The asymptotic dependence structure of the linear fractional Lévy motion
the managerial discretion theory
the managerial discretion theoryThe Managerial Discretion TheoryIntroduction:The managerial discretion theory is a popular theory in the field of management that explains how managers have the ability to exercise discretion in decision-making and shape the direction of their organization. This theory suggests that managers have a significant impact on organizational outcomes and that their discretion in decision-making plays a crucial role in determining the success or failure of an organization. In this essay, we will explore the various aspects of the managerial discretion theory, including its origins, key concepts, applications, and criticisms. Origins of the Managerial Discretion Theory:The managerial discretion theory emerged during the late 1960s and early 1970s, in response to the dominance of the bureaucratic management approach. This approach emphasized the importance of rules, procedures, and hierarchy in decision-making, leaving little room for managerial discretion. Theorists such as Richard Cyert and James March challenged this approach by arguing that managers should be allowed to exercise discretion and use their judgment in decision-making, as they possess unique knowledge and expertise about the organization and its environment.Key Concepts of the Managerial Discretion Theory:The managerial discretion theory is based on several key concepts that help to explain how managers exercise discretion and shape organizational outcomes. These concepts include bounded rationality, goal ambiguity, resource dependence, and institutionalpressures.Bounded rationality refers to the limitation of human rationality in decision-making. According to Cyert and March, managers are not capable of making fully rational decisions due to cognitive limitations, time constraints, and incomplete information. Instead, managers rely on heuristics and biases to make decisions, which may not always result in the optimal outcome.Goal ambiguity refers to the lack of clarity and consensus among organizational members about organizational goals. This ambiguity provides managers with room for discretion in interpreting and pursuing organizational goals. Managers can prioritize certain goals over others and allocate resources accordingly, based on their own judgment and interpretation of the situation.Resource dependence theory suggests that managers exercise discretion to manage their organization's resource dependencies. Organizations rely on external resources, such as capital, labor, and technology, to function effectively. Managers must negotiate and make decisions to acquire and allocate these resources, which gives them significant discretion in shaping the organization's strategy and direction.Institutional pressures refer to the external social, cultural, and political forces that influence managerial discretion. Managers face pressures from various stakeholders, such as employees, customers, suppliers, government agencies, and the broader society. These pressures shape the decision-making process and can limit orexpand the manager's discretion.Applications of the Managerial Discretion Theory:The managerial discretion theory has been extensively applied in organizational research to understand managerial decision-making and its impact on organizational outcomes. Researchers have examined how managers exercise discretion in various contexts, including strategic decision-making, organizational change, innovation, and corporate governance.Strategic decision-making is a key area where managers exercise discretion. They make choices about the organization's competitive positioning, resource allocation, product development, and diversification. The managerial discretion theory suggests that managers' cognitive biases, heuristics, and interpretation of organizational goals will influence these decisions and their subsequent impact on organizational performance.Organizational change is another area where managerial discretion plays a crucial role. Managers have discretion in initiating and implementing change initiatives, such as restructuring, mergers, acquisitions, and downsizing. The success of these change efforts depends on the manager's ability to exercise discretion effectively, navigate internal and external pressures, and align the organization's goals with the change initiative.Innovation is an important driver of organizational success and competitiveness. Managers play a critical role in fostering innovation within their organizations by creating a supportive culture, allocating resources, and providing necessary autonomyfor employees. The managerial discretion theory suggests that managers with high levels of discretion are more likely to support and promote innovation within their organizations.Corporate governance is the system of rules, practices, and processes by which a company is directed and controlled. The managerial discretion theory has been applied to understand how managers exercise discretion in corporate governance decisions, such as executive compensation, board composition, and shareholder relationships. Managers can shape the governance structure to align their interests with those of shareholders or other stakeholders, depending on their level of discretion.Criticisms of the Managerial Discretion Theory:While the managerial discretion theory has made significant contributions to the field of management, it is not without its criticisms. Some scholars argue that the theory overemphasizes the role of individual managers and neglects the importance of structural and contextual factors. They contend that managers' discretion is constrained by organizational structures, external pressures, and industry dynamics, which limit their ability to shape organizational outcomes.Another criticism of the theory is that it assumes managers always act in the best interest of the organization. However, managers may have their biases, self-interests, and personal agendas that can influence their decision-making and compromise organizational outcomes. This criticism raises questions about the ethical implications of managerial discretion and the need for accountability mechanisms to ensure that managers exercisediscretion responsibly.Conclusion:The managerial discretion theory provides valuable insights into how managers exercise discretion in decision-making and shape organizational outcomes. It emphasizes the importance of managers' knowledge, judgment, and interpretation of organizational goals in driving success. While the theory has been widely applied and has contributed to our understanding of managerial behavior, it is not without its limitations and criticisms. Future research should address these criticisms and further refine the theory to enhance its applicability and validity.。
第三阶段：GMAT OG13语法部分正确句子汇总
OG13 SC正确句子汇总1. In a review of 2,000 studies of human behavior that date back to the 1940s, two Swiss psychologists declared that since most of the studies had failed to control for variables such as social class and family size, none could be taken seriously2. Manufacturers rate batteries in watt-hours; if the higher the watt-hour rating, the longer the battery can be excepted to last.3. Although a surge in retail sales has raised hopes that a recovery is finally under way, many economists say that without a large amount of spending the recovery might not last.4. At the end of 1930s, Duke Ellington was looking for a composer to assisthim-——someone who could not only arrange music for his successful big band, but also mirror his eccentric writing style in order to finish the many pieces he had started but never completed.5. Of all the vast tides of migration that have swept through history, perhaps none was more concentrated than the wave that brought 12 million immigrants onto American shores in little more than three decades.6. Diabetes, together with its serious complications, ranks as the nation's third leading cause of death, surpassed only by heart disease and cancer.7. The intricate structure of the compound insect eye, with its hundreds of miniature eyes called ommatidia, helps explain why scientists have assumed that it evolved independently of the vertebrate eye.8. In late 1997, the chambers inside the pyramid of the Pharaoh Menkaure at Giza were closed to visitors for cleaning and repair because moisture exhaled by tourists had raised the humidity within them to such levels that salt from the stone was crystallizing and fungus was growing on the walls.9. In 1979 lack of rain reduced India's rice production to about 41 million tons, nearly 25 percent less than the 1978 harvest.10. The widely accepted big bang theory holds that the universe began in an explosive instant ten to twenty billion years ago and has been expanding ever since.11. Like the Brontes and Brownings, James Joyce and Virginia Woolf areoften subjected to kind of veneration that blurs the distinction between the artist and human being.12. Carnivorous mammals can endure what would otherwise be lethal levels of body heat because they have a heat-exchange network that keeps the brain from getting too hot.13. There are several ways to build solid walls using just mud or clay, but the most extensively used method has been to form the mud or clay into bricks, and, after some preliminary air drying or sun drying, to lay them in the wall in mud mortar.14. Rising inventories, if not accompanied by corresponding increases in sales, can lead to production cutbacks that would hamper economic growth.15. Many experts regarded the large increase in credit card borrowing in March not as a sign that households were pressed for cash and forced to borrow, but as a sign that households were confident they could safely handle new debt.16. A surge in new home sales and a drop in weekly unemployment claims suggest that the economy might not be as weak as some analysts previously thought.17. Sunspots, vortices of gas associated with strange electromagnetic activity, are visible as dark spots on the surface of the Sun but have never been sighted on the Sun's poles or equator.18. Warning that computers in the United States are not secure, the National Academy of Sciences has urged the nation to revamp computer security procedures, institute new emergency response teams, and create a special nongovernment organization to take charge of computer security planning.19. The exploits of Nellie Bly, a pioneer journalist, included circling the globe faster than Jules Verne's fictional Phileas Fogg.20. Retail sales rose 0.8 of 1 percent in August, intensifying expectations that personal spending in the July-September quarter would more than double the 1.4 percent growth rate in personal spending foe the previous quarter.21. The commission has directed advertisers to restrict the use of the word "natural" to foods that do not contain colour or flavor additives, chemical preservatives, or anything that has been synthesized.22. Plants are more efficient than fungi at acquiring carbon, in the form of carbon dioxide, and converting it to energy-rich sugars.23. The Iroquois were primarily planters, although they supplemented their cultivation of maize, squash, and beans with fishing and hunting.24. Unlike the honeybee, the yellow jacket can sting repeatedly without dying and carries a potent venom that cause intense pain.25. Neuroscientists, having amassed a wealth of knowledge over the past twenty years about the brain and its development from birth to adulthood, are now drawing solid conclusions about how the human brain grows and how babies acquire language.26. Tropical bats play important roles in the rain forest ecosystem, aiding in the dispersal of cashew, date, and fig seeds; pollinating banana, breadfruit, and mango trees; and indirectly helping to produce tequila by pollinating agave plants.27. None of the attempts to specify the causes of crime explains why most of the people exposed to the alleged causes do not commit crimes and, conversely, why so many of those not so exposed do.28. In virtually all types of tissue in every animal species, dioxin induces the production of enzymes that are the organism's attempt to metabolize, or render harmless, the chemical irritant.29. Emily Dickinson's letters to Susan Huntington Dickinson, which were written over a period beginning a few years before Susan's marriage to Emily's brother and ending shortly before Emily's death in 1886, outnumber her letters to anyone else.30. Paleontologists believe that fragments of a primate jawbone unearthed in Burma and estimated to be 40 to 44 million years old provide evidence of a crucial step along the evolutionary path that led to human beings.31. Even though many of her colleagues were convinced that genes were relatively simple and static, Barbara McClintock adhered to her own more complicated ideas about how genes might operate, and in 1983, at age of 81, was awarded a Nobel Prize for her discovery that the genes in corn are capable of moving from one chromosomal site to another.32. Galileo was convinced that natural phenomena, as manifestations of the laws of physics, would appear the same to someone on the deck of a ship moving smoothly and uniformly through the water as to a person standing on land.33. Because an oversupply of computer chips has sent prices plunging, the manufacturer has announced that it will cut production by closing its factories for two days a month.34. Beyond the immediate cash flow crisis that the museum faces, its survival depends on whether it can broaden its membership and leave its cramped quarters for a site where it can store and exhibit its more than 12,000 artifacts.35. By 1940, the pilot Jacqueline Cochran held seventeen official national and international speed records, earned at a time when aviation was still so new that many of the planes she flew were dangerously experimental design.36. Along with the drop in producer prices announced yesterday, the strong retail sales figures released today seem to indicate that the economy, although growing slowly, is not nearing a recession.37. Dressed as a man and using the name Robert Shurtleff, Deborah Sampson, the first woman to draw a soldier's pension, joined the Continental Army in 1782 at the age of 22, was injured three times, and was discharged in 1783 because she had become too ill to serve.38. Bengal-born writer, philosopher, and educated Rabindranath T agore had the greatest admiration for Mohandas K. Gandhi as a person and as a politician, butT agore was also skeptical of Gandhi's form of nationalism and his conservative opinions about India's cultural traditions.39. Although schistosomiasis is not often fatal, it is so debilitating that it has become an economic drain on many developing countries.40. The organization of Petroleum Exporting Countries (OPEC) had long been expected to announce a reduction in output to bolster sagging oil prices, but officials of the organization just recently announced that the group will pare daily production by 1.5 million barrels by the beginning of next year only if non-OPEC nations, including Norway, Mexico, and Russia, trim output by a total of 500,000 barrels a day.41. In 1850, Lucretia Mott published her discourse on Women, a treatise that argued for equal political and legal rights for women and for changes in the married women's property laws.42. T o develop more accurate population forecasts, demographers would have to know a great deal more than they do now about the social and economic determinants of fertility.43. Laos has a land area comparable to that of Great Britain but a population of only four million people, many of whom are members of hill tribes ensconced in the virtually inaccessible mountain valleys of the north.44. The plot of the Bostonians centres on the rivalry that develops between Olive Chancellor, an active feminist, and Basil Ransom, her charming and cynical cousin, when they find themselves drawn to the same radiant young woman whose talent for public speaking has won her ardent following.45. Quasars, at billions of light-years from Earth the most distant observable objects in the universe, are believed to be the cores of galaxies in an early stage of development.46. In ancient Thailand, much of the local artisan's creative energy was expended on the creation of Buddha images and on construction and decoration of the temples in which they were enshrined.47. In 1713, Alexander Pope began his translation of the Iliad, a work that took him seven years to complete and that literacy critic Samuel Johnson, Pope's contemporary, pronounced the greatest translation in any language.48. Though called a sea, the landlocked Caspian is actually the largest lake on Earth, covering more than four times the surface area of its closest rival in size, North America's Lake Superior.49. The automotive conveyor-belt system, which Henry Ford modeled after an seemly-line technique introduced by Ransom Olds, reduced the time required to assemble a Model T from a day and a half to 93 minutes.50. According to some analysts, the gains in the stock market reflect growing confidence that the economy will avoid the recession that many had feared earlier in the year and instead come in for a "soft landing," followed by a gradual increase in business activity.51. A new study suggests that the conversational pace of everyday life may be so brisk that it hampers the ability of some children to distinguish discrete sounds and words and, as a result, to make sense if speech.52. Long before it was fashionable to be an expatriate, Josephine Baker made Paris her home, and she remained in France during the Second World War as a performer and an intelligence agent for the Resistance.53. The nineteenth-century chemist Humphry Davy presented the results of his early experiments in his "Essay on heat and Light," a critique of all chemistry since Robert Boyle as well as a vision of a new chemistry that DAvy hoped to found. 54. The report recommended that the hospital eliminate unneeded beds, consolidate expensive services, and use space in other hospitals.55. Many house builders offer rent-to-buy programs that enable a family with insufficient savings for a conventional down payment to move into new housing and to apply part of the rent to a purchase later.56. Elizabeth Barber, the author of both Prehistoric T extiles, a comprehensive work on cloth in the early cultures of the Mediterranean, and Women's Work, a more general account of early cloth manufacture, is an authority on textiles in ancient societies.57. Many of the earliest known images of Hindu deities in India date from the time of the Kushan Empire and were fashioned either from the spotted sandstone of Mathura or from Gandharan grey schist.58. It can hardly be said that educators are at fault for not anticipating the impact of microcomputer technology: Alvin T offler, one of the most prominent students of the future, did not even mention microcomputers in Future Shock, published in 1970.59. A leading figure in the Scottish Enlightenment, Adam Smith wrote two major books that are to democratic capitalism what Marx's Das Kapital is to socialism.60. The Olympic Games helped to keep pace among the pugnacious states of the Greek world, for a sacred true was proclaimed during the month of the festival.61. While all states face similar industrial waste problems, the predominant industries and the regulatory environment of each state obviously determine the types and amounts of waste produced, as well as the cost of disposal.62. Rivaling the pyramids of Egypt or even the ancient cities if the Maya as an achievement, the army of terra-cotta warriors created to protect Qin Shi Huang, China's first emperor, in his afterlife is more than 2,000 years old and took 700,000 artisans more than 36 years to complete.63. When Congress reconvenes, some newly elected members from rural states will try to establish tighter restrictions on the amount of grain farmers will be allowed to grow and to encourage more aggressive sales of United States farm products overseas.64. Doctors generally agree that such factors as cigarette smoking, eating rich foods high in fats, and alcohol consumption not only do damage by themselves but also aggravate genetic predispositions toward certain diseases.65. Digging in sediments in northern China, scientists have gathered evidence suggesting that complex life-forms emerged much earlier than previous thought.66. In a plan to stop the erosion of East Coast Beaches, the Army Corps of Engineers proposed building parallel to shore a breakwater of rock that would rise six feet above the waterline and act as a buffer, absorbing the energy of crashing waves and protecting the beaches.67. The 32 species that make up dolphin family are closely related to whales and in fact include the animal known as the killer whale which can grow to be 30 feet long and is famous for its aggressive hunting pods.68. Outlining his strategy for nursing the troubled conglomerate back to health, the chief executive announced plans Wednesday to cut the company's huge debt by selling nearly $12 billion in assets over the next 18 months.69. Affording strategic proximity to the Strait of Gibraltar Morocco was also of interest to the French throughout the first half of the twentieth century because they assumed that without it their grip on Algeria would never be secure.70. The first trenches cut into a 500-acre site at T ell Hamoukar, Syria, have yielded strong evidence that centrally administered complex societies in northern regions of Middle East arose simultaneously with but independently of the more celebrated city-states of southern Mesopotamia, in what is now southern Iraq.71. Along the major rivers that traverse the deserts of northeast Africa, the Middle East, and northwest India, the combination of a reliable supply of water and good growing conditions encouraged farming traditions that have, in places, endured for at least 6,000 years.72. His studies of ice-polished rocks in his Alpine homeland, far outside the range of present-day glaciers, led Louis Agassiz in 1837 to propose the concept of an age in which great ice sheets existed in what are temperature areas.73. Unlike the original National Museum of Science and T echnology in Italy, where the models are encased in glass or operated only by staff member, the Virtual Leonardo Project, an online version of the museum, encourages visitors to "touch" each exhibit and thereby active the animated functions of the piece.74. Although it covers the entire planet, Earth's crust is neither seamless nor stationary, but rather fragmented into mobile semirigid plates.75. More and more in recent years, cities are stressing the arts as a means to greater economic development and investing millions of dollars in cultural activities, despite strained municipal budgets and fading federal support.76. Combining enormous physical strength with higher intelligence, the Neanderthals appear to have been equipped to face any obstacle the environment could put in their path, but their relatively sudden disappearance during the Paleolithic era indicates that an inability to adapt to some environmental change led to their extinction.77. A 1972 agreement between Canada and the United States reduced the amount of phosphates that municipalities are allowed to dump into the Great Lakes.78. A proposal has been made to trim the horns from rhinoceroses to discourage poachers; the question is whether tourists will continue to visit game parks to see rhinoceroses once the animals' horn have been trimmed.79. Ryunosuke Akutagawa's knowledge of the literatures of Europe, China, and Japan was instrumental in his development as a writer, informing both his literary style and the content of his fiction.80. The only way for growers to salvage frozen citrus is to have it quickly processed into juice concentrate before warmer weather returns and rots the fruit.81. Fossils of the arm of a sloth, found in Puerto Rico in 1991, have been dated at 34 million years old, making the sloth the earliest known mammal on the Greater Antilles Islands.82.Defense attorneys have occasionally argued that their clients' misconduct stemmed from a reaction to something ingested, but if criminal or delinquent behaviour is attributed to an allergy to some food, the perpetrators are in effect told that they are not responsible for their actions.83. A report by the American Academy for the Advancement of Science has concluded that many of the currently uncontrolled dioxins to which North Americans are exposed come from the incineration of wastes.84. Recently physicians have determined that stomach ulcers are caused not by stress, alcohol, or rich foods, but by a bacterium that dwells in the mucous lining of the stomach.85. According to a recent poll, owning and living in a freestanding house on its own land is still a goal of a majority of young adults, as it was of earlier generations. 86. In 2000, a mere two dozen products accounted for half the increase in spending on prescription drugs, a phenomenon that is explained not just by the fact that drugsare becoming more expensive but also by the fact that doctors are writing many more prescriptions for higher-cost drugs.87. According to scientists who monitored its path, an expanding cloud of energized particles ejected from the Sun recently triggered a large storm in the magnetic field that surrounds EArth, brightening the Northern Lights and possibly knocking out a communications satellite.88. Often visible as smog, ozone is formed in the atmosphere when hydrocarbons and nitrogen oxides, two major pollutants emitted by automobiles, react with sunlight.89. Salt deposits and moisture threaten to destroy the Mohenjo-Daro excavation in Pakistan, the site of an ancient civilization that flourished at the same time as the civilizations in the Nile Delta and the river valleys of the Tigris and Euphrates.90. The result of the company's cost-cutting measures are evident in its profits, which have increase 5 percent during the first 3 months of this year after failing over the last two years.91. In an effort to reduce their inventories, Italian vintners have cut prices; their wines are priced to sell, and they do.92.Jazz pianist and composer Thelonious Monk produced a body of work that was rooted in the stride-piano tradition of Willie (The Lion) Smith and Duke Ellington, yet in many ways he stood apart from the mainstream jazz repertory.93. Nobody knows exactly how many languages there are in the world, partly because of the difficulty of distinguishing between a language and the sublanguages or dialects within it, but those who have tried to count typically have found about five thousand.94. Heating-oil price are expected to be higher this year than last because refiners are paying about $5 a barrel more for crude oil than they were last year.95. One of the primary distinctions between our intelligence and that of other pirates may lie not so much in any specific skill as in our ability to extend knowledge gained in one context to new and different ones.96. Even though Clovis points, spear points with longitudinal grooves chipped onto their faces, have been found all over North America, they are named for the New Mexico site where they were fist discovered in 1932.97. Some anthropologists believe that the genetic homogeneity evident in theworld's people is the result of a "population bottleneck"——that at some time in the past our ancestors suffered an event that greatly reduced their numbers and thus our genetic variation.98. Ranked as one of the most important of Europe's young playwrights, Franz Xaver Kroetz has written 40 plays; his works——translated into more than 30 languages——as produced more often than those of any contemporary German dramatist.99. Like the planets, the stars are in motion, some of them at tremendous speed, but they are so faraway from Earth that their apparent positions in the sky do not change enough for their movement to be observed during a single human lifetime.100. Being heavily committed to a course of action, especially one that has worked well in the past, is likely to make an executive miss signs of incipient trouble or misinterpret them when they do appear.101. As rainfall began to decrease in the Southwest about the middle of the twelfth century, most of the the Monument Valley Anasazi abandoned their homes to join other clans whose access to water was less limited.102. Y ellow jackets number among the 900 or so species of the world's social wasps, wasps that live in a highly cooperative and organized society consisting almost entirely of females——the queen and her sterile female workers.103. El Nino, the periodic abnormal warming of the sea surface off Peru, is a phenomenon in which changes in the ocean and atmosphere combine to allow the warm water that has accumulated in the western Pacific to flow back to the east. 104. In her book illustration, which she carefully coordinated with her narratives, Beatrix Potter capitalized on her keen observation and love of the natural world.105. Marconi conceived of the radio as a tool for private conversation that could substitute for the telephone; instead, it has become precisely the opposite, atoll for communicating with a large, public audience.106. Originally developed for detecting air pollutants, a technique calledproton-induced X-ray emission, which can quickly analyze the chemical elects in almost any substance without destroying it, is finding uses in medicine, archaeology, and criminology.107. While the costs of running nuclear plants is about the same as for other types of power plants, the fixed costs that stem from building nuclear plants make the electricity they generate more expensive.108. Authoritative parents are more likely than permissive parents to have children who as adolescents are self-confident,high in self-esteem, and responsibly independent.109. Among the objects found in the excavated temple were small terra-cotta effigies left by supplicants who were either asking the goddess Bona Dea's aid in heating physical and mental ills or thanking her for such help.110. Published in Harlem, The Messenger was owned and edited by two young journalists, A. Philip Randolph, who would later make his reputation as a labor leader, and Chandler Owen.111. A mutual fund having billions of dollars in assets will typically invest that money in hundreds of companies, rarely holding more than one percent of the shares of any particular corporation.112. Construction of the Roman Colosseum, which was officially known as the Flavian Amphitheater, began in A.D. 69, during the reign of Vespasian, and was completed a decade later, during the reign of Titus, who opened the Colosseum with a one-hundred-day cycle of religious pageants, gladiatorial games and spectacles.113. A baby emerges from the darkness of the womb with a rudimentary sense of vision that would be rated about 20/500; an adult with such vision would be deemed legally blind.114. Starfish, with anywhere from five to eight arms, have a strong regenerative ability, and if one arm is lost it is quickly replaced, with the animal sometimes overcompensating and growing an extra one or two.115. Because the new maritime code provides that even tiny islets can be the basis for claims to the fisheries and oil fields of large sea areas, it has already stimulated international disputes over uninhabited islands.116. The original building and loan associations were organized as limited life funds, whose members made monthly payments on their share subscriptions and then took turns drawing on the funds for home mortgages.117. Gall's hypothesis that different mental functions are localized in different parts of the brain is widely accepted today.118.Mauritius was a British colony for almost 200 years, but except in the domains of administration and teaching, the English language was never really spoken on the island.119. George Sand (Aurore Lucile Dupin) was one of the first European writers to consider the rural poor legitimate subjects for literature and to portray them with sympathy and respect in her novels.120. The World Wildlife Fund has declared that global warming, a phenomenon that most scientists agree is caused by human beings' burning of fossil fuels, will create havoc among migratory birds by altering the environment in ways harmful to their habitats.121. New theories propose that catastrophic impacts of asteroids and comets may have caused reversals in the Earth's magnetic field, the onset of ice ages, the splitting apart continents 80 million years ago, and great volcanic eruptions.122. A firm that specializes in the analysis of handwriting claims to be able, from a one-page writing sample, to assess more than 300 personality traits, including enthusiasm, imagination, and ambition.123. Sales of wines declined in the late 1980s, but they began to grow again after the 1991 report that linked moderate consumption of alcohol, and particularly of red wine, with a reduced risk of heart disease.124. Less successful after she emigrated to New Y ork than she had been in her native Germany, photographer Lotte Jacobi nevertheless earned a small group of discerning admirers, and her photographs were eventually exhibited in prestigious galleries across the United States.125. T oday, because of improvements in agricultural technology, the same amount of acreage produces twice as many apples as it did in 1910.126. The use of lie detectors is based on the assumption that lying produces emotional reactions in an individual that, in turn, create unconscious physiological responses.127. Joan of Arc, a young Frenchwoman who claimed to be divinely inspired, turned the tide of English victories in her country by liberating the city of Orleans and persuaded Charles VII of France to claim his throne.128. Australian embryologists have found evidence to suggest that the elephant is descended from an aquatic animal and that its trunk originally evolved as a kind of snorkel.129. Cajuns speak a dialect brought to southern Louisiana by the 4,000 Acadians who migrated there in 1755; their language is basically seventieth-century French to which English, Spanish, and Italian words have been added.130. Over 75 percent of the energy produced in France derives from nuclear power, whereas nuclear power accounts for just over 33 percent of the energy produced in Germany.131. Although the term "psychopath" is popularly applied to an especially brutal criminal, in psychology it refers to someone who is apparently incapable of feeling compassion or the pangs of conscience.132. Although heirloom tomatoes, grown from seeds saved during the previous year, appear less appetizing than most of their round and red supermarket cousins——they are often green and striped, or have plenty of bumps and viruses——heirlooms are more flavourful and thus in increasing demand.133. Last week local shrimpers held a new conference to take some credit for the resurgence of the rare Kemp's ridley turtle, saying that their compliance with laws requiring turtle-excluder devices on shrimp nets is protecting adult sea turtles.134. Recently implemented "shift-work equations" based on studies of the human sleep cycle have reduced sickness, sleeping on the job, and fatigue among shift workers while raising production efficiency in various industries.135. Spanning more than 50 years, Friedrich Muller's career began in an unpromising apprenticeship as a Sanskrit scholar and culminated in virtually every honour that European governments and learned societies could bestow.136. Whereas in mammals the tiny tubes that convey nutrients to bone cells are arrayed in parallel lines, in birds the tubes form a random pattern.137. Joachim Raff and Giacomo Meyerbeer are examples of the kind of composer who receives popular acclaim while living, but whose reputation declines after death and never regains its former status.138. Most efforts to combat such mosquito-borne diseases as malaria and dengue have focused on either vaccinating humans or exterminating.。
TRNSYS16 _TYPE10_使用说明[译]
![TRNSYS16 _TYPE10_使用说明[译]](https://img.taocdn.com/s3/m/d7a29b6625c52cc58bd6beeb.png)
(Eq 5.12.2.3) and (Eq 5.12.2.4) can be solved with significantly less computational effort than (Eq 5.12.2.1) and (Eq 5.12.2.2). （公式 5.12.2.3） 和 （等式 5.12.2.4） 的求解 （公式 5.12.2.1） 和 （等式 5.12.2.2）
The results of many simulations of air heating systems in which (Eq 5.12.2.1) and (Eq 5.12.2.2) have been used to describe the rock bed behavior, have shown that the system performance has an asymptotic dependence upon ε. For values of e greater than ~10, (which is generally much lower than the values encountered in most practical designs) the system performance is independent of ε (l); ε may be increased without bound without affecting system performance significantly. 由（公式 5.12.2.1）和（公式 5.12.2.2）对空气加热系统进行的模拟所得出的 大量模拟结果结果， 已经被用于描述石块床的状态变化， 并且表明该系统的----？ 性能对ε有渐进相关的关系。当 e 的值大于 10（该值要远低于绝大多数的实际 设计中的值）时，该系统的性能与ε（l）无关;ε的值可无限制地增加且不显著 影响系统性能。
Scattering of solitons on resonance
We found that the scattering of solitary waves on resonance is a general effect for nonlinear equations described the wave propagation. In this work we investigate this effect for the simplest model. It allows to show the essence of this effect without unnecessary details.
1 Statement of the problem and result
Let us consider the perturbed NLSE
i∂tΨ + ∂x2Ψ + |Ψ|2Ψ = ε2f eiS/ε2,
金融幂律
金融幂律：实证，模型以及原理Thomas Lux1Department of EconomicsUniversity of Kiellux@bwl.uni-kiel.de为社会科学中的幂律而准备：发现社会科学的复杂性和非均衡动态，Claudio Cioffi,编者.概述：金融市场（股票市场，外汇市场以及其他市场）均以一系列普遍使用的幂律为特征，最突出的例子是以强健的，近似三次幂律（cubic power law）来描述大量回报（large returns）的分布这一独特发现。
一个几乎同样强健特征是对波动性的长期依赖（例如：其自相关函数的双曲线递减）。
最近的文献加入了交易量的时间标度（temporal scaling）和higher moments of returns的multi-scaling. 最近，对于这些特征的关注引起了人们对市场过程中这些关键特征之所以出现的原因进行理论解释的尝试。
理论上来讲，不用种类的动态过程可能造成了这些幂律。
在经济学文献中找到的例子包括乘法随机过程（multiplicative stochastic processes）和多均衡的动态过程。
尽管这两种过程dynamics均以间歇产生大规模活动爆发的间断行为为特征，而事实上它们则可能是基于对交易过程上根本性地不同的理解。
前面的章节既回顾了在经济学文献中提出的相关模型，又复习了出现在以上数据到产生机制中的幂律的分析背景。
一简介尽管关于收入和资产中的幂律研究可以追溯到19世纪（Pareto）, 但对于在金融数据中幂律的关注还是最近的事情。
幂律在金融中第一次体现可能是在Mandelbrot 的Journal of Business 中1963卷的具有开启意义的Variation of Certain Speculative Prices"一文中，随后紧接着Eugene Fama在随后的一篇名为“Mandelbrot and the Stable Paretian Hy-pothesis"的一文中，进一步阐述了同一个问题。
时间序列的带有乘积调整的半参密度估计
SEMIPARAMETRIC DENSITY ESTIMATION FOR TIME SERIESWITH MULTIPLICATIVE ADJUSTMENT1Kaiping Wang1,2and Lu Lin11School of Mathematics and System Sciences,Shandong UniversityJinan250100,P.R.China2School of Management,Shandong University,Jinan250100,P.R.Chinawkp@AbstractIn this paper,we extend a class of semiparametric density estimators to time series context.The asymptotic theory and simulation study are discussed.Theoretical results and numerical comparison show that,in the time series case,the estimators in this class are better than,or at least competitive with,the traditional kernel density estimator in a broad class of densities.Keywords:semiparametric density estimation,time series,multiplicative adjustment.1.INTRODUCTIONDensity estimation is one of the most fundamental areas in statistical analysis.Tradition-ally,there are two approaches for density estimation.One is called the parametric approach, the other,nonparametric.The parametric approach is attractive for a number of reasons.1This paper is supported by RFDP project(20070422034)of China.1One reason is its statistical simplicity,i.e.,estimation of the entire function boils down to inferring a few parameter values.Another reason is that,if the parametric assumption is justified,the density function can be estimated more efficiently than it can be by a nonpara-metric approach.However,the nonparametric approach has attractiveflexibility which can be used without the structural assumption that the underlying structure is controlled by a finite-dimensional parameter.A representative method for nonparametric density estimation is the traditional kernel density estimation.Most of the work focuses on independent random samples.For time series data,the kernel method has also been studied,see,e.g.the book by Bosq(1996).Let{X t}Tt=1be a realization from a stationary process with marginal density f.The kernel density estimator of f is defined by˜f(x)=T−1Tt=1K h(X t−x),(1.1)where K h(z)=h−1K(h−1z),K(·)is usually a nonnegative,symmetric and unimodal prob-ability density function withfinite values ofσ2K =z2K(z)dz and R(K)=K(z)2dz,andh is the bandwidth.Under certain mixing and smoothness conditions,the basic statistical properties are thatE[ˆf(x)]=f(x)+σ2K2f (x)h2+O(h4),V ar{ˆf(x)}=f(x)T h R(K)+o(1T h).(1.2)(Fan and Yao,2003).In recent years,there have been increasing interests and activities in the general area of semiparametric approaches.Let X1,X2,···,X n be independently and identically distributed2with density f,to estimate the density f from the data,Naito(2004)provided a class of semiparametric density estimators that have multiplicative adjustment,including estimators proposed by several authors(Hjort and Glad,1995,Hjort and Jones,1996)as special cases. In the proposed approach,a parametric density estimator g(x,ˆθ)is utilized,but it is seen as a crude guess of the true density f.This initial parametric approximation is adjusted via multiplication by an adjustment factorξ=ξ(x).ξis determined by minimization of the empirical version of the functionQ(x,ξ|α)=K h(t−x)[f(t)−g(t,ˆθ)ξ]2g(t,ˆθ)αdt,(1.3)for afixed target point x,whereαis a real number called the index.This method is called the local L2-fitting criterion.After omitting the irrelevant term,the empirical version of (1.3)can be expressed asQ n(x,ξ|α)=ξ2K h(t−x)g(t,ˆθ)2−αdt−2ξnni=1K h(X i−x)g(X i,ˆθ)1−α.The minimizer can be easily determined asˆξ=ˆξ(x)=arg minξQ n(x,ξ|α)=n−1ni=1K h(X i−x)g(X i,ˆθ)1−αK h(t−x)g(t,ˆθ)2−αdt.Using thisˆξ,a class of semiparametric density estimators is obtained byˆf α(x)=g(x,ˆθ)ˆξ=g(x,ˆθ)n−1ni=1K h(X i−x)g(X i,ˆθ)1−αK h(t−x)g(t,ˆθ)2−αdt.(1.4)Theoretical comparison reveals that the estimators in this class are better than,or at least competitive with,the traditional kernel estimator in a broad class of densities.3In this paper,we extend this semiparametric multiplicative approach to time series con-text.In Section2,we study the asymptotic behavior ofˆfα,forα-mixing time series.This approach is shown to be effective and yields a class of theoretically good estimators in the sense of mean integrated squared error(MISE).Finite sample performance of the proposed estimators,and comparison to the kernel density estimator(1.1)are investigated by Monte Carlo simulation in section3.Proofs of the theoretical results are presented in section4. 2.ASYMPTOTIC THEORYLet{X t}Tt=1be a realization from a stationary process with marginal density f.Sup-pose g(x,θ)be a given parametric family of densities,where the possibly multidimensional parameterθ=(θ1,...,θp) belongs to some open and connected region in p-space.Let the parametric-start estimate be g(x,ˆθ),whereˆθis an estimator of the least false valueθ0ac-cording to a certain distance measure between f and g(·,θ).For concreteness we here choseˆθas the maximum likelihood estimator and defineθas the minimizer of the kullback-Leibler distance onθ.From(1.4),the class of semiparametric multiplicative estimators of f isˆf α(x)=g(x,ˆθ)ˆξ=g(x,ˆθ)T−1Tt=1K h(X t−x)g(X t,ˆθ)1−αK h(t−x)g(t,ˆθ)2−αdt,(2.1)where K(·)is the kernel function as in(1.1).In this section,we investigate various statistically important quantities about(2.1),such as bias and variance.We will use the following assumptions:(a)Let{X t}be anα-mixing process with the mixing coefficient| (l)|≤cl−βfor some4c>0andβ>2.(b)Let g l(x,y)be the joint density of X1and X l+1and assume that g l(x,y) =sup(x,y)g l(x,y)is bounded.Remark2.1According to Collomb(1985),theα-mixing condition is the most suitable one when working with time series since the ARMA processes with continuous white noise satisfy it,among others(see Doukhan(1994)for a more complete discussion of theα-mixing condition).Theorem 1.Assume that conditions(a)and(b)hold,h→0in such a way thatT h→∞.If f has the continuous second derivative at an interior point x of the support of f,then,Biasˆfα(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h2T+h4+T−2),V arˆfα(x)=1T h R(K)f(x)+o(1T h).(2.2)Remark2.2Whenα=0,1and2,we have the following relationships:ˆf(x)=ˆf HJ(x),ˆf1(x)=ˆf LL(x),ˆf2(x)=ˆf HG(x),whereˆf HJ(x)andˆf LL(x)are two estimators proposed by Hjort and Jones(1996),andˆf HG(x) is the density estimator proposed by Hjort and Glad(1995).In Section3,we will compareˆfαwith˜f,ˆf HJ(x),ˆf LL(x)andˆf HG(x)in time series settings by Monte Carlo simulation and get some insights about the practically good choice ofα.Remark2.3From above theorem,we can see that,the results are very much like those for independent samples.The bias is unaffected by dependence and the asymptotic variance5is the same as in the i.i.d.case.However,the result for the asymptotic variance heavily depends on the strength of the dependence among the X t’s.Let z t=K h(X t−x)g0(X t)1−α, thenV ar(T−1Tt=1z t)=1TV ar(z1)+2TT−1l=1(1−lT)Cov(z1,z l+1)(2.3)Thefirst term on the right hand side of(2.3)is equal to the variance based on independent data.The second term reflects the extra variability due to the dependence of the X t’s.Thestrength of the dependence can be measured through the size of T−1l=1Cov(z1,z l+1).For anα-mixing process,a standard result is T−1l=1|Cov(z1,z l+1)|=o(h−1)(see Lemma1).SoV arˆfα(x)=1T hR(K)f(x)+o(1T h).However,if without condition(a),the size of the second term on the right side of(2.3)can be significantly larger and can dominate the usual leading variance term,leading to a worse rate of convergence ofˆfα(x).Remark2.4From(2.2)and(1.2),the AMISE ofˆfα(x)and˜f are,respectively,given byAMISE(ˆfα)=h44(σ2k)2 (ˆfα)+R(K)T handAMISE(˜f)=h44(σ2k)2 (˜f)+R(K)T h,where(ˆfα)=[(g0(x)1−αf(x))1−α−f(x)(g0(x)2−α)2−α]2dx,(˜f)=[f (x)]2dx.6So this class of new estimators is better than the traditional kernel density estimator in all cases where (ˆfα)is smaller in size than (˜f).Furthermore,if f is in the model{g(x,θ):θ∈Θ},that is,g0(x)=f(x),then the O(h2)term of the bias vanishes.Naito(2004) compared (ˆfα)with (˜f)for the case in which f belongs to a class of normal mixture densities used in Marron and Wand(1992).The class of normal mixture densities is a very broad one because any density can be approximated arbitrarily closely in various senses by a normal mixture(Marron and Wand,1992).Naito confirmed thatˆfαis better than,or at least competitive with,˜f for all cases in that comparison.3.A SIMULATION STUDYFinite sample performance of the class of proposed density estimators was investigated by Monte Carlo simulation.The process{X t}we considered was a stationary moving average process of order1,X t=εt−pεt−1,where p=0.2and{εt}is a sequence of independent and continuous random variables with common density function g.As a direct consequence,the marginal density of the process isf(x)=g(y)g(x+py)dy.(3.1)The Gaussian,skewed unimodal and separated bimodal distributions were considered as the density function g of the noiseε(see Marron and Wand(1992)for the definitions about the last two densities)because they typify some different challenges to curve estimation.7By(3.1),f is Gaussian,skewed unimodal and bimodal,respectively.In each case200 samples of size T=500were generated.The MISE(α,h)value for a given combination of(α,h)was estimated by the average of these200realizations of ISE(α,h).To obtain a precise approximation to the minimum MISE,a grid search of the combination(α,h)was implemented.The Gaussian kernel was used throughout.Letα0be the optimalαwhich we obtained by the grid search,the estimators compared in this study were˜f andˆfαforα=0, 1,2andα0.We utilized g(x,ˆθ)=φˆσ−1(x−ˆµ)for all cases,i.e.,we started with a Gaussian MA(1) approximation,where(ˆµ,ˆσ2)is the MLE of(µ,σ2)(see,e.g.,Brockwell and Davis(2002) for computing the MLE of an ARMA model).Values of105×minMISE are tabulated in Table1,where the minimum is taken over h. Also tabulated in parentheses are105times the standard error(SE)for each case.Table1:The value of estimated min h MISE(h)×105for samples of size T=500from three densities over.The standard error×105is given in parentheses for each case. 200simulations for˜f,ˆf0,ˆf1,ˆf2andˆfαValues of the optimal indexα0are listed in theα0column for each case.α0f˜fˆf0ˆf1ˆf2ˆfα#1Gaussian16.53 3.94 3.74 5.01 3.73 1.31(11)(4)(4)(4)(4)#2skewed unimodal25.5626.1621.6519.5719.55 1.91(15)(14)(13)(12)(12)#3bimodal28.4331.5828.4427.4127.36 1.83(15)(16)(15)(15)(15)First we see#1.This case is that f is in the parametric model so that the O(h2)term8of the bias ofˆfαvanishes,as mentioned in Remark(2.4).For#1all ofˆfαare significantly better than˜f and the optimalαis around1.For cases#2and#3,the estimatorˆfαis the best.Furthermore,it is worth noting that α0is around2.This reveals that the Hjort and Glad estimatorˆf HG=ˆf2is also good for these cases.4.PROOFSIn this section the proofs of theoretical results are presented.First we prepare the fol-lowing lemma.Lemma4.1.Assume that conditions(a)and(b)in section2hold.Suppose g(x,θ0)is afixed density.Let g0(x)=g(x,θ0)andf∗α(x)=g0(x)T−1Tt=1K h(X t−x)g0(X t)1−αK h(t−x)g0(t)2−αdt.Suppose that h→0in such a way that T h→∞.If f has the continuous second derivative at an interior point x of the support of f,thenBiasf∗α(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h4),V arf∗α(x)=1R(K)f(x)+o(1). Proof.By Taylor expansion,we haveBiasf∗α(x)=Ef∗α(x)−f(x)=g0(x)E[T−1Tt=1K h(X t−x)g0(X t)1−α]−f(x)K h(t−x)g0(t)2−αdtK h(t−x)g0(t)2−αdt,in which the denominator can be expressed asK(u)g0(x+hu)2−αdu=g0(x)2−α+O(h2),9and the numerator can be expressed asg0(x)[g0(x)1−αf(x)+12σ2kh2g0(x)1−αf (x)+σ2k h2(g0(x)1−α) f (x)+12σ2kh2(g0(x)1−α) f(x)+O(h4)]−[f(x)g0(x)2−α+f(x)σ2kh2(g0(x)2−α) +O(h4)]=1σ2kh2g0(x)[g0(x)1−αf (x)+2(g0(x)1−α) f (x)+(g0(x)1−α) f(x)]−σ2kh2(g0(x)2−α) f(x)+O(h4).ThenBiasf∗α(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h4).The varianceV arf∗α(x)=V ar[g0(x)T−1Tt=1K h(X t−x)g0(X t)1−αK h(t−x)g0(t)2−αdt]=g2(x)[K h(t−x)g0(t)2−αdt]2V ar[T−1Ti=1K h(X t−x)g0(X t)1−α].Let z t=K h(X t−x)g0(X t)1−α,thenV ar(T−1Tt=1z t)=1TV ar(z1)+2TT−1l=1(1−lT)Cov(z1,z l+1).Note that Ez1=E[K h(X t−x)g0(X t)1−α]=f(x)g0(x)1−α+O(h2)=O(1),by a change of variables and Taylor expansion,we haveV ar(z1)=E[K h(X t−x)g0(X t)1−α]2−(Ez1)2=1hK2(u)g0(x+hu)2(1−α)f(x+hu)du−(Ez1)2=1hR(K)g0(x)2(1−α)f(x)+o(h−1).10Thus,we need only to show thatT−1l=1|Cov(z1,z l+1)|=o(h−1).By using Billingsley’s inequality,we have|Cov(z1,z l+1)|≤4 (l) z1 ∞ z l+1 ∞≤4 (l)D/h2(4.1) for some constant D.On the other hand,|Cov(z1,z l+1)|=|Ez1z l+1−(Ez1)2|≤ ∞−∞∞−∞K h(u−x)K h(v−x)g0(u)g0(v)g l(u,v)dudv+(Ez1)2(4.2)Hence,the covariance is bounded by a constant C.Let d T→∞be a sequence of integers.Then,by(4.2), dT−1l=1|Cov(z1,z l+1)|≤Cd T.Using(4.1)and the assumption on the mixing coefficient,we haveT−1l=d T |Cov(z1,z l+1)|≤D∞l=d Tl−β/h2.By taking d T=h−2/β,we haveT−1l=1|Cov(z1,z l+1)|=O(h−2/β)=o(h−1),for someβ>2.Hence,wefinish the proof.Proof of Theorem1.Let x n=(x1,...,x n)be a sequence of real-valued and dependent random variables,with joint probability density function(p.d.f.)given byg(x1,...,x n,θ)=g(x n,θ).11The conditional p.d.f.of x i given x i−1isg i,θ=g(x i,θ|x i−1)=g(x i,θ)/g(x i−1,θ).Letθ0be the true but unknown value ofθ,and let I(X i)=J−1(∂/∂θ)log g i,θ,whereJ=−E f[(∂2/∂θ∂θT)log g i,θ].Under certain conditions(e.g.Bhat,1974),we haveˆθ=θ0+1nni=1I(X i)+dn+εn(4.3)whereεn=O p(1/n)with mean O(1/n2).Define u0(x)=∂log g(x,θ0)/∂θ,v0(x)=∂2log g(x,θ0)/∂θ∂θT.Using Taylor expansions,we can expandˆfαasˆf α(x)=f∗α(x)+V T(x)+12W T(x)+o p(T−1).We write V T(x)=¯BT(ˆθ−θ0),and W T(x)=(ˆθ−θ0) ¯C T(ˆθ−θ0),whereB t=K h(X t−x)g0(X t)1−αg0(x)η0(x)[(1−α)u0(X t)−2−αη0(x)η1(x)+u0(x)],C t=K h(X t−x)g0(X t)1−αg0(x)η0(x){−2(1−α)(2−α)η0(x)η1(x)u0(X t)T+2(1−α)u0(x)u0(X t)T+(1−α)[v0(X t)+(1−α)u0(X t)u0(X t)T]−2(2−α)η0(x)u0(x)η1(x)T+[v0(x)+u0(x)u0(x)T]+2(2−α)η0(x)2[(2−α)η1(x)η1(x)T−12η0(x)η2(x)]},whereη0(x)=K h(t−x)g0(t)2−αdt,η1(x)=K h(t−x)u0(t)g0(t)2−αdt,η2(x)=K h(t−x)[v0(t)+(2−α)u0(t)u0(t)T]g0(t)2−αdt.12From Lemma4.1,we already know that,Biasf∗α(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h4).Through(4.3),wefindEV T(x)=E[1TTt=1Bt(ˆθ−θ0)]=1T2E[nt=1BtTt=1I t]+1TE(Tt=1Bt)d+O(T−2),1 T2E(Tt=1BtTt=1I t)=1TE(BtI t)+2TT−1l=1(1−lT)E(B1I l+1).It is not difficult to see that EB t,EBtI t,EC t is of size O(h2).WhileT−1l=1(1−l/T)E(B1I l+1)≤T−1l=1|E(B1I l+1)|=T−1l=1|Cov(B1,I l+1)|≤T−1l=14α(l)C≤4CT−1l=1l−β,forβ>2, T−1l=1l−βconverges,we have2/TT−1l=1(1−l/T)E(B1I l+1)=O(1/T).Thus,EV T(x)=O(h2T+T−2).Similarly,EW T(x)=E[(ˆθ−θ0) ¯C T(ˆθ−θ0)]=O(h2T+T−2).We haveBiasˆfα(x)=h22σ2K[(g0(x)1−αf(x))g0(x)1−α−f(x)(g0(x)2−α)g0(x)2−α]+O(h2T+h4+T−2).13Next we turn to the variance.The variance of f∗α(x)is known from Lemma4.1.V ar(V T(x))=V ar[¯BT(ˆθ−θ0)]=V ar[¯BT ¯In]+O(T−2)=O(h4T+T−2).Similarly,W T(x)can be seen to have uninfluential variance O(h4T2).Finally,Cov[f∗(x),V T(x)]=O(h2T).This combines to giveV arˆfα(x)=1T hR(K)f(x)+o(1T h).ReferencesBhat,B.R.(1974).On the method of maximum-likelihood for dependent observations.J. Roy.Statist.Soc.Ser.B,36,48-53.Bosq,D.(1996).Nonparametric statistics for stochastic processes.New York:Springer-Verlag.Brockwell,P.J.and Davis,R.A.(2002).Introduction to Time Series and Forecasting.New York:Springer-Verlag.Collomb,G.(1985).Nonparametric time series analysis and prediction:uniform almost sure convergence.Statist.,2,297-307.Doukhan,P.(1994).Mixing:properties and examples.Berlin:Springer.Fan,J.Q.and Yao,Q.W.(2003).Nonlinear Time Series:Nonparametric and Parametric14Methods.New York:Springer-Verlag.Hjort,N.L.and Glad,I.K.(1995).Nonparametric density estimation with a parametric start.Ann.Statist.,23,882-904.Marron,J.S.and Wand,M.P.(1992).Exact mean integrated squared error.Ann.Statist., 20,712-736.Hjort,N.L.and Jones,M.C.(1996).Locally parametric nonparametric density estimation. Ann.Statist.,24,1619-1647.Naito,K.(2004).Semiparametric density estimation by local L2-fitting.Ann.Statist.,32, 1162-1191.15。
非线性偏微分方程
FINITE DIMENSIONAL REDUCTION OF NONAUTONOMOUS DISSIPATIVESYSTEMSAlain MiranvilleUniversit´e de Poitiers Collaborators:Long time behavior of equations of the formy′=F(t,y)For autonomous systems:y′=F(y)In many situations,the evolution of the sys-tem is described by a system of ODEs:y=(y1,...,y N)∈R N,F=(F1,...,F N)Assuming that the Cauchy problemy′=F(y),y(0)=y0,is well-posed,we can define the family of solv-ing operators S(t),t≥0,acting on a subset φ⊂R N:S(t):φ→φy0→y(t)This family of operators satisfiesS(0)=Id,S(t+s)=S(t)◦S(s),t,s≥0We say that it forms a semigroup onφQualitative study of such systems:goes back to Poincar´eMuch is known nowadays,at least in low di-mensionsEven relatively simple systems can generate very complicated chaotic behaviorsThese systems are sensitive to perturbations: trajectories with close initial data may diverge exponentially→Temporal evolution unpredictable on ti-me scales larger than some critical value→Show typical stochastic behaviorsExample:Lorenz systemx′=σ(y−x)y′=−xy+rx−yz′=xy−bzObtained by truncature of the Navier-Stokes equationsGives an approximate description of a layer of fluid heated from belowSimilar to what is observed in the atmosphereFor a sufficiently intense heating:sensitive dependence on the initial conditions,repre-sents a very irregular convection→Butterfly effectVery often,the trajectories are localized in some subset of the phase space having a very complicated geometric structure(e.g.,locally homeomorphic to the product of R m and a Cantor set)→Strange attractor(Ruelle and Takens)Main feature of a strange attractor:dimen-sionSensitivity to initial conditions:>2(dimen-sion of the phase space≥3,say,3)Contraction of volumes:its volume is equal to0→noninteger,strictly between2and3→Fractal dimensionExample:Lorenz system:dim F A=2.05...Distributed systems:systems of PDEsφis a subset of an infinite dimensional func-tion space(e.g.,L2(Ω)or L∞(Ω))Solution:y:R+→φt→y(t)x→y(t,x)If the problem is well-posed,we can define the semigroup S(t):S(t):φ→φy0→y(t)The analytic structure of a PDE is much more complicated than that of an ODE:the global well-posedness can be a very difficult problemSuch results are known for a large class of PDEs→it is natural to investigate whether the notion of a strange attractor extends to PDEsSuch chaotic behaviors can be observed in dissipative PDEsChaotic behaviors arise from the interaction of•Energy dissipation in the higher part of the Fourier spectrum•External energy income in the lower part•Energyflux from the lower to the higher modesThe trajectories are localized in a”thin”in-variant region of the phase space having a very complicated geometric structure→the global attractor1.The global attractor.S(t)semigroup acting on E:S(t):E→E,t≥0S(0)=Id,S(t+s)=S(t)◦S(s),t,s≥0 Continuity:x→S(t)x is continuous on E,∀t≥0A set A⊂E is the global attractor for S(t)if(i)it is compact(ii)it is invariant:S(t)A=A,t≥0(iii)∀B⊂A,lim t→+∞dist(S(t)B,A)=0dist(A,B)=supa∈A infb∈Ba−b EEquivalently:∀B⊂φbounded,∀ǫ>0,∃t0= t0(B,ǫ)s.t.t≥t0implies S(t)B⊂UǫThe global attractor is uniqueIt is the smallest closed set enjoying(iii)It is the maximal bounded invariant setTheorem:(Babin-Vishik)We assume that S(t)possesses a compact attracting set K, i.e.,∀B⊂E bounded,lim t→+∞dist(S(t)B,K)=0Then S(t)possesses the global attractor A.The global attractor is oftenfinite dimen-sional:the dynamics,restricted to A isfinite dimensionalFractal dimension:Let X be a compact setdim F X=lim supǫ→0+ln Nǫ(X)ǫNǫ(X):minimum number of balls of radius ǫnecessary to cover XIf Nǫ(X)≤c(1Theorem:(H¨o lder-Ma˜n´e theorem)Let X⊂E compact satisfy dim F X=d and N>2d be an integer.Then almost every bounded linear projector P:E→R N is one-to-one on X and has a H¨o lder continuous inverse.This result is not valid for other dimensions (e.g.,the Hausdorffdimension)If A hasfinite fractal dimension,then,fixing a projector P satisfying the assumptions of the theorem,we obtain a reduced dynamical system(S),S= P(A),which isfinite dimensional(in R N)and H¨o lder continuousDrawbacks:(S)cannot be realized as a system of ODEs which is well-posedReasonable assumptions on A which would ensure that the Ma˜n´e projectors are Lipschitz are not knownComplicated geometric structure of A and AThe lower semicontinuitydist(A0,Aǫ)→0asǫ→0is more difficult to prove and may not hold It may be unobservable:∂y∂x2+y3−y=0,x∈[0,1],ν>0y(0,t)=y(1,t)=−1,t≥0A={−1}There are many metastable”almost station-ary”equilibria which live up to t⋆≡eν−12.Inertial manifolds.A Lipschitzfinite dimensional manifold M⊂E is an inertial manifold for S(t)if(i)S(t)M⊂M,∀t≥0(ii)∀u0∈E,∃v0∈M s.t.S(t)u0−S(t)v0 E≤Q( u0 E)e−αt,α>0,Q monotonicM contains A and attracts the trajectories exponentiallyConfirms in a perfect way thefinite dimen-sional reduction principle:The dynamics reduced to M can be realized as a Lipschitz system of ODEs(inertial form)Perfect equivalence between the initial sys-tem and the inertial formDrawback:all the known constructions are based on a restrictive condition,the spectral gap condition→The existence of an inertial manifold is not known for several important equations, nonexistence results for damped Sine-Gordon equations3.Exponential attractors.A compact set M⊂E is an exponential at-tractor for S(t)if(i)It hasfinite fractal dimension(ii)S(t)M⊂M,∀t≥0(iii)∀B⊂E bounded,dist(S(t)B,M)≤Q( B E)e−αt,α>0,Q monotonicM contains AIt is stillfinite dimensional and one has a uni-form exponential control on the rate of at-traction of trajectoriesIt is no longer smoothDrawback:it is not unique→One looks for a simple algorithm S→M(S)Initial construction:non-constructible and valid in Hilbert spaces onlyConstruction in Banach spaces:Efendiev, Miranville,Zelik→Exponential attractors are as general as global attractorsMain tool:Compact smoothing property on the difference of2solutionsLet S:E→E.We consider the discrete dynamical system generated by the iterations of S:S n=S◦...◦S(n times)Theorem:(Efendiev,Miranville,Zelik)We consider2Banach spaces E and E1s.t.E1⊂E is compact.We assume that•S maps theδ-neighborhood Oδ(B)of a bounded subset B of E into B•∀x1,x2∈Oδ(B),≤K x1−x2 ESx1−Sx2 E1Then the discrete dynamical system gener-ated by the iterations of S possesses an ex-ponential attractor M(S)s.t.(i)M(S)⊂B,is compact in E anddim F M(S)≤c1(ii)S M(S)⊂M(S)(iii)dist(S k B,M(S))≤c2e−c3k,k∈N,c3>0 (iv)The map S→M(S)is H¨o lder continu-ous:∀S1,S2,dist sym(M(S1),M(S2))≤c4 S1−S2 c5,c5>0, wheredist sym(A,B)=max(dist(A,B),dist(B,A))S =supSh Eh∈Oδ(B)Furthermore all the constants only depend on B,E,E1,δand K and can be computed explicitly.Remarks:1)We have a mapping S→M(S)and,due to the H¨o lder continuity,we can construct continuous families of exponential attractors2)Exponential attractors for a continuous semigroup S(t):Prove that∃t⋆>0s.t.S⋆=S(t⋆)satisfies the assumptions of the theorem→M⋆for S⋆If(x,t)→S(t)x is Lipschitz(or H¨o lder)on B×[0,t⋆],setS(t)M⋆M=∪t∈[0,t⋆]We again have a mapping S(t)→M(S)which is H¨o lder continuous3)For damped hyperbolic equations:asymp-totically smoothing property4.Finite dimensional reduction of nonau-tonomous systems.Systems of the form∂yDrawback:the uniform attractor has infinite dimension in general.Example:∂yThe family{A(t),t∈R}is a pullback attrac-tor for U(t,τ)if(i)A(t)is compact in E,∀t∈R(ii)U(t,τ)A(τ)=A(t),∀t≥τ(iii)∀B⊂E bounded,dist(U(t,t−s)B,A(t))=0lims→+∞Remarks:1)The pullback attractor is unique2)If the system is autonomous,we recover the global attractor3)In general,A(t)hasfinite fractal dimen-sion,∀t∈RDrawback:The forward convergence does not hold in generalExample:y′=f(t,y),where f(t,y)=−y if y≤0,(−1+2t)y−ty2 if t∈[0,1],and y−y2if t≥1Then A(t)={0},∀t∈R,but every trajectory starting from a neighborhood of0leaves this neighborhood never to enter it againThe forward convergence does not hold be-cause the rate of attraction is not uniform in t→This can be solved by constructing ex-ponential attractorsWe can construct a family{M(t),t∈R}, called nonautonomous exponential attractor, s.t.(i)dim F M(t)≤c1,∀t∈R,c1independent of t(ii)U(t,τ)M(τ)⊂M(t),∀t≥τ,(iii)∀B⊂E bounded,dist(U(t,τ)B,M(t+τ))≤Q( B E)e−αt,t∈R,t≥τ,α>0,Q monotonic(iii)implies the pullback attraction,but also the forward attraction→(i)and(iii)yield a satisfactoryfinite di-mensional reduction principle for nonautono-mous systemsRemarks:1)The time dependence is arbitrary2)The map U(t,τ)→{M(t),t∈R}is also H¨o lder continuous。
29--拉曼光谱在石墨烯结构表征中的应用
* E-mail: jinzhang@ Received September 6, 2013; published November 3, 2013. Project supported by the National Natural Science Foundation of China (Nos. 21233001, 21129001, 51272006 and 51121091) and the Ministry of Science and Technology of the People’s Republic of China (No. 2011YQ0301240201 and 2011CB932601). 项目受国家自然科学基金(Nos. 21233001, 21129001, 51272006 和 51121091)和科技部项目(Nos. 2011YQ0301240201 和 2011CB932601)资助.
量的研究表明扭转的双层石墨烯由于层间耦合较弱其而当扭转角小于15左右时这个线性的色散关系会被破坏能带结构会变为抛物线型5a给出了单层石墨烯及其折叠区域即扭转的双层石墨烯的拉曼谱图在5145nm激光激发下折叠区域的g峰半峰宽较单层石墨烯更小频率向高波数位移当激光波长减小至488nm两者差异几乎消失了这是由于扭转的双层石墨烯层间耦合较弱其电子色散曲线并未发生裂分g峰仍表现为单个的洛伦兹峰型82如图5b所示与扭转的双层石墨烯类似少层石墨烯经折叠之后拉曼光谱仍然保持了未折叠区域的光谱特征41大多数扭转的双层石墨烯的拉曼光谱仍然保持了单层石墨烯的拉曼特征g峰表现为单个的洛伦兹峰型且其强度大于g但对于某些扭转角在某一特定波长的激光激发下峰强度会极大地增强其强度会达到单层石墨烯的数十倍388384图5c为633nm激光激发下单层石墨烯和扭转角为31027的双层石与单层石墨烯相比扭转的双层石墨cm1强度对角度有着较强的依赖性峰强度在扭转角为10左右时达到最大aba和abc堆垛的三层石墨烯的ag峰拉曼光谱5173插图为aramanspectraabcstackedtrilayergraphene5173insetsramanimagesbandrespectively综述actachim
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The purpose of this paper is to study the asymptotic dependence structure of the Linear fractional Levy motion (LFLM) and the Log-fractional Levy motion (LogFLM). These processes, which we denote by X = {X(t), --m < t < ~}, share two important characteristics: they are strictly a-stable, 0 < a < 2, and they are H-sssi. Strictly a-stable means that for any real t t, ..., t d, d >_. 1, there are numbers A > 0, B > 0 and C real (depending on t I .... , to) such that
*Institute of Mathematics and Cybernetics, Lithuanian Academy of Sciences. tCollege of Management Science, University of Lowell, Lowell Massachusetts. :~Department of Mathematics, Boston University, Boston Massachusetts. Published in Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 1, pp. 3-28, JanuaryMarch, 1991. Original article submitted September 7, 1989. 0363-1672/91/3101-0001512.50 9 Plenum Publishing Corporation !
0.>., t) =Ezxp{i(O,Y(t)+O.,Y(O))}iEexp{iO,
Y(t)}Eexp{iO.,Y(O)),
where 01 and 0 2 are real constants and Y is the increment process Y(t) = X (t + 1) - - X(t), - - ~ < t < ~. The function r(t) has some nice properties: it is zero when Y(t) and Y(0) are independent, it is asymptotically p r o p o r t i o n a l to the covariance of Y(t) if Y(t) is Gaussian, and it is always defined. W e shall see that r(t) - A t k as t --, 0% where A and k are constants, when Y(t) is the increment process of L F L M or L o g F L M . O u r goal is to determine k and to obtain an explicit expression for the constant A in terms of the p a r a m e t e r s characterizing the distribution, including 01, 02, a , and H. O u r results extend those obtained by Astrauskas [1] in the symmetric a - s t a b l e case (SaS) for one-sided L F L M . It is difficult in general to show that a given a-stable H-sssi process X is not L F L M . The results of this paper suggest the following technique: if Z(t) = X (t + 1) - - X(t) and if Y is the increment process for L F L M , then X is not L F L M if limt_, ~ rz(t)/ry(t ) r 1. This technique exploits the fact that we have an explicit expression for the constant A. It is used in a forthcoming paper to d e m o n s t r a t e that an a - s t a b l e H-sssi process, which arises as a limit of sums of renewal reward processes, is not LFLM.
( X (at,), . . . . . V (~,~)) "A- aH ( X it 0 . . . . . . .V 0 , ) ) .
(it) X has stationary increments, and hence, the increment process Y(t) = X (t + 1) -- X (t), - - ~ < t < w, is stationary. The LFLM and the LogFLM have many interesting properties. (See for example, Taqqu and Wolpert [11], Astrauskas [1], Maejima [6], [7], Kasahara and Maejima [3], Kasahara, Maejima and Vervaat [4], Cambanis and Maejima [2], Samorodnitsky and Taqqu [9].) They are both a-stable extensions of the Gaussian H-sssi process (0 < H < 1) Fractional Brownian motion (FBM), which was introduced by Kolmogorov [5] and studied in detail by Mandelbrot and Van Ness [8]. The Gaussian process FBM can be represented as a "moving-average"-type stochastic integral with respect to Gaussian noise. The a-stable process LFLM is defined in the next section, using a similar representation but with respect to a-stable noise, a < 2. If X(t) is (standard) FBM and Y(t) = X (t + 1) -- X (t) is its increment process, then Y has mean zero and covariance EY(s)Y(s + t) = 1/2 { It + 112M _ 21tlzn + tt _ 11TM} - H(2H - - 1)t 2H-2 as t ~ Qo. This covariance function characterizes the dependence structure: when H = 1/2, nonoverlapping increments are independent (FBM reduces to Brownian motion in this case), and when 1/2 < H < 1, the increments exhibit long-range dependence because they have a spectral density which diverges at the origin (see Taqqu [10]).
A (.r"'(t,) ......
v~,' (t,~) + ~ (.v'~' (r,) . . . . .
x"-', (~,)) - ~ c ( v 0,) . . . . . .
,- (t,)).
where X(1) and X(e) are independent copies of the process X and where ___d denotes equality in distribution. H-sssi means: (i) there is a parameter H > 0 (called the self-similarity parameter) such that for all tl,..., td, d ~ 1, andd e n c e structure of the L F L M (and the L o g F L M ) is more difficult to analyze because the covariance is not defined when a < 2. O n e can sometimes use the "covariation" to describe the d e p e n d e n c e but the covariation is itself not always defined when a <- 1 (see Samorodnitsky and Taqqu [9]). W e shall use the following function to describe the dependence: r(t)=r(O,,