scholarly journals On wave equations for the Majorana particle in (3+1) and (1+1) dimensions

2021 ◽  
Author(s):  
Salvatore De Vincenzo
Keyword(s):  
Complex System ◽  
Wave Function ◽  
Wave Equations ◽  
Scalar Potential ◽  
Point Of View ◽  
Relativistic Wave Equation ◽  
System Of Equations ◽  
Algebraic Point ◽  
Coupled Equations ◽  
Majorana Particle

Abstract In general, the relativistic wave equation considered to mathematically describe the so-called Majorana particle is the Dirac equation with a real Lorentz scalar potential plus the so-called Majorana condition. Certainly, depending on the representation that one uses, the resulting differential equation changes. It could be a real or a complex system of coupled equations, or it could even be a single complex equation for a single component of the entire wave function. Any of these equations or systems of equations could be referred to as a Majorana equation or Majorana system of equations because it can be used to describe the Majorana particle. For example, in the Weyl representation, in (3+1) dimensions, we can have two non-equivalent explicitly covariant complex first-order equations; in contrast, in (1+1) dimensions, we have a complex system of coupled equations. In any case, whichever equation or system of equations is used, the wave function that describes the Majorana particle in (3+1) or (1+1) dimensions is determined by four or two real quantities. The aim of this paper is to study and discuss all these issues from an algebraic point of view, highlighting the similarities and differences that arise between these equations in the cases of (3+1) and (1+1) dimensions in the Dirac, Weyl, and Majorana representations. Additionally, to reinforce this task, we rederive and use results that come from a procedure already introduced by Case to obtain a two-component Majorana equation in (3+1) dimensions. Likewise, we introduce for the first time a somewhat analogous procedure in (1+1) dimensions and then use the results we obtain.

scholarly journals CONFLICTS AND FAIR TESTING

2006 ◽  
Vol 17 (04) ◽  
pp. 797-813 ◽  
Author(s):  
ROBI MALIK ◽  
DAVID STREADER ◽  
STEVE REEVES
Keyword(s):  
Discrete Event Systems ◽  
Process Algebra ◽  
Discrete Event ◽  
Denotational Semantics ◽  
Point Of View ◽  
Algebraic Point ◽  
Event Systems ◽  
Common Task ◽  
Testing Theory ◽  
Process Algebraic

This paper studies conflicts from a process-algebraic point of view and shows how they are related to the testing theory of fair testing. Conflicts have been introduced in the context of discrete event systems, where two concurrent systems are said to be in conflict if they can get trapped in a situation where they are waiting or running endlessly, forever unable to complete their common task. In order to analyse complex discrete event systems, conflict-preserving notions of refinement and equivalence are needed. This paper characterises an appropriate refinement, called the conflict preorder, and provides a denotational semantics for it. Its relationship to other known process preorders is explored, and it is shown to generalise the fair testing preorder in process-algebra for reasoning about conflicts in discrete event systems.

Ansatz approach solution of the Duffin–Kemmer–Petiau equation for spin-1 particles with position-dependent mass in the presence of Kratzer-type potential

2014 ◽  
Vol 92 (12) ◽  
pp. 1565-1569 ◽  
Author(s):  
M.K. Bahar ◽  
F. Yasuk
Keyword(s):  
Wave Function ◽  
Scalar Potential ◽  
Energy Eigenvalues ◽  
Relativistic Spin ◽  
Ansatz Approach ◽  
Dependent Mass ◽  
Type Potential ◽  
Position Dependent Mass

The relativistic Duffin–Kemmer–Petiau equation for relativistic spin-1 particles with position-dependent mass in the presence of a vector Kratzer-type potential and the absence of a scalar potential is studied analytically. The energy eigenvalues and corresponding eigenfunctions are obtained using the wave function ansatz approach.

scholarly journals Localizability of unicycle mobiles robots: An algebraic point of view

2012 ◽  
Author(s):  
Hugues Sert ◽  
Wilfrid Perruquetti ◽  
Annemarie Kokosy ◽  
Xin Jin ◽  
Jorge Palos
Keyword(s):  
Point Of View ◽  
Algebraic Point

Semiotic analysis of symbolic logic using tagmemic theory: with implications for analytic philosophy

Semiotica ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Vern S. Poythress
Keyword(s):  
Complex System ◽  
Analytic Philosophy ◽  
Formal Languages ◽  
Point Of View ◽  
Symbolic Logic ◽  
Semiotic Analysis ◽  
The World

Abstract This article uses tagmemic theory as a semiotic framework to analyze symbolic logic. It attends particularly to the issue of context for meaning and the role of personal observer/participants. It focuses on formal languages, which employ no ordinary words and from one point of view have “no meaning.” Attention to the context and the theorists who deploy these languages shows that formal languages have meanings at a higher level, colored by the purposes of the analysts. In fact, there is an indefinitely ascending hierarchy of theories of theories, each of which analyzes and evaluates the theories at a lower level. By analogy with Kurt Gödel’s incompleteness theory, no level of the hierarchy can capture within formalism everything in a sufficiently complex system. The personal analysts always have to make judgments about how a formalized system is analogous to the world outside the system. Arguments in analytic philosophy can be useful in clarification, but neither clarification of terms nor clarification of the structure of arguments can eliminate the need for personal judgment.

Software Tool for Assessment of Complexity and Variability in Physiological Signals of Respiration

2011 ◽  
Vol 1 (2) ◽  
pp. 28-53
Author(s):  
Ireneusz Jablonski ◽  
Kamil Subzda ◽  
Janusz Mroczka
Keyword(s):  
Complex System ◽  
Experimental Data ◽  
Time Series ◽  
Data Analysis ◽  
Input Signal ◽  
Software Tool ◽  
Point Of View ◽  
Software Implementation ◽  
Physiological Signals ◽  
Event Time

In this paper, the authors examine software implementation and the initial preprocessing of data and tools during the assessment of the complexity and variability of long physiological time-series. The algorithms presented advance a bigger Matlab library devoted to complex system and data analysis. Commercial software is unavailable for many of these functions and is generally unsuitable for use with multi-gigabyte datasets. Reliable inter-event time extraction from input signal is an important step for the presented considerations. Knowing the distribution of the inter-event time distances, it is possible to calculate exponents due to power-law scaling. From a methodology point of view, simulations and considerations with experimental data supported each stage of the work presented. In this paper, initial calibration of the procedures with accessible data confirmed assessments made during earlier studies, which raise objectivity of measurements planned in the future.

MAGNETIC GROUP ON THE PSEUDOSPHERE

1992 ◽  
Vol 06 (21) ◽  
pp. 3525-3537 ◽  
Author(s):  
V. BARONE ◽  
V. PENNA ◽  
P. SODANO
Keyword(s):  
Magnetic Field ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Constant Magnetic Field ◽  
Coherent States ◽  
Compact Operators ◽  
Point Of View ◽  
Algebraic Point ◽  
Planar Limit ◽  
Discrete Part

The quantum mechanics of a particle moving on a pseudosphere under the action of a constant magnetic field is studied from an algebraic point of view. The magnetic group on the pseudosphere is SU(1, 1). The Hilbert space for the discrete part of the spectrum is investigated. The eigenstates of the non-compact operators (the hyperbolic magnetic translators) are constructed and shown to be expressible as continuous superpositions of coherent states. The planar limit of both the algebra and the eigenstates is analyzed. Some possible applications are briefly outlined.

scholarly journals Connectivity of pseudomanifold graphs from an algebraic point of view

2015 ◽  
Vol 353 (12) ◽  
pp. 1061-1065 ◽  
Author(s):  
Karim A. Adiprasito ◽  
Afshin Goodarzi ◽  
Matteo Varbaro
Keyword(s):  
Point Of View ◽  
Algebraic Point

A lattice of extension rings for a commutative ring

1978 ◽  
Vol 84 (2) ◽  
pp. 225-234 ◽  
Author(s):  
D. Kirby ◽  
M. R. Adranghi
Keyword(s):  
Point Of View ◽  
Local Rings ◽  
Algebraic Point ◽  
Multiple Points ◽  
One Dimensional ◽  
Maximal Ideals ◽  
Blowing Up ◽  
Abstract Case ◽  
Algebroid Curve

The work of this note was motivated in the first place by North-cott's theory of dilatations for one-dimensional local rings (see, for example (4) and (5)). This produces a tree of local rings as in (4) which corresponds, in the abstract case, to the branching sequence of infinitely-near multiple points on an algebroid curve. From the algebraic point of view it seems more natural to characterize such one-dimensional local rings R by means of the set of rings which arise by blowing up all ideals Q which are primary for the maximal ideals M of R. This set of rings forms a lattice (R), ordered by inclusion, each ring S of which is a finite R-module. Moreover the length of the R-module S/R is just the reduction number of the corresponding ideal Q (cf. theorem 1 of Northcott (6)). Thus the lattice (R) provides a finer classification of the rings R than does the set of reduction numbers (cf. Kirby (1)).

SPIN DEPENDENCE OF THE AHARONOV—BOHM EFFECT

1991 ◽  
Vol 06 (18) ◽  
pp. 3119-3149 ◽  
Author(s):  
C.R. HAGEN
Keyword(s):  
Wave Equations ◽  
Virial Coefficient ◽  
Arbitrary Spin ◽  
Relativistic Wave Equation ◽  
Spin Dependence ◽  
Polarized Beams ◽  
Bohm Effect ◽  
Spinless Case ◽  
Aharonov Bohm ◽  
Covariant Field

The problem of the proper inclusion of spin in Aharonov—Bohm scattering is considered. It is proposed that this should be accomplished by imposing the requirement that all singularities arising from the presence of spin in the associated wave equations be interpreted as limits of physically realizable flux distributions. This leads to results which confirm the usual cross section in the spinless case but imply nontrivial modifications for the scattering of a polarized spin one-half beam. By applying the technique to a calculation of the virial coefficient for a collection of flux carrying spin one-half particles, some severe obstacles to conventional views of the flux as a parameter which interpolates between bosonic and fermionic statistics are shown to occur. Although similar results for the scattering of arbitrary spin particles obtain in the Galilean limit, it is found that when spin one is considered in the context of a relativistic wave equation the singularity structure is too pathological to yield a consistent interpretation. The exact equivalence of the spin one-half Aharonov-Bohm effect to the Aharonov-Casher effect is also demonstrated and corresponding results for polarized beams are presented. Finally, it is shown that the Aharonov-Bohm effect for arbitrary spin in the Galilean limit is the exact solution in the two-particle sector of a Galilean covariant field theory.

Research on Integration of Connection and Layout about Comprehensive Transport Hub and Corridor within Municipal Area

2014 ◽  
Vol 587-589 ◽  
pp. 1963-1966
Author(s):  
Yan Hong Li ◽  
Jian Ming Feng ◽  
Xiao Nian Sun
Keyword(s):  
Complex System ◽  
System Theory ◽  
Point Of View ◽  
Theoretical Integration ◽  
Transport Economics ◽  
Transport Organization

Based on the concept of “integrated transportation”, this paper utilizes the collaborative theory, complex system theory and transport economics theory to analyze the matching relationship between the transportation hub and corridor from a macro perspective. Meanwhile, it also explores the coordination of their transport capability, transport organization, etc., from the microscopic point of view, ultimately achieving the theoretical integration and harmonization of the connection and layout of the integrated transport hub and corridor.

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