索赔次数为复合Poisson-Geometric过程的常利率风险模型的罚金函数

讨论了常利率下索赔次数为复合Poisson-Geometric过程的风险模型的罚金函数,得到了罚金函数的期望所满足的积分方程,并由所得到的积分方程推出了破产概率所满足的积分方程,初始盈余为0时,得到了罚金函数的期望及破产概率的精确解.     

Experimental examination of displacement field in an edge dislocation core in aluminum

The displacement field of an edge dislocation in aluminum was experimentally investigated. Three typical theoretical models were discussed. High-resolution transmission electron microscopy (HRTEM) and geometric phase analysis (GPA) were used to map the displacement field of an edge dislocation. The displacement field near the dislocation core was determined. The experimental show that Peierls-Nabarro model is the most appropriate theoretical model for displacement field of dislocation in aluminum.     

Classification of sets satisfying the geometric characterization

The geometric characterization identifies the sets of nodes such that the Lagrange polynomials are products of factors of first degree. We offer a detailed classification of all known sets satisfying the geometric characterization in the plane. The defect, which takes into account the number of lines containing more nodes than the degree, plays a fundamental role in this classification. Partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo.     

Multi-level lot sizing and job shop scheduling with compressible process times: A cutting plane approach

This paper proposes an integer linear programming formulation for a simultaneous lot sizing and scheduling problem in a job shop environment. Among others, one of our realistic assumptions is dealing with flexible machines which enable the production manager to change their working speeds. Then, a number of valid inequalities are developed based on problem structures. As the valid inequalities can help in reducing the non-optimal parts of the solution space, they are dealt with as some cutting planes. The proposed cutting planes are used to solve the problem in (i) cut-and-branch, and (ii) branch-and-cut approaches. The performance of each cutting plane is investigated with CPLEX 12.2 on a set of randomly-generated test data. Then, some performance criteria are identified and the proposed cutting planes are ranked by TOPSIS method.     

Time-dependent harmonic oscillator in a magnetic field and an electric field on the non-commutative plane

In the non-commutative space, wave functions and geometric phases are derived for the time-dependent harmonic oscillator in external time-dependent magnetic and electric field. Explicit forms of the coherent states are also given, which are not the minimum uncertainty states for the coordinates and momenta.     

Helly-Type Theorems for Line Transversals to Disjoint Unit Balls

We prove Helly-type theorems for line transversals to disjoint unit balls in ℝ ^d . In particular, we show that a family of n≥2d disjoint unit balls in ℝ ^d has a line transversal if, for some ordering ≺ of the balls, any subfamily of 2d balls admits a line transversal consistent with ≺. We also prove that a family of n≥4d−1 disjoint unit balls in ℝ ^d admits a line transversal if any subfamily of size 4d−1 admits a transversal. Andreas Holmsen was supported by the Research Council of Norway, prosjektnummer 166618/V30. Otfried Cheong and Xavier Goaoc acknowledge support from the French-Korean Science and Technology Amicable Relationships program (STAR).     

A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight-sided quadrilateral plates

A four-node discrete singular convolution (DSC) method is developed for free vibration analysis of arbitrary straight-sided quadrilateral plates. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the plate are transformed from the physical domain into a square computational domain. Numerical examples illustrating the accuracy and convergence of the DSC method for skew, trapezoidal, rhombic and arbitrary quadrilateral plates are presented. The results obtained by DSC method were compared with those obtained by the other numerical methods.     

Simulation of forming processes by FEM with a Bingham fluid model

We model the forming process as a fluid flow. A finite element program, FIDAP, which analyses flow problems, was used to calculate velocity and strain rates at points throughout the material during the deformation process. This allows predictions to be made on the shape and quality of the resulting part. The stress-strain relation we used models the plastic flow of metals (Bingham fluids). The FEM approximation of such a fluid is tested by comparing results for a simple analytical example. In forming processes provision must be made for friction between dye and workpiece, and the program was modified accordingly. Two classical ring forming simulations are compared to published results.     

Grab vs. composite sampling of particulate materials with significant spatial heterogeneity—A simulation study of “correct sampling errors”

Sampling errors can be divided into two classes, incorrect sampling and correct sampling errors. Incorrect sampling errors arise from incorrectly designed sampling equipment or procedures. Correct sampling errors are due to the heterogeneity of the material in sampling targets. Excluding the incorrect sampling errors, which can all be eliminated in practice although informed and diligent work is often needed, five factors dominate sampling variance: two factors related to material heterogeneity (analyte concentration; distributional heterogeneity) and three factors related to the sampling process itself (sample type, sample size, sampling modus). Due to highly significant interactions, a comprehensive appreciation of their combined effects is far from trivial and has in fact never been illustrated in detail. Heterogeneous materials can be well characterized by the two first factors, while all essential sampling process characteristics can be summarized by combinations of the latter three. We here present simulations based on an experimental design that varies all five factors. Within the framework of the Theory of Sampling, the empirical Total Sampling Error is a function of the fundamental sampling error and the grouping and segregation error interacting with a specific sampling process. We here illustrate absolute and relative sampling variance levels resulting from a wide array of simulated repeated samplings and express the effects by pertinent lot mean estimates and associated Root Mean Squared Errors/sampling variances, covering specific combinations of materials’ heterogeneity and typical sampling procedures as used in current science, technology and industry. Factors, levels and interactions are varied within limits selected to match realistic materials and sampling situations that mimic, e.g., sampling for genetically modified organisms; sampling of geological drill cores; sampling during off-loading 3-dimensional lots (shiploads, railroad cars, truckloads etc.) and scenarios representing a range of industrial manufacturing and production processes. A new simulation facility “SIMSAMP” is presented with selected results designed to show also the wider applicability potential. This contribution furthers a general exposé of all essential effects in the regimen covered by “correct sampling errors”, valid for all types of materials in which non-bias sampling can be achieved.     

Geometric and Topological Thinking in Organic Chemistry

The beginning student of organic chemistry is often bewildered by what appears to be an enormous maze of random structural variations and reactions that can be mastered only by tedious memorization. To the organic chemist, however, the same subject is often a beautifully ordered discipline of elegant simplicity. An important value of learning organic chemistry is the mastering of “organic thinking,” an approach to intellectual processing whereby the “sameness” of many families of structures and reactions is revealed. This article offers the author's personal views of organic thinking and explores the intellectual and scientific foundations of organic chemistry and of the powerful methods that provide the field with a platform for making rapid conceptual and experimental advances. It is proposed that these methods involve a geometric and topological approach to scientific reasoning within the framework of scientific paradigms that guide experimental design and execution. The basis of this approach is considered in relation to day-to-day thinking, problem solving, and the psychological drive for intellectual closure. The power of the approach is illustrated by the analysis of several photochemical and chemiluminescent reactions.