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The Greek sailor Constantine Phaulkon, born to Catholic parents on a small island under Venetian control, joined the English East India Company, changed his religion to Anglicanism, and came to Siam as a merchant in 1675. A gifted linguist, he learned Thai, Malay, Portuguese, and English, becoming so skilled that he was appointed the prime counselor of King Narai. The English relied on him to promote their interests against the Dutch, with whom they had been at war. Then he converted to Catholicism, married a Christian woman of combined Japanese, Portuguese, and Bengali ancestry, and accumulated great wealth and power at the Siamese court. Aided by local Jesuits, he acted on behalf of the French against the English and Dutch. Louis XIV made him a citizen of France and a member of the French nobility, and the French had hopes of converting the king to Catholicism. Phaulkon continued to prosper in trade. He ordered jewels from the American Elihu Yale, President of the East India Company in Madras, who later founded Yale University, but returned them when he discovered that their price was too high. The French sent a military expedition to Siam in 1685, but their efforts to invade the country failed, forcing them to withdraw in 1688 in the face of intense hostility from the local population.
In 1959 Richard Nixon (1913–1994), vice president of the USA, traveled to the USSR to accompany Nikita Khrushchev (1894–1971), Soviet premier, to the opening of an exhibition on the American home. The contrast between the two men was striking. Khrushchev came from a peasant background, had supported the purges of the 1930s, and was a close associate of Joseph Stalin. He had commanded troops in the Battle of Stalingrad and had previously been First Secretary of the Russian Communist Party.
Except for military service, Nixon too had spent his life in politics. Serving in the South Pacific during the war, he had been elected to the House of Representatives and Senate from California. He had come to national prominence in 1948 as a member of the House Un-American Activities Committee and had played a leading role in the investigation of whether a former State Department official, Alger Hiss, had been a secret communist and passed government papers to the Soviets. The committee’s findings were inconclusive but Hiss was later convicted of perjury.
As they wended their way through the exhibition, Khrushchev and Nixon, followed by reporters, fell into debate that grew more intense, stopping in front of a section of the show devoted to the American kitchen; the debate that followed became known as the “kitchen debate.” Nixon invited the Soviet premier to look round and observe “a house, a car, a television set – each the newest and most modern of its type we can produce.” Nixon noted that while the USSR might be ahead of the USA in regard to missile thrust, the USA was superior in color television.
Virtual work method has many applications. It is more powerful than the traditional method in solving problems of frames and machines. It is especially suitable for problems involving degrees of freedom. The principle of virtual work is applicable to both types of problems: in static equilibrium and in dynamic condition. D’Alembert's principle is used to convert dynamic problem into static problem.
8.2 Degrees of freedom
To describe the physical motion of a system, a set of variables or coordinates are required. These are called generalized coordinates. The minimum number of independent coordinates needed to describe the motion of the system is called degrees of freedom.
A free particle is shown in Figure 8.1a. It requires three coordinates to completely specify its location. So, the degree of freedom of a particle in space is three.
In the years after 1500, the whole human family came into contact for the first time in thousands of years. For millennia Amerindians, Eurasians, and Polynesians had developed separately from one another with no knowledge of the existence of other members of the human race. Then in a few decades around 1500 long-lost peoples rediscovered one another. Amerindians and Europeans who had existed independently for at least 14,000 years suddenly came into contact. This same encounter occurred at many points throughout the world.
Within decades Europeans, Americans, and Asians were involved in a gigantic exchange that forever affected their menus and their agricultural life. Mineral and agricultural products crossed both the Atlantic and the Pacific in massive quantities, transforming production methods and daily consumption. From the Americas, Europeans imported turkeys, cranberries, potatoes, tomatoes, and tobacco. Asians obtained maize, peanuts, chili peppers, and most important, silver and gold in exchange for porcelain, silk, and tea. From Europe, Amerindians learned about horses, apples, barley, coffee, and wheat. Not all exchanges were productive. Crab grass comes from Europe as well as measles, malaria, cholera and bubonic plague, while smallpox devastated previously unexposed populations of the New World and Asia. From America came syphilis and hepatitis.
From an applications viewpoint, the main reason to study the subject of this book is to help deal with the complexity of describing random, time-varying functions. A random variable can be interpreted as the result of a single measurement. The distribution of a single random variable is fairly simple to describe. It is completely specified by the cumulative distribution function F(x), a function of one variable. It is relatively easy to approximately represent a cumulative distribution function on a computer. The joint distribution of several random variables is much more complex, for in general it is described by a joint cumulative probability distribution function, F(x1, x2, …, xn), which is much more complicated than n functions of one variable. A random process, for example a model of time-varying fading in a communication channel, involves many, possibly infinitely many (one for each time instant t within an observation interval) random variables. Woe the complexity!
This book helps prepare the reader to understand and use the following methods for dealing with the complexity of random processes:
• Work with moments, such as means and covariances.
• Use extensively processes with special properties. Most notably, Gaussian processes are characterized entirely by means and covariances, Markov processes are characterized by one-step transition probabilities or transition rates, and initial distributions. Independent increment processes are characterized by the distributions of single increments.
• Appeal to models or approximations based on limit theorems for reduced complexity descriptions, especially in connection with averages of independent, identically distributed random variables. The law of large numbers tells us, in a certain sense, that a probability distribution can be characterized by its mean alone. The central limit theorem similarly tells us that a probability distribution can be characterized by its mean and variance. These limit theorems are analogous to, and in fact examples of, perhaps the most powerful tool ever discovered for dealing with the complexity of functions: Taylor's theorem, in which a function in a small interval can be approximated using its value and a small number of derivatives at a single point.
The hype around globalization in early-twenty-first-century political and economic debates may convey an impression that we now are in an entirely new phase of economic development. This chapter will show that the presumption is wrong. A dose of elementary economic history is often helpful when the popular media forget about the past.
Globalization is market integration on a world scale. Market integration means that domestic markets are increasingly dependent on international markets. Prices and hence factor rewards will reflect global rather than local demand and supply conditions. Globalization is the product of intensified trade, capital mobility and migration. In that process prices, interest rates and – with a time lag – wages tend to converge and react faster to international shocks. The first wave of globalization started in the middle of the nineteenth century when barriers to trade, migration and capital mobility were abolished or weakened at the same time as the speed of information transmission increased. In most respects markets were as globalized around 1900 as they were at the beginning of the present century. In fact labour mobility across borders was less restricted before 1914 than it is now. However, there was an anti-globalization backlash early in the twentieth century with two World Wars and the Great Depression. That policy reversal affected commodity, labour and capital markets to the extent that the late-nineteenth-century globalization level was not regained until the 1970s or 1980s, when the second globalization period gained momentum.
Market integration operates through trade and arbitrage and the ultimate manifestation of a fully integrated market is the law of one price. The law of one price proposes that the price of identical goods that are traded is the same in all geographical locations. This is strictly true, of course, only if transport and transaction costs are zero, which they are not.
This edition has been thoroughly revised and a large amount of new material has been added reflecting new research results and the recent development of the European economy. Paul Sharp, my former PhD student and now Professor at the University of Southern Denmark in Odense, has assisted me in this work and he has the principal responsibility for Chapters 8 and 9.
We thank Marc Klemp for revising the Glossary and for his comments and suggestions on Chapter 3.
Claudia Riani has contributed to the development of the companion website and we thank Martin Lundrup Ingerslev for research assistance.