A Generic Position Based Method for Real Root Isolation of Zero-Dimensional Polynomial Systems

We improve the local generic position method for isolating the real roots of a zero-dimensional bivariate polynomial system with two polynomials and extend the method to general zero-dimensional polynomial systems. The method mainly involves resultant computation and real root isolation of univariate polynomial equations. The roots of the system have a linear univariate representation. The complexity of the method is $\tilde{O}_B(N^{10})$ for the bivariate case, where $N=\max(d,\tau)$, $d$ resp., $\tau$ is an upper bound on the degree, resp., the maximal coefficient bitsize of the input polynomials. The algorithm is certified with probability 1 in the multivariate case. The implementation shows that the method is efficient, especially for bivariate polynomial systems.Comment: 24 pages, 5 figure

Multiplicity Preserving Triangular Set Decomposition of Two Polynomials

In this paper, a multiplicity preserving triangular set decomposition algorithm is proposed for a system of two polynomials. The algorithm decomposes the variety defined by the polynomial system into unmixed components represented by triangular sets, which may have negative multiplicities. In the bivariate case, we give a complete algorithm to decompose the system into multiplicity preserving triangular sets with positive multiplicities. We also analyze the complexity of the algorithm in the bivariate case. We implement our algorithm and show the effectiveness of the method with extensive experiments.Comment: 18 page

Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation

In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the roots of the equation system are represented as linear combinations of roots of several univariate polynomial equations. The main advantage of this representation is that the precision of the roots can be easily controlled. In fact, based on the linear univariate representation, we can give the exact precisions needed for roots of the univariate equations in order to obtain the roots of the equation system to a given precision. As a consequence, a root isolation algorithm for a zero-dimensional polynomial equation system can be easily derived from its linear univariate representation.Comment: 19 pages,2 figures; MM-Preprint of KLMM, Vol. 29, 92-111, Aug. 201

Using micro genetic algorithm for solving scheduling problems

Job Shop Scheduling Problem (JSSP) and Timetable scheduling are known to be computationally NP–hard problems. There have been many attempts by many researchers to develop reliable scheduling software, however, many of these software have only been tested or applied on an experimental basis or on a small population with minimal constraints. However in actual model JSSP, the constraints involved are more complicated compared to classical JSSP and feasible schedule must be suggested within a short period of time. In this thesis, an enhanced micro GA, namely micro GA with local search is proposed to solve an actual model JSSP. The scheduler is able to generate an output of a set of feasible production plan not only at a faster rate but which can generate a plan which can reduce the makespan as compare to those using manual. Also, in this thesis, the micro GA is applied to the timetabling problem of Faculty of Electrical Engineering Universiti Teknologi Malaysia which has more than 3,000 students. Apart from having more students, the faculty also offers various different type s of specialized courses. Various constraints such as elective subjects, classrooms capacity, multiple sections students, lecturer, etc have to be taken into consideration when designing the solution for this problem. In this thesis , an enhanced micro GA is proposed for timetable scheduling in the Faculty to overcome the problems. The enhanced micro GA algorithm is referred to as distributed micro GA which has local search to speed up the scheduling process. Comparisons are made with simple GA methods such that a more optimal solution can be achieved. The proposed algorithm is successfully implemented at the Faculty meeting a variety of constraints not achievable using manual methods

The anodic dissolution of cadmium in aqueous solutions

The purpose of this investigation was to study the effect of cadmium ions on the anodic dissolution of cadmium in salt solutions of ·constant ionic strength. The concentration of the cadmium ions was varied from 0.001 to 1 N and the current density ranged from 0.001 to 0.1 amp•cm-2. The temperature was controlled at 25°C. ....A mathematical model was postulated expressing the anodic dissolution rate as the sum of electrochemical, local corrosion, and disintegration rates. --Abstract, page iii

A study of the anodic oxidation of ethylene on gold and gold-platinum alloys

The distinctive features of electrochemical energy conversion is the direct conversion of the chemical energy of a reaction into electrical energy without going through the intermediary of heat, thereby avoiding the Carnot limitation. Since it is theoretically possible to obtain electrical energy to the extent of the free energy change of the chemical reaction, the overall thermal efficiencies expected are nearly 100 percent. However, the observed efficiencies of most electrochemical energy converters are considerably lower than this due to a slowness of one or more of the intermediate steps of the overall reaction. There has been a recent surge of studies on the electro-oxidation of hydrocarbons because of their possible use as fuels in electrochemical conversion. The widespread use of fuel cells hinges on a cheap and readily available fuel such as natural gas, propane, or methane that can be oxidized at moderate temperatures. From the economic standpoint, hydrocarbons have a clear advantage over other fuels suggested for use. They also have a further advantage of being easily handled and distributed through established systems. Therefore, it is important that these specialized fuel cells are developed and commercialized. Since most fuel cells studies have been concerned with technological aspects, the results are usually too complex to allow electrode kinetic analysis. The more fundamental aspects of several organic systems have been studied. Previous studies of the electro-oxidation of ethylene on Au in acid had not been directed toward determining all the reaction parameters which are useful in diagnosing a mechanism. It has been reported that Pt alloys have shown an even higher catalytic activity then pure Pt black. This refers particularly to alloys of the Pt-Ru system and to a lesser degree of alloys with Ir and Rh. These catalysts were found to be active for the oxidation of a number of organic fuels such as methanol and selected hydrocarbons. The object of this reported investigation was to establish the mechanisms for the anodic oxidation of ethylene on Au and Au-Pt alloy electrodes in aqueous solutions. It was believed that this research would lead to a better understanding of the rate processes of electrochemical reactions in general on alloy electrodes --Introduction, page 1-2

Astromag data system concept

A feasible, top-level data system is defined that could accomplish and support the Astromag Data System functions and interfaces necessary to support the scientific objectives of Astromag. This data system must also be able to function in the environment of the Space Station Freedom Manned Base (SSFMB) and other anticipated NASA elements