scholarly journals Support Neighbourly Edge Irregular Graphs

2019 ◽  
Vol 8 (3) ◽  
pp. 5329-5332
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Basic Properties ◽  
New Family ◽  
Necessary And Sufficient ◽  
Irregular Graphs

In this paper, we introduce a new family of irregular graphs called support neighbourly edge irregular graphs based on degree in edge sense. In any graph, the support of an edge is the sum of the edge degrees of its neighbours. A graph is said to be support neighbourly edge irregular(or simply SNEI), if any two adjacent edges have different support. Basic properties of theses graphs are studied. A necessary and sufficient condition for a graph to be SNEI has been obtained and several methods to construct SNEI graph from other graphs have been discussed.

Comaximal factorization of lifting ideals

2020 ◽  
pp. 2250044
Author(s):  
Esmaeil Rostami ◽  
Sina Hedayat ◽  
Reza Nekooei ◽  
Somayeh Karimzadeh
Keyword(s):  
Commutative Ring ◽  
Proper Ideal ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
New Approach ◽  
Ideal Formula ◽  
Basic Properties ◽  
Necessary And Sufficient

A proper ideal [Formula: see text] of a commutative ring [Formula: see text] is called lifting whenever idempotents of [Formula: see text] lift to idempotents of [Formula: see text]. In this paper, many of the basic properties of lifting ideals are studied and we prove and extend some well-known results concerning lifting ideals and lifting idempotents by a new approach. Furthermore, we give a necessary and sufficient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal lifting ideals.

Properties of bisect-diagonal quadrilaterals

2017 ◽  
Vol 101 (551) ◽  
pp. 214-226 ◽  
Author(s):  
Martin Josefsson
Keyword(s):  
General Class ◽  
The Other ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Basic Properties ◽  
Necessary And Sufficient

The general class of quadrilaterals where one diagonal is bisected by the other diagonal has appeared very rarely in the geometrical literature, but they have been named several times in connection with quadrilateral classifications. Günter Graumann strangely gave these objects two different names in [1, pp. 192, 194]: sloping-kite and sliding-kite. A. Ramachandran called them slant kites in [2, p. 54] and Michael de Villiers called them bisecting quadrilaterals in [3, pp. 19, 206]. The latter is a pretty good name, although a bit confusing: what exactly is bisected?We have found no papers and only two books where any theorems on such quadrilaterals are studied. In each of the books, one necessary and sufficient condition for such quadrilaterals is proved (see Theorem 1 and 2 in the next section). The purpose of this paper is to investigate basic properties ofconvexbisecting quadrilaterals, but we have chosen to give them a slightly different name. Let us first remind the reader that a quadrilateral whose diagonals have equal lengths is called an equidiagonal quadrilateral and one whose diagonals are perpendicular is called an orthodiagonal quadrilateral.

scholarly journals Friezes and continuant polynomials with parameters

2018 ◽  
Vol 36 (2) ◽  
pp. 57-81
Author(s):  
Véronique Bazier-Matte ◽  
David Racicot-Desloges ◽  
Tanna Sánchez McMillan
Keyword(s):  
Finite Type ◽  
Type A ◽  
Cluster Algebras ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
New Family ◽  
Laurent Phenomenon ◽  
Necessary And Sufficient ◽  
Positive Integers

Frieze patterns (in the sense of Conway and Coxeter) are related to cluster algebras of type A and to signed continuant polynomials. In view of studying certain classes of cluster algebras with coefficients, we extend the concept of signed continuant polynomial to define a new family of friezes, called c-friezes, which generalises frieze patterns. Having in mind the cluster algebras of finite type, we identify a necessary and sufficient condition for obtaining periodic c-friezes. Taking into account the Laurent phenomenon and the positivity conjecture, we present ways of generating c-friezes of integers and of positive integers. We also show some specific properties of c-friezes.

scholarly journals a*-families of analytic functions

1984 ◽  
Vol 7 (3) ◽  
pp. 435-442 ◽  
Author(s):  
G. P. Kapoor ◽  
A. K. Mishra
Keyword(s):  
Analytic Function ◽  
Taylor Series ◽  
Analytic Functions ◽  
Extreme Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
New Family ◽  
Symmetric Points ◽  
Necessary And Sufficient

Using convolutions, a new family of analytic functions is introduced. This family, calleda*-family, serves in certain situations to unify the study of many previously well known classes of analytic functions like multivalent convex, starlike, close-to-convex or prestarlike functions, functions starlike with respect to symmetric points and other such classes related to the class of univalent or multivalent functions. A necessary and sufficient condition on the Taylor series coefficients so that an analytic function with negative coefficients is in ana*-family is obtained and sharp coefficents bound for functions in such a family is deduced. The extreme points of ana*-family of functions with negative coefficients are completely determined. Finally, it is shown that Zmorvic conjecture is true if the concerned families consist of functions with negative coefficients.

Hecke **-algebras on locally compact hypergroups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Seyyed Mohammad Tabatabaie ◽  
Bentolhoda Sadathoseyni
Keyword(s):  
Compact Group ◽  
Hecke Algebras ◽  
Locally Compact Group ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Basic Properties ◽  
Necessary And Sufficient

AbstractIn this paper, for a discrete hypergroup K and its subhypergroup H, we initiate the related Hecke {*}-algebra which is an extension of the classical one, and study its basic properties. Especially, we give a necessary and sufficient condition (named (β)) for this algebra to be associative. Also, we show that this new structure is an associative {*}-algebra if and only if K is a locally compact group.

scholarly journals Optimization of the reducible objective functions with monotone factors subject to FRI constraints defined with continuous t-norms

2018 ◽  
pp. 1-19
Keyword(s):  
Objective Function ◽  
Special Kind ◽  
Sufficient Condition ◽  
Objective Functions ◽  
Necessary And Sufficient Condition ◽  
Basic Properties ◽  
Binary Operator ◽  
Necessary And Sufficient ◽  
Decreasing Functions

In this paper, we investigate a special kind of optimization with fuzzy relational inequalities constraints where a continuous t-norm is considered as the fuzzy composition and the objective function can be expressed as in which and are increasing and decreasing functions, respectively, and is a commutative and monotone binary operator. Some basic properties have been extended a necessary and sufficient condition is presented to realize the feasibility of the problem. Also, an algorithm is given to optimize the objective function on the region of the FRI constraints. Finally, five examples are appended with two continuous t-norms, Lukasiewicz and Yager, and different objective functions, for illustrating.

(G) Fuzzy Integral on Fuzzy Set

2014 ◽  
Vol 926-930 ◽  
pp. 2863-2866
Author(s):  
Gui Ling Li
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Convergence Theorem ◽  
Fuzzy Integral ◽  
Monotone Convergence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Basic Properties ◽  
Monotone Convergence Theorem ◽  
Necessary And Sufficient

In this paper, the concept of (G) fuzzy integral on a fuzzy set is given and the basic properties of it are discussed. Monotone Convergence Theorem and Fatou Lemma are proved. Finally, A necessary and sufficient condition on which (G) fuzzy integrals of two fuzzy measurable functions on fuzzy sets are always equal is given.

scholarly journals Pseudo-distributive near-rings

1975 ◽  
Vol 12 (3) ◽  
pp. 449-456 ◽  
Author(s):  
Henry E. Heatherly ◽  
Steve Ligh
Keyword(s):  
Group Rings ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Matrix Rings ◽  
Basic Properties ◽  
Necessary And Sufficient

In the study of the theory of rings, matrix rings, group rings, algebras, and so on, play a very important role. However, the analogous systems may not exist in the theory of near-rings. Recently Ligh obtained a necessary and sufficient condition for the set of n × n matrices with entries from a near-ring to be a near-ring. This opens the door for the study of other structures such as group near-rings, algebras, and so on. In this paper we initiate a study of the basic properties of pseudo-distributive near-rings, which is exactly the class of near-rings needed to carry out the construction of matrix near-rings, group near-rings, polynomials with near-ring coefficients, and so on.

scholarly journals Optimization of the reducible objective functions with monotone factors subject to FRI constraints defined with continuous t-norms

2018 ◽  
pp. 1-19 ◽  
Keyword(s):  
Objective Function ◽  
Special Kind ◽  
Sufficient Condition ◽  
Objective Functions ◽  
Necessary And Sufficient Condition ◽  
Basic Properties ◽  
Binary Operator ◽  
Necessary And Sufficient ◽  
Decreasing Functions

In this paper, we investigate a special kind of optimization with fuzzy relational inequalities constraints where a continuous t-norm is considered as the fuzzy composition and the objective function can be expressed as in which and are increasing and decreasing functions, respectively, and is a commutative and monotone binary operator. Some basic properties have been extended a necessary and sufficient condition is presented to realize the feasibility of the problem. Also, an algorithm is given to optimize the objective function on the region of the FRI constraints. Finally, five examples are appended with two continuous t-norms, Lukasiewicz and Yager, and different objective functions, for illustrating.

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