The Ruelle zeta-function of the geodesic flow on the sphere bundle S(X) of an even-dimensional compact locally symmetric space X of rank 1 is a meromorphic function in the complex plane that satisfies a functional equation relating its values in s and -s . The multiplicity of its singularity in the central critical point 5 = 0 only depends on the hyperbolic structure of the flow and can be calc...

A symmetric dataset is defined as an n x n dataset that when transposed, it is equal to that of prior transposed. In data mining algorithms that employ vertical data structure, symmetric datasets are used, for example, in clustering gene expression pattern and density-based clustering algorithms. In the former, a symmetric dataset is the pre-computed pairwise similarity of genes, while in the l...

In this paper, we study sharp heat kernel estimates for a large class of symmetric jump-type processes in Rd for all t > 0. A prototype of the processes under consideration are symmetric jump processes on Rd with jumping intensity 1 Φ(|x− y|) Z [α1,α2] c(α, x, y) |x− y|d+α ν(dα), where ν is a probability measure on [α1, α2] ⊂ (0, 2), Φ is an increasing function on [0,∞) with c1e2 β ≤ Φ(r) ≤ c3e...

In a recent paper, Pawale [22] investigated quasi-symmetric 2-(v, k, λ) designs with intersection numbers x > 0 and y = x+ 2 with λ > 1 and showed that under these conditions either λ = x + 1 or λ = x + 2, or D is a design with parameters given in the form of an explicit table, or the complement of one of these designs. In this paper, quasi-symmetric designs with y−x = 3 are investigated. It is...

The famous Frobenius characteristic map is a bijection from the space of characters of a symmetric group S n to the space of homogeneous symmetric functions of degree n. In this note, we prove a formula for the inverse map. More precisely, we express the generating function for the values of an arbitrary virtual character of S n in terms of the symmetric function which is the Frobenius image of...

‎let $r$ be a noncommutative prime ring of‎ ‎characteristic different from $2$‎, ‎$u$ the utumi quotient ring of $r$‎, ‎$c$ $(=z(u))$ the extended centroid‎ ‎of $r$‎. ‎let $0neq ain r$ and $f(x_1,ldots,x_n)$ a multilinear‎ ‎polynomial over $c$ which is noncentral valued on $r$‎. ‎suppose‎ ‎that $g$ and $h$ are two nonzero generalized derivations of $r$‎ ‎such that $a(h(f(x))f(x)-f(x)g(f(x)))in ...

We define a new family F̃w(X) of generating functions for w ∈ S̃n which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions such as their symmetry and conjecture certain positivity properties. As an application, we relate these functions to the k-Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur functions of Postnikov. ...

This paper is concerned with the approximation of the effective conductivity σ(A,μ) associated to an elliptic operator ∇xA(x, η)∇x where for x ∈ R , d ≥ 1, A(x, η) is a bounded elliptic random symmetric d×d matrix and η takes value in an ergodic probability space (X,μ). Writing A(x, η) the periodization of A(x, η) on the torus T d N of dimension d and side N we prove that for μ-almost all η lim...

This paper studies the elementary symmetric polynomials Sk(x) for x ∈ Rn. We show that if |Sk(x)|, |Sk+1(x)| are small for some k > 0 then |S`(x)| is also small for all ` > k. We use this to prove probability tail bounds for the symmetric polynomials when the inputs are only t-wise independent, which may be useful in the context of derandomization. We also provide examples of t-wise independent...