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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Identities, inequalities and congruences for odd ranks and k-marked odd Durfee symbols
奇数秩 k标记 奇数杜菲符号 恒等式 不等式 全等
2023/4/23
In 2007, Andrews introduced the odd rank of odd Durfee symbols. Let N^0 (m,n) denote the number of odd Durfee symbols of n with odd rank m, and N^0 (r,m;n) be the number of odd Durfee symbols of n wit...
INTEGRAL IDENTITIES AND MINKOWSKI TYPE INEQUALITIES INVOLVING SCHOUTEN TENSOR
INTEGRAL IDENTITIES MINKOWSKI TYPE INEQUALITIES INVOLVING SCHOUTEN TENSOR
2014/4/3
New formulas for the integration of the k-th elementary symmetric functions of the Shouten tensor are derived and applied to deduce some
Minkowski type inequalities.
Integral and series transformations via Ramanujan's identities and Salem's type equivalences to the Riemann hypothesis
Mellin transform Riemann zeta-function Kontorovich-Lebedev transform modified Bessel functions Lambert transform
2012/6/21
We consider integral and series transformations, which are associated with Ramanujan's identities, involving various arithmetic functions and a ratio of products of Riemann's zeta functions of differe...
Exponential-Uniform Identities Related to Records
records planar Poisson process distributional identities
2012/6/21
We consider a rectangular grid induced by the south-west records from the planar Poisson point process in $R^2_+$. A random symmetry property of the matrix whose entries are the areas of tiles of the ...
The pseudorelativistic Hartree equation with a general nonlinearity: existence, non existence and variational identities
The pseudorelativistic Hartree equation general nonlinearity non existence variational identities Analysis of PDEs
2012/6/21
We prove several existence and non existence results of solitary waves for a class of nonlinear pseudo-relativistic Hartree equations with general nonlinearities. We use variational methods and some n...
Partition Identities for Ramanujan's Third Order Mock Theta Functions
mock theta function Ramanujan's identities partition identity Fine's theorem involution
2014/6/3
We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions φ(-q) and ψ(-q). We also give an involution for Fine's partition identity on th...
Simple G-graded algebras and their polynomial identities
graded algebra polynomial identity
2011/9/19
Abstract: Let G be any group and F an algebraically closed field of characteristic zero. We show that any two G-graded finite dimensional G-simple algebras over F are G-graded isomorphic if and only i...
Actions and identities on set partitions
Actions and identities set partitions Combinatorics
2011/9/16
Abstract: A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group $A$. Inspired by the action of the linear characters of the unitria...
Proofs of some binomial identities using the method of last squares
binomial identities method of last squares Proofs Combinatorics
2011/8/26
Abstract: We give combinatorial proofs for some identities involving binomial sums that have no closed form.
Conformal Killing vector fields and Rellich type identities on Riemannian Manifolds, II
Riemannian Manifolds Killing vector fields Rellich identities
2011/1/21
We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds ad...
Skyrmions, Rational Maps & Scaling Identities
Skyrmions Rational Maps & Scaling Identities
2010/12/28
Starting from approximate Skyrmion solutions obtained using the rational map ansatz, improved approximate Skyrmions are constructed using scaling arguments.Although the energy improvement is small, th...
Identities and congruences for a new sequence
congruence Euler polynomial identity p-regular function
2011/2/22
Let [x] be the greatest integer not exceeding x. In the paper we introduce the sequence {Un} given by U0 = 1 and Un = −2P[n/2] k=1 n 2kUn−2k (n 1), and establish many recursi...
Generating functions for the Bernstein polynomials: A unified approach to deriving identities for the Bernstein basis functions
Bernstein polynomials generating function Szasz-Mirakjan basis functions
2011/2/28
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and different...
Operator algebras with contractive approximate identities
Operator algebras contractive approximate identities
2010/11/22
We give several applications of a recent theorem of the second author, which solved a conjecture of the first author with Hay and Neal, concerning contractive approximate identities; and another of H...
A field-theoretic approach to nonequilibrium work identities
Work identities Stochastic dynamics Supersymmetry
2010/12/16
We study nonequilibrium work relations for a space-dependent field with stochastic dynamics
(Model A). Jarzynski’s equality is obtained through symmetries of the dynamical action in the
path integra...