Reshetnyak’s Theory of Subharmonic Metrics
Despite the fundamental role played by Reshetnyak's work in the theory of surfaces of bounded integral curvature, the proofs of his results were only available in his original articles, written in Russian and often hard to find. This situation used to be a serious problem for experts in the field. This book provides English translations of the full set of Reshetnyak's articles on the subject. Together with the companion articles, this book provides an accessible and comprehensive reference for the subject. In turn, this book should concern any researcher (confirmed or not) interested in, or active in, the field of bounded integral curvature surfaces, or more generally interested in surface geometry and geometric analysis. Due to the analytic nature of Reshetnyak's approach, it appears that his articles are very accessible for a modern audience, comparing to the works using a more synthetic approach. These articles of Reshetnyak concern more precisely the work carried bythe author following the completion of his PhD thesis, under the supervision of A.D. Alexandrov. Over the period from the 1940's to the 1960's, the Leningrad School of Geometry, developed a theory of the metric geometry of surfaces, similar to the classical theory of Riemannian surfaces, but with lower regularity, allowing greater flexibility. Let us mention A.D. Alexandrov, Y.D. Burago and V.A. Zalgaller. The types of surfaces studied by this school are now known as surfaces of bounded curvature. Particular cases are that of surfaces with curvature bounded from above or below, the study of which gained special attention after the works of M. Gromov and G. Perelman. Nowadays, these concepts have been generalized to higher dimensions, to graphs, and so on, and the study of metrics of weak regularity remains an active and challenging field. Reshetnyak developed an alternative and analytic approach to surfaces of bounded integral curvature. The underlying idea is based on the theorem of Gauss which states that every Riemannian surface is locally conformal to Euclidean space. Reshetnyak thus studied generalized metrics which are locally conformal to the Euclidean metric with conformal factor given by the logarithm of the difference between two subharmonic functions on the plane. Reshetnyak's condition appears to provide the correct regularity required to generalize classical concepts such as measure of curvature, integral geodesic curvature for curves, and so on, and in turn, to recover surfaces of bounded curvature. Chapter-No.7, Chapter-No.8, Chapter-No.12 and Chapter-No.13 are available open access under Creative Commons Attribution-NonCommercial 4.0 International License via link.springer.com.
Observations On Reversionary Payments
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A History of Japanese Mathematics
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Principles of the Algebra of Physics
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A Shilling Arithmetic
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Spiral Slide Rule
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Examples of Analytical Geometry of Three Dimensions
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Five-Figure Mathematical Tables
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An Elementary Treatise on the Integral Calculus
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Five-Figure Mathematical Tables
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A Practical System of Algebra in Theory and Practice in Two Parts
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A Text Book of Algebra
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Rational Geometry
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Geometrical Lectures
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A History of Japanese Mathematics
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A Course in Mathematical Analysis; Volume 1
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Objects and Structures
From modern neuroscience we now know that everything we think, understand, perceive, and experience, is a construct of brain function. Objects and Structures (Object Theory) is an approach to mathematics in this context. It is not, in itself, mathematics as we know it, rather, it is metamathematics. It is a way of looking at mathematics and mathematical structures, and at numbers and the relations between numbers, in essence. Firstly, we recognise that all our structures of understanding must be related to dynamic structures of brain function. Secondly, we recognise that numbers and their relations correlate to objects and phenomena, and their relations in the material world, when understood in terms of numbers. Thirdly, we recognise that the material world as we encounter it is a structure of brain function. Fourthly, we recognise that our comprehension and understanding of any "proof" of the traditional kind in mathematics, or indeed other mathematical architecture, we also only encounter as a structure of brain function. Taking these points together we can consider all things simply in terms of structures of relations between distinct objects. These objects are not neurons in the brain, or networks of neurons, but rather, just what we conceive as "objects". They are whatever we consider to be an object, and any object of thought. Whilst Object Theory does deal with numbers, its viewpoint is from an ultranumeric position - a viewpoint in which we abandon any intellectually intuitive belief that numbers and the mathematical structures that arise from their relations, should be fundamental to our deepest understanding. Rather we focus on how all phenomena and objective concept-structures can be considered at the highest level of abstraction as structures of relations between distinct objects. This then also allows a way of understanding infinities and their relations both to numbers and other infinities. A core concept is the infinite iteration process or IIP. In a "real world" context, in terms of empirical mathematics, the natural structures of the Mandelbrot and Julia sets, for example, because they are created in the first instance through IIPs, can be explored on the basis of IIPs as objects. This then gives rise to insights on the relation between the real numbers and the continuum.
The Principles and Methods of Geometrical Optics
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Ray's New Primary Arithmetic for Young Learners, Book 1
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Theory of Groups of Finite Order
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Chapters On The Modern Geometry Of The Point, Line, And Circle
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Concrete Geometry for Beginners
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Mathematical Tables
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Elements of Projective Geometry
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A Treatise on the Construction, Properties, and Analogies of the Three Conic Sections
The Principles of Logic
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Mathematical Papers. Edited by N.M. Ferrers
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Numerical Methods for Engineering Students
Numerical methods is an important subject in the study of engineering. It is the study of approximate solution of algebraic, transcendental equations and interpolation. This book on numerical methods, meant for undergraduate students, covers solution of equations and interpolation.In this book, each topic has been thoroughly covered from the examination point of view.
The Elliptic Cylinder Function Of Class K
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Treatise on the Arrangement, Application, and Use of Slide Rules
Der Barycentrische Calcul
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On Multi-objective Integer Linear Programming Problem
Multi-Objective Integer Linear Programming Problems is really wide range to study its theory and algorithms it is really difficult for us to come with the decision that book is complete. The basic idea is to classify and analyze the Multi -Objective Integer Linear Programming theory and its applications. Our objectives are mainly based on: To study and solve the single-objective integer linear programming problems Bi-objective integer linear programming problems, Multi-objective integer linear programming problems and developed some algorithms.
Key To The Publications Of The United States Census, 1790-1887
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An Elementary Treatise on Conic Sections by the Methods of Co-ordinate Geometry
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An Introduction to the Elements of Algebra
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The Moon
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Solid Geometry, With Problems and Applications
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High School Algebra
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Weights and Measures
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