Showing papers in "The Mathematical Gazette in 1991"
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects
3,424 citations
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TL;DR: RANDOM EVENTS and their probabilities: Classes of random events and their potentials as mentioned in this paper, classes of Random Events and their possibilities, and their properties: Independence of random Events Probabilities Independence of Random Event Probabilities Probability Independency of Random events Diverse Properties of Random Variables and their Probabilities RANDOM VARIABLUEVIABLES, DISTRIBUTIONS, and BASIC CHARACTERISTICS: Distribution Functions of Random Variable Expectations Expectations and Conditional Expectations, Characteristic and Generating Functions Infinitely Divisible and St
Abstract: RANDOM EVENTS AND THEIR PROBABILITIES: Classes of Random Events Probabilities Independence of Random Events Diverse Properties of Random Events and their Probabilities RANDOM VARIABLES, DISTRIBUTIONS AND BASIC CHARACTERISTICS: Distribution Functions of Random Variables Expectations and Conditional Expectations Independence of Random Variables Characteristic and Generating Functions Infinitely Divisible and Stable Distributions Normal Distribution The Moment Problem Characterization Properties of some Probability Distributions Diverse Properties of Random Variables LIMIT THEOREMS: Various Kinds of Convergence of Sequences of Random Variables Laws of Large Numbers Weak Convergence of Probability Measures and Distributions Central Limit Theorem Diverse Limit Theorems STOCHASTIC PROCESSES: Basic Notation on Stochastic Processes Markov Processes Stationary Processes and some Related Topics Discrete-Time Martingales Continuous-Time Martingales Poisson Process and Wiener Process Diverse Properties of Stochastics Processes Index.
99 citations
85 citations
Journal Article•
TL;DR: Realism: Pre-theoretic realism Realism in philosophy Realism and truth realism in mathematics Perception and intuition: What is the question? Perception Intuition Godelian Platonism Numbers: What numbers could not be Numbers as properties Frege numbers Axioms: Reals and sets of reals Axiomization Open problems Competing theories The challenge Monism and beyond: Monism Field's nominalism Structuralism as mentioned in this paper
Abstract: Realism: Pre-theoretic realism Realism in philosophy Realism and truth Realism in mathematics Perception and intuition: What is the question? Perception Intuition Godelian Platonism Numbers: What numbers could not be Numbers as properties Frege numbers Axioms: Reals and sets of reals Axiomization Open problems Competing theories The challenge Monism and beyond: Monism Field's nominalism Structuralism.
83 citations
55 citations
TL;DR: Lifetime distributions the mean lifetime, the residual lifetime some important distributions some other models life tables and censoring estimation of the survivor function estimation and inference from censored samples estimation and inferred for other models stochastic models 1 stochastics models 2 renewal processes.
Abstract: Lifetime distributions the mean lifetime, the residual lifetime some important distributions some other models life tables and censoring estimation of the survivor function estimation and inference from censored samples estimation and inference for other models stochastic models 1 stochastic models 2 renewal processes some simple availability models explanatory variables - the proportional hazards model analysis for the proportional hazards model bayesian methods for reliability bayesian analysis in a reliability context.
TL;DR: In this article, a discussion of number theory, covering factorization and primality testing, is presented, which is part of a series of undergraduate texts in mathematics, including a discussion on the primality test.
Abstract: This is a discussion of number theory, covering factorization and primality testing. It is part of a series of undergraduate texts in mathematics.
TL;DR: In this paper, the authors addressed to students on various levels, to mathematicians, scientists, engineers, and teachers, and tried to help the genuinely interested reader by throwing light on the interconnections and purposes of the whole.
Abstract: From the Preface: (...) The book is addressed to students on various levels, to mathematicians, scientists, engineers. It does not pretend to make the subject easy by glossing over difficulties, but rather tries to help the genuinely interested reader by throwing light on the interconnections and purposes of the whole. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters. Numerous examples and problems are given at the end of various chapters. Some are challenging, some are even difficult; most of them supplement the material in the text. In an additional pamphlet more problems and exercises of a routine character will be collected, and moreover, answers or hints for the solutions will be given. This first volume of concerned primarily with functions of a single variable, whereas the second volume will discuss the more ramified theories of calculus (...).
TL;DR: For many years the mathematicians visiting Stanford enjoyed guided tours through pages of the Polya photograph album, led by Polya himself as discussed by the authors, accompanied by remarks taken from tapes of Polya's conversations with his visitors.
Abstract: For many years the mathematicians visiting Stanford enjoyed guided tours through pages of the Polya photograph album, led by Polya himself. This is a selection of the photographs accompanied by remarks taken from tapes of Polya's conversations with his visitors.
TL;DR: In this article, the authors collected together some of the known properties of this polynomial and presented some additional properties which appear to be new. But they did not seem to be known to the present generation of mathematical students.
Abstract: Ever since I was a schoolboy, my favourite polynomial has been It is a wonderful polynomial, with lots of beautiful and useful properties which, alas, do not seem to be known to the present generation of mathematical students. To remedy this, we collect together some of the known properties of this polynomial and present some additional properties which appear to be new.
TL;DR: In this article, the Simpson's paradox is discussed starting from a complex number situation, but the real occurrences of the paradox stem from real occurrences, and not from a fictional example.
Abstract: Note 74.11 from Nick Lord in the March 1990 Gazette looks at the fascinating Simpson's paradox starting from a complex number situation; and in the same issue John Haigh, reviewing Cox and Snell's Analysis of Binary Data, gives a (fictitious) example; but the fascination of the paradox stems from the real occurrences.