Design of anisotropic structures: Calculation,optimization, and tests

Conclusions A computational procedure based on a limiting state has been worked out which proposes the performance of tests of samples, small-scale models, and full-scale structures and a statistical analysis of the experimental data. Advantages of the method are shown in comparison with the computational method based on fracturing loads which pertain to estimating the accuracy of the computational scheme of structures and determining their safety coefficients. An optimality criterion is formulated within the framework of the method which is related to ensuring a maximum of the limiting (fracturing or critical) load with a constant mass of the structure.Applications of the method are given to estimation of the strength and stability of structures made out of polymeric and metal CM with the use of the Gol'denblat-Kopnov criterion and solutions based on linear shell theory. The conditions for realization of the optimality criterion of structures are determined. Recommendations are made for the rational reinforcement of structures made out of filamentary CM, and a procedure is proposed for the rational design of reinforced structures.As an example of the tests for stability of cylindrical shells made out of aluminum-magnesium alloy under external pressure, the legitimacy of the cause of the disagreement between the calculated and experimental critical loads, which consists of a discrepancy in the nature of wave formation at the instant of stability loss and initial imperfections, and the effectiveness of the computational method based on a limiting state are confirmed. Refined computational formulas for the critical loads of cylindrical shells made out of fiberglass, carbon fiber, and boraluminum under typical kinds of loading are proposed within the framework of the method and on the basis of an analysis of the results of tests, and a comparison is made of the effectiveness of the reinforcement of shells made out of aluminum-magnesium alloy and carbon fiber. The values of the safety coefficients of structures which guarantee their reliability are determined.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 262–271, March–April, 1980.     

组合的分组测试算法的近似控制标准

对于给定的一个集合,分组测试问题是通过一系列的测试去确定这个集合的一个子集. 在文中, 作者首先运用动态规划的理论与方法, 建立了一个近似控制标准, 目的是对分组测试算法的构建过程进行有效控制, 使所构建的算法达到最优. 其次, 应用该近似控制标准研究了在n个硬币集合中确定一个伪硬币的最小平均测试数的问题. 文中所涉及的近似控制问题, 给出了在一个给定集合中去确定这个集合的一个子集的最优分组测试算法, 该最优分组测试算法是在平均测试步骤最少意义下的最优分组测试算法.     

Job-shop local-search move evaluation without direct consideration of the criterion’s value

This article focuses on the evaluation of moves for the local search of the job-shop problem with the makespan criterion. We reason that the omnipresent ranking of moves according to their resulting value of a criterion function makes the local search unnecessarily myopic. Consequently, we introduce an alternative evaluation that relies on a surrogate quantity of the move’s potential, which is related to, but not strongly coupled with, the bare criterion. The approach is confirmed by empirical tests, where the proposed evaluator delivers a new upper bound on the well-known benchmark test yn2. The line of the argumentation also shows that by sacrificing accuracy the established makespan estimators unintentionally improve on the move evaluation in comparison to the exact makespan calculation, in contrast to the belief that the reliance on estimation degrades the optimization results.     

Four types of nonlinear scalarizations and some applications in set optimization

There are two types of criteria of solutions for the set-valued optimization problem, the vectorial criterion and set optimization criterion. The first criterion consists of looking for efficient points of set valued map and is called set-valued vector optimization problem. On the other hand, Kuroiwa–Tanaka–Ha started developing a new approach to set-valued optimization which is based on comparison among values of the set-valued map. In this paper, we treat the second type criterion and call set optimization problem. The aim of this paper is to investigate four types of nonlinear scalarizing functions for set valued maps and their relationships. These scalarizing functions are generalization of Tammer–Weidner’s scalarizing functions for vectors. As applications of the scalarizing functions for sets, we present nonconvex separation type theorems, Gordan’s type alternative theorems for set-valued map, optimality conditions for set optimization problem and Takahashi’s minimization theorems for set-valued map.     

Limit analysis and numerical modeling of spherically porous solids with Coulomb and Drucker-Prager matrices

The first goal of this work was to develop efficient limit analysis (la) tools to investigate the macroscopic criterion of a porous material on the basis of the hollow sphere model used by Gurson, here with a Coulomb matrix. Another goal was to give the resulting rigorous lower and upper bounds to the macroscopic criterion to enable comparisons and validations with further analytical or numerical studies on this micro-macro problem. In both static and kinematic approaches of la, a quadratic formulation was used to represent the stress and displacement velocity fields, in triangular finite elements. A significant improvement of the quality of the results was obtained by superimposing, on the fem fields, analytical fields which are the solutions to the problem under isotropic loadings.The final problems result in conic optimization, or linear programming after linearization of the criterion, so as to determine the “Porous Coulomb” criterion. A fine iterative post-analysis strictly restores the admissibility of the static and kinematic solutions. After presenting the results for various values of the porosity and internal friction angle, a comparison with a heuristic Cam-Clay-like criterion shows that this criterion cannot be considered a precise general approximation. Then a comparison with the “Porous Drucker-Prager” criterion treated by specific 3D codes is presented. With the same numerical tools, a final analysis of recent results in the literature is detailed, and tables of selected numerical data are presented in the appendices.     

Stochastic dominance based comparison for system selection

We present two complementing selection procedures for comparing simulated systems based on the stochastic dominance relationship of a performance metric of interest. The decision maker specifies an output quantile set representing a section of the distribution of the metric, e.g., downside or upside risks or central tendencies, as the basis for comparison. The first procedure compares systems over the quantile set of interest by a first-order stochastic dominance criterion. The systems that are deemed nondominant in the first procedure could be compared by a weaker almost first-order stochastic dominance criterion in the second procedure. Numerical examples illustrate the capabilities of the proposed procedures.     

An Optimum Multivariate Stratified Sampling Design with Nonresponse: A Lexicographic Goal Programming Approach

In a multivariate stratified sample survey with L strata and p > 1 characteristics, defined on each unit of the population, let the estimation of all the p-population means be of interest. As discussed by Cochran (1977), since the optimum allocation for one characteristic will not in general be optimum for other characteristics some compromise must be reached in a multiple characteristics stratified surveys. Various authors worked out allocations that are based on a compromise criterion. The resulting allocations are optimal for all characteristics in some sense, for example an allocation that minimizes the trace of the variance-covariance matrix of the estimators of the population means or an allocation that minimizes the weighted average of the variances or an allocation that maximizes the total relative efficiency of the estimators as compared to the corresponding individual optimum allocations. In the present paper the problem of optimum allocation in multivariate stratified random sampling in the presence of nonresponse has been formulated as a multiobjective integer nonlinear programming problem and a solution procedure is developed using goal programming technique. Three numerical examples are worked out to illustrate the computational details. A comparison of the proposed method with some well known methods is also carried out to show the practical utility of the proposed method.     

Methods of the Convex Cone Theory in the Feasibility Problem of Multicommodity Flow

The feasibility problem of multicommodity flow is reduced to finding out if a multidimensional vector determined by the network parameters belongs to a convex polyhedral cone determined by the set of paths in the network. It is shown that this representation of the feasibility problem makes it possible to formulate the feasibility criterion described in [1] in a different form. It is proved that this criterion is sufficient. The concepts of reference vectors and networks are defined, and they are used to describe a method for solving the feasibility problem for an arbitrary network represented by a complete graph.     

Quasi-optimal control of axisymmetric temperature displacements in a given section of a body using internal heat sources

For a thermoelastic half-space we study the problem of constructing in the space of continuous functions a quasi-optimal control of the axisymmetric vertical displacements in a given section parallel to the boundary surface in the form of a sequence that minimizes the original optimality criterion. For a half-space heated over a circular region by a heat flux of constant intensity we carry out a numerical analysis of the behavior of the elements of the minimizing sequence. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 104–109.     

The efficiency criteria problem for stochastic processes

This paper is concerned with the problem of finding a suitable (asymptotic) efficiency criterion for inference concerning parameters of stochastic processes. Special attention is aid to conditional exponential families of stochastic processes and to three tests based on the maximum likelihood estimate as well as to the likelihood ratio test. A contiguity calculation is used to show that a previously suggested criterion is inadequate and itself provides a partial solution to the problem. A heuristic argument is also put forward to support a proposition implying the optimality of the maximum likelihood estimate in a certain sense. Two examples which illustrate the theory are discussed.     

DISPERSION COMPARISONS OF TWO PROBABILITY VECTORS UNDER MULTINOMIAL SAMPLING

We consider testing hypotheses concerning comparing dispersions between two parameter vectors of multinomial distributions in both one-sample and two-sample cases. The comparison criterion is the concept of Schur majorization. A new dispersion index is proposed for testing the hypotheses. The corresponding test for the one-sample problem is an exact test. For the two-sample problem, the bootstrap is used to approximate the null distribution of the test statistic and the p-value. We prove that the bootstrap test is asymptotically correct and consistent. Simulation studies for the bootstrap test are reported and a real life example is presented.     

Multicriteria tour planning for mobile healthcare facilities in a developing country

A multiobjective combinatorial optimization (MOCO) formulation for the following location-routing problem in healthcare management is given: For a mobile healthcare facility, a closed tour with stops selected from a given set of population nodes has to be found. Tours are evaluated according to three criteria: (i) An economic efficiency criterion related to the tour length, (ii) the criterion of average distances to the nearest tour stops corresponding to p-median location problem formulations, and (iii) a coverage criterion measuring the percentage of the population unable to reach a tour stop within a predefined maximum distance. Three algorithms to compute approximations to the set of Pareto-efficient solutions of the described MOCO problem are developed. The first uses the P-ACO technique, and the second and the third use the VEGA and the MOGA variant of multiobjective genetic algorithms, respectively. Computational experiments for the Thiès region in Senegal were carried out to evaluate the three approaches on real-world problem instances.     

正态分布方差变点的检验

本文讨论了正态分布方差只有一个变点的检验问题，我们构造了三个检验统计量，其中L检验基于非参数U统计量，B检验基于Bayes方法，R检验由极大似然比方法导出．本文给出了L、B、R检验的渐近临界值，并用MonteCarlo模拟方法研究了这三个检验与平方的CUSUM检验以及LM检验的势，并进行了比较。当变点在序列的前一半位置时，L和R检验较好，当变点在序列的后一半位置时，平方的CUSUM和B检验较好．     

Investigation of secondary flow instability on an infinite yawed cylinder with 15 per cent. Thick joukowski profile as section

This paper contains a theoretical investigation of the secondary flow instability in the incompressible boundary layer on an infinite yawed cylinder with chordwise section as Joukowski profile of 15 per cent. thickness at zero incidence and with homogeneous suction, the suction mass flow coefficient being equal to 0·2085. Values of the instability criterion are obtained at different points of the wing section and for various angles of sweepback. It is found that the values of the criterion increase with the increasing sweepback whether the pressure gradient is favourable or adverse. The effect of adverse pressure gradient on the variation of the criterion is more pronounced than that of a favourable pressure gradient. At some points in adverse pressure gradients, there are two values of the criterion for a given sweepback. It is also found that the flow is intermittently laminar and turbulent for low values of the chordwise free stream Reynolds number and consists of an irregular sequence of laminar and turbulent regions.     

Local networks for computer communications: A. WEST and P. JANSON (Eds.) Proceedings of the IFIP Working Group 6.4, International Workshop on Local Networks,Zürich,Switzerland, August 27–29, 1980, North-Holland,Amsterdam, 1981, xiii + 470 pages,Dfl.125.00

In this paper we present two lower bounds for the p-median problem, the problem of locating p facilities (medians) on a network. These bounds are based on two separate lagrangean relaxations of a zero-one formulation of the problem with subgradient optimisation being used to maximise these bounds. Penalty tests based on these lower bounds and a heuristically determined upper bound to the problem are developed and shown to result in a large reduction in problem size. The incorporation of the lower bounds and the penalty tests into a tree search procedure is described and computational results are given for problems with an arbitrary number of medians and having up to 200 vertices. A comparison is also made between these algorithms and the dual-based algorithm of Erlenkotter.     

A generalized Neyman–Pearson lemma for g-probabilities

This paper is concerned with hypothesis tests for g-probabilities, a class of nonlinear probability measures. The problem is shown to be a special case of a general stochastic optimization problem where the objective is to choose the terminal state of certain backward stochastic differential equations so as to minimize a g-expectation. The latter is solved with a stochastic maximum principle approach. Neyman–Pearson type results are thereby derived for the original problem with both simple and randomized tests. It turns out that the likelihood ratio in the optimal tests is nothing else than the ratio of the adjoint processes associated with the maximum principle. Concrete examples, ranging from the classical simple tests, financial market modelling with ambiguity, to super- and sub-pricing of contingent claims and to risk measures, are presented to illustrate the applications of the results obtained.     

Choice of weights in FMA estimators under general parametric models

The choice of weights in frequentist model average estimators is an important but difficult problem. Liang et al. (2011) suggested a criterion for the choice of weight under a general parametric framework which is termed as the generalized OPT (GOPT) criterion in the present paper. However, no properties and applications of the criterion have been studied. This paper is devoted to the further investigation of the GOPT criterion. We show that how to use this criterion for comparison of some existing weights such as the smoothed AIC-based and BIC-based weights and for the choice between model averaging and model selection. Its connection to the Mallows and ordinary OPT criteria is built. The asymptotic optimality on the criterion in the case of non-random weights is also obtained. Finite sample performance of the GOPT criterion is assessed by simulations. Application to the analysis of two real data sets is presented as well.     

A comparative study of methods for testing the equality of two or more ROC curves

The problem of comparing the accuracy of diagnostic tests is usually carried out through the comparison of the corresponding receiver operating characteristic (ROC) curves. This matter has been approached from different perspectives. Usually, ROC curves are compared through their respective areas under the curve, but in cases where there is no uniform dominance between the involved curves other procedures are preferred. Although the asymptotic distributions of the statistics behind these methods are, in general, known, resampling plans are considered. With the purpose of comparing the performance of different approaches, with different ways of calibrating the distribution of the tests, a simulation study is carried out in order to investigate the statistical power and the nominal level of each methodology.     

Local Bahadur efficiency of rank tests for the independence problem

In previous papers [Approximate and local Bahadur efficiency of linear rank tests in the two-sample problem, Ann. Statist.7, 1246–1255, 1979; Local comparison of linear rank tests in the Bahadur sense, Metrika, 1979] the author developed for linear rank tests of the one-sample symmetry and the k-sample problem (k ≥ 2) a theory of local comparison, based on the concept of Bahadur efficiency. In the present article this theory is carried over to rank tests of the independence problem.     

Optimal prediction of human postural response under anterior–posterior platform tilting

Previous studies have suggested that human beings movements can be related to the problem of cost function minimization. But at the present time it is not clear that which objective function(s) and constraints are used by central nervous system (CNS) to produce optimal reactions under perturbations. Present study has been done experimentally and by numerical simulations to explore the stability constraints which should be used in combination with energy based cost function (weighted minimum torque) to estimate the motor planning criterion is used by CNS for disturbance rejections. The influence of three stability criterions (ZMP, extrapolated center of mass and a vertical force criterion) in combination with minimum torque model on the optimal trajectory formation is investigated. First, the response of 10 male healthy persons to platform oscillation was recorded by motion analysis system and the hip, knee and ankle angular trajectories were derived from recorded data. Second, the dynamic simulation of a four-segment, three actuated degrees of freedom mechanical model of the human body was performed using predictive dynamic method which leads to an optimization problem. The simulated trajectories were then compared to the experimental data. With comparison between experimental results, the weighting coefficients of the objective function were found to achieve best estimation. It was seen that the minimum torque objective function with weighting coefficients gives trajectories that are mostly matched with experimental observation. Moreover, the results showed that between stability criterions, the ZMP predictions are near to experimental results. Although by using vertical force criterion some nearness to experimental results are lost (in comparison with ZMP criterion) but a secured flat-foot posture for the model is obtained which this posture is more applicable than others in humanoid implementations.