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.

scholarly journals C*-ALGEBRAS THAT ARE ISOMORPHIC AFTER TENSORING AND FULL PROJECTIONS

2004 ◽  
Vol 47 (3) ◽  
pp. 659-668
Author(s):  
Kazunori Kodaka
Keyword(s):  
Matrix Algebra ◽  
Subject Classification ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Primary 46L05 ◽  
C Algebra ◽  
C Algebras ◽  
Necessary And Sufficient

AbstractLet $A$ be a unital $C^*$-algebra and for each $n\in\mathbb{N}$ let $M_n$ be the $n\times n$ matrix algebra over $\mathbb{C}$. In this paper we shall give a necessary and sufficient condition that there is a unital $C^*$-algebra $B$ satisfying $A\not\cong B$ but for which $A\otimes M_n\cong B\otimes M_n$ for some $n\in\mathbb{N}\setminus\{1\}$. Also, we shall give some examples of unital $C^*$-algebras satisfying the above property.AMS 2000 Mathematics subject classification: Primary 46L05

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 HILBERT MODULAR PSEUDODIFFERENTIAL OPERATORS OF MIXED WEIGHT

2003 ◽  
Vol 46 (2) ◽  
pp. 269-277 ◽  
Author(s):  
Min Ho Lee ◽  
Hyo Chul Myung
Keyword(s):  
Pseudodifferential Operator ◽  
Modular Forms ◽  
Pseudodifferential Operators ◽  
Discrete Subgroup ◽  
Subject Classification ◽  
Sufficient Condition ◽  
Hilbert Modular Forms ◽  
Necessary And Sufficient Condition ◽  
Hilbert Modular ◽  
Necessary And Sufficient

AbstractWe introduce an action of a discrete subgroup $\varGamma$ of $SL(2,\mathbb{R})^n$ on the space of pseudodifferential operators of $n$ variables, and construct a map from the space of Hilbert modular forms for $\varGamma$ to the space of pseudodifferential operators invariant under such a $\varGamma$-action, which is a lifting of the symbol map of pseudodifferential operators. We also obtain a necessary and sufficient condition for a certain type of pseudodifferential operator to be $\varGamma$-invariant.AMS 2000 Mathematics subject classification: Primary 11F41; 35S05

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 (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.

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