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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Pleijel identity
Pleijel恒等式 光滑边界 Blaschke–Petkantschin
2023/10/16
Let K be a planar convex body with C^1 boundary. Consider a random line G intersecting K. In [1] Pleijel discovered an identity expressing the integral functional of the length of the chord G ∩ K in t...
A NEW IDENTITY FOR PARSEVAL FRAMES
Bessel sequence Frame Hilbert space Parseval frame Parseval Frame Identity
2015/9/29
In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss ...
Function-Private Identity-Based Encryption: Hiding the Function in Functional Encryption
Function privacy identity-based encryption functional encryption
2015/8/5
In light of such an inherent difficulty, any meaningful notion of function privacy must be based
on the minimal assumption that, from the adversary's point of view, identities that correspond to...
On the Permanents of Complements of the Direct Sum of identity Matrices
Complement, permanent magnet straight, identity matrix
2015/7/14
On the Permanents of Complements of the Direct Sum of identity Matrices.
Combinatorial Telescoping for an Identity of Andrews on Parity in Partitions
creative telescoping combinatorial telescoping partition q-little Jacobi polynomial
2014/6/3
Recently Andrews proposed a problem of finding a combinatorial proof of an identity on the q-little Jacobi polynomials. We give a classification of certain triples of partitions and find bijections ba...
The Mikheev identity in right Hom-alternative algebras
Right Hom-alternative algebra Mikheev identity Rings and Algebras
2012/5/9
It is shown that in every multiplicative right Hom-alternative algebra, a Hom-type generalization of the Mikheev identity holds. It is then inferred that a multiplicative right Hom-alternative algebra...
Real analytic expansion of spectral projection and extension of Hecke-Bochner identity
Coxeter group Hecke-Bochner identity Heisenberg group Laguerre polynomials spherical harmonics twisted convolution
2012/4/16
In this article, we review the Weyl correspondence of bigraded spherical harmonics and use it to extend the Hecke-Bochner identities for the spectral projections $f\times\varphi_k^{n-1}$ for function ...
A binomial identity on the least prime factor of an integer
binomial identity least prime factor of an integer Number Theory
2011/9/22
Abstract: An identity for binomial symbols modulo an odd positive integer $n$ relating to the least prime factor of $n$ is proved. The identity is discussed within the context of Pell conics.
An identity on the $2m$-th power mean value of the generalized Gauss sums
2m-th power mean exact calculating formula generalized quadratic Gauss sums Number Theory
2011/9/5
Abstract: In this paper, using combinatorial and analytic methods, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m\geq 2$. This sol...
Extension of Euler Lagrange identity by superquadratic power functions
Euler Lagrange Identity Bohr’s inequality Convexity Superquadracity
2011/9/2
Abstract: Using convexity and superquadracity we extend in this paper Euler Lagrange identity, Bohr's inequalitiy and the triangle inequality.
Abstract: The AZ identity is a generalization of the LYM-inequality. In this paper, we will give a generalization of the AZ identity.
Denominator identity for affine Lie superalgebras with zero dual Coxeter number
Denominator identity affine Lie superalgebras zero dual Coxeter number
2011/2/28
We prove a denominator identity for non-twisted affine Lie superalgebras with zero dual Coxeter number.
A recursion identity for formal iterated logarithms and iterated exponentials
recursion identity formal iterated logarithms iterated exponentials
2011/1/18
We prove a recursive identity involving formal iterated logarithms and for-mal iterated exponentials. These iterated logarithms and exponentials appear in a nat-ural extension of the logarithmic forma...
A simple proof of a generalization of the Chu-Vandermonde identity
simple proof generalization Chu-Vandermonde identity
2011/1/18
We provide a simple proof of a generalization of the multivariate Chu-Vandermonde identity recently derived in Favaro et al. (2010a). Exploiting known results for rising factorials and fourth Lauricel...
Polynomial identity rings as rings of functions, II
Polynomial identity ring central simple algebra trace ring
2011/1/18
In characteristic zero, Zinovy Reichstein and the author generalized the usual relationship between irreducible Zariski closed subsets of the affine space.