All symmetric designs are determined for which the automorphism group is 2-transitive on the set of points. This note contains a proof of the following result. Theorem. Let D be a symmetric design with v > 2k such that Aut D is 2-transitive on points. Then D is one o f the following: (i) a projective space; (ii) the unique Hadamard design with v = I 1 and k = 5; (iii) a unique design with v = 1...

The paper develops a construction for finding fully symmetric integration formulas of arbitrary degree 2k + t in n-space such that the number of evaluation points is O ((2n)k/k t), n ~ . Formulas of degrees 3, 5, 7, 9, are relatively simple and are presented in detail. The method has been tested by obtaining some special formulas of degrees 7, 9 and 1 t but these are not presented here.

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means subordination, analytic parts which are reciprocal starlike (or convex) functions. Further, combining graph function, discuss bound Bloch constant and norm pre-Schwarzian derivative for classes.

In the present article, using subordination principle, authors employed certain generalized multiplier transform to define two new subclasses of analytic functions with respect symmetric and conjugate points. particular, bi-univalent conditions for function f(z) belonging these their relevant connections famous Fekete-Szegö inequality |a3−va22| were investigated a succinct mathematical approach.

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means subordination, analytic parts which are reciprocal starlike (or convex) functions. Further, discuss geometric properties classes, such as integral expression, coefficient estimation, distortion theorem, Jacobian growth estimates, and covering theorem.

The problem was first proposed by Blum [1] and Blum and Langley [2]. Ever since, the first nontrivial algorithm was given by [4], which runs in time n0.7kpoly(log 1/δ, 2k, n), for general juntas and n 2 3 poly(log 1/δ, 2k, n) for symmetric juntas. We give an algorithm for symmetric juntas which runs in time nk/3(1+o(1))poly(log 1/δ, 2k, n). We further show that when k is bigger than some large ...