scholarly journals On Refined Neutrosophic Matrices and Their Application in Refined Neutrosophic Algebraic Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Mohammad Abobala
Keyword(s):  
Sufficient Condition ◽  
Algebraic Equations ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The objective of this paper is to introduce the concept of refined neutrosophic matrices as matrices such as multiplication, addition, and ring property. Also, it determines the necessary and sufficient condition for the invertibility of these matrices with respect to multiplication. On the contrary, nilpotency and idempotency properties will be discussed.

A birth, death and migration process by immigration

1975 ◽  
Vol 7 (01) ◽  
pp. 44-60
Author(s):  
M. Aksland
Keyword(s):  
Sufficient Condition ◽  
Algebraic Equations ◽  
Necessary And Sufficient Condition ◽  
Migration Process ◽  
Immigration Process ◽  
Special Cases ◽  
And Migration ◽  
Necessary And Sufficient ◽  
Sequence Of Functions ◽  
Birth Death

A finite number of colonies, each subject to a simple birth-death and immigration process is studied under the condition of migration between the colonies. Kolmogorov's backward equations for the process are solved for some special cases, and a sequence of functions uniformly converging to the p.g.f. of the process is given for the general case. Further, a set of algebraic equations for the extinction probabilities are studied for the process without immigration, and a necessary and sufficient condition that the extinction probability be one is obtained.

scholarly journals Solutionally complete varieties

1979 ◽  
Vol 28 (1) ◽  
pp. 82-86 ◽  
Author(s):  
Harald Hule
Keyword(s):  
Amalgamation Property ◽  
Subject Classification ◽  
Sufficient Condition ◽  
Algebraic Equations ◽  
Necessary And Sufficient Condition ◽  
Solvable System ◽  
Necessary And Sufficient

AbstractA veristy is called solutionally complete if any solvable system of algebraic equations over an algebra A in which has at most one solution in every extension of A in has the solution in A. A necessary and sufficient condition for solutional completeness is given which is a weaker form of the strong amalgamation property.Subject classification (Amer. Math. Soc. (MOS) 1970): 08 A 15.

A birth, death and migration process by immigration

1975 ◽  
Vol 7 (1) ◽  
pp. 44-60 ◽  
Author(s):  
M. Aksland
Keyword(s):  
Sufficient Condition ◽  
Algebraic Equations ◽  
Necessary And Sufficient Condition ◽  
Migration Process ◽  
Immigration Process ◽  
Special Cases ◽  
And Migration ◽  
Necessary And Sufficient ◽  
Sequence Of Functions ◽  
Birth Death

A finite number of colonies, each subject to a simple birth-death and immigration process is studied under the condition of migration between the colonies.Kolmogorov's backward equations for the process are solved for some special cases, and a sequence of functions uniformly converging to the p.g.f. of the process is given for the general case. Further, a set of algebraic equations for the extinction probabilities are studied for the process without immigration, and a necessary and sufficient condition that the extinction probability be one is obtained.

scholarly journals On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohammad Abobala
Keyword(s):  
Linear Equations ◽  
Direct Application ◽  
Sufficient Condition ◽  
Algebraic Equations ◽  
Necessary And Sufficient Condition ◽  
Algebraic Properties ◽  
Invertible Elements ◽  
Necessary And Sufficient

This paper studies the problem of determining invertible elements (units) in any n-refined neutrosophic ring. It presents the necessary and sufficient condition for any n-refined neutrosophic element to be invertible, idempotent, and nilpotent. Also, this work introduces some of the elementary algebraic properties of n-refined neutrosophic matrices with a direct application in solving n-refined neutrosophic algebraic equations.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

Sign in / Sign up

Export Citation Format

Share Document