The Geometry Of Higher Dimensional Polytopes
DOWNLOAD
FREE 30 Days
Download The Geometry Of Higher Dimensional Polytopes PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Geometry Of Higher Dimensional Polytopes book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Geometry Of Higher Dimensional Polytopes
DOWNLOAD
FREE 30 Days
Author : Zhizhin, Gennadiy Vladimirovich
language : en
Publisher: IGI Global
Release Date : 2018-08-03
The Geometry Of Higher Dimensional Polytopes written by Zhizhin, Gennadiy Vladimirovich and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-03 with Technology & Engineering categories.
The majority of the chemical elements form chemical compounds with molecules of higher dimension (i.e., substantially exceeding three). This fact is very important for the analysis of molecular interactions in various areas: nanomedicine, nanotoxicology, and quantum biology. The Geometry of Higher-Dimensional Polytopes contains innovative research on the methods and applications of the structures of binary compounds. It explores the study of geometry polytopes from a higher-dimensional perspective, taking into account the features of polytopes that are models of chemical compounds. While highlighting topics including chemical compounds, symmetry transformation, and DNA structures, this book is ideally designed for researchers, academicians, and students seeking current research on dimensions present in binary compounds.
The Classes Of Higher Dimensional Polytopes In Chemical Physical And Biological Systems
DOWNLOAD
FREE 30 Days
Author : Zhizhin, Gennadiy Vladimirovich
language : en
Publisher: IGI Global
Release Date : 2022-04-08
The Classes Of Higher Dimensional Polytopes In Chemical Physical And Biological Systems written by Zhizhin, Gennadiy Vladimirovich and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-08 with Mathematics categories.
The study of the geometry of structures that arise in a variety of specific natural systems, such as chemical, physical, biological, and geological, revealed the existence of a wide range of types of polytopes of the highest dimension that were unknown in classical geometry. At the same time, new properties of polytopes were discovered as well as the geometric patterns to which they obey. There is a need to classify these types of polytopes of the highest dimension by listing their properties and formulating the laws to which they obey. The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems explains the meaning of higher dimensions and systematically generalizes the results of geometric research in various fields of knowledge. This book is useful both for the fundamental development of geometry and for the development of branches of science related to human activities. It builds upon previous books published by the author on this topic. Covering areas such as heredity, geometry, and dimensions, this reference work is ideal for researchers, scholars, academicians, practitioners, industry professionals, instructors, and students.
Normal Partitions And Hierarchical Fillings Of N Dimensional Spaces
DOWNLOAD
FREE 30 Days
Author : Zhizhin, Gennadiy Vladimirovich
language : en
Publisher: IGI Global
Release Date : 2020-12-25
Normal Partitions And Hierarchical Fillings Of N Dimensional Spaces written by Zhizhin, Gennadiy Vladimirovich and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-25 with Mathematics categories.
In the study of the structure of substances in recent decades, phenomena in the higher dimension was discovered that was previously unknown. These include spontaneous zooming (scaling processes), discovery of crystals with the absence of translational symmetry in three-dimensional space, detection of the fractal nature of matter, hierarchical filling of space with polytopes of higher dimension, and the highest dimension of most molecules of chemical compounds. This forces research to expand the formulation of the question of constructing n-dimensional spaces, posed by David Hilbert in 1900, and to abandon the methods of considering the construction of spaces by geometric figures that do not take into account the accumulated discoveries in the physics of the structure of substances. There is a need for research that accounts for the new paradigm of the discrete world and provides a solution to Hilbert's 18th problem of constructing spaces of higher dimension using congruent figures. Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces aims to consider the construction of spaces of various dimensions from two to any finite dimension n, taking into account the indicated conditions, including zooming in on shapes, properties of geometric figures of higher dimensions, which have no analogue in three-dimensional space. This book considers the conditions of existence of polytopes of higher dimension, clusters of chemical compounds as polytopes of the highest dimension, higher dimensions in the theory of heredity, the geometric structure of the product of polytopes, the products of polytopes on clusters and molecules, parallelohedron and stereohedron of Delaunay, parallelohedron of higher dimension and partition of n-dimensional spaces, hierarchical filling of n-dimensional spaces, joint normal partitions, and hierarchical fillings of n-dimensional spaces. In addition, it pays considerable attention to biological problems. This book is a valuable reference tool for practitioners, stakeholders, researchers, academicians, and students who are interested in learning more about the latest research on normal partitions and hierarchical fillings of n-dimensional spaces.
Regular Polytopes
DOWNLOAD
FREE 30 Days
Author : H. S. M. Coxeter
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Regular Polytopes written by H. S. M. Coxeter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.
The Visual Guide To Extra Dimensions
DOWNLOAD
FREE 30 Days
Author : Chris McMullen
language : en
Publisher: CreateSpace
Release Date : 2008-08-17
The Visual Guide To Extra Dimensions written by Chris McMullen and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-17 with Mathematics categories.
Watch a tesseract unfold. See how the 3D cross section of a hypercube changes as the hypercube rotates. View 4D wheels with axles with a spherinder or cubinder structure. Imagine climbing a 4D staircase. Find 10 out of 120 dodecahedra of a hecatonicosachoron highlighted... all on this visual tour of the fourth dimension.The book is much more visual and conceptual than algebraic, yet it is detailed and technical, with the intention of satisfying the needs of mathematically-minded readers familiar with the fundamentals of algebra, geometry, and graphing.
Convex Polytopes
DOWNLOAD
FREE 30 Days
Author : P. McMullen
language : en
Publisher: CUP Archive
Release Date : 1971-07-02
Convex Polytopes written by P. McMullen and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-07-02 with Mathematics categories.
Lectures In Geometric Combinatorics
DOWNLOAD
FREE 30 Days
Author : Rekha R. Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Lectures In Geometric Combinatorics written by Rekha R. Thomas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the statepolytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Grobner bases of toric ideals and other methods fromcommutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.
Higher Dimensional Geometry Over Finite Fields
DOWNLOAD
FREE 30 Days
Author : D. Kaledin
language : en
Publisher: IOS Press
Release Date : 2008-06-05
Higher Dimensional Geometry Over Finite Fields written by D. Kaledin and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-05 with Mathematics categories.
Number systems based on a finite collection of symbols, such as the 0s and 1s of computer circuitry, are ubiquitous in the modern age. Finite fields are the most important such number systems, playing a vital role in military and civilian communications through coding theory and cryptography. These disciplines have evolved over recent decades, and where once the focus was on algebraic curves over finite fields, recent developments have revealed the increasing importance of higher-dimensional algebraic varieties over finite fields. The papers included in this publication introduce the reader to recent developments in algebraic geometry over finite fields with particular attention to applications of geometric techniques to the study of rational points on varieties over finite fields of dimension of at least 2.
Nanotechnologies And Clusters In The Spaces Of Higher Dimension Emerging Research And Opportunities
DOWNLOAD
FREE 30 Days
Author : Zhizhin, Gennadiy Vladimirovich
language : en
Publisher: IGI Global
Release Date : 2020-10-09
Nanotechnologies And Clusters In The Spaces Of Higher Dimension Emerging Research And Opportunities written by Zhizhin, Gennadiy Vladimirovich and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-09 with Technology & Engineering categories.
Research on nanomaterials and their applications has become a trending area in various fields of study and practice. Its properties and abilities open a variety of scientific advancements that weren’t possible in past years. One specific area of research that is benefiting from the implementation of nanotechnology is the study of higher-dimensional compounds that include metallic atoms and other polytypes. There is vast potential in the study of how nanomaterials are currently being used for producing clusters in higher dimensions of space. Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities provides emerging research exploring the theoretical and practical aspects of the production of intermetallic clusters in high dimensional spaces using nanotechnology. Featuring coverage on a broad range of topics such as intermetallic compounds, incident conservation law, and applied mathematics, this book is ideally designed for practitioners, scientists, engineers, researchers, educators, physicists, mathematicians, students, and academicians seeking current research on the use of nanomaterials in interdimensional science.
Attractors And Higher Dimensions In Population And Molecular Biology Emerging Research And Opportunities
DOWNLOAD
FREE 30 Days
Author : Zhizhin, Gennadiy Vladimirovich
language : en
Publisher: IGI Global
Release Date : 2019-06-28
Attractors And Higher Dimensions In Population And Molecular Biology Emerging Research And Opportunities written by Zhizhin, Gennadiy Vladimirovich and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-28 with Science categories.
In studying biology, one of the more difficult factors to predict is how parents attributes will affect their children and how those children will affect their own children. Organizing and calculating those vast statistics can become extremely tedious without the proper mathematical and reproductive knowledge. Attractors and Higher Dimensions in Population and Molecular Biology: Emerging Research and Opportunities is a collection of innovative research on the methods and applications of population logistics. While highlighting topics including gene analysis, crossbreeding, and reproduction, this book is ideally designed for academics, researchers, biologists, and mathematicians seeking current research on modeling the reproduction process of a biological population.