A bump triangular dynamic factorization algorithm for the simplex method

A dynamic factorization algorithm is developed which algebraically partitions the basis inverse in such a manner so that the simplex method can be executed from a series of small inverses and the basis itself. This partition is maintained dynamically so that the additional memory required to represent the basis inverse reduces to this series of small inverses for in-core implementations.The algorithm is intended for use in solving general large-scale linear programming problems. This new method of basis representation should permit rather large problems to be solved completely in-core.Preliminary computational experience is presented and comparisons are made with Reid's sparsity-exploiting variant of the Bartels—Golub decomposition for linear programming bases. The computational experience indicated that a significant reduction in memory requirements can usually be obtained using the dynamic factorization approach with only a slight (up to about 20%) degradation of execution time.This research was supported in part by the Air Force Office of Scientific Research, Air Force System Command, USAF, under AFOSR Contract/Grant Number AFOSR-74-2715.     

Full analogy of Sharkovsky's theorem for lower semicontinuous maps

A full analogy of the celebrated Sharkovsky cycle coexistence theorem is established for lower semicontinuous (multivalued) maps on metrizable linear continua. This result is further extended to triangular maps.     

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

This paper provides a thorough investigation on the resolution of a finite system of fuzzy relational equations with sup-T composition, where T is a continuous triangular norm. When such a system is consistent, although we know that the solution set can be characterized by a maximum solution and finitely many minimal solutions, it is still a challenging task to find all minimal solutions in an efficient manner. Using the representation theorem of continuous triangular norms, we show that the systems of sup-T equations can be divided into two categories depending on the involved triangular norm. When the triangular norm is Archimedean, the minimal solutions correspond one-to-one to the irredundant coverings of a set covering problem. When it is non-Archimedean, they only correspond to a subset of constrained irredundant coverings of a set covering problem. We then show that the problem of minimizing a linear objective function subject to a system of sup-T equations can be reduced into a 0–1 integer programming problem in polynomial time. This work generalizes most, if not all, known results and provides a unified framework to deal with the problem of resolution and optimization of a system of sup-T equations. Further generalizations and related issues are also included for discussion.     

Construction of triangular DP surface and its application

In this paper, a new type of bivariate basis on a triangle is presented, which is constructed by extending the univariate NTP basis proposed by Delgado and Peña. Some algebraic properties and its recursive formulae are given. Then a new type of surfaces that is called triangular DP surface is defined, and its recursive evaluation algorithm is obtained. Also, in the case of low degree, its subdivision algorithm and degree elevation algorithm are derived. It is shown that this type of surfaces is obviously more advantageous than triangular Bézier surface, and hence extremely useful for geometric design, especially for the situation in which the surface needs to be evaluated quickly.     

Numerical analysis for factorial data analysis. Part II: Special purpose hardware—the programmable systolic array SARDA

The second part of this paper deals with the systolic implementation of the computational kernel for factorial data analysis, defined in Part I, on special-purpose hardware. The framework of the study is that a sequence of different algorithms has to be performed on a unique hardware array. This fact has led us to the design of the programmable systolic array SARDA: this is a triangular array which consists of programmable nodes with local memory and programmable orthogonal connections.     

K2Fe2B2O7: A transparent nonlinear optical crystal with frustrated magnetism

A new noncentrosymmetric ferroborate crystal, K₂Fe₂B₂O₇, has been grown from high temperature melt. Structure solution from single crystal X-ray diffraction shows that the title compound crystallizes in a trigonal space group P321 with cell dimensions of a=8.7475(12) Å and c=8.5124(17) Å. In the structure, FeO₄ tetrahedron shares its three basal oxygen atoms with BO₃ triangles forming a two-dimensional layer in the ab plane and the layers are connected by the apical Fe-O bonds along the c direction. The crystal is transparent in the visible and near infrared region from 500 to 2000 nm with three pronounced absorption bands ascribed to d-d transitions of tetrahedrally coordinated Fe³⁺ ions. Though, structurally analog to K₂Al₂B₂O₇, the further twisting of the BO₃ groups between adjacent layers reduces its optical nonlinearity to a second-harmonic generation intensity of about 0.4 times that of KDP. Spin-glass behavior is observed at 20 K which is probably due to geometrically magnetic frustration of the triangular Fe net in the ab plane.     

Development of a triangular-plate MEMS tunable capacitor with linear capacitance-voltage response

This paper introduces a modified structure for parallel-plate-based MEMS tunable capacitors. The capacitor has triangular electrodes with geometric and structural asymmetry, which enhances its performance. The device structure is also equipped with a set of cantilever beams between capacitor’s electrodes, called middle beams. These beams provide extra stiffness as tuning voltage increases and delay the pull-in which results in a higher tunability. They also reduce the high sensitivity of the capacitance to the voltage change and linearize the C-V response. An analytical model is developed to optimize the capacitor’s dimensions for maximum linearity of the response. Numerical simulations demonstrate tunabilities over 150% where more than 2/3 of which is highly linear. Capacitors fabricated with PolyMUMPs verify that the design technique proposed in this paper can improve the linearity of the device and increase the maximum tunability. The proposed design has a simple geometry and is fabricated using three structural layers, and therefore, it can be easily integrated in tunable filters or other RF circuits.     

Selecting green suppliers based on GSCM practices: Using fuzzy TOPSIS applied to a Brazilian electronics company

Due to an increased awareness and significant environmental pressures from various stakeholders, companies have begun to realize the significance of incorporating green practices into their daily activities. This paper proposes a framework using Fuzzy TOPSIS to select green suppliers for a Brazilian electronics company; our framework is built on the criteria of green supply chain management (GSCM) practices. An empirical analysis is made, and the data are collected from a set of 12 available suppliers. We use a fuzzy TOPSIS approach to rank the suppliers, and the results of the proposed framework are compared with the ranks obtained by both the geometric mean and the graded mean methods of fuzzy TOPSIS methodology. Then a Spearman rank correlation coefficient is used to find the statistical difference between the ranks obtained by the three methods. Finally, a sensitivity analysis has been performed to examine the influence of the preferences given by the decision makers for the chosen GSCM practices on the selection of green suppliers. Results indicate that the four dominant criteria are Commitment of senior management to GSCM; Product designs that reduce, reuse, recycle, or reclaim materials, components, or energy; Compliance with legal environmental requirements and auditing programs; and Product designs that avoid or reduce toxic or hazardous material use.