We dedicate this work to the memory of a great mathematician-Abstract The concepts of regular generalized functions in Gaussian analysis are presented. Spaces of regular generalized functions are characterized and equipped with an innnite dimensional calculus. Finally, these concepts are applied in the theory of stochastic (partial) diier-ential equations of Wick type and a generalized Clark-Oc...

In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the generalized order-k Pell numbers.

In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (0F1) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these 0F1 functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arb...

We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with ?-coefficients). This complements Filipazzi’s with connected fibres. It is then applied to obtain subadjunction log centers pairs. As another application, we show that image an anti-nef pair has structure numerically trivial pair. readily implies result Chen–Zhang. Along way Shokurov t...

A strong convergence theorem for the common zero for a finite family of Generalized Lipschitz operators in a uniformly smooth Banach space is proved when atleast one of the operator is Generalized Φaccretive, using a new iteration formula. Similar result for Generalized Lipschitz and Generalized Φpseudocontractive map is also proved. Our result extends the convergence results of Chidume [4] to ...

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several generalizations of formula for generalized functions polynomials. As a consequence, give new addition an integral representation these Finally, introduce family Lebesgue spaces show that some special belong to them.

Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

Abstract Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two alternative formulas to calculate their generalized Hamming weights. Lastly, we determine their weight distribution and generalized Hamming weights partial...

In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators [Formula: see text] in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutator...