scholarly journals Multigraph decomposition into multigraphs with two underlying edges

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Miri Priesler ◽  
Michael Tarsi
Keyword(s):  
Decision Problem ◽  
Sufficient Conditions ◽  
Simple Graph ◽  
Necessary And Sufficient Conditions ◽  
International Audience ◽  
Necessary And Sufficient ◽  
The Given

International audience Due to some intractability considerations, reasonable formulation of necessary and sufficient conditions for decomposability of a general multigraph G into a fixed connected multigraph H, is probably not feasible if the underlying simple graph of H has three or more edges. We study the case where H consists of two underlying edges. We present necessary and sufficient conditions for H-decomposability of G, which hold when certain size parameters of G lies within some bounds which depends on the multiplicities of the two edges of H. We also show this result to be "tight" in the sense that even a slight deviation of these size parameters from the given bounds results intractability of the corresponding decision problem.

scholarly journals Defect Effect of Bi-infinite Words in the Two-element Case

2001 ◽  
Vol Vol. 4 no. 2 ◽  
Author(s):  
Ján Maňuch
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Alphabet ◽  
Infinite Words ◽  
Infinite Word ◽  
The Family ◽  
International Audience ◽  
Necessary And Sufficient ◽  
Primitive Roots ◽  
Element Set

International audience Let X be a two-element set of words over a finite alphabet. If a bi-infinite word possesses two X-factorizations which are not shiftequivalent, then the primitive roots of the words in X are conjugates. Note, that this is a strict sharpening of a defect theorem for bi-infinite words stated in \emphKMP. Moreover, we prove that there is at most one bi-infinite word possessing two different X-factorizations and give a necessary and sufficient conditions on X for the existence of such a word. Finally, we prove that the family of sets X for which such a word exists is parameterizable.

scholarly journals More on the annihilator-ideal graph of a commutative ring

2019 ◽  
Vol 18 (08) ◽  
pp. 1950160
Author(s):  
M. J. Nikmehr ◽  
S. M. Hosseini
Keyword(s):  
Commutative Ring ◽  
Sufficient Conditions ◽  
Simple Graph ◽  
Necessary And Sufficient Conditions ◽  
Star Graph ◽  
Annihilator Ideal ◽  
Vertex Set ◽  
Necessary And Sufficient

Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be the set of ideals of [Formula: see text] with nonzero annihilator. The annihilator-ideal graph of [Formula: see text], denoted by [Formula: see text], is a simple graph with the vertex set [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. In this paper, we study the affinity between the annihilator-ideal graph and the annihilating-ideal graph [Formula: see text] (a well known graph with the same vertices and two distinct vertices [Formula: see text] are adjacent if and only if [Formula: see text]) associated with [Formula: see text]. All rings whose [Formula: see text] and [Formula: see text] are characterized. Among other results, we obtain necessary and sufficient conditions under which [Formula: see text] is a star graph.

scholarly journals Hypersurface Family with a Common Isoasymptotic Curve

Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ergin Bayram ◽  
Emin Kasap
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Necessary And Sufficient ◽  
The Given

We handle the problem of finding a hypersurface family from a given asymptotic curve in R4. Using the Frenet frame of the given asymptotic curve, we express the hypersurface as a linear combination of this frame and analyze the necessary and sufficient conditions for that curve to be asymptotic. We illustrate this method by presenting some examples.

Some Relationships between Filters*

1967 ◽  
Vol 10 (2) ◽  
pp. 257-260
Author(s):  
Ivan Baggs
Keyword(s):  
Sufficient Conditions ◽  
Theoretical Concept ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
The Given

A filter is a set theoretical concept and as such, its structure is independent of any topology which can be put on the given space. However, an O-filter, whose counterpart in the theory of nets is the O-nets of Robertson and Franklin [2], is defined with respect to the topology on the given space. The purpose of this paper is to give necessary and sufficient conditions for every O-filter to be an ultrafilter and for every Cauchy filter to be an O-filter.

scholarly journals The factorial moments of additive functions with rational argument

2006 ◽  
Vol 81 (3) ◽  
pp. 425-440
Author(s):  
J. Šiaulys ◽  
G. Stepanauskas
Keyword(s):  
Weak Convergence ◽  
Limit Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Additive Functions ◽  
Factorial Moments ◽  
Rational Argument ◽  
Necessary And Sufficient ◽  
The Given

AbstractWe consider the weak convergence of the set of strongly additive functions f(q) with rational argument q. It is assumed that f(p) and f(1/p) ∈ {0, 1} for all primes. We obtain necessary and sufficient conditions of the convergence to the limit distribution. The proof is based on the method of factorial moments. Sieve results, and Halász's and Ruzsa's inequalities are used. We present a few examples of application of the given results to some sets of fractions.

scholarly journals (Anti-)Hermitian Generalized (Anti-)Hamiltonian Solution to a System of Matrix Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Juan Yu ◽  
Qing-Wen Wang ◽  
Chang-Zhou Dong
Keyword(s):  
Least Squares ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Optimal Approximation ◽  
Matrix Equations ◽  
Approximation Solution ◽  
Numerical Examples ◽  
System Of Matrix Equations ◽  
Necessary And Sufficient ◽  
The Given

We mainly solve three problems. Firstly, by the decomposition of the (anti-)Hermitian generalized (anti-)Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-)Hermitian generalized (anti-)Hamiltonian solutions to the system of matrix equationsAX=B,XC=Dare derived, respectively. Secondly, the optimal approximation solutionmin⁡X∈K⁡∥X^-X∥is obtained, whereKis the (anti-)Hermitian generalized (anti-)Hamiltonian solution set of the above system andX^is the given matrix. Thirdly, the least squares (anti-)Hermitian generalized (anti-)Hamiltonian solutions are considered. In addition, algorithms about computing the least squares (anti-)Hermitian generalized (anti-)Hamiltonian solution and the corresponding numerical examples are presented.

DECOMPOSITION OF MULTIUNIVERSE FUZZY TRUTH FUNCTIONS

2001 ◽  
Vol 09 (05) ◽  
pp. 623-643
Author(s):  
DERYA ALTUNAY ◽  
TURHAN ÇİFTÇİBAŞI
Keyword(s):  
Propositional Logic ◽  
Sufficient Conditions ◽  
Fuzzy Relation ◽  
Necessary And Sufficient Conditions ◽  
Fuzzy Relations ◽  
Decomposition Problem ◽  
The Common ◽  
Necessary And Sufficient ◽  
The Given

This paper focuses on the decomposition problem of fuzzy relations using the concepts of multiuniverse fuzzy propositional logic. Given two fuzzy propositions in different universes, it is always possible to construct a fuzzy relation in the common universe through a prescribed combination. However, the converse is not so obvious, if possible at all. In other words, given a fuzzy relation, how would we know if it really represents a certain relationship between some fuzzy propositions? It is important to recognize whether the given fuzzy relation is a meaningful representation of information according to certain criteria applicable to some fuzzy propositions that constitute the fuzzy relation itself. Two basic structures of decomposition are investigated. Necessary and sufficient conditions for decomposition of multiuniverse fuzzy truth functions in terms of one-universe truth functions are presented. An algorithm for decomposition is proposed.

scholarly journals Continuous Representability of Interval Orders: The Topological Compatibility Setting

2015 ◽  
Vol 23 (03) ◽  
pp. 345-365 ◽  
Author(s):  
G. Bosi ◽  
A. Estevan ◽  
J. Gutiérrez García ◽  
E. Induráin
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Interval Order ◽  
Topological Spaces ◽  
Interval Orders ◽  
Finite Support ◽  
Order Representation ◽  
Necessary And Sufficient ◽  
The Given

In this paper, we go further on the problem of the continuous numerical representability of interval orders defined on topological spaces. A new condition of compatibility between the given topology and the indifference associated to the main trace of an interval order is introduced. Provided that this condition is fulfilled, a semiorder has a continuous interval order representation through a pair of continuous real-valued functions. Other necessary and sufficient conditions for the continuous representability of interval orders are also discussed, and, in particular, a characterization is achieved for the particular case of interval orders defined on a topological space of finite support.

Spacelike Surfaces with a Common Line of Curvature in Lorentz-Minkowski 3-Space

2021 ◽  
Vol 20 ◽  
pp. 207-217
Author(s):  
M. Khalifa Saad ◽  
Abu Zaid Ansari ◽  
M. Akram ◽  
F. Alharbi
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Spacelike Curve ◽  
Common Line ◽  
Necessary And Sufficient ◽  
Spacelike Surfaces ◽  
The Given ◽  
Line Of Curvature

This paper aims to study spacelike surfaces from a given spacelike curve in Minkowski 3–space. Also, we investigate the necessary and sufficient conditions for the given space-like curve to be the line of curvature on the space-like surface. Depending on the causal character of the curve, the necessary and sufficient conditions for the given space-like curve to satisfy the line of curvature and the geodesic (resp. asymptotic) requirements are also analyzed. Furthermore, we give with illustration some computational examples in support of our main results.

An Analysis of Undercut Conditions and of Appearance of Contact Lines Envelope Conditions of Gears

1978 ◽  
Vol 100 (3) ◽  
pp. 423-432 ◽  
Author(s):  
F. L. Litvin
Keyword(s):  
Necessary Conditions ◽  
Contact Point ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Contact Lines ◽  
Mating Surface ◽  
Worm Gears ◽  
Necessary And Sufficient ◽  
The Given ◽  
Special Case

Necessary conditions of undercutting of gears, necessary and sufficient conditions of the existence of the contact lines envelope on the generating surface are found. The conditions are studied under which the contact lines envelope appears in the vicinity of the given contact point of the generating surface with beginning of undercutting simultaneously on the mating surface. The Wildhaber-Baxter problem of the limit normal location is a special case of the theory suggested. It is proved that the appearance of a contact lines envelope on the generating surface of skew worm-gears can be avoided and meshing conditions improved.

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