Mathematical Physics

1411 Submissions

[7] viXra:1411.0587 [pdf] submitted on 2014-11-28 17:17:03

A Simple Lecture on Mubs

Authors: M. D. Sheppeard
Comments: 5 Pages.

This is a concise summary of the concept of mutually unbiased bases, including the concrete examples up to d=6.
Category: Mathematical Physics

[6] viXra:1411.0178 [pdf] replaced on 2015-10-31 15:26:43

Quaternions and Hilbert Spaces

Authors: J.A.J. van Leunen
Comments: 51 Pages.

This is a compilation of quaternionic number systems, quaternionic function theory, quaternionic Hilbert spaces and Gelfand triples. The difference between quaternionic differential calculus and Maxwell based differential calculus is explained.
Category: Mathematical Physics

[5] viXra:1411.0175 [pdf] submitted on 2014-11-15 16:14:30

Skeleton Relational Structures

Authors: J.A.J. van Leunen
Comments: 10 Pages.

The theory of skeleton relational structures is very useful in the investigation of the isomorphism between structures in which relations play an important role. It is an important tool for model designers. This theory is also known as lattice theory.
Category: Mathematical Physics

[4] viXra:1411.0112 [pdf] submitted on 2014-11-14 03:40:42

Modelling and Simulation of Crowds

Authors: Shreyak Chakraborty, Salil Batabyal
Comments: 50 Pages.

In this project, we extend the work already done in [1.] to include a generalised mathematical framework for studying and explaining the dynamics and behavior of crowds of humans. The method is both analytical and numerical. The numerical methods are used to solve the differential equations of crowds that are derived analytically. The analytical and numerical solutions are compared and their relevance is shown. In this project, we study mainly two types of responses of a crowd: Position Response and Density Response. The latter is formulated using stressors using an approach similar to [2.] which also enables us to derive the General Adaptation Syndrome (GAS) Model in a very generalised form. Finally, we extend stressors to define inter-crowd and intra-crowd interactions using a parameterisation linking it directly to a generalisation of the stressdensity equation.
Category: Mathematical Physics

[3] viXra:1411.0085 [pdf] submitted on 2014-11-10 11:16:11

About the Replacement of Metric Tensor

Authors: sangwha Yi
Comments: 6 Pages.

In the general relativity theory, study the replacement of the metric tensor in the Einstein gravity field equation.
Category: Mathematical Physics

[2] viXra:1411.0032 [pdf] replaced on 2014-12-09 08:41:56

Metamorphoses of Resonance Curves for Two Coupled Oscillators: the Case of Small Nonlinearities in the Main Mass Frame

Authors: Jan Kyziol
Comments: 10 pages

We study dynamics of two coupled periodically driven oscillators in general case. Periodic steady-state solutions of the system of two equations are determined within the Krylov-Bogoliubov-Mitropolsky approach. The orresponding amplitude profiles, A(omega), B(omega), which are given by two implicit equations, F(A,B,omega)=0, G(A,B,omega)=0, where omega is frequency of the driving force, are computed. These two equations, each describing a surface, define a 3D curve - intersection of these surfaces. In the present paper we carry out preliminary investigation of metamorphoses of this curve, induced by changes of control parameters. The corresponding changes of dynamics near singular points of the curve are studied.
Category: Mathematical Physics

[1] viXra:1411.0015 [pdf] replaced on 2014-11-10 05:51:44

Variational Principle of Extremum in Electromechanical and Electrodynamic Systems \\ Вариационный принцип экстремума в электромеханических и электродинамических системах

Authors: Solomon I. Khmelnik
Comments: 360 Pages.

Here we shall formulate and prove the variational optimum principle for electromechanical systems of arbitrary configuration, in which electromagnetic, mechanical, thermal, hydraulic or other processes are going on. The principle is generalized for systems described by partial differential equations, including also Maxwell equations. The presented principle permits to expand the Lagrange formalism and extend the new formalism on dissipative systems. It is shown that for such systems there exists a pair of functionals with a global saddle point. A high-speed universal algorithm for such systems calculation with any perturbations is described. This algorithm realizes a simultaneous global saddle point search on two functionals. The algorithms for solving specific mathematical and technical problems are cited. The book contains numerous examples, including those presented as M-functions of the MATLAB system and as functions of the DERIVE system. The programs in systems MATLAB and DERIVE are published as a separate annex in the form of an electronic book. Programs are not required to understand the theory. \\ Формулируется и доказывается вариационный принцип оптимума для электромеханических систем произвольной конфигурации, в которых протекают электромагнитные, механические, тепловые, гидравлические и др. процессы. Принцип обобщается на системы, описываемые уравнениями в частных производных и, в т.ч., уравнениями Максвелла. Предложенный принцип позволяет расширить лагранжев формализм и распространить новый формализм на диссипативные системы. Показывается, что для таких систем существует пара функционалов с глобальной седловой точкой. Описывается быстродействующий универсальный алгоритм расчета таких систем при любых возмущающих воздействиях. В этом алгоритме реализуется метод поиска глобальной седловой точки одновременно на двух функционалах. Приводятся алгоритмы решения конкретных математических и технических задач. Книга содержит многочисленные примеры, в т.ч. в виде М-функций системы MATLAB и в виде функций системы DERIVE. Программы в системах MATLAB и DERIVE изданы как отдельное приложение в виде электронной книги. Программы не являются обязательными для понимания теории.
Category: Mathematical Physics