二层次消费与投资决策优化动态规划模型

在动态多阶段情形,投资者面临的环境不仅只有投资环境,还包括消费环境.投资者关于投资与消费的决策具有层次性.因为消费事关人的生存需要,是优先要考虑的问题,且投资的最终目的还是为了消费,所以使消费最大化应是高一层次的目标,而使投资最大化则应是次一级的目标.因此,试图建立一个二层次消费与投资决策优化动态规划模型,以便更好地模拟现实世界的情况.讨论了该模型的动态决策过程和最优解的性质.     

J. Howard Redfield 1879–1944

During much of his life J. Howard Redfield earned his living as an engineer but his main interests lay elsewhere. He performed and wrote music and was a gifted linguist, familiar with almost all European languages, as well as with some African and Asian tongues. In middle age he turned his attention towards combinatorial mathematics but it was not until many years after his death that the mathematical world realized that he had obtained significant results.     

The rejected parts of Brouwer's dissertation on the foundations of mathematics

Brouwer launched his intuitionist attack on the formalistic trends in mathematics in his now famous dissertation “On the Foundations of Mathematics” in 1904. In the autumn of 1976, the author found what turned out to be the first version of Brouwer's dissertation. He also discovered that his supervisor disapproved and rejected what Brouwer considered to be the most important part of his dissertation. The extreme solipsistic views held by Brouwer in his later years are well known. The first version of the dissertation shows that these views were held before Brouwer began his intuitionist campaign and that they determined his philosophy of mathematics. The deleted parts not found in the final version of the dissertation are presented here in an English translation. In a brief introduction the author gives some of the historical background, based partly on the correspondence between Brouwer and his supervisor, Korteweg.     

Cultivating a research imperative: Mentoring mathematics at Stockholms Högskola, 1882–1887

Though the central role of Gösta Mittag-Leffler in the promotion of specialized, research-oriented mathematics at Stockholms Högskola is widely acknowledged, the specific social and technical means by which he sought to cultivate a fledgling research community there during the early- to mid-1880s have received little attention. In particular, a detailed study of the relationship of his own research activity to that of his first Swedish students is absent from the existing literature.Through the juxtaposition of their research activities and unpublished correspondence, this paper explores Mittag-Leffler's active and deliberate efforts to engage his students Ivar Bendixson and Edvard Phragmén in open problems within his own research agenda, support them through his institutional connections, and instill within them norms concerning research ideologies, practices of communication and criticism, and frameworks for shared knowledge. It also illuminates the extent to which his teachings took root in at least one student to emerge from his program, who would perpetuate the mathematical practices set in place by his teacher and set forth on the international stage to promote his newly-acquired system of values.     

Shiing-Shen Chern��s Centenary

Shiing-Shen Chern was an editor of our journal Results in Mathematics from 1984 to 2004, the year he passed away at Tianjin. This article honors one of the greatest mathematicians of the twentieth century, in particular remembering his studies at Hamburg University during the years 1934?C1936. This period strongly influenced his mathematical work and was decisive for his later career. We survey the situation of the Department of Mathematics there, Chern??s studies, his visits to Germany in later years, his honours and awards from German institutions, and finally exemplarily his influence on the next generations of Chinese mathematicians studying in Germany.     

Boscovich's geometrical principle of continuity,and the “mysteries of the infinity”

In this paper we give a detailed account of Boscovich's geometrical principle of continuity. We also compare his ideas with those of his forerunners and successors, in order to cast some light on his possible sources of inspiration and to underline the elements of novelty in his approach to the subject.     

Pure mathematics applied in early twentieth-century America: The case of T.H. Gronwall,consulting mathematician

Thomas Hakon Gronwall (1877–1932) was a Swedish-American mathematician with a broad range of interests in mathematical analysis, physics, and engineering. Though he was primarly known for his results in pure mathematics, his career as a “consulting mathematician” in America from 1912 to his death in 1932 provides a backdrop against which one can discuss contemporary issues involved in the increasing application of mathematics to engineering, industrial, and scientific problems. This paper attempts a summary of his major mathematical contributions to industrial, governmental, and academic institutions while relating his often difficult life during these years.     

Robert Patterson: American ‘revolutionary’ mathematician

You will not see Robert Patterson’s name mentioned in many mathematics books. While his mathematical works survive, his name is more likely to appear in American history books dealing with the Colonial period, given his associations with the most influential men of that time. In this article, we will examine his mathematical work, as well as his contributions to a newly-formed nation. Most of what we know about Robert Patterson’s ancestors and life is due to his grandson, William Ewing DuBois, who wrote a family history in 1847. For other information, I have drawn upon diaries and a great many letters. All spelling and syntax are copied exactly as they appear.     

Anton Kazimirovich Suschkewitsch (1889–1961)

Anton Kazimirovich Suschkewitsch was a Russian mathematician who spent most of his working life at Kharkov State University in the Ukraine. In the 1920s, he embarked upon the first systematic study of semigroups, placing him at the very beginning of algebraic semigroup theory and, arguably, earning him the title of the world's first semigroup theorist. Owing to the political circumstances under which he lived, however, his work failed to find a wide audience during his lifetime. We give a brief account of his life and his researches into semigroup theory.     

Kenneth O. May, 1915–1977 : His early life to 1946

Kenneth Ownsworth May graduated from the University of California at Berkeley in 1936 with highest honors in mathematics. The following year he received his Masters degree and became a fellow of the Institute of Current World Affairs, and during the next two years he traveled to England, Europe, and Russia. On his return to the United States he became active in the Communist Party, the consequences of which would plague him for years. He joined the United States Army in 1942, serving with distinction, and after the war returned to Berkeley, where he obtained his Ph.D. in 1946. He immediately accepted an assistant professorship at Carleton College in Northfield, Minnesota, later moving to the University of Toronto.This part of May's biography focuses on the events up to his accepting a position at Carleton College. In this early phase his openness, his emphasis on good communications in the process of education, and his interest in practical procedures emerge which later set the background for his successful career as a leading historian of mathematics and the founding editor of Historia Mathematica.     

Peano's concept of number

Giuseppe Peano's development of the real number system from his postulates for the natural numbers and some of his views on definitions in mathematics are presented in order to clarify his concept of number. They show that his use of the axiomatic method was intended to make mathematical theory clearer, more precise, and easier to learn. They further reveal some of his reasons for not accepting the contemporary “philosophies” of logicism and formalism, thus showing that he never tried to found mathematics on anything beyond our experience of the material world.     

Gauss as a geometer

In an attempt to reveal the breadth of Gauss's interest in geometry, this account is divided into six chapters. The first mentions the fundamental theorem of algebra, which can be proved only with the aid of geometric ideas, and in return, an application of algebra to geometry: the connection between the Fermat primes and the construction of regular polygons. Chapter 2 shows his essentially ‘modern’ approach to quaternions. Chapter 3 is a sample of his work in trigonometry. Chapter 4 deals with his approach to the geometry of numbers. Chapter 5 sketches his differential geometry of surfaces: his use of two parameters, the elements of distance and area, his theorema egregium, and the total curvature of a geodesic polygon. Finally, Chapter 6 shows that he continually returned to the subject of non-Euclidean geometry, which was so precious and personal that he would not publish anything of it during his lifetime, and yet did not wish to let it perish with him.     

Ky Fan (1914�C2010), he spent every waking moment thinking about mathematics

This survey article on Dr. Ky Fan summarizes his versatile achievements and fundamental contributions in the fields of topological groups, nonlinear and convex analysis, operator theory, linear algebra and matrix theory, mathematical programming, and approximation theory, etc., and as well reveals Fan’s exemplary mathematical formation opening up the beauty of pure mathematics, with natural conditions, concise statements and elegant proofs. This article contains a brief biography of Dr. Fan and epitomizes his life. He was not only a great mathematician, but also a very serious teacher known to be extremely strict to his students. He loved his motherland and made generous donations for promoting mathematical development in China. He devoted his life to mathematics, continued his research and published papers till 85 years old.     

Extension of the partition sieve

We demonstrate the correspondence which lies behind certain partition identities used by Andrews in his partition sieve. This leads to an extension of his methods and a generalization of his results.     

According to Davis: Connecting principles and practices

In this article, the author allows Robert B. Davis to state for himself his own Principles concerning how children learn, and how teachers can best teach them. These principles are put forward in Davis’ own words along with detailed documentation. The author goes on compare Davis’ words with his practices. A single Davis video (Towers of Hanoi) is analyzed to determine if, and to what extent, his principles are evident in his teaching of this lesson.     

Interactions between subgoals and understanding of problem situations in mathematical problem solving

The purpose of this paper is to investigate solver's use of subgoals in mathematical problem solving processes. For this purpose, the process in which a solver tackled a rather difficult problem will be analyzed, focusing on how he established subgoals and how these subgoals affected his solving activity. This analysis will imply an interactive relation between subgoals established by the solver and his understanding of the problem situation. That is, his understanding of the situation supported his generation of subgoals, and those subgoals influenced his understanding positively or negatively. His use of subgoals will be also examined from the viewpoint of metacognition, and this examination will suggest the difficulty of escaping from the influence of a subgoal.     

Charles Peirce's place in philosophy

Peirce's publications on the method of scientific investigation (as distinct from his work in formal logic and mathematics) are his most important and valuable contributions to philosophy. His views on this subject are superior in clarity and cogency to his voluminous writings on metaphysics and cosmology. He subscribed to a fallibilistic conception of knowledge that is poles apart from a wholesale skepticism; his formulations of the conditions for meaningful discourse and of the pragmatic maxim, though not free from difficulties, have been fruitful sources of much subsequent philosophical and scientific analyses; and his classification of and discussions of types of argument or reasoning employed in scientific inquiry continue to be valuable and insightful clarifications of this important subject. In contrast to his account of scientific method, Peirce's evolutionary theory of ultimate reality, though marked by originality and ingenious speculation, has little merit as a contribution to genuine knowledge.     

Louis Charles Karpinski,historian of mathematics and cartography

Louis C. Karpinski was best known for his publications on the history of mathematics, and secondarily as a historian of cartography. This survey of his life includes an account of his contributions to the teaching of mathematics and of his avocational interests as a collector, chess player, and gadfly attacking what he saw as poor thinking and abuses of power in both the universities and in the public domain. It is followed by a note on archives, a list of the Ph.D. theses he supervised, and a complete bibliography.     

Tracing Robert's use of representations to solve counting problems: A 16-year case study

This study describes how Robert used his external representations (formulae, notations, sketches, models, and figures) to solve progressively more challenging counting tasks over a 16-year period. In his explorations of counting tasks, Robert discovered intricate connections between solutions to problems that looked different on the surface. Using video data from Robert's problem solving, analyses of his solutions are presented that shed light on how he built new ideas from existing ideas and how he modified external representations to make new mathematical discoveries and provide justifications for his solutions.