Related papers: La formule de Cauchy dans les alg\`ebres
We review recent results on the Cauchy-Kowalevsky structure of theories with higher derivatives in vacuum. We prove genericity of regularity of solutions under the assumption of analyticity. Our approach is framed in the general context of…
Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
A general solution to the Complex Monge-Amp\`ere equation in a space of arbitrary dimensions is constructed.
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…
In this paper we develop generalized d'Alembert's formulas for abstract fractional integro-differential equations and fractional differential equations on Banach spaces. Some examples are given to illustrate our abstract results, and the…
In the article, a general solution of an equation with a generalized Hilfer derivative, which has a degeneration, is constructed. Particular solutions are presented through the Kilbas-Saigo function. A representation of the solution of the…
An expansion formula of a new type with the rest term of Cauchy type is derived in the operator formulation of generalized umbral calculus
After reviewing classical Schur-Weyl duality, we present some other contexts which enjoy similar features, relating to Brauer algebras and classical groups.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
The deformation bicomplex of a module-algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module-coalgebras,…
We survey the classical results of the Dirichlet Approximation Theorem.
Quaternions often appear in wide areas of applied science and engineering such as wireless communications systems, mechanics, etc. It is known that are two types of non-isomorphic generalized quaternion algebras, namely: the algebra of…
Some identities that involve the elliptic version of the Cauchy matrices are presented and proved. They include the determinant formula, the formula for the inverse matrix, the matrix product identity and the factorization formula.
In this paper we present a generalization of Faulhaber's formula to sums of arbitrary complex powers $m\in\mathbb{C}$. These summation formulas for sums of the form $\sum_{k=1}^{\lfloor x\rfloor}k^{m}$ and $\sum_{k=1}^{n}k^{m}$, where…
A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…
In this note we propose a definition of weak solution for an abstract Cauchy problem in a Hilbert space, and we discuss existence and uniqueness results.
We revisit Hardy's inequality in the scope of regular Dirichlet forms following an analytical method. We shall give an alternative necessary and sufficient condition for the occurrence of Hardy's inequality. A special emphasis will be given…
We present new results concerning the solvability, of lack thereof, in the Cauchy problem for the debar operator, with initial values assigned on a weakly pseudoconvex hypersurface, and provide illustrative examples.