A new approach based on the surrogating method in the project time compression problems

This paper develops a mathematical model for project time compression problems in CPM/PERT type networks. It is noted this formulation of the problem will be an adequate approximation for solving the time compression problem with any continuous and non-increasing time-cost curve. The kind of this model is Mixed Integer Linear Program (MILP) with zero-one variables, and the Benders' decomposition procedure for analyzing this model has been developed. Then this paper proposes a new approach based on the surrogating method for solving these problems. In addition, the required computer programs have been prepared by the author to execute the algorithm. An illustrative example solved by the new algorithm, and two methods are compared by several numerical examples. Computational experience with these data shows the superiority of the new approach.     

Synthesis and cyclization of 1-arylalk-1-ene-3,5-diynylamines

An investigation of the reaction of 1-lithio-1,3-diynes, generated in situ, with nitriles has been carried out. In the case of aromatic nitriles 1-arylalk-1-ene-3,5-diynylamines are formed, which undergo dimerization and cyclization on isolation, giving 3-(alka-1,3-diynyl)-4-(alk-2-ynyl)-2,6-diarylpyridines. The effect of the nature of the substituent in the benzonitrile molecule on the selectivity of the reaction and the yield of the products has been determined. A scheme is proposed for the conversions and the structures of the intermediates have been established. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 701–710, May, 2006.     

On the solution of Maxwell's equations in polygonal domains

This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H² when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H², and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd.     

微分算子扰动问题的值域研究

本文研究作用在C2周期函数空间上的微分算子u→u″ g(u) ,其中g(u)为连续有界函数.我们将证明上述微分算子的值域限制在周期函数空间的“超曲面”中.     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

Algorithms for finding connected separators between antipodal points

A set (or a collection of sets) contained in the Euclidean space Rm is symmetric if it is invariant under the antipodal map. Given a symmetric unicoherent polyhedron X (like an n-dimensional cube or a sphere) and an odd real function f defined on vertices of a certain symmetric triangulation of X, we algorithmically construct a connected symmetric separator of X by choosing a subcollection of the triangulation. Each element of the subcollection contains the vertices v and u such that f(v)f(u)?0.     

A Bayesian analysis for the seismic data on Taiwan

A Bayesian approach is used to analyze the seismic events with magnitudes at least 4.7 on Taiwan. Following the idea proposed by Ogata (1988,Journal of the American Statistical Association,83, 9–27), an epidemic model for the process of occurrence times given the observed magnitude values is considered, incorporated with gamma prior distributions for the parameters in the model, while the hyper-parameters of the prior are essentially determined by the seismic data in an earlier period. Bayesian inference is made on the conditional intensity function via Markov chain Monte Carlo method. The results yield acceptable accuracies in predicting large earthquake events within short time periods.     

Commutators, C0-semigroups and resolvent estimates

We study the existence and the continuity properties of the boundary values on the real axis of the resolvent of a self-adjoint operator H in the framework of the conjugate operator method initiated by Mourre. We allow the conjugate operator A to be the generator of a C₀-semigroup (finer estimates require A to be maximal symmetric) and we consider situations where the first commutator [H,iA] is not comparable to H. The applications include the spectral theory of zero mass quantum field models.     

Effect of Hydrolysis Conditions on the Direct Formation of Nanoparticles of Ceria–Zirconia Solid Solutions from Acidic Aqueous Solutions

The effect of the cation concentration, hydrolysis temperature, and composition in the CeO₂–ZrO₂ system on the direct precipitation of ceria–zirconia solid solutions and the structure of the precipitates from acidic aqueous solutions of (NH₄)₂Ce(NO₃)₆ and ZrOCl₂ by hydrolysis under hydrothermal conditions were investigated. Nanometer-sized (8–10 nm) ceria–zirconia solid solution particles in a composition range of 0 to 60 mol% ZrO₂ were directly precipitated from the solutions with total metal cation concentration less than 0.2 mol/dm³ by simultaneous thermal hydrolysis at 150–240°C. The crystalline phase of the precipitates gradually changed from cubic and/or tetragonal to monoclinic with increasing the cation concentration of the solution from 0.2 to 0.8 mol/dm³ at the starting composition of 50 mol% ZrO₂ under hydrolysis condition of 150°C for 48 h, which was attributed to decrease in the supply of hydrolyzed Ce component caused by decrease in the hydrolysis ratio of (NH₄)₂Ce(NO₃)₆. Ceria–zirconia solid solutions containing large amount of ZrO₂ maintained high specific surface area and small-sized crystallite after heat-treatment at 900–1000°C for 1 h.     

Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128.