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

Algebraic Properties ◽

Invertible Elements ◽

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 class of sub-almost distributive lattices in an associate almost distributive lattice through a filter

Asian-European Journal of Mathematics ◽

10.1142/s1793557120501363 ◽

2019 ◽

Vol 13 (07) ◽

pp. 2050136

Author(s):

S. Ramesh ◽

Jogarao Gunda

Keyword(s):

Boolean Algebra ◽

Distributive Lattice ◽

Distributive Lattices ◽

Sufficient Condition ◽

Algebraic Properties ◽

In this paper, we introduce a class of sub-almost distributive lattices in an associate almost distributive lattice through a filter. We obtain several algebraic properties on the class of sub-almost distributive lattices and prove that the above class forms a distributive lattice. We derive a necessary and sufficient condition that the class to become a Boolean algebra.

A birth, death and migration process by immigration

Advances in Applied Probability ◽

10.1017/s0001867800040283 ◽

1975 ◽

Vol 7 (01) ◽

pp. 44-60

Author(s):

M. Aksland

Keyword(s):

Sufficient Condition ◽

Algebraic Equations ◽

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.

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

Journal of Mathematics ◽

10.1155/2021/5531093 ◽

2021 ◽

Vol 2021 ◽

pp. 1-5

Author(s):

Mohammad Abobala

Keyword(s):

Sufficient Condition ◽

Algebraic Equations ◽

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.

Solutionally complete varieties

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700014944 ◽

1979 ◽

Vol 28 (1) ◽

pp. 82-86 ◽

Cited By ~ 1

Author(s):

Harald Hule

Keyword(s):

Amalgamation Property ◽

Subject Classification ◽

Sufficient Condition ◽

Algebraic Equations ◽

Solvable System ◽

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

Advances in Applied Probability ◽

10.2307/1425852 ◽

1975 ◽

Vol 7 (1) ◽

pp. 44-60 ◽

Cited By ~ 10

Author(s):

M. Aksland

Keyword(s):

Sufficient Condition ◽

Algebraic Equations ◽

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.

Positive Solutions for Neutral Difference Equations with Continuous Arguments

Georgian Mathematical Journal ◽

10.1515/gmj.2007.699 ◽

2007 ◽

Vol 14 (4) ◽

pp. 699-710

Author(s):

Xianyi Li

Keyword(s):

Asymptotic Behavior ◽

Positive Solutions ◽

Comparison Principle ◽

Difference Equations ◽

Linear Equations ◽

Sufficient Condition ◽

Neutral Difference Equations ◽

Abstract Some “sharp” conditions are established for a kind of linear neutral difference equations with continuous arguments not to possess eventually positive solutions. The existence and asymptotic behavior are obtained for positive solutions of the kind of equations. The results for linear cases are further extended to nonlinear ones. A comparison principle, which is a necessary and sufficient condition, for linear equations not to possess eventually positive solutions is also presented.

A necessary and sufficient condition for nonoscillatory behavior of the solutions of a system of two linear equations of the first order

Mathematical Notes ◽

10.1007/bf01105581 ◽

1974 ◽

Vol 16 (2) ◽

pp. 742-746 ◽

Cited By ~ 1

Author(s):

I. V. Kamenev

Keyword(s):

Linear Equations ◽

Sufficient Condition ◽

First Order ◽

A class of Lie racks associated to symmetric Leibniz algebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498822502309 ◽

2021 ◽

pp. 2250230 ◽

Cited By ~ 1

Author(s):

Hamid Abchir ◽

Fatima-ezzahrae Abid ◽

Mohamed Boucetta

Keyword(s):

Sufficient Condition ◽

Leibniz Algebras ◽

Algebraic Properties ◽

We classify symmetric Leibniz algebras in dimensions 3 and 4 and we determine all associated Lie racks. Some of such Lie racks give rise to nontrivial topological quandles. We study some algebraic properties of these quandles and we give a necessary and sufficient condition for them to be quasi-trivial.

Multidimensional Iterative Interpolation

Canadian Journal of Mathematics ◽

10.4153/cjm-1991-016-4 ◽

1991 ◽

Vol 43 (2) ◽

pp. 297-312 ◽

Cited By ~ 27

Author(s):

Gilles Deslauriers ◽

Jacques Dubois ◽

Serge Dubuc

Keyword(s):

Euclidean Space ◽

Discrete Subgroup ◽

Interpolation Process ◽

Sufficient Condition ◽

Interpolation Function ◽

Schwartz Distributions ◽

Algebraic Properties ◽

Iterative Interpolation ◽

AbstractWe define an iterative interpolation process for data spread over a closed discrete subgroup of the Euclidean space. We describe the main algebraic properties of this process. This interpolation process, under very weak assumptions, is always convergent in the sense of Schwartz distributions. We find also a convenient necessary and sufficient condition for continuity of each interpolation function of a given iterative interpolation process.