Number crunching vs. number theory: computers and FLT,from Kummer to SWAC (1850–1960), and beyond

The present article discusses the computational tools (both conceptual and material) used in various attempts to deal with individual cases of FLT, as well as the changing historical contexts in which these tools were developed and used, and affected research. It also explores the changing conceptions about the role of computations within the overall disciplinary picture of number theory, how they influenced research on the theorem, and the kinds of general insights thus achieved. After an overview of Kummer’s contributions and its immediate influence, I present work that favored intensive computations of particular cases of FLT as a legitimate, fruitful, and worth-pursuing number-theoretical endeavor, and that were part of a coherent and active, but essentially low-profile tradition within nineteenth century number theory. This work was related to table making activity that was encouraged by institutions and individuals whose motivations came mainly from applied mathematics, astronomy, and engineering, and seldom from number theory proper. A main section of the article is devoted to the fruitful collaboration between Harry S. Vandiver and Emma and Dick Lehmer. I show how their early work led to the hesitant introduction of electronic computers for research related with FLT. Their joint work became a milestone for computer-assisted activity in number theory at large.     

AUTOMATIC DECISION-MAKING： NEURAL FIRING AND RESPONSE

1. Introduction This is the fourth exposition on theAnalytic Hierarchy Process. It is true thatmany decisions we make subconsciously ariseout of our physical and biological needs andderive from the pressure to survive physically.We also make subconsciou…     

MAN-MACHINE COLLABORATED KNOWLEDGE CREATION IN HWMSE

1 Introduction Science of complexity and complex systems is a relatively new area In wide fields from chemistry, biology, environment, geo-science, climatology to economics and sociology, complexity has been studied from diverse views and understandings Systems science, which could be traced back to Ludwig von Bertalanffy’foundational work on general system theory, plays an active role in complexity studies From system perspectives, relevant concepts often include interaction, feedback, evol…     

Preparation and characteristics of flexible all-organic thin-film field-effect transistor

Much attention has been attracted to organic thin-film field-effect transistors (OTFFETs) in the past decades[1—4]. Because of their lower cost and easier preparation, OTFFETs are considered to be useful in driving liquid crystal displays (LCD) and organic light-emitting diodes (OLED). Furthermore, flexible OTFFETs will be one of the most useful electronic devices for flexible active matrix driving circuits. OTFFETs based on pentacene single crystal have been reported to be of g…     

GROUP SIZE AND PARALLELISM EFFECTS IN TASKS WITHHETEROGENEOUS LEVELS OF DIFFICULTY：A STOCHASTIC ORDER APPROACH

We consider tasks where in order to perform them it is sufficient that one member of a group will know how to do it. We are interested in the effect of task difficulty, and variability of that difficulty, on group performance, and in particular on the marginal contribution of an additional number to the performance of groups of different size. We explore the implications of various stochastic orders over task difficulty and variability. Some intuitive conjectures are shown to be false.     

STUDIES ON HORIZONTAL COMPETITION AMONG HOMOGENOUS RETAILERS THROUGH AGENT-BASED SIMULATION

1. Introduction A supply chain is a network composed osuppliers, manufacturers, retailers, etc., whichcooperate to offer a kind of goods or servicesThese supply chain members cooperate andcompete with each other to maximize theiown profits. For example,…     

Resonance Light-Scattering Spectroscopy Study on Interaction between Gold Colloid and Thiol Containing Pharmaceutical

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Phylogeny constructed by using diversity increment

A new approach based on the concept of the diversity increment is applied to reconstruct a phylogeny. The phylogeny of the Eutherian orders use concatenated H-stranded amino acid sequences, and the result is consistent with the commonly accepted one for the Eutherians. Foundation item: Supported by the National Natural Science Foundation of China ( 30170214) and the Open Foundation of the State Key Laboratory of Software Engineer, Wuhan University, China. Biography: Shi Feng ( 1966- ), male, Ph. D, Associate professor, research direction: bioinformatics.     

Fundamentals of the analytic network process — Dependence and feedback in decision-making with a single network

The Analytic Network Process (ANP) is a multicriteria theory of measurement used to derive relative priority scales of absolute numbers from individual judgments (or from actual measurements normalized to a relative form) that also belong to a fundamental scale of absolute numbers. These judgments represent the relative influence, of one of two elements over the other in a pairwise comparison process on a third element in the system, with respect to an underlying control criterion. Through its supermatrix, whose entries are themselves matrices of column priorities, the ANP synthesizes the outcome of dependence and feedback within and between clusters of elements. The Analytic Hierarchy Process (AHP) with its independence assumptions on upper levels from lower levels and the independence of the elements in a level is a special case of the ANP. The ANP is an essential tool for articulating our understanding of a decision problem. One had to overcome the limitation of linear hierarchic structures and their mathematical consequences. This part on the ANP summarizes and illustrates the basic concepts of the ANP and shows how informed intuitive judgments can lead to real life answers that are matched by actual measurements in the real world (for example, relative dollar values) as illustrated in market share examples that rely on judgments and not on numerical data. Thomas L. Saaty holds the Chair of University Professor, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA, and obtained his Ph.D. in mathematics from Yale University. Before that he was a professor at the Wharton School of the University of Pennsylvania for ten years. Prior to that he spent seven years at the Arms Control and Disarmament Agency in the State Department in Washington, DC, that carried out the arms reduction negotiations with the Soviets in Geneva. His current research interests include decision-making, planning, conflict resolution and synthesis in the brain. As a result of his search for an effective means to deal with weapons tradeoffs at the Disarmament Agency and, more generally, with decision-making and resource allocation, Professor Saaty developed The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP). He is co-developer of the software Expert Choice and of the software Super Decisions for decisions with dependence and feedback. He has authored or co-authored twelve books on the AHP/ANP. Professor Saaty has also written a number of other books that embrace a variety of topics, including Modern Nonlinear Equations, Nonlinear Mathematics, Graph Theory, The Four Color Problem, Behavioral Mathematics, Queuing Theory, Optimization in Integers, Embracing the Future and The Brain: Unraveling the Mystery of How It Works. His most recent book is Creative Thinking, Problem Solving & Decision Making. The book is a rich collection of ideas, incorporating research by a growing body of researchers and practitioners, profiles of creative people, projects and products, theory, philosophy, physics and metaphysics...all explained with a liberal dose of humor. He has published more than 300 refereed articles in a wide variety of professional journals. He has been on the editorial boards of Mathematical Reviews, Operations Research, Naval Research Logistics Quarterly, Mathematical and Computer Modeling, Socio-Economic Planning Sciences, Applied Mathematics Letters, and several others. He also served as consultant to many corporations and governments.     

Synthesis of CaCO3 crystals using hydroxypropylmethyl cellulose hydrogel as template

Calcium carbonate crystallization was performed in hydrogel of hydroxypropylmethyl cellulose (HPMC). Results showed that the polyhydroxy functionalities in HPMC gel network facilitated the nucleation of aragonite which was not found in experiment without HPMC hydrogel and in experiment using methylcellulose (MC) hydrogel as template. On the other hand, due to the unique assembly of the macromolecules in HPMC hydrogel network, which was different from other hydrogels used in some previous reports, particular crystal morphology, corncob-like CaCO_3, was obtained for the first time.