In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...

The paper is devoted to prove a version of Milnor-Moore Theorem for connected braided bialgebras that are infinitesimally cocommutative. Namely in characteristic different from 2, we prove that, for a given connected braided bialgebra A having a λ-cocommutative infinitesimal braiding for some regular element λ 6= 0 in the base field, then the infinitesimal braiding of A is of Hecke-type of mark...

This paper determines all arc-transitive pentavalent graphs of order 4pq, where q > p > 5 are primes. The cases p = 1, 2, 3 and p = q is a prime have been treated previously by Hua et al. [Pentavalent symmetric graphs of order 2pq, Discrete Math. 311 (2011), 2259-2267], Hua and Feng [Pentavalent symmetric graphs of order 8p, J. Beijing Jiaotong University 35 (2011), 132-135], Guo et al. [Pentav...

We study the classification problem for left-symmetric algebras with commutation Lie algebra gl(n) in characteristic 0. The problem is equivalent to the classification of étale affine representations of gl(n). Algebraic invariant theory is used to characterize those modules for the algebraic group SL(n) which belong to affine étale representations of gl(n). From the classification of these modu...

Abstract. In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions, in particular as they form a subalgebra of the algebra of symmetric functions. This subalgebra is generated by the odd power sum symmetric functions...

and Applied Analysis 3 We will prove this theorem by contradiction. The idea is similar to the proof of Theorem 1. Suppose ψ is a rotationally symmetric harmonic diffeomorphism from P(a) onto D∗ with the metric σ 2 d|u|, with the form ψ = g(r)e, then substituting ψ, σ 2 to u, σ in (2), respectively, we can get

The relationship between financial development and economic growth is the crucial issues which could grab economists and policy makers' attention to it. Financial market plays an essential role on each economy, because it conducts funds to those individuals or firms which have productive investment opportunities. If the financial system does not perform this role efficiently, the economic effic...

This paper studies the algebraic structure of transposition hypergroups with idempotent identity. Their subhypergroups and their properties are examined. Right, left and double cosets are defined through symmetric subhypergroups and their properties are studied. Further- more, this paper examines the homomorphisms, the behaviour of attrac- tive and non-attractive elements through them, as well ...

We present new lower bounds for the symmetric border rank of the n × n determinant for all n. Further lower bounds are given for the 3 × 3 permanent.

Let Γ be a graph admitting an arc-transitive subgroup G of automorphisms that leaves invariant a vertex partition B with parts of size v ≥ 3. In this paper we study such graphs where: for B, C ∈ B connected by some edge of Γ , exactly two vertices of B lie on no edge with a vertex of C; and as C runs over all parts of B connected to B these vertex pairs (ignoring multiplicities) form a cycle. W...