We study the combinatorics of constructing non-singular geometrically irreducible projective curves that do not admit rational points over finite solvable extensions of the base field. A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a non-solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c...

INTRODUCTION Recently, the use of Groebner bases and Buchberger algorithm [BUC1,2,4] has been generalised from the case of commutative polynomials to finitely generated algebras R over a field k, R = k, s.t. for each i < j, for some cij ∈ k, for some commutative polynomial pij ∈ k[X1,...,Xn], one has xj xi cij xi xj = pij(x1,...,xn). The first results in this direction were due to Ga...

Abstract In this paper we deal with the class $$\mathcal {C}$$ C of decomposable solvable Lie groups having dimension six. We determine those in and their subgroups which are multiplication Mult ( L ) inner mapping Inn for three-dimensional connected simply topological loops . This result completes classifica...

A difficult problem in the character theory of solvable groups is to show that the number c.d. (G) of irreducible character degrees of a solvable group G is equal to or greater than d.l. (G), the derived length of G. Isaacs [4] has shown that d.l. (G) ^ 3 c.d. (G)-2 for every solvable group. Berger [1] subsequently proved that d.l. (G) < c.d. (G) when | G | is odd. This problem belongs to the c...

Motivated by recently discovered privacy attacks on social networks, we study the problem of anonymizing the underlying graph of interactions in a social network. We call a graph (k, l)anonymous if for every node in the graph there exist at least k other nodes that share at least l of its neighbors. We consider two combinatorial problems arising from this notion of anonymity in graphs. More spe...

Abstract. We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Although integral equation methods are widely used for the numerical solution of such problems, to date there is no formulation which is known to be uniquely solvable in the 3D case. We consider a novel Brakhage-Werner type integral equation formulation of this problem, base...

In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and unconditionally uniquely solvable. Furthermore, we show that the discrete phase variable is bounded in L∞ (0, T ;L∞) and the discrete chemical potential is bou...

‎let $g$ be a finite group and let $n$ be a normal subgroup of $g$‎. ‎suppose that ${rm{irr}} (g | n)$ is the set of the irreducible characters of $g$ that contain $n$ in their kernels‎. ‎in this paper‎, ‎we classify solvable groups $g$ in which the set $mathcal{c} (g) = {{rm{irr}} (g | n) | 1 ne n trianglelefteq g }$ has at most three elements‎. ‎we also compute the set $mathcal{c}(g)$ for suc...

We investigate subgroups of the group PLo(I) of piecewise-linear, orientation preserving homeomorphisms of the unit interval with finitely many breaks in slope, and also subgroups of Thompson’s group F . We find geometric criteria determining the derived length of any such group, and use this criteria to classify the solvable and non-solvable subgroups of PLo(I) and of F . Let H be a subgroup o...

A graph G = ( b’. El has bandwidth k under a layout L : V 4’ ’ { 1. . . . , 1 VJ} if, for all {s. y} E E. jL(x 1 -L(y)] s k. Bandwidth constraints on several problems that are complete for [Fp (under log space reductions) are considered. In particular, the solvable path system problem and the and/or graph accessibility problem under various bandwidth constraints are used to prove results about ...