We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4 and S5, such logics are useful, as shown in previous work by Baltag, Coecke and the first au...

In this work, we present a new constructive technique which is based on Green’s functional concept. According to this technique, a linear completely nonhomogeneous nonlocal problem for a second-order ordinary differential equation is reduced to one and only one integral equation in order to identify the Green’s solution. The coefficients of the equation are assumed to be generally variable nons...

We study the different guises of the projective objects in Cocont(Q): they are the “completely distributive” cocomplete Q-categories (the left adjoint to the Yoneda embedding admits a further left adjoint); equivalently, they are the “totally continuous” cocomplete Q-categories (every object is the supremum of the presheaf of objects “totally below” it); and also are they the Q-categories of re...

For an integer k ≥ 1, the k-th interlacing adjoint of a digraph G is the digraph ιk(G) with vertex-set V (G) k , and arcs ((u1, . . . , uk), (v1, . . . , vk)) such that (ui, vi) ∈ A(G) for i = 1, . . . , k and (vi, ui+1) ∈ A(G) for i = 1, . . . , k − 1. For every k we derive upper and lower bounds for the chromatic number of ιk(G) in terms of that of G. In particular, we find tight bounds on th...

We derive the well-known continuity principle for adjoint variables for preannounced or anticipated changes in parameters for continuoustime, infinite-horizon, perfect foresight optimization models. For easy and intuitive numerical computation of the resulting multi point boundary value problem we suggested to simulate the resulting differential algebraic system representing the first order con...

Voevodsky’s derived category of motives is the main arena today for the study of algebraic cycles and motivic cohomology. In this paper we study whether the inclusions of three important subcategories of motives have a left or right adjoint. These adjoint functors are useful constructions when they exist, describing the best approximation to an arbitrary motive by a motive in a given subcategor...

In this paper, we use soft linear operators to introduce the notion of discrete frames on Hilbert spaces, which extends classical spaces context algebraic structures sets. Among other results, show that frame operator associated a is bounded, self-adjoint, invertible and with bounded inverse. Furthermore, prove every element in space satisfies decomposition theorem. This theoretical framework p...

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

Let G be an adjoint simple algebraic group over an algebraically closed field of characteristic p; let be the root system of G, and take t ∈ N. Lawther has proven that the dimension of the set G[t] = {g ∈G : g = 1} depends only on and t . In particular the value is independent of the characteristic p; this was observed for t small and prime by Liebeck. Since G[t] is clearly a disjoint union of ...