in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

Cloud computing is one of the widest phenomena embraced in information technology. This result from numerous advantages associated with it making many organizations and individuals offload their data to cloud. Encryption schemes restrict access unauthorized clients, helping attain confidentiality privacy. The modification ciphertext clients’ on cloud demand downloading, deciphering, editing, fi...

The study of constraint satisfaction problems definable in various fragments of Datalog has recently gained considerable importance. We consider constraint satisfaction problems that are definable in the smallest natural recursive fragment of Datalog monadic linear Datalog with at most one EDB per rule, and also in the smallest non-linear extension of this fragment. We give combinatorial and al...

The semiring-based constraint satisfaction problems (semiring CSPs), proposed by Bistarelli, Montanari and Rossi [3], is a very general framework of soft constraints. In this paper we propose an abstraction scheme for soft constraints that uses semiring homomorphism. To find optimal solutions of the concrete problem, the idea is, first working in the abstract problem and finding its optimal sol...

We give a structure theorem for a ring homomorphism of a commutative regular Banach algebra into another commutative Banach algebra. In particular, it is shown that: (i) A ring homomorphism of a commutative C∗-algebra onto another commutative C∗-algebra with connected infinite Gelfand space is either linear or anti-linear. (ii) A ring automorphism of L1(R ) is either linear or anti-linear. (iii...

Given a countable Borel equivalence relation E on a Polish space, let IE denote the σ-ideal generated by the Borel partial transversals of E. We show that there is a Borel homomorphism from IE to IF if and only if there is a smooth-to-one Borel homomorphism from a finite index Borel subequivalence relation of E to F . As a corollary, we see that IE is homogeneous in the sense of Zapletal (2007,...

Let D denote the partially ordered sets of homomorphism classes of finite directed graphs, ordered by the homomorphism relation. Order theoretic properties of this poset have been studied extensively, and have interesting connections to familiar graph properties and parameters. This paper studies the generalized duality pairs in D: it gives a new, short proof for the Foniok Nešetřil Tardif theo...

Let Fg denote the closed orientable surface of genus g. What is the least order finite group, Gg, for which there is a homomorphism ψ : π1(Fg) → Gg so that no nontrivial simple closed curve on Fg represents an element in Ker(ψ)? For the torus it is easily seen that G1 = Z2 × Z2 suffices. We prove here that G2 is a group of order 32 and that an upper bound for the order of Gg is given by g . The...

Following the last talk on graph homomorphisms, we continue to discuss some examples of graph homomorphisms. But this time we will focus on some models, that is, the homomorphism G → H for the graph H with fixed weights. The main reference is Section 1 in [2].

We show that if a graph H is k-colorable, then (k−1)-branching walks on H exhibit long range action, in the sense that the position of a token at time 0 constrains the configuration of its descendents arbitrarily far into the future. This long range action property is one of several investigated herein; all are similar in some respects to chromatic number but based on viewing H as the range, in...