LetW := exp( Q), where Q is of smooth polynomial growth at1, for example Q(x) = jxj ; > 1. We call W 2 a Freud weight. Let fxjngnj=1 and f jngnj=1 denote respectively the zeros of the nth orthonormal polynomial pn for W 2 and the Christo¤el numbers of order n. We establish converse quadrature sum inequalities associated with W , such as k (PW ) (x) (1 + jxj) kLp(R) C n X j=1 jnW 2 (xjn) jPW j (...

An n-ary quasigroup (Q, A) such that for some i ∈ {1, . . . , n} the identity A(A(x1 ), A(x n−1 2 , x1), . . . , A(xn, x n−1 1 )) = xi holds is called an i-Weisner n-quasigroup ( i-W-n-quasigroup ). iW-nquasigroups represent a generalization of quasigroups satisfying Schröder law (xy · yx = x) and quasigroups satisfying Stein’s third law (xy · yx = y). Properties of i-W-n-quasigroups which are ...

Let X be a nonsingular algebraic curve of genus g ≥ 3, and let M ξ denote the moduli space of stable vector bundles of rank n ≥ 2 and degree d with fixed determinant ξ over X such that n and d are coprime and d > n(2g − 2). We assume that if g = 3 then n ≥ 4 and if g = 4 then n ≥ 3. Let W ξ (L) denote the vector bundle over M ξ defined by the direct image p M ξ * (U ξ ⊗ p * X L) where U ξ is a ...

A kind of fixed-point problem in the area of discrete tomography is proposed and investigated. Our chief concern in this paper is the case of square windows in the plane. Dealing with the arrays which are bounded, of polynomial growth, and finite-ring-valued, one comes across several interesting phenomena of combinatorial and arithmetic nature. keywords: discrete tomography; fixed point; square...

We are concerned with function approximation and image representation using Iterated Function Systems (IFS) over L p (X;): An N-map IFS with grey level maps (IFSM), to be denoted as (w;), is a set w of N contraction maps w i : X ! X over a compact metric space (X; d) (the \base space") with an associated set of maps i : R ! R. Associated with each IFSM is a contractive operator T with xed point...

Š + Z s x Z v ¬ \ » W y ~ x ì 7 g ~ ¬ Ý Z K̈ +M Å @ Z e$ Ô Z & b z # b Z z g ] Æ n W c* ì X Z s x Z q§ ] 6, z g Š + ì ) 1 ( å Ÿ $ î E 0 § ] Z z g Z qY ì Š 2 g ) 2 ( ì X Z v ¬ \ ä Ñ < * i w Û â ð ì Z k ~ t & ¢A g ¿ ì z { CÙ q w ~ Š * Å g É ð TM n Ô Z z g CÙ 2 w ~ p | ] · Z v m z Å Z v ¬ \ Æ W y ~ g Î w X Æ Š Z ], { t ] Ã 5+ k, Z K̈ +M » ‚ B Š } n Z z g CÙ i â y z k y 6, ” Z z g Z $+ Z Ñ !...

In this paper, we are concerned with the symmetry and regularity of positive solutions of the following integral system: u(x) = ∫ Rn Gα (x–y)wr (y)vq(y) |y|β dy, v(x) = ∫ Rn Gα (x–y)up(y)wr (y) |y|β dy, w(x) = ∫ Rn Gα (x–y)up(y)vq(y) |y|β dy, where Gα (x) is the αth-order Bessel kernel, n≥ 3, 0≤ β < α < n, 1 < p,q, r < n–β β and 1 p+1 + 1 q+1 + 1 r+1 > 2n–α+β n . We show that every positive sol...

1. Compute the center manifold (to second order), and the reduced system on it (to third order), and conclude regarding the behavior of the systems near the origin (draw phase portrait) for F(x, y) = (x + xy − y 2 , 1 2 y + x 2). Solution. Let us write the map in the form: x n+1 = x n + x n y n − y 2 n y n+1 = 1 2 y n + x 2 n (1) Note that the origin (0, 0) is the fixed point. Calculate the Jac...

Consider two graphs X and Y, each with n vertices. The friends-and-strangers graph FS(X,Y) of Y is a vertex set consisting all bijections σ:V(X)↦V(Y), where σ, σ′ are adjacent if only they differ precisely on vertices X, the corresponding mappings in Y. most fundamental question that one can ask about these whether or not connected. Recently, Alon, Defant Kravitz showed independent random G(n,p...

Let X,Y be Banach spaces and consider the w′-topology (the dual weak operator topology) on the space (L(X,Y ), ‖.‖) of bounded linear operators from X into X with the uniform operator norm. L ′ (X,Y ) is the space of all T ∈ L(X,Y ) for which there exists a sequence of compact linear operators (Tn) ⊂ K(X,Y ) such that T = w′ − limnTn. Financial support from the National Council for Science and ...