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 |Sl(x)| is also small for all l > k. We use this to prove probability tail bounds for the symmetric polynomials when the inputs are only t-wise independent, that may be useful in the context of derandomization. We also provide examples of t-wise independent ...

d, where X = fX (t); t 2 0; 1]g is a symmetric stable process of index 2 (0; 2], and is a nite measure on 0; 1]. Under general assumptions upon , we prove that lim x!0 x =2 log P(;; < x) = ?c ;;. The constant c ;; is formulated as the solution to a variational problem , and its value is explicitly given when X is a symmetric Cauchy process (= 1) or Brownian motion (= 2).

Let (X,S) be an association scheme where X is a finite set and S is a partition of X × X. We say that (X,S) is symmetric if σs is symmetric for each s ∈ S where σs is the adjacency matrix of s, and integral if ⋃ s∈S ev(σs) ⊆ Z where ev(σs) is the set of all eigenvalues of σs. For an association scheme (X,T ) we say that (X,T ) is a fusion of (X,S) if each element of T is a union of elements of ...

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 ∈ Rd, 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 AN (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 ...

A generalization of the concept of PT −symmetric Hamiltonians H = p + V (x) is presented. For the usual analytic potentials V (x) (with singularities) and for the recently widely accepted “PT −symmetric” asymptotic boundary conditions for wave functions ψ(x) (selected inside a pair of complex wedges generalizing the usual x → ±∞ asymptotics), non-equivalent quantum toboggans are defined as inte...

Let X be a locally symmetric variety, i.e., the quotient of a bounded symmetric domain by a (say) neat arithmetically-defined group of isometries. Let X exc and X denote its excentric Borel-Serre and toroidal compactifications respectively. We determine their least common modification and use it to prove a conjecture of Goresky and Tai concerning canonical extensions of homogeneous vector bundl...

Symmetricity of an optimal solution of SemiDefinite Program (SDP) with certain symmetricity is discussed based on symmetry property of the central path that is traced by a primaldual interior-point method. Introducing some operators for rearranging elements of matrices and vectors, three types of symmetric SDPs are defined by using those operators. The symmetricity of the solution on the centra...

Centrioles are cylindrical cell organelles with a ninefold symmetric peripheral microtubule array that is essential to template cilia and flagella. They are built around a central cartwheel assembly that is organized through homo-oligomerization of the centriolar protein SAS-6, but whether SAS-6 self-assembly can dictate cartwheel and thereby centriole symmetry is unclear. Here we show that Lei...

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X −→ X such that the set A = {x ∈ X : ||R(x)|| → ∞} is non-empty and nowhere dense in X . Moreover, if x ∈ X \ A then some subsequence of (R(x)) n=1 converges weakly to x. This answers in the negative a recent conjecture of Prǎjiturǎ. The result can be extended to any Ba...

We establish several conditions which are equivalent to |[Bx, x]| ≤ 〈Ax, x〉 , ∀x ∈ H , where A is a nonnegative operator and B is a complex symmetric operator on a separable complex Hilbert space H. Along the way, we also prove a new factorization theorem for complex symmetric operators. Mathematics Subject Classification (2000). 47B99.