By Mordecai Avriel, Erwin Diewert, Siegfried Schaible, Israel Zang
Initially released in 1988, this enduring textual content is still the main accomplished publication on generalized convexity and concavity. The authors current generalized concave services in a unified framework, exploring them essentially from the domain names of optimization and economics.
Concavity of a functionality is a standard estate utilized in lots of the very important theorems referring to houses of optimization difficulties in mathematical economics, operations learn, mathematical programming, engineering, and administration technological know-how. Generalized concavity offers with the various nonconcave capabilities that experience homes just like these of concave features.
particular issues coated during this e-book include:a overview of concavity and the fundamentals of generalized concavity; purposes of generalized concavity to economics; particular functionality kinds akin to composite kinds, items, ratios, and quadratic capabilities; fractional programming; and concave transformable capabilities.
Audience: Mathematicians, economists, computational mathematicians, administration scientists, operations researchers, and optimization theorists will locate this ebook invaluable.
Contents: Preface to the Classics version; Preface; bankruptcy 1: advent; bankruptcy 2: Concavity; bankruptcy three: Generalized Concavity; bankruptcy four: program of Generalized Concavity to Economics; bankruptcy five: certain practical types I: Composite services, items, and Ratios; bankruptcy 6: specified useful varieties II: Quadratic features; bankruptcy 7: Fractional Programming; bankruptcy eight: Concave Transformable capabilities; bankruptcy nine: extra Generalizations of Concavity; Supplementary Bibliography; writer Index; topic Index.
By Philippe Dennery
First-class textual content offers thorough historical past in arithmetic had to comprehend brand new extra complex issues in physics and engineering. issues comprise thought of features of a fancy variable, linear vector areas, tensor calculus, Fourier sequence and transforms, particular capabilities, extra. Rigorous theoretical improvement; difficulties solved in nice element. Bibliography. 1967 variation.
By J. R. Quine, Peter Sarnak
This quantity is an outgrowth of the AMS distinctive consultation on Extremal Riemann Surfaces held on the Joint arithmetic assembly in San Francisco, January 1995. The publication bargains with quite a few extremal difficulties on the topic of Riemann surfaces. a few papers care for the identity of surfaces with longest systole (element of shortest nonzero size) for the size spectrum and the Jacobian. Parallels are interested in classical questions regarding extremal lattices. different papers care for maximizing or minimizing services outlined by way of the spectrum reminiscent of the warmth kernel, the zeta functionality, and the determinant of the Laplacian, a few from the viewpoint of selecting an extremal metric.There are discussions of Hurwitz surfaces and surfaces with huge cyclic teams of automorphisms. additionally mentioned are surfaces that are ordinary applicants for fixing extremal difficulties similar to triangular, modular, and mathematics surfaces, and curves in a variety of staff theoretically outlined curve households. different allied subject matters are theta identities, quadratic classes of Abelian differentials, Teichmuller disks, binary quadratic kinds, and spectral asymptotics of degenerating hyperbolic 3 manifolds. This quantity: comprises papers by way of a number of the most excellent specialists on Riemann surfaces; outlines fascinating connections among Riemann surfaces and parallel fields; follows up on investigations of Sarnak pertaining to connections among the idea of utmost lattices and Jacobians of Riemann surfaces; and, includes papers on numerous themes in relation to Riemann surfaces
By V. A. Zorich
This softcover variation of a truly renowned two-volume paintings offers a radical first direction in research, prime from actual numbers to such complicated themes as differential types on manifolds, asymptotic equipment, vital transforms, and distributions. specifically outstanding during this path is the truly expressed orientation towards the traditional sciences and its casual exploration of the essence and the roots of the fundamental suggestions and theorems of calculus. readability of exposition is matched through a wealth of instructive workouts, difficulties and clean purposes to components seldom touched on in actual research books.
The moment quantity expounds classical research because it is this present day, as part of unified arithmetic, and its interactions with sleek mathematical classes akin to algebra, differential geometry, differential equations, complicated and useful research. The ebook offers a company starting place for complicated paintings in any of those directions.
By Eric Chin, Sverrir Olafsson, Dian Nel
Mathematical finance calls for using complicated mathematical suggestions drawn from the idea of chance, stochastic approaches and stochastic differential equations. those components are quite often brought and built at an summary point, making it complex whilst utilizing those thoughts to sensible concerns in finance. difficulties and recommendations in Mathematical Finance quantity I: Stochastic Calculus is the 1st of a four-volume set of books targeting difficulties and options in mathematical finance. This quantity introduces the reader to the elemental stochastic calculus recommendations required for the learn of this crucial topic, delivering a number of labored examples which allow the reader to construct the mandatory beginning for simpler oriented difficulties within the later volumes. via this program and via operating throughout the quite a few examples, the reader will safely comprehend and delight in the basics that underpin mathematical finance. Written as a rule for college kids, practitioners and people taken with instructing during this box of research, Stochastic Calculus offers a worthwhile reference e-book to enrich one's additional knowing of mathematical finance.
By Klaus-Dieter Bierstedt, Benno Duchssteiner
Those lawsuits from the Symposium on practical research discover advances within the frequently separate components of semigroups of operators and evolution equations, geometry of Banach areas and operator beliefs, and Frechet areas with functions in partial differential equations.
By R. Narasimhan
Those notes shape the contents of a Nachdiplomvorlesung given on the Forschungs institut fur Mathematik of the Eidgenossische Technische Hochschule, Zurich from November, 1984 to February, 1985. Prof. ok. Chandrasekharan and Prof. Jurgen Moser have inspired me to write down them up for inclusion within the sequence, released by way of Birkhiiuser, of notes of those classes on the ETH. Dr. Albert Stadler produced exact notes of the 1st a part of this direction, and intensely intelligible class-room notes of the remainder. with out this paintings of Dr. Stadler, those notes shouldn't have been written. whereas i've got replaced a few issues (such because the facts of the Serre duality theorem, right here performed solely within the spirit of Serre's unique paper), the current notes stick to Dr. Stadler's rather heavily. My unique target in giving the path was once twofold. i needed to offer the elemental theorems concerning the Jacobian from Riemann's personal standpoint. Given the Riemann-Roch theorem, if Riemann's equipment are expressed in sleek language, they fluctuate little or no (if in any respect) from the paintings of recent authors.