Operational Research in the U.K. in 1977: The Causes and Consequences of a Myth?

Instead of maintaining the original ideal of having a broad scientific basis for practical Operational Research, it is suggested that the O.R. community has uncritically accepted a myth which views O.R. as a "Hard" (Physical or even Mathematical) Science. It is argued that this has had profound consequences which explain the present difficulties O.R. workers have with problems involving major Social or Behavioural features. It is concluded that the "Hard" Science myth must be replaced, and a return made to the original conception of O.R., if we are to assist effectively in the complex social issues we face today.     

The Metastable Behavior of the Three Dimensional Ising Model

The problem of metastability has attracted a great attention in the recent decade.In particular, it has been extensively investigated the 2-dimensional Ising model ina finite torus [CFQ]、[NS]、[Sch]. In this paper, the 3-dimensional Ising model withGlauber dynamics under a positive magnetic field is considered. We characterize themetastable behavior in the pathwise approacb, find out all metastable states, anddetermine naturally the critical droplet. We give a general and clear view of the sub-stance of the passage from all spins down (- 1) to all spins up (+ 1). For a largeclass of initial states, the logarithmic asymptotics of the hitting time of - 1 or + 1 areaccurately estimated, and the shrink and growth of droplets are described.     

The Metastable Behavior of the Two Dimensional Ising Model

There are continuous efforts in recent years in order to have a better understan-ding of metastable bekavior of a statistical mechanics system. We consider it in twodimensions, solve problems proposed in [Sch]. By the idea of [FW] we are able toshapen the previous results [NS], and to identify the critical droplet naturally.Let Λ be a 2-dimensional lattice torus, and X = { - 1, + 1}~Λ. For η∈X assignthe Hamiltonian     

The fundamental theorem of calculus: visually?

The paper wants to show how it is possible to develop based on an adequate basic idea (so-called “Grundvorstellung”) of the derivative a visual understanding of the (first) Fundamental theorem of Calculus.     

The Inequality Process Versus the Saved Wealth Model: Which Is the More Likely to Imply an Analogue of Thermodynamics in Social Science?

The Inequality Process (IP) and the Saved Wealth Model (SW) are theories of income distribution. The IP's social science metatheory requires its stationary distribution to fit the distribution of labor income conditioned on education. The SW is a modification of the particle system model of the kinetic theory of gases (KTG), the basis of gas thermodynamics. The IP is a particle system similar to the SW and KTG. This article shows that the IP passes the empirical test required of it by social science theory better than the SW. The IP's advantage increases as the U.S. labor force becomes more educated. The IP may the better bet to imply an analogue of thermodynamics in social science.     

The Asymptotic Behavior of Solutions of Some Doubly Degenerate Nonlinear Parabolic Equations

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The Existence and Local Behavior of Multivariate Algebraic Function Approximations

The existing scheme of rational polynomial approximants, defined by multivariate power series, is extended to define approximants with branch points. The existence theorem is obtained. The basic properties used to define the rational approximants can be preserved almost intactly. Especially, the local behavior of the     

The evolution of metanorms: quis custodiet ipsos custodes?

How are norms maintained? Axelrod (in Am. Political Sci. Rev. 80(4): 1095–1111, 1986) used an evolutionary computational model to proffer a solution: the metanorm (norm to enforce norm enforcement). Although often discussed, this model has neither been sufficiently replicated nor explored. In this paper we replicate and extend that model. Results were generally supportive of the original. Speculations in the original regarding the requirement to link sanctions underlying the metanorm structure were not supported, as differentiating punishment likelihoods against defectors from punishment likelihoods against shirkers (non-enforcers of the norm against defection) lead to more efficient and effective sanctioning structures that allowed norm emergence. Replications of the Groups game (two groups differing in numbers and power) generally supported the original reports, but true norms against defection emerged only if sanctioning structures were differentiated, resulting in the Strong group developing a dominant norm against others defecting (Metavengeance). That is, when groups are involved with differential power, Metanorms fail unless a more sophisticated sanctioning structure (Metavengeance) is supported.     

The Local Asymptotic Behavior of Solutions of Second Order Linear Differential Equations in a Nutshell

1.IntroductionGiven a second order linear differential equation with meromorphic coefficienta(x)y” b(x)y’ c(x)y=0 (1.1)in,a domain D the local analytic theory for such equations is well developed,see e.g.[8].If x_0 is a regular point for(1.1)then the theory advocates to utilize Taylor seriesexpansions of two linearly indepentdent solutions of(1.1).If x_0 is a regular singular pointfor(1.1),Frobenius’method tells us to follow sometimes a laborious procedure which     

The End of Moral Realism?

The author considers how constructivism, presently known to us essentially as a theory for generating rules of social cooperation, embodies a certain conception of justification that in turn may be thought of as a general theory. It is argued that moral realism and projectivism are by turns platitudinous and unsatisfactory as conceptions of justification; by contrast the general conception of justification in constructivism makes sense of reason giving and coherent rivalry. The author argues that once the right picture of justification is in place, the picture constructivism illustrates or embodies, the problem of moral ontology disappears.

The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model

The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.     

The Measurement of Volume: Why Do Young Children Measure Inaccurately?

A total of 257 children in grades 2–5 were individually interviewed to find the grade level at which they demonstrated transitive reasoning and unit iteration in the measurement of volume. In the transitivity task, the children were asked if a larger, empty container could be used to compare the quantity of popcorn kernels (about 350 cc) in two containers that looked very different. The unit‐iteration task was similar except that children were asked if a small cup could be used to compare similar quantities of rice in two containers. It was found that a majority of children (51%) demonstrated transitive reasoning by third grade and that a majority (56%) demonstrated unit iteration by fourth grade. A conclusion reached is that the standard of the National Council of Teachers of Mathematics (2000) expecting children to understand units of measurement by grade 2 is unrealistic. Better principles of teaching are also suggested to encourage children to think logically.     

The Asymptotic Behavior of the Stochastic Nonlinear Schrdinger Equation With Multiplicative Noise

The nonlinear Schrdinger equation is one of the basic models for nonlinear waves.In some circumstances,randomness has to be taken into account and it often occurs through a random potential.Here,we consider the following equation     

Restricted set addition: The exceptional case of the Erd?s-Heilbronn conjecture

Let A≠B be nonempty subsets of the group of integers modulo a prime p. If p?|A|+|B|−2, then at least |A|+|B|−2 different residue classes can be represented as a+b, where a∈A, b∈B and a≠b. This result complements the solution of a problem of Erd?s and Heilbronn obtained by Alon, Nathanson, and Ruzsa.     

Shortcomings of Mathematics Education Reform in The Netherlands: A Paradigm Case?

This article offers a reflection on the findings of three PhD studies, in the domains of, respectively, subtraction under 100, fractions, and algebra, which independently of each other showed that Dutch students' proficiency fell short of what might be expected of reform in mathematics education aiming at conceptual understanding. In all three cases, the disappointing results appeared to be caused by a deviation from the original intentions of the reform, resulting from the textbooks' focus on individual tasks. It is suggested that this “task propensity”, together with a lack of attention for more advanced conceptual mathematical goals, constitutes a general barrier for mathematics education reform. This observation transcends the realm of textbooks, since more advanced conceptual mathematical understandings are underexposed as curriculum goals. It is argued that to foster successful reform, a conscious effort is needed to counteract task propensity and promote more advanced conceptual mathematical understandings as curriculum goals.     

The ?ojasiewicz exponent of nondegenerate surface singularities

We give some estimations of the ?ojasiewicz exponent of nondegenerate surface singularities in terms of their Newton diagrams. We also give an exact formula for the ?ojasiewicz exponent of such singularities in some special cases. The results are stronger than Fukui inequality?[8]. It is also a multidimensional generalization of the Lenarcik theorem?[13].