相关论文: Jordan s-identities in three variables
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
We prove a number of new Rogers-Ramanujan type identities involving double, triple and quadruple sums. They were discovered after an extensive search using Maple. The main idea of proofs is to reduce them to some known identities in the…
A Jordan H\"older theorem is established for derived module categories of piecewise hereditary algebras. The resulting composition series of derived categories are shown to be independent of the choice of bounded or unbounded derived module…
We state and discuss numerous mathematical identities involving Jacobi elliptic functions sn(x,m), cn(x,m), dn(x,m), where m is the elliptic modulus parameter. In all identities, the arguments of the Jacobi functions are separated by either…
The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological…
We find the conditions for bi-Lipschitz equivalence of self-similar Jordan arcs which are the attractors of self-similar zippers.
Some ramifications of the identity of Chaundy and Bullard are presented. We discuss its homogeneous form and its relations to other identities, as well as extensions to more variables and more parameters.
We discuss some aspects of the theory of recognition of two-dimensional shapes by means of fingerprints of Jordan curves. An interesting approach to problems on shape recognition suggested by P.~Ebenfelt, D.~Khavinson, and H.~Shapiro and…
Using the model of words, we give bijective proofs of Gould-Mohanty's and Raney-Mohanty's identities, which are respectively multivariable generalizations of Gould's identity $$\sum_{k=0}^{n}{x-kz\choose k}{y+kz\choose n-k}=…
It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers-Ramanujan identities (L. J. Slater, Further identities of the Rogers-Ramanujan type, \emph{Proc. London Math Soc. (2)} \textbf{54} (1952),…
We give explicit bounds for Jordan constants of groups of birational automorphisms of rationally connected threefolds over fields of zero characteristic, in particular, for Cremona groups of ranks 2 and 3.
In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a…
We derive generalizations of the Cherednik-Macdonald constant term identities associated to root systems which depend, besides on the usual multiplicity function, symmetrically on two quasi-periods. They are natural analogues of the…
For a given ring $\mathfrak{R}$ and a locally finite pre-ordered set $(X, \leq)$, consider $I(X, \mathfrak{R})$ to be the incidence algebra of $X$ over $\mathfrak{R}$. Motivated by a Xiao's result which states that every Jordan derivation…
We developed a new proper method for classifying $n$-dimensional derived Jordan algebras, and apply it to the classification of $3$-dimensional derived Jordan algebras. As a byproduct, we have the algebraic classification of $3$-dimensional…
In a recent paper, Griffin, Ono and Warnaar present a framework for Rogers-Ramanujan type identities using Hall-Littlewood polynomials to arrive at expressions of the form \[\sum_{\lambda : \lambda_1 \leq m}…
We use derivatives to prove the equivalences between MacWilliams identity and its four equivalent forms, and present new interpretations for the four equivalent forms. Our results explicitly give out the relationships between MacWilliams…
Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant…
We derive three identities of symmetry in two variables and eight in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by unramified roots of unity. The case…
We generalize Menon's identity by considering sums representing arithmetical functions of several variables. As an application, we give a formula for the number of cyclic subgroups of the direct product of several cyclic groups of arbitrary…