Download or read book Chemical Equilibrium Problems Treated by Geometric and Transcendental Programming written by Gideon Lidor and published by . This book was released on 1975 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chemical equilibrium problem--finding the equilibrium composition of a multiphase, multicomponent system--is of interest in the study of chemical systems in general, with many potential applications in biochemistry and biomedicine. The problem can be posed as a nonlinear program, where a convex 'free energy' function is minimized, subject to linear mass balance equations. There is an associated dual chemical problem, equivalent to a geometric program when the system is ideal. This work studies the chemical duality and applies the existing theory of geometric programming to analyze and solve chemical problems. Some general characteristics of free energy functions are developed and are used to analyze the properties of equilibrium solutions. Chemical duality is applied to formulate and solve a class of related problems which are of a different nature than the original chemical equilibrium problem. A dual cutting-plane algorithm is adapted from a method developed for geometric programs and is tested and compared to a standard chemical equilibrium code. Geometric programming theory is extended to include forms having variables as exponents. The resulting 'transcendental geometric programs' are shown to be a generalization of chemical problems, where the system is not ideal.
Download or read book Advances in Geometric Programming written by Mordecai Avriel and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1961, C. Zener, then Director of Science at Westinghouse Corpora tion, and a member of the U. S. National Academy of Sciences who has made important contributions to physics and engineering, published a short article in the Proceedings of the National Academy of Sciences entitled" A Mathe matical Aid in Optimizing Engineering Design. " In this article Zener considered the problem of finding an optimal engineering design that can often be expressed as the problem of minimizing a numerical cost function, termed a "generalized polynomial," consisting of a sum of terms, where each term is a product of a positive constant and the design variables, raised to arbitrary powers. He observed that if the number of terms exceeds the number of variables by one, the optimal values of the design variables can be easily found by solving a set of linear equations. Furthermore, certain invariances of the relative contribution of each term to the total cost can be deduced. The mathematical intricacies in Zener's method soon raised the curiosity of R. J. Duffin, the distinguished mathematician from Carnegie Mellon University who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polynomials. Interes tingly, the investigation of optimality conditions and properties of the optimal solutions in such problems were carried out by Duffin and Zener with the aid of inequalities, rather than the more common approach of the Kuhn-Tucker theory.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1976 with total page 1056 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin of Thermodynamics and Thermochemistry written by and published by . This book was released on 1977 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Systems Optimization Project Progress Report written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1975 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin of Chemical Thermodynamics written by and published by . This book was released on 1977 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Annual Index written by and published by . This book was released on 1975 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1987 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Chemical Equilibrium Problem written by James Harold Bigelow and published by . This book was released on 1968 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has long been known that the problem of determining the equilibrium composition of a solution of chemically reacting species could be formulated as a constrained minimum problem. Previous methods for solving the chemical equilibrium problem in this form have had much success. However, all such methods run into trouble whenever degeneracy or near-degeneracy occurs during the computational procedure. The paper shows that the constrained minimum formulation of the chemical equilibrium problem is equivalent to a generalized linear program which can in turn be replaced by a quadratic program. In these alternative forms, degeneracy is more easily accomodated than in previous methods. (Author).
Download or read book Degeneracy in Ideal Chemical Equilibrium Problems written by Stanford University. Department of Operations Research. Operations Research House and published by . This book was released on 1970 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: A single- or multi-phase chemical equilibrium problem may be though of as the problem of minimizing a particular nonlinear function (the free energy) of composition subject to the conditions that the composition vector be nonnegative and satisfy a system of linear equations (the mass-balance laws). It was pointed out in a previous paper (AD-706 018) that the free energy is convex and homogeneous of degree one, but that as a variable approaches zero, the free energy may behave badly. In this paper, the phase 'chemical equilibrium problem' refers only to a problem with a particular mathematical form. Problems of this form arise in many situations that are not classically denoted chemical equilibrium problems. (Author).
Download or read book Applications of Interval Arithmetic in Signomial Programming written by Louis Joseph Mancini and published by . This book was released on 1975 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in engineering design can be found formulated as a nonlinear program where a criterion function of the design variables is minimized, or maximized, subject to certain inequality and equality constraints which define the problem. Such a formulation allows the engineer to use optimization theory and numerical algorithms to find the best design, or global solution, among the possibily infinite number of reasible designs. However, optimization methods are guaranteed to yield the global solution only if the nonlinear program has a certain structure; and in many cases only a solution which is guaranteed to be locally optimal can be obtained. The problem of multiple local solutions in nonlinear programs is of major concern to both the engineer and operations researcher. If all the functions in the nonlinear program are sums of power functions, then the nonlinear program is a signomial program. All the methods presented here use interval arithmetic, a generalization of ordinary arithmetic in which the basic elements are closed intervals of the real line. This study brings interval arithmetic and signomial programming together.
Download or read book Computing Equilibrium Compositions of Ideal Chemical Systems written by Stanford University. Department of Operations Research. Operations Research House and published by . This book was released on 1970 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin Institute of Mathematical Statistics written by Institute of Mathematical Statistics and published by . This book was released on 1976 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Chemical Equilibrium Problem ba Special Case of Nonlinear Programming written by James Harold Bigelow and published by . This book was released on 1969 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Programming for Communication Systems written by Mung Chiang and published by Now Publishers Inc. This book was released on 2005 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently Geometric Programming has been applied to study a variety of problems in the analysis and design of communication systems from information theory and queuing theory to signal processing and network protocols. Geometric Programming for Communication Systems begins its comprehensive treatment of the subject by providing an in-depth tutorial on the theory, algorithms, and modeling methods of Geometric Programming. It then gives a systematic survey of the applications of Geometric Programming to the study of communication systems. It collects in one place various published results in this area, which are currently scattered in several books and many research papers, as well as to date unpublished results. Geometric Programming for Communication Systems is intended for researchers and students who wish to have a comprehensive starting point for understanding the theory and applications of geometric programming in communication systems.
Download or read book Index to American Doctoral Dissertations written by and published by . This book was released on 1974 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Announcements written by and published by . This book was released on 1975-09-19 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
