scholarly journals Certain Types of Interval-Valued Fuzzy Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Akram ◽  
Noura Omair Alshehri ◽  
Wieslaw A. Dudek
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Irregular Interval ◽  
Intuitionistic Fuzzy Graphs ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Interval Valued

We propose certain types of interval-valued fuzzy graphs including balanced interval-valued fuzzy graphs, neighbourly irregular interval-valued fuzzy graphs, neighbourly total irregular interval-valued fuzzy graphs, highly irregular interval-valued fuzzy graphs, and highly total irregular interval-valued fuzzy graphs. Some interesting properties associated with these new interval-valued fuzzy graphs are investigated, and necessary and sufficient conditions under which neighbourly irregular and highly irregular interval-valued fuzzy graphs are equivalent are obtained. We also describe the relationship between intuitionistic fuzzy graphs and interval-valued fuzzy graphs.

Insensitivity and reversed Markov processes

1983 ◽  
Vol 15 (4) ◽  
pp. 752-768 ◽  
Author(s):  
W. Henderson
Keyword(s):  
Markov Processes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
The Relationship

This paper is concerned with the relationship between insensitivity in a certain class of Markov processes and properties of that process when time is reversed. Necessary and sufficient conditions for insensitivity are established and linked to already proved results. A number of examples of insensitive systems are given.

Semicritical Rings and the Quotient Problem

1984 ◽  
Vol 27 (2) ◽  
pp. 160-170
Author(s):  
Karl A. Kosler
Keyword(s):  
Quotient Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Prime Ideals ◽  
Regular Elements ◽  
The Right ◽  
Minimal Prime ◽  
Necessary And Sufficient ◽  
Quotient Rings ◽  
The Relationship

AbstractThe purpose of this paper is to examine the relationship between the quotient problem for right noetherian nonsingular rings and the quotient problem for semicritical rings. It is shown that a right noetherian nonsingular ring R has an artinian classical quotient ring iff certain semicritical factor rings R/Ki, i = 1,…,n, possess artinian classical quotient rings and regular elements in R/Ki lift to regular elements of R for all i. If R is a two sided noetherian nonsingular ring, then the existence of an artinian classical quotient ring is equivalent to each R/Ki possessing an artinian classical quotient ring and the right Krull primes of R consisting of minimal prime ideals. If R is also weakly right ideal invariant, then the former condition is redundant. Necessary and sufficient conditions are found for a nonsingular semicritical ring to have an artinian classical quotient ring.

scholarly journals The Q0-matrix completion problem

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kalyan Sinha
Keyword(s):  
Matrix Completion ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
Necessary And Sufficient ◽  
The Relationship

A matrix is a Q0-matrix if for every k∈{1,2,…,n}, the sum of all k×k principal minors is nonnegative. In this paper, we study some necessary and sufficient conditions for a digraph to have Q0-completion. Later on we discuss the relationship between Q and Q0-matrix completion problem. Finally, a classification of the digraphs of order up to four is done based on Q0-completion.

Insensitivity and reversed Markov processes

1983 ◽  
Vol 15 (04) ◽  
pp. 752-768 ◽  
Author(s):  
W. Henderson
Keyword(s):  
Markov Processes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
The Relationship

This paper is concerned with the relationship between insensitivity in a certain class of Markov processes and properties of that process when time is reversed. Necessary and sufficient conditions for insensitivity are established and linked to already proved results. A number of examples of insensitive systems are given.

scholarly journals Process tree-based analysis method of DECLARE relation constraints in acyclic bridge-less well-structured workflow nets

2019 ◽  
Vol 13 (2) ◽  
pp. 104-111
Author(s):  
Shingo Yamaguchi ◽  
Mohd Anuaruddin Bin Ahmadon
Keyword(s):  
Polynomial Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Analysis Method ◽  
Declarative Language ◽  
Tree Representation ◽  
Workflow Nets ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Process Tree

In this paper, we proposed a method to analyze workflows’ constraints whose templates are defined in a declarative language called DECLARE. Checking such constraints is important but known to be intractable in general. Our results show three things. First, utilizing a tree representation of workflow process called {\it process tree}, we provided necessary and sufficient conditions on the constraints. Second, those conditions enable us to not only check a given constraint in polynomial time but also find a clue for improving the net if it violates the constraint. Third, we revealed the relationship among the constraint templates.

Magic labeling on interval-valued intuitionistic fuzzy graphs

2017 ◽  
Vol 33 (6) ◽  
pp. 3999-4006 ◽  
Author(s):  
P.K. Kishore Kumar ◽  
S. Lavanya ◽  
Hossein Rashmanlou ◽  
Mostafa Nouri Jouybari
Keyword(s):  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs ◽  
Interval Valued

On the representation of analytic functions by infinite series

1953 ◽  
Vol 245 (900) ◽  
pp. 429-468 ◽  
Keyword(s):  
General Theory ◽  
Infinite Series ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Methods ◽  
Basic Series ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Product Sets

Given a set of functions {p k {z)}, necessary and sufficient conditions are known under which the basic series ∑ (k=0) ∞ II k f (0)p k (z) will represent all functions f ( z ) in certain classes. The various cases are included in a general theory given in part II. Questions of uniqueness are discussed, and an attempt is made to initiate a theory of representation by series of the form ∑ (k=0) ∞ α k p k (z) which are not necessarily basic. Topological methods are used, and part I is devoted largely to preliminaries. In part III is discussed the relationship between given sets and various associated sets such as the inverse and product sets.

scholarly journals Demand functions and demand manifolds

2021 ◽  
Author(s):  
Alan Beggs
Keyword(s):  
Demand Function ◽  
Firm Behavior ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Static Properties ◽  
Demand Functions ◽  
Necessary And Sufficient ◽  
The Relationship

AbstractMrázová and Neary (2017) introduce the notion of the Demand Manifold which expresses the relationship between the elasticity and curvature of a demand function. They argue that this determines many important comparative static properties of firm behavior. This paper gives necessary and sufficient conditions for two demand functions to have the same demand manifold and so to have similar comparative static properties.

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