Do not leave your luggage unattended.

Keep an eye on your belongings, especially in the Renfe * Do not be afraid of people asking for money on the train. You may see musicians on trains, especially Renfe, who will entertain you, but do not feel obliged to give them money. On the other hand, we see women with babies begging on the trains. * Do not get nervous if there are delays on the trains of Renfe, is quite common.

Consider these tips about trains from Barcelona and have an enjoyable and safe. To learn more about trains in Barcelona see the article Traveling by train in Barcelona and its surroundings.

"A Christmas Circus" New Light On Ong, Calcutta

I spent my three weeks of vacation in August in Calcutta, India, in a volunteer project of the NGO World Cooperating. The project was to fill the free time and leisure than 200 children who welcomed the NGO New Light. Through the program, called "Once Upon a circus?, We tried to approach the smaller alternatives to the use of free time and transmit values ​​associated with the circus, such as confidence, responsibility towards others, the concentration, solidarity ... The children are mostly children of prostitutes in Calcutta's red light district. New Light offers safe shelter, educational opportunities and health and legal assistance for children and women of his community. The 16 volunteers have taken a program full of activities we have developed during the afternoon and we've gone to a theater on the last day a success and a very special day for children and families who attended to him. Personally, I am convinced that this experience gives me much more to me than boys. These almost three weeks I have shared time with some children loving, with a high level of receptivity, joyful and open to everything we wanted to teach ever with a beautiful smile.

I have joined New Light, which does an admirable job, and Urmi Basu and her team. Urmi is the director of the organization and is certainly the most inspiring person, generous and sensitive that I have known in my life. This experience also underscores my social awareness and sensitivity to my childhood too. These three weeks I have also come to the reality of India, knowing so many different life forms, customs, smells and scenes very impressive. Furthermore, this experience so intense, it has transformed my fellow volunteer friends. Three weeks in Calcutta make you discover an unknown part of you and puts you on tessituras not lived so far. One is known better when you experience this kind of adventure. Everything good and bad of this experience has taught me something valuable. And indeed, I consider myself richer after having lived. On the other hand, I believe in long-term cooperation, ie in sustainable projects in time. I think developing countries need to receive assistance in infrastructure, training, but who should lead the future projects are themselves. So I do not believe in these volunteer projects as sustainable means of improving society. Volunteers go and come back.

They are.

However, despite these ideas of mine, these volunteer projects are an injection of hope, fresh approach and different worlds. These projects are fully compatible with long-term cooperation of the speaker. You need financial support to these organizations that do work so quiet and indispensable. Support is needed in the dissemination of their activities. Support is needed face time. And, yes, it takes projects like a circus There once to put a grain of sand in the sample of new and different aspects of leisure, so important in the growth of all, and are required to publicize the work of organizations both here and there, are helping to change society. Now I feel that all financial and personal effort I made in India was worth it just for the first hour I spent in New Light with children. Children in India have a penetrating gaze, with eyes so dark, and the New Light, you know you conquer anything because you hug and kiss like you're his best friend, caress you, you smile ...

And you and you feel hooked melt them in a way that you hardly happens here. India is a wonderful country full of contrasts, but tough. Calcutta is a shock to all the senses that is difficult to explain and perhaps only be understood by living it in person. Calcutta, in its poorest neighborhoods, is a source of misery, with images that you stick in the memory and you can not ever erase, for example the image of a baby sleeping naked on a sidewalk. Live there. Born here, is being fed, washed his family there. Calcutta in August is hot and humid monsoon rains surprises you with its sudden, and never stop sweating. Dirt and smells like incense. The streets collect garbage in the corners and sounds of horns and crows become deafening. Hygiene is poor and is easy to spend a few days when health is weakened. They miss the comforts to which we are accustomed. But despite this, Calcutta India, and India's spirituality is melting pot of cultures, religions. India is a mixture of past and future.

India is a society of peace, with a huge number of people with needs that never make you feel insecure. The feeling of peace and security has not left us a single moment during the three weeks is impressive considering the misery that is and what a Westerner calls attention in its streets. In this context, in a caste society already abolished but still very much alive, New Light is carrying out what I consider a social revolution slowly and safely. If your mother was a prostitute, you have little chance to be anything in life. Have no chance of education or health, and be part of the social status they came from. Breaking the chain is nearly impossible. New Light offers education and a future for these children. New Light breaks, with hard work, effort and enthusiasm in the chain. From my experience I encourage you to read about the work you do Mundo from Spain Cooperating with projects in Colombia, Ecuador, India, Kenya and Ethiopia, to inform the work of New Light. I encourage you to cooperate economically with the causes they believe. I encourage you to be part of a project like the one I've been lucky enough to live.

To learn more about how it was was once a circus, this was the blog where we have been counting the project from the beginning and every day from India: www.barhaparty.com Here you can see some pictures: http://www .youtube.com / watch? v = N_gF4843Bqw Please take a few minutes of your time to read me and let me tell you how you can enjoy the holiday of a different form than usual.

Cheap flights to New Zealand

Well. If you are extremely rich, I would stop reading here. Total 1000 Euros more or less not going to matter much, right? For the rest of us who do our best to get get the most out of our hard-earned money sweat, and we have the same right as any other to travel to New Zealand to explore this natural paradise, when choosing flights New Zealand is an experience not suitable for individuals with heart problems. And is that the impact of flights generally do not drop below 1400 Euros after taxes are added several extras and is brutal. 1400 Euros?? Many people can not even win this in a single salary! We note as well if you look on us as if we ask specialized agencies, the numbers always end up hanging around this figure, and that we are talking about the famous tourist class, the supposedly cheaper! And that's when we see some anomalies. Our colleague from the UK tells us that went to New Zealand for 500 Euros. Some French friends tell us they were for 600 Euros. Something smells bad. Very bad. What is happening?

It's simple. New Zealand is a very new market for Spain, Spanish only 10,000 trips a year to the country and very few are truly specialized agencies on their pages but otherwise reported.

For I tell you, find cheap flights to New Zealand from Spain is possible, but must know how to find them. First of all, 2 tips: 1. I never find in the website or calling an airline. 2. I never find in typical search engines such as Opodo, Expedia, Edream, etc.. 3. I never find in a conventional agency as a commission ranging from 10-15% with what interests them charge a relatively high price to take your work more savings! Where then? Well, given my position, I have to say that this is confidential information, although you can move to cheap flights to New Zealand are always in small agencies, called in English "Travel Consolidators" dedicated to purchase travel in packs to baratísimos the airlines. These are a few seats away from winning blow over a bit of money and the burden is on these small agencies to try to sell them and make a small profit. In our low-cost agency, for example, we find flights from approximately 550 Euros. With a bit of flexibility that is usually quite easy to get. In the worst cases, the flights could get to touch the 1000 Euros, but never the terrible 1400 Euros which are usually charged for this trip.

Just finish by saying that, as I always like to point out, New Zealand is for everyone, not just for those who have much money. Every lover of nature has the opportunity to discover this paradise. And yes, cheap flights to New Zealand from Spain are not fiction, is a reality that every day is closer to everyone. Just open your eyes.

Lowcost Holidays In Las Vegas

Glowing neon signs, luxury hotels, limousines to walk the streets and billboards with the faces of celebrities. This is the image that the vast majority of people are in Las Vegas and therefore consider it impossible to enjoy a cheap holiday.

However, the reality is quite different because Las Vegas has been able to reserve a space for each purchasing power. While the millionaires spend fortunes in the exclusive Bobby'sRoom Bellagio, a large part of the tourists can enjoy the American dream without spending too much and without being restricted.

Getting there

Whenever considering starting date for the days between Sunday and Thursday, you can find cheap flights from Europe and that fewer people are traveling these days and ticket prices are cheaper. Obviously, avoid significant dates such as Christmas and New Year and the January, July and August.

Many of these flights arrive to the city of Los ANGELES. For this reason many people choose to hire for the adventure of traveling hundreds of miles of desert. While this may be a tempting plan, the truth is that the different deals offered by these hotels are even more convenient. In addition to considerable time savings in these offers domestic flights out totally free or at a bargain price.

Where to sleep?

Las Vegas Stripacapara 19 of the 25 largest hotels in the world and exquisite. This means that higher prices are exorbitant rooms at these hotels just design. However, in the interior streets you can find cheap hotels that, although more modest, offer impeccable service.

If you still want to indulge a little whim and just staying in Las Vegas Strip, Excalibur and then CicusCircus hotels are cheaper. For special offers, the minimum price of around $ 70 per night.

Economic Attractions

Visit Las Vegas and try your luck is like going to Paris and not know the Eiffel Tower. How to play without spending too much? First you must know that almost every shop, restaurant or hotel in Las Vegas offers coupons which you can start playing. In addition, there are casinos like the Luxor which are held every Friday free poker tournaments with a prize of one thousand dollars and also offer lessons in the afternoons free alguno.Aún so, the golden rule is: do not enter a casino with more money we are willing to spend.

The fashionvictim also have the opportunity to approach the American fashion without paying excessive prices. Nothing better than coming to the Las Vegas Premium Outlet, and if they match the discount period, you will find attractive prices.

Finally, if you want to try the delicacies of fine dining, then it is highly recommendable to decide for lunch and dinner that prices tend to be much higher.

Tips For Travel To India In Summer

India has always been a favorite destination for tourists from around the world. Travel to India is synonymous with exotic places, culture, mythology, landscapes and culinary arts, as well as spirituality and recogimiento.En this article offer tips and useful information to travel to India in summer time when India hosts the largest number of visitors. Passports: First, as in most foreign travel, we must have an updated passport and valid, ie, the passport should not win in the six months period following the presentation to customs. Also we have the tourist visa that is valid for six months. Generally, both an original photocopy of round trip tickets and itinerary preset that will give us the travel agency we contratado.Moneda: The official currency of India is the Indian Rupee, the easiest way is to take money from the country of departure, or traveler's checks, this will always be cheaper than secillo and change the currency once it has arrived. The coins are legal tender only be changed in the houses we cambio.Si euros, in India we find places where we can change.

Thus there is no need to change U.S. dollars previously estadounidenses.Vacunas: dsi travels to India in the summer, we should have an international certificate of vaccination against yellow fever present 10 days before entering the country. Now, it is recommended to those who decide to vacation there, as a precautionary measure, also be vaccinated against Hepatitis A and B, tetanus and typhoid. Special emphasis is placed on the recruitment of a medical insurance before carrying out the trip and once there, the conditions are not the most optimal. It is also recommended to drink bottled water should be boiled or sterilized in order to not take risks or disease during the estancia.Por other hand, being summer, we should not forget to bring insectos.Higiene repellent: women do not find certain products easily. Therefore, it is advisable to take the necessary hygiene and transfers íntima.Taxis: in some places, the taxi fare may be paid depending on the route in advance we make. If not, they should not warn the driver that is our first time in that territory or that we are tourists, we often charge more than the payment correspondiente.Por other hand, it also happens that taxi drivers charge certain fees for bringing a passenger to different places.

Thus, we should not pay attention when we report our hotel is full, we should another room, etc.. They are resources for daily false away from our destination and charge a comisión.Vestimenta: the costumes of women in India is very different from Europe or America. In the summer, and almost any time of year, use of clothing is not tight or provocative. It is convenient to the body something loose (baggy pants, blouses) and rather cortas.Alimentación sleeves: not recommended accepting drinks, tea or food of any kind if we are not sure of its origin. To read travel articles like this, visit the Travel Blog Quehoteles.com.

The different neighborhoods of New York

New York, especially Manhattan, has some of the most unique and diverse in the world. Whatever you are looking, no doubt you'll find it at one of these amazing and interesting neighborhoods in the Big Apple.

NoLita

Until recently, this magnificent neighborhood in New York did not exist. Located halfway between Little Italy, SoHo and Lower East Side, this small neighborhood is filled with beautiful boutiques, galleries, thrift stores filled with treasures and eclectic restaurants whose delicious dishes to suit all tastes. If you make a trip to New York, not to be missed.

The Flatiron District

Famous for the 20-story Flatiron Building, the Flatiron district is home to a variety of boutiques, shops and department stores. The neighborhood is considered one of the most popular shopping areas. Located between Chelsea and Gramercy, Flatiron district is named after its main attraction, the magnificent 20-story Flatiron Building. Thanks to the abundance of nightclubs, bars and restaurants, is one of the trendiest neighborhoods in New York. Nor can lose Gothic architecture typical of the area. Also, while you're there, be sure to visit the Flatiron Building, Gramercy Park, New York Public Library and the Empire State Building.

Chinatown (Chinatown)

Chinatown, home to the largest population of Americans of Chinese descent in the country, is a must for any traveler who cares exotic. This neighborhood of New York comes alive in January, a month when we celebrate the Chinese New Year in style. For typical Asian products and visit the street markets and shops east, there is no place like Chinatown.

Little Italy (Little Italy)

Next to Chinatown is a piece of Italy. Little Italy has some of the best cafes and restaurants in New York, and needless to say the food is fantastic. If you like gangster movies, you can not miss Little Italy, for here were filmed several scenes of The Godfather and other mafia movies.

Midtown

The prestigious Fifth Avenue divides the Midtown neighborhood into two halves: the west and the east. Midtown East, including the fashionable neighborhood of Murray Hill, is famous for its excellent shopping, fantastic restaurants and attractions. So if you are interested in buying Hermès, a trip to the architectural marvel that is the Chrysler Building or eat some sushi or pizza before heading to MoMA, Midtown East is a must between the neighborhoods of New York.

Midtown West is the heart of New York in regard to business, shopping, entertainment and tourism in the city. When you scroll to the Midtown West, be sure to visit the eclectic neighborhoods of Hell's Kitchen and Clinton. Melting pot of cultures, races, religions and tastes: this neighborhood in New York will delight all who visit the Big Apple.

Greenwich Village

Broadway separates the Greenwich Village neighborhood in two halves: East Village and West Village. No doubt this is the most artistic neighborhood of New York. If you are attracted to poetry readings, jazz bars or punk rock, you'll love Greenwich Village. As is also home to the University of New York, has many rock night clubs, places where a pizza and a beer and coffee. Greenwich Village has something for everyone.

SoHo

SoHo is the most fashionable district of New York, famous for its magnificent art of sidewalks, studios, galleries and art cafes. At night, the neighborhood becomes alive and full of vitality and color. Do not miss a trip to one of the restaurants or bars.

Chelsea

Would you like to visit one of the most beautiful neighborhoods in New York? Then go to the wealthy neighborhood of Chelsea in their next visit to the Big Apple. Home of the Chelsea Piers, Union Square and Madison Square Park, Chelsea has many gay bars and a variety of restaurants, theaters and nightclubs. Another of its charms is its location in the heart of the Garment District (Fashion District) of New York, so buying here is a pleasure.

Upper West Side and Upper East Side

The Upper West Side is famous for its cosmopolitan charm as well. It is much more relaxed than the Upper East Side and enjoys great popularity among executives and families. It is a pleasure to shop in Zabars, Fairway Market, Hugo Boss, Morgenthal Frederics Eyewear and Crabtree & Evelyn. The Lincoln Center, the Children's Museum of Manhattan and the New York Historical Society will meet their cultural needs.

Home to some of the wealthier citizens of New York, the Upper East Side is very popular and is the ideal place if you love shopping. With places like Barneys, Madison Avenue and Bloomingdales, it is easy to see why it enjoys such popularity.

Tribeca

To the west of SoHo lies Tribeca neighborhood, which is also fashionable with its galleries, markets and incredible nightlife. It is the district of New York publishing, and therefore hosts several bookstores and many restaurants will not know which to choose.

Every neighborhood in New York is totally unique and has its own attractions, some of which we have mentioned here. To enjoy the best attractions on your trip to New York should consider the New York Pass, which will provide entry to over 55 attractions in New York.

The New University Thought Trends

"The universities and educational institutions play an important role in today's world characterized by the challenges that poses the knowledge society, a strategic role in the transition from one paradigm to another more dynamic, where economic development and conditioned by social factors is unavoidable, such as having to do with the progress of the investigation and the progress of science and technology? With the emergence of a new model imposed by today's knowledge society, academia, its agencies and people involved therein, are committed to facilitate adjustments, alterations and major alternatives in its structure, to make the scholarship, of teaching, research and extension, the basis for change to induce a new model of socio-economic development. This step is platform and record the ideas of Martí, when nearly a century taught us that the new world a new university belongs to the express?: "In times theology, theological college. In time scientists, scientific university?. (J. Martí 1963: T8 34)

The developments today's world is experiencing economic, educational, social, political and cultural, together with the great advances in science, technology and information in these times has produced a new socio-historical context where human society every day must embrace change and challenges imposed by the information society and knowledge. These important changes have impacted the university education system in the world by establishing a new philosophical conception of teachers and institutions of higher education. This reality leads to the emergence of new requirements and management practices for the teacher to respond efficiently and effectively to the changes we experience today in this sector. The versed in the area: Daniel Bell wrote his book in Spanish universities were investigated very little. Today the reality is different: The search for scientific and technical is composed an important part of the regular fit and universities, but did not achieve in quantitative terms, the average production levels, we can say that most university teachers applies to the production of knowledge. But now, universities are not the only institutions that produce knowledge.

Not since its creation in the Middle Ages, they have been in exclusive and in times of deep crisis of the universities, as in the eighteenth century, much of the technical creation took place outside thereof. But from the second third of the twentieth century, especially after the Second World War, when scientific research is addressed systematically by arms companies and other non-university institutions, producing as much or more knowledge in the academies .

The 21 century leaders

IT IS L? DER by its very existence.



The man likes to win, exercise and maintain power, many times we turn to the truth for a profit, because we realize that all around us no loyalty or sincerity in action, and we commit or / a sympathize with the famous phrase that does not tranz = not advance =, we have seen men march through history that will eventually be recognized as leaders in thought and hope that thanks to his eloquence, presence or his innocent face showing, to their messages that bombarded us until they had the opportunity to satisfy their interests, little help from a Machiavellian advertising and our agreement, as currently the character who wants to succeed has publicly advertising platform, if you are motivated by good you will by the current that drags us or at other times it was said = that moves not in the photo = y, we realize that one of the most important points to overcome these states of man is to recognize the existing mediocrity education, but this should not generalize, but if we have to recognize that there is, which is something we as humans going on and why we are paying a high price, we need a higher dose of valuation of our rights and Of course, our obligations, that we recognize and enforce them will automatically lead to a higher level of self-esteem and competence.

A competition but not as we conventionally, and that the conduct against an opponent, we need to see the competition against ourselves, making ourselves a leader. Concluding that if we're on the right path, we will be able to sow the good in our environment.

The UNAD, faces the challenges ahead

The Open University and Distance, faces the challenges of globalization through innovation, capturing from various perspectives of managing an education that responds to the knowledge society.

The XXI century education demands that new generations have the capacity to meet the challenges of globalization with new skills and knowledge. That addresses the management of technology and eradicate stratified differences in education.

Transforming and renewing higher education, it is intended that the company has the ability to compete not only locally but globally. In this leads UNAD under its various programs to build citizens able to tackle the various challenges that we face the twenty-first century.

This development of the education system is fundamental to the transformation of higher education today, where UNAD integrated through the participation of all, some innovative and sustainable developments in education for the future, as in this Colombian .

In this, the Open University and Distance working on a teaching model based on autonomy, under the constant reflection that combines theoretical and practical knowledge to the management of ICT thus achieving an international dimension to seek an exchange with quality and relevance .

The National Open University and Distance (UNAD) under its mission in mind the need of our society which competes and is facing a globalization that brings with it a transformative dynamic, so sailing distances to combat not only physical but intellectual among developed societies others like ours in the process of development.

Among his main interest is the advantage of technological advances to contribute to social change, knowledge, and thus development. That the actors act with responsibility and autonomy, to develop an entrepreneurial spirit and always looking for the advancement of projects productive for a society vulnerable, active or changing.

In the words of Germain Pilonieta "authentic pedagogical action is one that could develop within a dynamic view of history, educational projects that provide for democratic principles, technological, epistemological methodological strategies and supports to match the dynamics of the concrete reality of the community. (1987, 115). In this, the present managing UNAD ideal education in our society.



REFERENCES

MORENO, L. A. (2010). OPEN AND DISTANCE LEARNING UNIVERSITY: PROSPECTS AND CHALLENGES.

Pilonieta, German (1987) The relevant curriculum in distance education. IN: PEREIRA, Francisco The Distance Education in Latin America. Volume I. National Open University, Vice President for Academic Publishing Fund. Caracas: Editorial Kapelusz Venezuela.

Essentials in Combinatorics

What is essential in Combinatorics. R. Reytor. Isbn. 9789591607430? Index. Page Foreword ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. 3 An introduction necessary ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 4 A little history ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 6 Chapter 1. General rules of combinatorics ... ... ... ... ... ... ... ... ... ... ... ... 9 1.1 .- Principle Additive ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 10 1.2 Principle Multiplicative ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 12 1.3 .- Exercises ... ... ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... 15 Chapter II .- Variations and permutations ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 18 2.1 Platform variations without repetition ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .22 Training and number of permutations without repetition ... ... ... ... ... ... ... ... ... 23 2.1 Permutations without repetition ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. 28 2.3 Circular Permutations ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 34 2.4 Permutations with repetition ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 37 2.5 Training and number of permutations with repetition ... ... ... ... ... ... ... .. 38 2.6 Variations with repetition ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. 40 2.6 Exercises Chapter II ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. 49 Chapter III. Combinations ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 56 1.3 Training and number of combinations without repetition ... ... ... ... ... ... ... 57 3.2 Combinations with Repetition ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 61 3.3 Relationship between combinations with and without repetition ... ... ... ... ... ... .. 63 3.4 Repeated exercise in Chapter III ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 64 Solutions and Answers ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 68 Preface. The development of combinatorial thinking is hard work and patience in this sense plays a big role in the system of pulses as a spring has to teach combinatorics. On many occasions, at the end of receiving a combinatorial topic, students do not have enough weapons to cope by themselves to solving problems, because the system of impulses in the appropriation of these concepts has been insufficient. The work of the teacher is important in this regard because they highlight the characteristics that defined concepts or facilitate appropriate description or characterization of these is ensuring success in the teaching process.

This text has been intended to highlight the treatment of combinatorial concepts in order to secure them properly giving attention to the process of identifying them, especially when we are dealing with problems. There are, of course, some trends algoritmizar try to work with sequences of combinatorial problems proposed indications for its solution, but, when these signs have a strong heuristic, further activate the learning process. Success in teaching combinatorics lies essentially in the drive system is used to set these concepts. This, undoubtedly, was the character that has tried to print this text. Had he succeeded, the goal will be fulfilled. The author. An introduction necessary. The combination is a section of mathematics that is useful for various representatives of various specialties. With the combinatorial problems are faced by biologists, physicists, chemists, mathematicians, linguists, engineers and many others. The study of combinatorics is the base that supports the analysis and solution of many problems of probability theory and its practical applications. This paper explains in simple language and combinatorial methods to solve the problems on this issue are proposed.

The exhibition has been made so that it can be understood by individuals with an average instruction. It may be useful to students and teachers of secondary education institutions, students from faculties of education in the fields of Mathematics, Physics, Chemistry, Biology and Elementary Education from the Higher Pedagogical Institute of Cuba especially in the first years of their respective specialties where they must face in the practical work with various combinatorial problems. This sets out the general rules of combinatorics, additive and multiplicative Principles, variations, permutations and combinations with and without repetition. these concepts are defined and described, emphasizing the characteristics that identify them in practical work, we deduce the formulas for combinatorial and are in the form of theorems with their proofs. Special emphasis is placed on the treatment should be given to the combinatorial defined concepts and their application to solving problems. It also includes many examples and exercises to help fix and systematized. Although this text has been respected mathematical rigor in the treatment of the concepts, the main objective of this is to analyze in some ways the combinatorial nature of the elements present in the problems and show some ways to solve them.

A little history. The part of mathematics that studies the problems of how many or which combinations (under certain conditions) can be performed with certain objects is called combinatorics. Historians place the emergence of combinatorics in the early sixteenth century, and was coined almost exclusively in the aristocracy of the time, for this society, generally spent his time in games of chance in which great fortunes won or lost. Playing dice or cards were won or lost large fortunes. Playing dice or cards were won or lost bright garments valuable thoroughbreds, etc.. At this time they were released several types of lotteries which occupied his days of knights and ladies of the time. It is understandable then, that in its inception, the problems is fundamentally about gambling, trying to figure out how many ways could be obtained favorable events in a number of tests. Thus, for example tried to find out how many ways you could draw a specific number by throwing several dice or how many ways you could draw two kings in a deck of 52 cards. These and other games were the driving force of combinatorics and probability, theory that runs parallel to it.

History records the name of Tartaglia as one of the pioneers in combinatorics. This famous Italian compiled a table showing all the ways you can fall "n? given, but did not anticipate that the same amount of points could be obtained in different ways (eg 4 +1 +3 = 4 +2 +2). The theoretical study of combinatorics is considered a fact from the year 1600 (XVII century) when the French Blaise Pascal and Fermat began collecting samples of experiments performed at the gaming tables and statistically recorded to study the laws and regularities in the which were governed. A particularly important role was played here the problem of the division of a wager Pascal proposed by a friend named Mere, passionate player by others. The problem was this: if a coin is tossed, the championship will continue until one player has won 6 games, but is interrupted when one won 5 and the other 4. How to split bet then? It was evident that the 5:4 ratio was not fair. Pascal solved the problem using some combinatorial methods and also proposed a solution method for the general case, when a player will remain "r" games to win and the other player will remain "s" matches.

A similar solution to this problem was given by Fermat. The subsequent development of combinatorics is linked to the names of famous mathematicians and Jacob Bernoulli, Leibniz and Euler. However, for these, also the fundamental role it were the applications to different types of games. Already in recent years, combinatorial entered a period of intense development related to the general growth of interest in the problems of discrete mathematics. Combinatorial methods are used to solve transportation problems, timetabling problems on, production plans and the mechanization of these and to determine the genetic characteristics in obtaining laboratory animal breeds. The combination is used for making and deciphering codes and to solve problems of information theory. And also, why not? To decide not too distant future the most effective way of preserving life on our planet. Chapter I. General rules of combinatorics. Combinatorial problems are classified according to the number of operations needed to solve to make: • Combinatorial Problems simple: those who are resolved by combining a single operation. • Problems combinatorial compounds are those which are resolved by using more than one operation combinations.

In the development of the following chapters exemplify these classifications. In discrete mathematics there are problems that are resolved by using certain formulas (depending on the combinatorial nature of the elements present in them) but most can be solved by two general principles: 1. The additive principle or rule of Sum. 2. The Multiplication Principle or Rule of the Product. The Multiplication Principle is generally associated with the procedure used in the early school years to find the number of items containing certain set, hence the majority of teachers recognize it as "Counting Method?. As is often the number of combinations or arrangements can be made with the elements of a set admits that appear in every election one and only one class of combinations, then the additive principle can be expressed as follows: '1.1.-Principle Additive "The total number of combinations that can be done with all kinds of items in a set is equal to the sum of the combinations of each of the classes?. Note: Class is defined as all subsets that form the elements of the set in question. Through the analysis and solution of the following example can be seen the application of this method.

Example 1: Mark has 3 shirts and 4 pants. Mark how many ways you can combine the shirts and pants? Denote the shirts with the letters a, b, c. pants and the x, y, z, u. if we set the distribution can be made between the shirts and pants can be seen that: Look at you that each sample consisting appears once and only once. The total number of samples are easily obtained by adding all combinations obtained by the above process: 1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 = 12 12 times because the number of combinations each class is one. Example 2: In a study team there are 3 girls and 2 boys. How many different pairs can be formed to study? Similar to the above, we can form two sets of different nature: all the girls: Diana, Claudia, Susan and the children: Rafael, Alejandro. The selection of duets can be performed using a network diagram as follows: The lines connecting the circles is 10. Obviously the total number of possible samples is obtained by counting the lines formed. 1 +1 +1 +1 +1 +1 +1 +1 +1 +1 = 10 10 times Example 3: How many three-digit numbers must not repeat?

a) Start with 23. Previously analyzed the place of the units may be occupied in each sample by one and only one of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8.9. If we form each sample is obtained: 230, 231, 234, 235, 236, 237, 238, 239. As can be seen the number of combinations of each class is 1 so the total number of combinations of all classes is 8. The additive principle? provides information about the composition of all samples from an experiment? issue that is important, especially in the early grades of education for the contribution they make in the field of combinatorial development of thinking in schoolchildren. Obviously "their inconvenience is that its application is rational only in cases where the total number of samples that make up the experiment is not very high?. The above examples can be addressed by further analysis, in which you can get to know the total number of samples that make up an experiment without having to form each of the samples that comprise them. In this sense we state the following principle. 1.2 .- Multiplication Principle. "If any one thing can happen in m different ways and if it occurred after any of these ways, anything can happen in n ways, then the two things in that order, m can occur n ways?.

This principle states that if two things happen one after the other, the total number of ways that can occur both by multiplying the number of ways from the first by the number of ways in the second. Example 4: How many syllables of two letters, beginning with a consonant, in Spanish there? In this case the method of counting additive slows down the work by the number of samples that have the experiment. The first thing is choosing the first letter (a consonant) and the second, the choice of a vowel. And Spanish are 24 consonants and 5 vowels only, the second choice may occur of 5 ways. In total can be obtained from 24 × 5 = 120 syllables. The multiplicative principle can be extended to more than two things. Example 5: "The numbers 2, 3, 4 and 5 can be multiplied for each other in different orders. Write down all the possible ways of considering the 2 as the first facto?. In this case we have 3 different things. The first is to place the second factor of the product (considering the order from left to right), for which there are three possibilities, the second place the third factor, we can have a chance.

Depending on the multiplicative principle we can multiply the numbers of 3 × 2 × 1 = 6 different ways. Clearly, they can easily see that all samples obtained up this experiment. Sometimes both methods can be applied to solve certain problems. Example 6: How many numbers of two or three non-repeating numbers can be formed with the digits 1 to 4? Applying the Multiplication Principle, to determine all 2-digit numbers we do not repeat the approach: 4 × 3 = 12 2-digit numbers are not repeated. Similarly to determine the amount of 3-digit numbers do not get repeated (4 × 3) × 2 = 24 numbers. Then applying the additive principle gives: 12 +24 = 36 numbers in two or three figures are not repeated. The combinatorial stranded allows the application of analytical methods for the solution of problems in the following example shows one way in which a problem can be solved. Example 7: To make a trip from city A to city B can be used three buses and to go from city B to city C only 2. How many different ways you can travel from city A to city C?

The following diagram shows how you can make the trip. In this diagram each segment represents a journey between two cities mentioned in the problem. To make the full trip is necessary to select two segments. Can be clearly seen that there are many possibilities as there are segments between city A and C, ie 6th this result is easily reached using the Multiplication Principle. In practice it is necessary to use a diagram like this, but if it does, it helps to understand the problem, which in more complex cases is essential. This type of diagram is called a diagram? Tree branches because every point in the same way as does a tree. Exercises. 1. How many ways can you choose a vowel and a consonant of the word number? 2. At the top of a mountain roads lead 5. How many ways can upload and download a camper using these roads? What if the ascent and descent are carried on different paths? 3. How many ways can choose two dominoes, of the 28's in a game table, so that can be applied with each other?

4. At a meeting there are 18 people. All greet each other and no two people greet each other more than once. How many hands greetings given? 5. In a clothing store there are men's shirts in 4 different sizes and three different colors in each size. How many different types of shirts in the store? 6. Of copies of a text after Algebra 2 Geometry Trigonometry and 2 must choose a copy of each. How many ways there are to do? 7. How many different ways can write the letters A, B, C, D, one after another without repeating any? 8. How many two digit numbers can be formed with the numbers 1, 2, 3, 4, 5, 6, 7? How many of them have their two numbers equal? 9. How many three-digit numbers can be formed with the figures of the number 24 356? How many are even? 10. How many are three-digit numbers that are multiples of two? 11. How many 4-digit numbers are there? 12. How many 4-digit natural numbers exist that do not contain the number 7? 13. How many odd numbers are 3 digits and are less than 500? 14. How many natural numbers between 100 and 999 have their different figures?

15. How many of the first 1000 positive integers are all different numbers? 16. How many three-digit natural numbers are such that the sum of its digits is 5? What are they? 17. How many ways can be indicated on a chessboard two squares: one white and one black? 18. In a corporation employed 67 people. Of these, 47 are fluent in English, 35 French and 23 in both languages. How many people do not speak of the corporation or English or French? 19. From a group of 19 young people like mathematics, plastic arts 17, 11 history, 12 prefer math and fine arts, history and mathematics 7, 5 visual arts and history. 2 people like the three subjects and 5 none of them. How many young people are in the group? 20. to transmit information by telegraph using Morse code. In this code the letters, numerals and punctuation marks are represented by dots and dashes. For example, the letter t is represented by a dot (.) And L for three points and a line (.-.). Using up to two signs, how many letters can be encoded? 21. there are three types of envelopes without stamps and four types of stamps of the same value.

How many ways you can choose an envelope and a stamp to send a letter? 22. How many ways can you choose a vowel and a consonant in the word Martí? 23. How many ways can you choose a vowel and a consonant in the word Maceo? 24. On a shelf there are three copies of a text in Spanish, 7 and 6 math history. How many ways you can choose a copy? 25. A person has 8 copies of a book of arithmetic and the other has 9 books of algebra. How many ways you can choose a copy? Chapter II. Variations and permutations. Previously studied combinatorial principles used to solve most problems that arise in combinatorial theory, however, there are some special cases that occur frequently and for which it is possible to obtain simple formulas. But if it is true that these formulas expedite the calculation, it is necessary to establish a prior work of identifying combinatorial experiment present in the problem. In this sense we may include combinatorial problems into two groups: the problems dealing with variations and combinations that address. Establishing this division, we will study each concept separately, highlighting the characteristics of the term that defines the specific purpose of identifying them in solving problems.

Of the anterior division first study the variations. This set of variations, in turn divide into 2 subgroups: without repeating variations and variations with repetition. The strategy we use to identify randomized experiments represent it in the following scheme: • Strategy for the Identification of a random experiment. The logic of the proposed strategy is based on the existence of a combinatorial experiment of unknown nature. To identify those parts of the formation of some samples of the same (at most 3) and analyze their characteristics, focusing our attention in order. The analysis leads to decision making related to the type of random experiment: if the distinctive element in the analysis of samples is the order, the experiment deals with random variations, otherwise, is about combinations. Once the decision is analyzed if the samples were again supported by repetition and decide: is a variation with repetition or a combination with repetition. This decision marked the combinatorial experiment samples and allows us to identify. If the random experiment was made, because he was formed by several simple random experiments, we start again and repeat the cycle analysis. With this logic will be discussed the concepts of combinatorial analysis.

For its part, the solution of combinatorial problems has been one of the most difficult barriers to overcome for the students because they do not use an appropriate strategy for solving them. The strategy for solving the combinatorial problems expressed in the following scheme: General scheme for solving a combinatorial problem. The logic of the strategy is the first time the identification of random experiment to implement the Strategy for Identification. The second step is to select the path to calculate the number of samples that make up the experiment using any of the calculation procedures known in the combinatorial theory: use of diagrams, general principles or formulas. The third stage is the implementation of the selected route calculation, with which we know the number of samples that make up the experiment. Validation of the way of calculation applied to the solution of the problem is the fourth moment of the strategy. This step takes on characteristics peculiar to the problems of discrete mathematics because it is very difficult to check the solution in relation to the text of the problem, except in very simple cases. Validation should be performed using a route other than the one chosen to give the solution and compare the results.

On the above conditions, we will treat the random experiments and solving problems on Combinatorial Theory. II.I. - Variations without repetition. Definition. Variations are called without repetition of n objects taken pap (or variations of order p) all p possible orderings of n objects taken from the given objects where repetition is not supported. The characteristics that identify the signs of an experiment without repetition variations are: Two different samples: • Or in the order of its elements. • Or at least one item. • Items not repeated in the same sample. Example 1: Train all numbers from 2 different numbers with the digits 1,2, 3, 4. 12 21 31 41 13 23 32 42 14 24 34 43 As can be seen, it is easy to analyze the samples made using the standard features mentioned. Samples 12 and 21 are different, since the order of the items taken is essential (obviously the numbers 12 and 21 are different). If we select the samples 12 and 14 the difference is an element (2 and 4) and samples 12 and 43 differ in its entirety. It is essential to the mastery of these characteristics for subsequent application to the analysis of combinatorial problems.

• Training and number of permutations without repetition. Variations without repeating a certain number of given objects, for example, the numbers 1, 2, 3, 4, you can go in succession, ie, first appears variations where only one element (Monari variations), then the binary the tertiary, etc.. The method involves adding a certain order every variation of each of the numbers not listed. The variations are evidently Monari: 1, 2 3, 4. To form the binary variation is added to each Monari, the remaining numbers, we get: 12 21 31 41 13 23 32 42 14 24 34 43 They are now ternary, adding to each binary numbers that do not appear in them. Applying the Principle Multiplicative we have: there are 12 binary variations and each one can add 4-2 numbers, thus obtaining 12 × 2 = 24 ternary variations. 123 231 321 412 124 213 312 421 132 241 342 423 134 214 324 432 142 234 314 413 124 243 341 431 Similarly the analysis is performed for variations quaternary or fourth order. In variations without repeating the training process concludes when sample order (p, number of elements in the sample) matches the number of elements in the set (N). Following the procedure described above can be variations without repetition of n objects taken pa p.

Theorem: The number of permutations without repetition of "n" objects taken pap is: • V (N) = N (N-1) (N-2) ... (N-p +1) with n ≥ p, N p are natural numbers, N ≥ 1. Demonstration. (Complete induction on n) • For n = p = 1 we have V (1,1) = 1. • For N = p is: V (p, p) = p (p-1) (p-2) ... (p-(p +2)) (p-(p +1)) are obtained without repeating variations of p elements from pap, for which it holds for n = p. • Suppose that is true for n = k. V (k, p) = k (k-1) (k-2) ... (k - (p +2)) (k - (p +1)) • validity for n = k it follows the validity for n = k +1 V (K +1, p) = (k +1) K (k-1) (k-2) (k-3) ... (k - (p +2)) (k - (p +1)) The formula is composed of p factors arranged in descending order starting with n and terminated by p. The following example shows the process of solving a combinatorial problem. Example 2: How many different three-digit numbers can be formed with the digits making up the number 24756? In this problem we have as elements the digits 2, 4, 7, 5, 6, a total of 5 elements and 3 samples must be different elements, it is important to note the fact of non-repetition of the elements the samples.

Formed a few samples of the experiment. 247, 724.245. It is easy to observe compliance with the relevant characteristics to changes without repeating two samples differ: • Or in the order of its elements (247, 724) • Or at least one item. (247 and 245) • The elements are not repeated in the same sample. Found that the combinatorial element present in the problem without repeating variations undoubtedly we can easily determine the number of elements in the set (N = 5) and the number of elements with the samples (p = 3). Applying the formula for calculating and making them get V (5.3) = 5x4x3 = 60 three-digit numbers. To validate the result we can apply the Multiplication Principle: We can designate the hundreds place by the variable m, n and the dozens of units by p. The site can be occupied m 5 forms, n and p 4 ways 3 ways. The number of times that can occur in that order of things is: = 5x4x3 = 60 mxnxp Analysis of combinatorial problems is the key to determine the nature of this random experiment in it. Sometimes the difference between combinational elements is so subtle that it is not easy to determine whether the analysis is superficial.

Example 3: In a group of 8 people have to choose a president, vice president and secretary. How many ways can you do? They form groups of three people to whom to be designated responsibilities, no matter the order of choice of people and if the order in which they are appointed positions. We form three samples of the experiment. As the charges are not repeated and the designation of responsibilities differs in each sample formed, the experiment shows that variation is not repeated. N = 8 and p = 3 V (8.3) = 8x7x6 = 336. The validation and retrospective analysis of the problem we can make it similar to Example 2. If you change slightly the structure of the problem such as: In a group of 8 people have to choose a group of three to participate in an event. How many ways can you do? Formed a few samples of this experiment. First group: Paul, John, Jonah. Second group: John, Paul, John. Third group: Paul, Rachel, John. No matter what order to take the members of the groups, since if they have the same members, it is the same group is what happens with the first and second groups.

In the analysis of samples we can realize that they are different the first and third groups or the second and third.

















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