scholarly journals A-topology for Minkowski space

1979 ◽  
Vol 21 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Sribatsa Nanda
Keyword(s):  
Minkowski Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
One Dimensional ◽  
Group Of Homeomorphisms ◽  
Dimensional Space Time ◽  
The One ◽  
Induced Topology ◽  
Time Continuum ◽  
Inhomogeneous Lorentz Group

AbstractWe consider in this paper a topology (which we call the A-topology) on Minkowski space, the four-dimensional space–time continuum of special relativity and derive its group of homeomorphisms. We define the A-topology to be the finest topology on Minkowski space with respect to which the induced topology on time-like and light-like lines is one-dimensional Euclidean and the induced topology on space-like hyperplanes is three- dimensional Euclidean. It is then shown that the group of homeomorphisms of this topology is precisely the one generated by the inhomogeneous Lorentz group and the dilatations.

Disorders of Orientation in Space-Time

1966 ◽  
Vol 112 (488) ◽  
pp. 661-670 ◽  
Author(s):  
William Gooddy
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Indefinite Number ◽  
The World ◽  
Dimensional Space Time ◽  
In Virtue Of ◽  
Time Continuum

“The non-mathematician is seized by a mysterious shuddering when he hears of ‘four-dimensional’ things, by a feeling not unlike that awakened by thoughts of the occult. And yet there is no more commonplace statement than that the world in which we live is a four-dimensional space-time continuum. By this we mean that it is possible to describe the position of a point at rest by means of three numbers (co-ordinates) x, y, z, and that there is an indefinite number of points in the neighbourhood of this one, the position of which can be described by co-ordinates such as x1, y1, z1, which may be as near as we choose to the respective values of the co-ordinates x, y, z of the first point. In virtue of the latter property we speak of a ‘continuum’, and owing to the fact that there are three co-ordinates we speak of it as being ‘three-dimensional’.

Study on Dynamics Model of Solid Trajectory Analysis and Pneumatics Based on Space-Time Four-Dimensional Data

2014 ◽  
Vol 556-562 ◽  
pp. 3856-3859
Author(s):  
Jun Zhang
Keyword(s):  
Mathematical Model ◽  
Dimensional Space ◽  
Space Time ◽  
Flight Trajectory ◽  
Time Data ◽  
One Dimensional ◽  
Dimensional Space Time ◽  
The One ◽  
Steady State Simulation ◽  
The Mathematical Model

In this paper we use elastic-plastic mechanics and air dynamic to establish the mathematical model of badminton flight trajectory and deformation, and use the ANSYS software to do simulation on badminton flight process, and obtain the flight path and deformation of badminton. In order to analyze the badminton four-dimensional space-time data, we establish the one-dimensional time measurement, and use one-dimensional time transient stress to establish flight trajectory and deformation, and design the four-dimensional space-time steady-state simulation process. Through calculation we eventually get the force of badminton flight process and deformation nephogram. Comparing four times results of numerical simulation results, the mathematical model of this design model meets the design requirements. It provides technical reference for badminton athlete's training and teaching.

Linearized Two-Dimensional Fluid Transients

1984 ◽  
Vol 106 (2) ◽  
pp. 227-232 ◽  
Author(s):  
E. B. Wylie
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Low Velocity ◽  
Flow Problems ◽  
Spatial Dimensions ◽  
Dimensional Space Time ◽  
Fluid Transients ◽  
Explicit Procedure ◽  
The One

A numerical analysis of low-velocity two-dimensional transient fluid flow problems is presented. The method is similar in concept to the one-dimensional method of characteristics, but does not follow the traditional characteristics theory for two spatial dimensions. Distinct paths are defined in the three-dimensional space-time domain along which compatibility equations are integrated. The explicit procedure is explained, and validated by comparisons with analytical solutions.

ON THE PHYSICAL PROPERTIES RELATED TO THE ALGEBRAIC STRUCTURE OF THE DIRAC EQUATION IN THREE-DIMENSIONAL SPACE–TIME

1998 ◽  
Vol 13 (09) ◽  
pp. 1523-1542
Author(s):  
C. A. LINHARES ◽  
JUAN A. MIGNACO
Keyword(s):  
Dirac Equation ◽  
Algebraic Structure ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Four Dimensions ◽  
Dimensional Space Time ◽  
The One ◽  
Physical Consequences ◽  
Three Dimensional Space

We look for the physical consequences resulting from the SU(2) ⊗ SU(2) algebraic structure of the Dirac equation in three-dimensional space–time. We show how this is obtained from the general result we have proven relating the matrices of the Clifford–Dirac ring and the Lie algebra of unitary groups. It allows the introduction of a notion of chirality closely analogous to the one used in four dimensions. The irreducible representations for the Dirac matrices may be labelled with different chirality eigenvalues, and they are related through inversion of any single coordinate axis. We analyze the different discrete transformations for the space of solutions. Finally, we show that the spinor propagator is a direct sum of components with different chirality; the photon propagator receive separate contributions for both chiralities, and the result is that there is no generation of a topological mass at one-loop level. In the case of a charged particle in a constant "magnetic" field we have a good example where chirality plays a determinant role for the degeneracy of states.

Three-dimensional uncertain heat equation

2021 ◽  
pp. 2250012
Author(s):  
Tingqing Ye ◽  
Xiangfeng Yang
Keyword(s):  
Heat Source ◽  
Heat Equation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Uncertainty Distribution ◽  
Change Rate ◽  
One Dimensional ◽  
Liu Process ◽  
The One ◽  
Three Dimensional Space

Heat equation is a partial differential equation describing the temperature change of an object with time. In the traditional heat equation, the strength of heat source is assumed to be certain. However, in practical application, the heat source is usually influenced by noise. To describe the noise, some researchers tried to employ a tool called Winner process. Unfortunately, it is unreasonable to apply Winner process in probability theory to modeling noise in heat equation because the change rate of temperature will tend to infinity. Thus, we employ Liu process in uncertainty theory to characterize the noise. By modeling the noise via Liu process, the one-dimensional uncertain heat equation was constructed. Since the real world is a three-dimensional space, the paper extends the one-dimensional uncertain heat equation to a three-dimensional uncertain heat equation. Later, the solution of the three-dimensional uncertain heat equation and the inverse uncertainty distribution of the solution are given. At last, a paradox of stochastic heat equation is introduced.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Sign in / Sign up

Export Citation Format

Share Document