We study model theoretic properties of valued fields (equipped with a real-valued multiplicative valuation), viewed as metric structures in continuous first order logic. For technical reasons we prefer to consider not the valued field (K, |·|) directly, but rather the associated projective spaces KP, as bounded metric structures. We show that the class of (projective spaces over) metric valued ...

The purpose of this article is to give a rather thorough understanding of the compact support property for measure-valued processes corresponding to semi-linear equations of the form ut = Lu+ βu− αu p in R × (0,∞), p ∈ (1, 2]; u(x, 0) = f(x) in R; u(x, t) ≥ 0 in R × [0,∞). In particular, we shall investigate how the interplay between the underlying motion (the diffusion process corresponding to...

For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints‎, ‎we define a new gap function that generalizes the definitions of this concept in other articles‎. ‎Then‎, ‎we characterize the efficient‎, ‎weakly efficient‎, ‎and properly efficient solutions of the problem utilizing this new gap function‎. ‎Our results are based on $(Phi,rho)-$invexity‎,...

We look at extensions (i.e., stronger logics in the same language) of the Belnap-Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap-Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterize the reduced algebraic models of these new logics and prove a completeness result for the first ...

A group of analytical formulas formulas for calculating the global maximal and minimal ranks and inertias of the quadratic matrix-valued function φ(X) = (AXB + C )M(AXB + C) +D are established and their consequences are presented, where A, B, C and D are given complex matrices with A and C Hermitian. As applications, necessary and sufficient conditions for the two general quadratic matrix-value...

Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite matrices in applications. The cone-valued class of generalised Gamma convolutions is studied. In particular, a characterisation in terms of an Itô-Wiener integ...

In this paper we investigate inverse limits of two related parameterized families of upper semi-continuous set-valued functions. We include a theorem one consequence of which is that certain inverse limits with a single bonding function from one of these families are the closure of a topological ray (usually with indecomposable remainder). Also included is a theorem giving a new sufficient cond...

We introduce in the present paper a Gauss–Newton-type method for solving generalized equations defined by sums of differentiable mappings and set-valued mappings in Banach spaces. Semi-local convergence and local convergence of the Gauss–Newton-type method are analyzed.

A modified mapping method is presented to derive a variable separation solution with two arbitrary functions of the (2+1)-dimensional generalized Nizhnik–Novikov–Veselov equation. By selecting appropriate functions in the variable separation solution, we discuss interaction behaviours among special solitons, constructed by multi-valued functions, including the compacton-like dromion, compacton-...

In this paper we present a sequence f2, f3, f4, . . . of upper semi-continuous set-valued functions with the property that the graph of fn n is not connected but the graph of fk n is connected for 1 ≤ k < n. Thus, for each positive integer n, lim ←−n is not connected but the difficulty of detecting this fact increases with n.