We present some results on character degree sums in connection with several important characteristics of finite groups such as p-solvability, solvability, supersolvability, and nilpotency. Some of them strengthen known results in the literature.

We introduce a version of Post Correspondence Problem (PCP, in short) generalized to words over partially commutative alphabets. Several observations are presented about the algorithmic status of the introduced problem. In particular solvability is shown for the partially commutative PCP for two special cases: the binary case of PCP (denoted by PCP(2) ), and the case with one periodic morphism....

Dominance solvability is one of the most straightforward solution concepts in game theory. It is based on two principles: dominance (according to which players always use their dominant strategy) and iterated dominance (according to which players always act as if others apply the principle of dominance). However, existing experimental evidence questions the empirical accuracy of dominance solva...

In Part I, we studied linear network coding over finite commutative rings and made comparisons to the wellstudied case of linear network coding over finite fields. Here, we consider the more general setting of linear network coding over finite (possibly non-commutative) rings and modules. We prove the following results regarding the linear solvability of directed acyclic networks over various f...

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on one hand, and abelian extensions and congruence solvability on the other hand. In particular, we show that a loop is congruence solvable (that is, an iterated...

In this paper we prove the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of a Hollomon’s power-law plastic beam subject to an axial compression and nonlinear lateral constrains. For certain ranges of the acting axial compression force, the solvability of the equations follows from the monotonicity of the fourth order nonlinear differ...

The solvability in Sobolev spaces W 1,2 p is proved for nondivergence form second order parabolic equations for p > 2 close to 2. The leading coefficients are assumed to be measurable in the time variable and two coordinates of space variables, and almost VMO (vanishing mean oscillation) with respect to the other coordinates. This implies the W 2 p -solvability for the same p of nondivergence f...

The well-known positive real lemma characterizes positive realness of transfer functions of timeinvariant linear systems via the solvability of certain linear matrix inequalities. In this paper, we propose an extension of the positive real lemma and the underlying linear matrix inequalities to descriptor systems. We show that the solvability of these linear matrix inequalities is sufficient and...

In this paper we survey some results concerning polynomial and/or strongly polynomial solvability of some classes of quadratic programming problems. The discussion on polynomial solvability of continuous convex quadratic programming is followed by a couple of models for quadratic integer programming which, due to their special structure, allow polynomial (or even strongly polynomial) solvabilit...

We study the solvability in the whole Euclidean space of coercive quasi-linear and fully nonlinear elliptic equations modeled on ∆u±g(|∇u|) = f(u), u ≥ 0, where f and g are increasing continuous functions. We give conditions on f and g which guarantee the availability or the absence of positive solutions of such equations in R . Our results considerably improve the existing ones and are sharp o...