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    The Steiner Ratio

    Posted By: AvaxGenius
    The Steiner Ratio

    The Steiner Ratio by Dietmar Cieslik
    English | PDF | 2001 | 247 Pages | ISBN : 0792370155 | 15.5 MB

    Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space.

    Matrix Groups: An Introduction to Lie Group Theory

    Posted By: AvaxGenius
    Matrix Groups: An Introduction to Lie Group Theory

    Matrix Groups: An Introduction to Lie Group Theory by Andrew Baker
    English | PDF | 2002 | 332 Pages | ISBN : 1852334703 | 35.2 MB

    Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter.

    Mathematical Models (Repost)

    Posted By: AvaxGenius
    Mathematical Models (Repost)

    Mathematical Models: From the Collections of Universities and Museums – Photograph Volume and Commentary by Gerd Fischer
    English/Deutsch | PDF (True) | 2017 | 228 Pages | ISBN : 3658188642 | 169.5 MB

    This book presents beautiful photos of mathematical models of geometric surfaces made from a variety of materials including plaster, metal, paper, wood, and string. The construction of these models at the time (of Felix Klein and others) was not an end in itself, but was accompanied by mathematical research especially in the field of algebraic geometry. The models were used to illustrate the mathematical objects defined by abstract formulas, either as equations or parameterizations. In the second part of the book, the models are explained by experts in the field of geometry.

    Introduction to computational geometry

    Posted By: yoyoloit
    Introduction to computational geometry

    Introduction to computational geometry
    by Samuel R. Buss

    English | 2024 | ISBN: 1774698471 | 254 pages | True PDF | 99.05 MB

    Complex Systems in Biomedicine

    Posted By: AvaxGenius
    Complex Systems in Biomedicine

    Complex Systems in Biomedicine by Alfio Quarteroni, Luca Formaggia, Alessandro Veneziani
    English | PDF (True) | 2006 | 299 Pages | ISBN : 8847003946 | 7 MB

    Mathematical modeling of human physiopathology is a tremendouslyambitioustask. It encompasses the modeling of most diverse compartments such as the cardiovaslar,respiratory,skeletalandnervoussystems,aswellasthemechanicalandbioch- ical interaction between blood ?ow and arterial walls, and electrocardiac processes and electric conduction in biological tissues. Mathematical models can be set up to simulate both vasculogenesis (the aggregation and organization of endothelial cells dispersed in a given environment) and angiogenesis (the formation of new vessels sprouting from an existing vessel) that are relevant to the formation of vascular networks, and in particular to the description of tumor growth. The integration of models aimed at simulating the cooperation and interrelation of different systems is an even more dif?cult task. It calls for the setting up of, for instance, interaction models for the integrated cardio-vascular system and the interplay between the central circulation and peripheral compartments, models for the mid-to-long range cardiovascular adjustments to pathological conditions (e.g., to account for surgical interventions, congenital malformations, or tumor growth), models for integration among circulation, tissue perfusion, biochemical and thermal regulation, models for parameter identi?cation and sensitivity analysis to parameter changes or data uncertainty – and many others.

    Mixing: Chaos and Turbulence

    Posted By: AvaxGenius
    Mixing: Chaos and Turbulence

    Mixing: Chaos and Turbulence by H. Chaté, E. Villermaux, J.-M. Chomaz
    English | PDF | 1999 | 395 Pages | ISBN : 0306461951 | 43.8 MB

    Mixing may be thought of as the operation by which a system evolves from one state of simplicity (initial segregation) to another state of simplicity (complete uniformity). Between these two extremes, complex patterns emerge and die. Questions naturally arise- how can the geometry of complex patterns be characterised, what is the time scale of the process, what structures are involved in the flow?

    Biometrics: Advanced Identity Verification: The Complete Guide

    Posted By: AvaxGenius
    Biometrics: Advanced Identity Verification: The Complete Guide

    Biometrics: Advanced Identity Verification: The Complete Guide by Julian Ashbourn
    English | PDF | 2000 | 215 Pages | ISBN : 1852332433 | 42.1 MB

    Biometric identity verification (BIV) offers a radical alternative to passports, PIN numbers, ID cards and driving licences. It uses physiological or behavioural characteristics such as fingerprints, hand geometry, and retinas to check a person's identity. It is therefore much less open to fraudulent use, which makes it ideal for use in voting systems, financial transactions, benefit payment administration, border control, and prison access.

    Minimal Surfaces I: Boundary Value Problems

    Posted By: AvaxGenius
    Minimal Surfaces I: Boundary Value Problems

    Minimal Surfaces I: Boundary Value Problems by Ulrich Dierkes , Stefan Hildebrandt , Albrecht Küster , Ortwin Wohlrab
    English | PDF | 1992 | 528 Pages | ISBN : N/A | 47.4 MB

    Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.

    Complex Analytic Desingularization (Repost)

    Posted By: AvaxGenius
    Complex Analytic Desingularization (Repost)

    Complex Analytic Desingularization by José Manuel Aroca , Heisuke Hironaka , José Luis Vicente
    English | EPUB (True) | 2019 | 356 Pages | ISBN : 4431702180 | 19.4 MB

    [From the foreword by B. Teissier] The main ideas of the proof of resolution of singularities of complex-analytic spaces presented here were developed by Heisuke Hironaka in the late 1960s and early 1970s. Since then, a number of proofs, all inspired by Hironaka's general approach, have appeared, the validity of some of them extending beyond the complex analytic case. The proof has now been so streamlined that, although it was seen 50 years ago as one of the most difficult proofs produced by mathematics, it can now be the subject of an advanced university course. Yet, far from being of historical interest only, this long-awaited book will be very rewarding for any mathematician interested in singularity theory. Rather than a proof of a canonical or algorithmic resolution of singularities, what is presented is in fact a masterly study of the infinitely near “worst” singular points of a complex analytic space obtained by successive “permissible” blowing ups and of the way to tame them using certain subspaces of the ambient space. This taming proves by an induction on the dimension that there exist finite sequences of permissible blowing ups at the end of which the worst infinitely near points have disappeared, and this is essentially enough to obtain resolution of singularities. Hironaka’s ideas for resolution of singularities appear here in a purified and geometric form, in part because of the need to overcome the globalization problems appearing in complex analytic geometry.

    Advanced Composites

    Posted By: AvaxGenius
    Advanced Composites

    Advanced Composites by Shadia Jamil Ikhmayies
    English | EPUB (True) | 2023 (2024 Edition) | 655 Pages | ISBN : 3031427300 | 118.7 MB

    This book presents a comprehensive collection of reviews and experimental research findings in the realm of composite materials. It explores manufacturing technologies and applications, as well as recent breakthroughs in nanomaterial-based composites, polymer-based composites, titanium matrix composites (TMCs), conducting polymers, natural polymers, graphene polymers, graphene composites, and organosulfur polymeric composites, alongside reinforced aluminum matrix composites. The mechanical and tribological aspects take center stage, with a focus on aluminum alloy composites as a superior alternative to traditional gear materials. The book also addresses cutting-edge composite materials developed for drug removal via adsorption techniques, radiation shielding, and their use as shielding absorbers for ionizing radiation. Furthermore, the significance of electrical contact materials and their performance is explored. The book unveils fabrication methods, sample preparation techniques, properties, and various applications of these remarkable composites.

    Functional Analysis: An Introduction to Banach Space Theory

    Posted By: AvaxGenius
    Functional Analysis: An Introduction to Banach Space Theory

    Functional Analysis: An Introduction to Banach Space Theory by Terry J. Morrison
    English | PDF | 2000 | 370 Pages | ISBN : 0471372145 | 17.6 MB

    A powerful introduction to one of the most active areas of theoretical and applied mathematics.

    Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions (Repost)

    Posted By: AvaxGenius
    Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions (Repost)

    Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions by Michel L. Lapidus , Machiel Frankenhuysen
    English | PDF | 2000 | 277 Pages | ISBN : 0817640983 | 21.76 MB

    A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo­ metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di­ mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string.

    Hyperbolic Geometry

    Posted By: AvaxGenius
    Hyperbolic Geometry

    Hyperbolic Geometry by James W. Anderson
    English | PDF | 1999 | 239 Pages | ISBN : 1852331569 | 18.15 MB

    The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.

    Relativistic Electrodynamics and Differential Geometry

    Posted By: AvaxGenius
    Relativistic Electrodynamics and Differential Geometry

    Relativistic Electrodynamics and Differential Geometry by Stephen Parrott
    English | PDF | 1987 | 317 Pages | ISBN : 1461291135 | 38.8 MB

    The aim of this book is to provide a short but complete exposition of the logical structure of classical relativistic electrodynamics written in the language and spirit of coordinate-free differential geometry. The intended audience is primarily mathematicians who want a bare-bones account of the foundations of electrodynamics written in language with which they are familiar and secondarily physicists who may be curious how their old friend looks in the new clothes of the differential-geometric viewpoint which in recent years has become an important language and tool for theoretical physics.

    The Stationary Semiconductor Device Equations

    Posted By: AvaxGenius
    The Stationary Semiconductor Device Equations

    The Stationary Semiconductor Device Equations by Peter A. Markowich
    English | PDF | 1986 | 202 Pages | ISBN : 3211818928 | 16.1 MB

    In the last two decades semiconductor device simulation has become a research area, which thrives on a cooperation of physicists, electrical engineers and mathe­ maticians. In this book the static semiconductor device problem is presented and analysed from an applied mathematician's point of view. I shall derive the device equations - as obtained for the first time by Van Roosbroeck in 1950 - from physical principles, present a mathematical analysis, discuss their numerical solu­ tion by discretisation techniques and report on selected device simulation runs. To me personally the most fascinating aspect of mathematical device analysis is that an interplay of abstract mathematics, perturbation theory, numerical analysis and device physics is prompting the design and development of new technology.