Search results for "Numerical"

Complexity of gauge bounded Cartier algebras

2019

We show that a gauge bounded Cartier algebra has finite complexity. We also give an example showing that the converse does not hold in general.Communicated by Graham J. Leuschke

Elementary hypergeometric functions, Heun functions, and moments of MKZ operators

2019

We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementary functions. The higher order moments of these operators are expressed in terms of elementary functions and polylogarithms. Other applications are concerned with the expansion of certain Heun functions in series or finite sums of elementary hypergeometric functions.

Indefinite integrals of quotients of Gauss hypergeometric functions

2018

A method recently applied to obtain indefinite integrals involving quotients of some common special functions is applied to obtain indefinite integrals of some quotients of Gauss hypergeometric fun...

Indefinite integrals of quotients of special functions

2018

ABSTRACTA new method is presented for deriving indefinite integrals involving quotients of special functions. The method combines an integration formula given previously with the recursion relations obeyed by the function. Some additional results are presented using an elementary method, here called reciprocation, which can also be used in combination with the new method to obtain additional quotient integrals. Sample results are given here for Bessel functions, Airy functions, associated Legendre functions and the three complete elliptic integrals. All results given have been numerically checked with Mathematica.

On a class of compactly epi-Lipschitzian sets

2003

The paper is devoted to the study of the so-called compactly epi-Lipschitzian sets. These sets are needed for many aspects of generalized differentiation, particulary for necessary optimality conditions, stability of mathematical programming problems and calculus rules for subdifferentials and normal cones. We present general conditions under which sets defined by general constraints are compactly epi-Lipschitzian. This allows us to show how the compact epi-Lipschitzness properties behave under set intersections.

Further results on generalized centro-invertible matrices

2019

[EN] This paper deals with generalized centro-invertible matrices introduced by the authors in Lebtahi et al. (Appl. Math. Lett. 38, 106¿109, 2014). As a first result, we state the coordinability between the classes of involutory matrices, generalized centro-invertible matrices, and {K}-centrosymmetric matrices. Then, some characterizations of generalized centro-invertible matrices are obtained. A spectral study of generalized centro-invertible matrices is given. In addition, we prove that the sign of a generalized centro-invertible matrix is {K}-centrosymmetric and that the class of generalized centro-invertible matrices is closed under the matrix sign function. Finally, some algorithms ha…

Compactness and $s$-numbers for polynomials

2018

Positive linear maps on normal matrices

2018

For a positive linear map [Formula: see text] and a normal matrix [Formula: see text], we show that [Formula: see text] is bounded by some simple linear combinations in the unitary orbit of [Formula: see text]. Several elegant sharp inequalities are derived, for instance for the Schur product of two normal matrices [Formula: see text], [Formula: see text] for some unitary [Formula: see text], where the constant [Formula: see text] is optimal.

Abelian Gradings on Upper Block Triangular Matrices

2012

AbstractLet G be an arbitrary finite abelian group. We describe all possible G-gradings on upper block triangular matrix algebras over an algebraically closed field of characteristic zero.

Special elements in a ring related to Drazin inverses

2013

In this paper, the existence of the Drazin (group) inverse of an element a in a ring is analyzed when amk = kan, for some unit k and m; n 2 N. The same problem is studied for the case when a* = kamk-1 and for the fk; s+1g-potent elements. In addition, relationships with other special elements of the ring are also obtained