Hypersurface Family with a Common Isoasymptotic Curve

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.

A Note on Parametric Surfaces in Minkowski 3-Space

The Scientific World JOURNAL ◽

10.1155/2014/618340 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6

Author(s):

Esra Betul Koc Ozturk

Keyword(s):

Linear Combination ◽

Sufficient Conditions ◽

Ruled Surface ◽

Frenet Frame ◽

Parametric Surface ◽

Parametric Surfaces ◽

Null Curve ◽

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some interesting examples are illustrated about these surfaces.

Surfaces family with common Smarandache asymptotic curve

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v34i1.24392 ◽

2016 ◽

Vol 34 (1) ◽

pp. 9-20

Author(s):

Gulnur Saffak Atalay ◽

Emin Kasap

Keyword(s):

Linear Combination ◽

Sufficient Conditions ◽

Frenet Frame ◽

The Family ◽

In this paper, we analyzed the problem of constructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficients to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache curve.

On the Construction of a Surface Family with Common Geodesic in Galilean Space G3

Open Physics ◽

10.1515/phys-2016-0041 ◽

2016 ◽

Vol 14 (1) ◽

pp. 360-363 ◽

Cited By ~ 3

Author(s):

Zühal Küçükarslan Yüzbaşı ◽

Mehmet Bektaş

Keyword(s):

Sufficient Conditions ◽

Parametric Representation ◽

Geodesic Curve ◽

Frenet Frame ◽

Parametric Surfaces ◽

Galilean Space ◽

AbstractIn this paper, we investigate the parametric representation for a family of surfaces through a given geodesic curve G3. We provide necessary and sufficient conditions for this curve to be an isogeodesic curve on the parametric surfaces using Frenet frame in Galilean space. Also, for the sake of visualizing of this study, we plot an example for this surfaces family.

Injectivity of linear combinations in $\mathcal{B}(\mathcal{H})$

Electronic Journal of Linear Algebra ◽

10.13001/ela.2021.5049 ◽

2021 ◽

Vol 37 ◽

pp. 359-369

Author(s):

Marko Kostadinov

Keyword(s):

Linear Combination ◽

Necessary Conditions ◽

Sufficient Conditions ◽

Linear Combinations ◽

Special Cases ◽

Sufficient And Necessary Conditions ◽

Alpha Beta ◽

The aim of this paper is to provide sufficient and necessary conditions under which the linear combination $\alpha A + \beta B$, for given operators $A,B \in {\cal B}({\cal H})$ and $\alpha, \beta \in \mathbb{C}\setminus \lbrace 0 \rbrace$, is injective. Using these results, necessary and sufficient conditions for left (right) invertibility are given. Some special cases will be studied as well.

Linear combinations of polynomials with three-term recurrence

Publications de l Institut Mathematique ◽

10.2298/pim2124029t ◽

2021 ◽

Vol 110 (124) ◽

pp. 29-40

Author(s):

Khang Tran ◽

Maverick Zhang

Keyword(s):

Linear Combination ◽

Chebyshev Polynomials ◽

Sufficient Conditions ◽

Linear Combinations ◽

Zero Distribution ◽

Linear Polynomials

We study the zero distribution of the sum of the first n polynomials satisfying a three-term recurrence whose coefficients are linear polynomials. We also extend this sum to a linear combination, whose coefficients are powers of az + b for a, b ? R, of Chebyshev polynomials. In particular, we find necessary and sufficient conditions on a, b such that this linear combination is hyperbolic.

Some Relationships between Filters*

Canadian Mathematical Bulletin ◽

10.4153/cmb-1967-025-4 ◽

1967 ◽

Vol 10 (2) ◽

pp. 257-260

Author(s):

Ivan Baggs

Keyword(s):

Sufficient Conditions ◽

Theoretical Concept ◽

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.

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.

On a Certain Subclass of Analytic Functions Involving Integral Operator Defined by Polylogarithm Function

Mathematics ◽

10.3390/math7010066 ◽

2019 ◽

Vol 7 (1) ◽

pp. 66

Author(s):

Danyal Soybaş ◽

Santosh B. Joshi ◽

Haridas Pawar

Keyword(s):

Integral Operator ◽

Linear Combination ◽

Analytic Functions ◽

Sufficient Conditions ◽

Distortion Theorem ◽

Partial Sums ◽

Polylogarithm Function ◽

In the present paper, we have introduced a new subclass of analytic functions involving integral operator defined by polylogarithm function. Necessary and sufficient conditions are obtained for this class. Further distortion theorem, linear combination and results on partial sums are investigated.