Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation

In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painlevé equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models.     

Phase behavior of ternary blends containing dimethylpolycarbonate,tetramethylpolycarbonate and poly[styrene‐co‐(methyl methacrylate)] copolymers (or polystyrene)

The miscibility and phase behavior of ternary blends containing dimethylpolycarbonate (DMPC), tetramethylpolycarbonate (TMPC) and poly[styrene‐co‐(methyl methacrylate)] copolymer (SMMA) have been explored. Ternary blends containing polystyrene (PS) instead of SMMA were also examined. Blends of DMPC with SMMA copolymers (or PS) did not form miscible blends regardless of methyl methacrylate (MMA) content in copolymers. However, DMPC blends with SMMA (or PS) blends become miscible by adding TMPC. The miscible region of ternary blends is compared with the previously determined miscibility region of binary blends having the same chemical components and compositions. The region where the ternary blends are miscible is much narrower than that of binary blends. Based on lattice fluid theory, the observed phase behavior of ternary blends was analyzed. Even though the term representing the Gibbs free energy change of mixing for certain ternary blends had a negative value, blends were immiscible. It was revealed that a negative value of the Gibbs free energy change of mixing was not a sufficient condition for miscible ternary blends because of the asymmetry in the binary interactions involved in ternary blends. Copyright © 2004 Society of Chemical Industry     

Reduced modified quadratures for quadratic membrane finite elements

Reduced integration is frequently used in evaluating the element stiffness matrix of quadratically interpolated finite elements. Typical examples are the serendipity (Q8) and Lagrangian (Q9) membrane finite elements, for which a reduced 2 × 2 Gauss–Legendre integration rule is frequently used, as opposed to full 3 × 3 Gauss–Legendre integration. This ‘softens’ these element, thereby increasing accuracy, albeit at the introduction of spurious zero energy modes on the element level. This is in general not considered problematic for the ‘hourglass’ mode common to Q8 and Q9 elements, since this spurious mode is non‐communicable. The remaining two zero energy modes occurring in the Q9 element are indeed communicable. However, in topology optimization for instance, conditions may arise where the non‐communicable spurious mode associated with the elements becomes activated. To effectively suppress these modes altogether in elements employing quadratic interpolation fields, two modified quadratures are employed herein. For the Q8 and Q9 membrane elements, the respective rules are a five and an eight point rule. As compared to fully integrated elements, the new rules enhance element accuracy due to the introduction of soft, higher‐order deformation modes. A number of standard test problems reveal that element accuracy remains comparable to that of the under‐integrated counterparts. Copyright © 2004 John Wiley & Sons, Ltd.     

Decreasing miscibility with greater heterogeneity in ternary polymer blend: poly(cyclohexyl methacrylate), poly(α‐methyl styrene) and poly(4‐methyl styrene)

A ternary blend system comprising poly(cyclohexyl methacrylate) (PCHMA), poly(α‐methyl styrene) (PαMS) and poly(4‐methyl styrene) (P4MS) was investigated by thermal analysis, optical and scanning electron microscopy. Ternary phase behaviour was compared with the behaviour for the three constituent binary pairs. This study showed that the ternary blends of PCHMA/PαMS/P4MS in most compositions were miscible, with an apparent glass transition temperature (T_g) and distinct cloud‐point transitions, which were located at lower temperatures than their binary counterparts. However, in a closed‐loop range of compositions roughly near the centre of the triangular phase diagram, some ternary blends displayed phase separation with heterogeneity domains of about 1 µm. Therefore, it is properly concluded that ternary PCHMA/PαMS/P4M is partially miscible with a small closed‐loop immisciblity range, even though all the constituent binary pairs are fully miscible. Thermodynamic backgrounds leading to decreased miscibility and greater heterogeneity in a ternary polymer system in comparison with the binary counterparts are discussed. © 2003 Society of Chemical Industry     

多目标二次规划非劣解集的理论生成及应用

本文对多目标二次规划问题非劣解集的理论生成进行了探讨,在介绍二次规划单目标问题优化解求法的基础上,提出了在决策平面上互切点,共交点轨迹的概念.由此导出了非劣解集的一般解析式(对切点解问题)和另一类交点解问题时的非劣解集求法,然后介绍了在目标平面非劣解集的解析表达式.使多目标二次规划问题整个非劣解集的推求严格、明确和方便,有理论和实际意义。文中以一个综合利用水库参数的多目标优选作为例子阐述了应用,并求出了最终的最佳协调解.     

Application d'une méthodologie expérimentale à l'étude du diagramme ternaire d'un gel

Nous avons montré sur l'exemple d'un gel, mélange de trois constituants (C12–C15 Alcohols Benzoate, Cyclomethicone et Ethylene Vinyl Acetate Copolymer) qu'il est possible d'optimiser une formulation en un nombre preécis d'essais en faisant appel à une stratégic expérimentale optimale. Le gel avait déjàétéétudié par Chang,¹ mais par approches successives.
Nous avons utlisé les matrices d'expériences développées dans le cas des mélanges par Scheffe sous le nom de 'reseaux-simplex'. Prévoyant des intéractions de 2éme ordre entre les constituants nous avons retenu le modéle appelé'cubique réduit'. Cette approche permet l'exploration systémique de tout le domaine.
Les réponses étudiées sont la compatibilité (gel homogène ou non), la consistance, la blancheur et le coût. Le meilleur gel étant celui qui se rapproche le plus de la vaseline.
A partir des résultats, nous avons tracé des courbes d'isoréponse en blancheur, consistance et coût. La superposition des diagrammes conduit à la détermination d'une zone où les réponses sont optimales.
En ajoutant la réponse supplémentaire: 'facilité d'étalement sur la peau'on arrive au meilleur gel avec un nombre réduit d'essais.
La même méthode s'appliquerait à des mélanges de plus de trois constituants.
Study of a ternary diagram gel according to a methodology of experimental research     

关于布尔函数的二次逼近

本文首先利用矩阵形式引入了二阶ｗａｌｓｈ谱的概念并讨论了其性质，其次引入了二次ｂｅｎｔ函数的概念，同时论述了二次ｂｅｎｔ函数的密码学意义。     

Existence of discrete-time LQG-controllers

Existence results for the LQG-controller are investigated. An infimal Riccati equation based controller may potentially give closed loop eigenvalues on the unit circle. Assuming left and right invertibility it is shown that there exists an optimal controller if and only if the Riccati equation based controller stabilizes the closed loop system after removal of all its unobservable and uncontrollable modes. Furthermore this reduced controller is the optimal controller, and its transfer function is unique. This existence condition is a considerable simplification of the more general geometric condition recently derived by Trentelman and Stoorvogel.     

Metaheuristic downhill simplex method in combinatorial optimization

The concept of combinatorial objects is formalized. It allows strict definition of a combinatorial optimization problem (COP). An efficient metaheuristic method to solve COPs (H-method) is considered. It includes stochastic local search algorithms as a built-in procedure. A parallel implementation of the H-method is set forth and analyzed. The results from a numerical experiment and solution of some well-known COPs on personal computers and on the SKIT cluster supercomputer are presented. The study was supported by INTAS (Project 06-1000017-8909). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 70–79, November–December 2007.