The absolute value equations (AVE) problem is an algebraic of solving . So far, most the research has focused on methods for AVE, but we address itself by analyzing properties AVE and corresponding solution set. In particular, investigate topological set, such as convexity, boundedness, or connectedness, whether it consists finitely many solutions. Further, problems related to nonnegativity sol...

Abstract The solvability of several new constrained quaternion matrix equations is investigated, and their unique solutions are presented in terms the weighted MPD inverse DMP suitable matrices. It interesting to consider some exceptional cases these corresponding solutions. Determinantal representations for as mentioned earlier established sums appropriate minors. In order illustrate obtained ...

ELEMENTARY CLASSES RAMI GROSSBERG AND SEBASTIEN VASEY Abstract. In the context of abstract elementary classes (AECs) with a monster model, several possible definitions of superstability have appeared in the literature. Among them are no long splitting chains, uniqueness of limit models, and solvability. Under the assumption that the class is tame and stable, we show that (asymptotically) no lon...

in this paper, an attempt is made to present an extension of darbo's theorem, and its applicationto study the solvability of a functional integral equation of volterra type.

We analyse dominance solvability (by iterated elimination of weakly dominated strategies) of voting games with three candidates and provide sufficient and necessary conditions for the Borda Count to yield a unique winner. We find that Borda is the unique scoring rule that is dominance solvable both (i) under unanimous agreement on a best candidate and (ii) under unanimous agreement on a worst c...

We study the partially eponymous model of distributed computation, which simultaneously generalizes the anonymous and the eponymous models. In this model, processors have identities, which are neither necessarily all identical, nor necessarily unique; processors receive inputs and must reach outputs that respect a relation. We focus on the partially eponymous ring R, and we are interested in th...

An inverse problem for a system of equations modeling oxygen transport in the brain is studied. The consists finding right-hand side equation blood transport, which linear combination given functionals describing average concentration neighborhoods ends arterioles and venules. overdetermination condition determined by values these evaluated on solution. unique solvability proven without any sma...

Some new necessary and sufficient conditions for the existence of analytic resolving families operators to linear equation with a distributed Riemann–Liouville derivative in Banach space are established. We study unique solvability natural initial value problem fractional derivatives corresponding inhomogeneous equations. These abstract results applied class boundary problems equations time pol...

Some general conditions sufficient for unique solvability of the boundary-value problem for a system of linear functional differential equations of the second order are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations and neutral equations. An example is presented to illustrate the general theory. 1....