Some Relationships between Filters*

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.

Hypersurface Family with a Common Isoasymptotic Curve

Geometry ◽

10.1155/2014/623408 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Ergin Bayram ◽

Emin Kasap

Keyword(s):

Linear Combination ◽

Sufficient Conditions ◽

Frenet Frame ◽

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.

The factorial moments of additive functions with rational argument

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700014403 ◽

2006 ◽

Vol 81 (3) ◽

pp. 425-440

Author(s):

J. Šiaulys ◽

G. Stepanauskas

Keyword(s):

Weak Convergence ◽

Limit Distribution ◽

Sufficient Conditions ◽

Additive Functions ◽

Factorial Moments ◽

Rational Argument ◽

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.

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

Mathematical Problems in Engineering ◽

10.1155/2014/539215 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Juan Yu ◽

Qing-Wen Wang ◽

Chang-Zhou Dong

Keyword(s):

Least Squares ◽

Sufficient Conditions ◽

Optimal Approximation ◽

Matrix Equations ◽

Approximation Solution ◽

Numerical Examples ◽

System Of Matrix Equations ◽

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

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488501001095 ◽

2001 ◽

Vol 09 (05) ◽

pp. 623-643

Author(s):

DERYA ALTUNAY ◽

TURHAN ÇİFTÇİBAŞI

Keyword(s):

Propositional Logic ◽

Sufficient Conditions ◽

Fuzzy Relation ◽

Fuzzy Relations ◽

Decomposition Problem ◽

The Common ◽

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.

Continuous Representability of Interval Orders: The Topological Compatibility Setting

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488515500142 ◽

2015 ◽

Vol 23 (03) ◽

pp. 345-365 ◽

Cited By ~ 10

Author(s):

G. Bosi ◽

A. Estevan ◽

J. Gutiérrez García ◽

E. Induráin

Keyword(s):

Topological Space ◽

Sufficient Conditions ◽

Interval Order ◽

Topological Spaces ◽

Interval Orders ◽

Finite Support ◽

Order Representation ◽

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

WSEAS TRANSACTIONS ON MATHEMATICS ◽

10.37394/23206.2021.20.22 ◽

2021 ◽

Vol 20 ◽

pp. 207-217

Author(s):

M. Khalifa Saad ◽

Abu Zaid Ansari ◽

M. Akram ◽

F. Alharbi

Keyword(s):

Sufficient Conditions ◽

Spacelike Curve ◽

Common Line ◽

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

Journal of Mechanical Design ◽

10.1115/1.3453946 ◽

1978 ◽

Vol 100 (3) ◽

pp. 423-432 ◽

Cited By ~ 3

Author(s):

F. L. Litvin

Keyword(s):

Necessary Conditions ◽

Contact Point ◽

Sufficient Conditions ◽

Contact Lines ◽

Mating Surface ◽

Worm Gears ◽

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.

THE RIEMANN HOMOGENEOUS BOUNDARY VALUE PROBLEM IN THE CLASS OF ANALYTIC FUNCTIONS WITH THE GIVEN INDICATOR UNDER THE ENTIRE ORDER

Mathematical Modelling and Analysis ◽

10.3846/13926292.1998.9637081 ◽

1998 ◽

Vol 3 (1) ◽

pp. 7-13

Author(s):

A. G. Alehno

Keyword(s):

Boundary Value Problem ◽

Analytic Functions ◽

Boundary Value ◽

Sufficient Conditions ◽

The Riemann homogeneous boundary value problem is investigated in the class of piecewise analytic functions. The necessary and sufficient conditions are obtained for the existence of the solution.

Necessary and Sufficient Conditions for Group Consensus of Agents With Third-Order Dynamics in Directed Networks

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4045779 ◽

2020 ◽

Vol 142 (4) ◽

Author(s):

Onur Cihan ◽

Mehmet Akar

Keyword(s):

Directed Graph ◽

Sufficient Conditions ◽

Group Consensus ◽

Directed Networks ◽

Third Order ◽

Systematic Method ◽

The Given ◽

Theoretical Results

Abstract In this paper, we investigate the group consensus problem in directed networks where agents have third-order dynamics. Necessary and sufficient conditions on the controller parameters are obtained to ensure K-equilibria group consensus where K is determined by the structure of the directed graph. It is theoretically shown that, for an arbitrary directed graph, there exist controller parameters that satisfy the given conditions. A systematic method for choosing the controller parameters to guarantee group consensus is suggested and theoretical results are verified by numerical examples.

On the Existence of Mayer’s Potential

Journal of Applied Mechanics ◽

10.1115/1.2788936 ◽

1997 ◽

Vol 64 (3) ◽

pp. 606-612 ◽

Cited By ~ 1

Author(s):

V. M. Cˇovic´ ◽

M. M. Lukacˇevic´

Keyword(s):

Dynamical Systems ◽

Complete Solution ◽

Sufficient Conditions ◽

Hamilton’S Principle ◽

Hamilton's Principle ◽

Nonconservative Systems ◽

The Given ◽

Special Case

A complete solution of the well-known Mayer’s problem, which is concerned with the possibility of extending Hamilton’s principle expressed in the form valid for conservative dynamical systems to one special case of nonconservative systems (Appell, 1911), is obtained. Namely, the necessary and sufficient conditions which have to be satisfied by the coefficients of the given nonconservative generalized forces so that the Mayer’s potential (and, as a consequence, the descriptive function of the system) can be constructed, are established. This result is illustrated by an example.