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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...
Anti de Sitter quantum field theory and a new class of hypergeometric identities
hypergeometric identities High Energy Physics - Theory Anti de Sitter quantum field theory
2011/10/9
Abstract: We use Anti-de Sitter quantum field theory to prove a new class of identities between hypergeometric functions related to the K\"all\'en-Lehmann representation of products of two Anti-de Sit...
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.
Ghirlanda-Guerra identities and ultrametricity: An elementary proof in the discrete case
spin glasses Sherrington-Kirkpatrick model ultrametricity
2011/7/28
Abstract: In this paper we give another proof of the fact that a random overlap array, which satisfies the Ghirlanda-Guerra identities and whose elements take values in a finite set, is ultrametric wi...
Ward-Takahashi identities for the colored Boulatov model
Group field theory Ward-Takahashi identities
2011/7/27
Abstract: Ward-Takahashi identities of the colored Boulatov model are derived using a generic unitary field transformation. In a specific instance, this generic transformation turns out to be a symmet...
Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics
Pohozhaev Morawetz Identities Elastostatics Elastodynamics
2011/7/27
Abstract: We construct identities of Pohozhaev type, in the context of elastostatics and elastodynamics, by using the Noetherian approach. As an application, a non-existence result for forced semi-lin...
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...