Bipolarization of posets and natural interpolation

The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of n[0,1]. We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their natural triangulation, as in the work of Koshevoy.A second aim of the paper is to define a general mechanism for the bipolarization of ordered structures. Bisets (or signed sets), as well as bisubmodular functions, bicapacities, bicooperative games, as well as the Choquet integral defined for them can be seen as particular instances of this scheme.Lastly, an application to multicriteria aggregation with multiple reference levels illustrates all the results presented in the paper.     

Bayesian estimation of system reliability in Brownian stress-strength models

A stress-strength system fails as soon as the applied stress,X, is at least as much as the strength,Y, of the system. Stress and strength are time-varying in many real-life systems but typical statistical models for stress-strength systems are static. In this article, the stress and strength processes are dynamically modeled as Brownian motions. The resulting stress-strength system is then governed by a time-homogeneous Markov process with an absorption barrier at O. Conjugate as well as non-informative priors are developed for the model parameters and Markov chain sampling methods are used for posterior inference of the reliability of the stress-strength system. A generalization of this model is described next where the different stress-strength systems are assumed to be exchangeable. The proposed Bayesian analyses are illustrated in two examples where we obtain posterior estimates as well as perform model checking by cross-validation.     

Stationary probability distributions for multiresponse linear learning models

A necessary and sufficient condition is given for the existence of stationary probability distributions of a non-Markovian model with linear transition rule. Similar to the Markovian case, stationary probability distributions are characterized as eigenvectors of nonnegative matrices. The model studied includes as special cases the Markovian model as well as the linear learning model and has applications in psychological and biological research, in control theory, and in adaption theory.     

Notions of equivalence through ratios: Students with and without learning disabilities

Students with learning disabilities (LD) specific to mathematics historically underperform in foundational content such as rational number equivalence. This study examined the strategy usage and multiplicative thinking of three third grade children (i.e., Bill, a child identified as having a learning disability specific to mathematics, Carl, a child labeled as low achieving in mathematics, and Albert, a child labeled as typically achieving) before, during, and after participating in tutoring sessions consisting of student-centered pedagogy and equivalence tasks presented through an underutilized interpretation of rational number: namely, the ratio interpretation. Constant comparison analysis of the children's work during the tutoring sessions as well as responses to tasks during two clinical interviews seemed to indicate that all three children increased their use of viable strategies, with notable differences in the sophistication of the strategies as well as the level of multiplicative thinking utilized before and after the ratio-based tutoring sessions. Yet, Bill's continued use of rudimentary strategies reflects a need for continued research to investigate why the use of such strategies persists and how supporting the development of more sophisticated strategies (especially among children with LD) can be achieved.     

Cones for the Moulton planes

We present a two-parameter family of affinely connected surfaces which admit the cylinder group as a collineation group of their geodesics. The Moulton Planes in the radial model of Betten, the circular cone, as well as the real affine plane, are part of this family. The Moulton Planes occur in this family in the same way as the real affine plane is contained in a family of cones with decreasing steepness.      

强Khler-Finsler流形上(p,q)形式的中值Laplace算子(英文)

本文给出了强Khler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等。与Khler流形上利用逆变基本张量及其在Finsler流形上的变形作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强Khler-Finsler流形上的逆变密切Khler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强Khler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广。     

EXISTENCE，UNIQUENESS AND PROPERTIES OF THE SOLUTIONS OF A DEGENERATE PARABOLIC EQUATION WITH DIFFUSION－ADVECTION－ABSORPTION

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社会网络分析方法在管理民间信仰活动的应用研究

民间信仰活动是一种复杂的社会现象,其信众群体是一个独特的社会关系网络。本文在国内首次运用社会网络分析的思维和方法,在对冀南地区民间信仰抽样调查的基础上,建立网络模型,通过对民间信仰主体和客体各结点的中心性、凝聚性等进行量化分析,进而探究民间信仰网络的社会结构及其属性,得出信众群体特征、信仰动因、活动特点、社会心态等有益结论,为民间信仰活动的社会治理和政府管理提供科学依据.     

不带微结构的连续统中新的能量守恒定律和C-D不等式

对连续统力学中的基本定律和均衡方程以及C-D不等式进行了认真的再研究.指出了现有的动量矩均衡定律和能量守恒定律以及Clausius-Duhem不等式的不完整性,并且提出了不带微结构的局部和非局部非对称连续统中新的而且更为普遍的能量守恒定律和相应的能量均衡方程以及C-D不等式.     

On semiclassical linear functionals of class s=2: classification and integral representations

In this paper, we obtain all the semiclassical linear functionals of class two taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention in their integral representations. Thus, some linear functionals very well known in the literature, associated with perturbations of classical linear functionals, as well as new linear functionals appear which have not been studied as far as we know.     

Sequential entry and exit decisions with an ergodic performance criterion

We consider a variant of an optimisation problem involving sequential entry and exit decisions that has emerged in the economics literature as a real option model. The problem that we solve aims at maximising an ergodic, or long-term average, performance criterion in a pathwise as well as in an expected sense. Such a performance index is probably better suited to decision making within a sustainable economic environment. Our results include a complete characterisation of the optimal strategy, which can take qualitatively different forms depending on the problem's data, as well as explicit expressions for the maximal value of the associated performance index.     

Advanced supply chain planning with mixtures of backorders,lost sales,and lost contract

This paper investigates a supply chain system in which a supplier prepares for the selling season by building stock levels prior to the beginning of the season and shortages realized at the beginning of the season are represented as mixtures of backorders and lost sales. Backlogged items are replenished as soon as possible through an emergency procurement as opposed to waiting until the next scheduled delivery as in many continuous review scenarios, and the backorder rate is modeled as a piecewise linear function of the magnitude of the shortage. The often intangible cost associated with lost sales and customer goodwill is also quantified. In particular, the buyer and supplier are engaged in a contractual agreement and the loss of customer goodwill from the supplier’s perspective is represented as the expected cost associated with violating the conditions of the contract. The likelihood of contract cancellation is also represented as a function of the magnitude of shortage. The optimal solution is derived in closed form for the case of exponential demand distribution, and an example problem is illustrated with numerical data in order to demonstrate calculation of the optimal solution and corresponding sensitivity analysis for demand distributions in which the solution cannot be expressed in closed form.     

An evolving framework for describing student engagement in classroom activities

Student engagement in classroom activities is usually described as a function of factors such as human needs, affect, intention, motivation, interests, identity, and others. We take a different approach and develop a framework that models classroom engagement as a function of students’ conceptual competence in the specific content (e.g., the mathematics of motion) of an activity. The framework uses a spatial metaphor—i.e., the classroom activity as a territory through which students move—as a way to both capture common engagement-related dynamics and as a communicative device. In this formulation, then, students’ engaged participation can be understood in terms of the nature of the “regions” and overall “topography” of the activity territory, and how much student movement such a territory affords. We offer the framework not in competition with other instructional design approaches, but rather as an additional tool to aid in the analysis and conduct of engaging classroom activities.     

Spectral properties of the massless relativistic quartic oscillator

An explicit solution of the spectral problem of the non-local Schrödinger operator obtained as the sum of the square root of the Laplacian and a quartic potential in one dimension is presented. The eigenvalues are obtained as zeroes of special functions related to the fourth order Airy function, and closed formulae for the Fourier transform of the eigenfunctions are derived. These representations allow to derive further spectral properties such as estimates of spectral gaps, heat trace and the asymptotic distribution of eigenvalues, as well as a detailed analysis of the eigenfunctions. A subtle spectral effect is observed which manifests in an exponentially tight approximation of the spectrum by the zeroes of the dominating term in the Fourier representation of the eigenfunctions and its derivative.     

Projecting average family size in rural India by the analytic hierarchy process

In this study, cultural, economic as well as certain crucial demographic factors are considered as the determinants for projecting the average family size in rural India. We use the Analytic Hierarchy Process to analyze influences of the factors which enter implicitly in a rural couple's decision‐making to determine the number of children they want to have as time goes by. We did not attempt to make distinctions among the regional differences in rural India. The outcome projected in our analysis compares favorably with the results of other demographic studies.     

Forecasting the value effect of seasoned equity offering announcements

Seasoned Equity Offers (SEOs) by publicly listed firms generally result in unexpected negative share price returns, being often perceived as a signal of overvalued share prices and information asymmetries. Hence, forecasting the value effect of such announcements is of crucial importance for issuers, who wish to avoid share price dilution, but also for professional fund managers and individual investors alike. This study adopts the OR forecasting paradigm, where the latest part of the data is used as a holdout, on which a competition is performed unveiling the most effective forecasting techniques for the matter in question. We employ data from a European Market raising in total €8 billion through 149 SEOs. We compare economic and econometric models to forecasting techniques mostly applied in the OR literature such as Nearest Neighbour approaches, Artificial Neural Networks as well as human Judgment. Evaluation in terms of statistical accuracy metrics indicates the superiority of the econometric models, while economic evaluation based on trading strategies and simulated profits attests expert judgement and nearest-neighbour approaches as top performers.     

Pairings for cryptographers

Many research papers in pairing-based cryptography treat pairings as a “black box”. These papers build cryptographic schemes making use of various properties of pairings. If this approach is taken, then it is easy for authors to make invalid assumptions concerning the properties of pairings. The cryptographic schemes developed may not be realizable in practice, or may not be as efficient as the authors assume.The aim of this paper is to outline, in as simple a fashion as possible, the basic choices that are available when using pairings in cryptography. For each choice, the main properties and efficiency issues are summarized. The paper is intended to be of use to non-specialists who are interested in using pairings to design cryptographic schemes.     

A generalized Fourier transform and convolution on time scales

In this paper, we develop some important Fourier analysis tools in the context of time scales. In particular, we present a generalized Fourier transform in this context as well as a critical inversion result. This leads directly to a convolution for signals on two (possibly distinct) time scales as well as several natural classes of time scales which arise in this setting: dilated, closed under addition, and additively idempotent. We explore the properties of these time scales and demonstrate the utility of these concepts in discrete convolution, Mellin convolution, and transformations of a random variable.     

Convergence analysis of finite volume scheme for nonlinear aggregation population balance equation

In this work, we introduce the convergence analysis of the recently developed finite volume scheme to solve a pure aggregation population balance equation that is of substantial interest in many areas such as chemical engineering, aerosol physics, astrophysics, polymer science, pharmaceutical sciences, and mathematical biology. The notion of the finite volume scheme is to conserve total mass of the particles in the system by introducing weight in the formulation. The consistency of the finite volume scheme is also analyzed thoroughly as it is an influential factor. The convergence study of the numerical scheme shows second order convergence on uniform, nonuniform smooth (geometric) as well as on locally uniform meshes independent of the aggregation kernel. Moreover, the first‐order convergence is shown when the finite volume scheme is implemented on oscillatory and random meshes. In order to check the accuracy, the numerical experimental order of convergence is also computed for the physically relevant as well as analytically tractable kernels and validated against its analytical results.