We study continuity and equicontinuity of semigroups on norming dual pairs with respect to topologies defined in terms of the duality. In particular, we address the question whether continuity of a semigroup already implies (local/quasi) equicontinuity. We apply our results to transition semigroups and show that, under suitable hypothesis on E, every transition semigroup on Cb(E) which is conti...

Let X be a separable complete metric space. We characterize completely the innnitesimal generators of semigroups of linear transformations in C b (X), the bounded real-valued continuous functions on X, that are induced by strongly continuous semigroups of continuous transformations in X. In order to do this, C b (X) is equipped with a locally convex topology known as the strict topology. Introd...

For families of partial differential equations (PDEs) with particular boundary conditions, strict Lyapunov functions are constructed. The PDEs under consideration are parabolic and, in addition to the diffusion term, may contain a nonlinear source term plus a convection term. The boundary conditions may be either the classical Dirichlet conditions, or the Neumann boundary conditions or a period...

In a recent paper, Faloutsos et al. [1] found that the inter Autonomous System (AS) topology exhibits a power-law vertex degree distribution. This result was quite unexpected in the networking community and stirred significant interest in exploring the possible causes of this phenomenon. The work of Barabasi and Albert [2] and its application to network topology generation in the work of Medina...

In this paper we develop the theory of quasispaces (for a Grothendieck topology) and of concrete quasitopoi, over a suitable base category. We introduce the notion of f-regular category and of f-regular functor. The f-regular categories are regular categories in which every family with a common codomain can be factorized into a strict epimorphic family followed by a (single) monomorphism. The f...

For—according to the lore—any attempt at pullingoff this featwill reduce themtomaterial implicationand that is decidedlynot agoodwayof assigning truth-conditions to ordinary indicative if s. That is too bad since it seems like they are bounded from above by strict implication (they are true when their antecedents straight out imply their consequents), are bounded from below by material implicat...

In this article, we study geometric unitaries of JB-algebras (in particular, self-adjoint parts of C∗-algebras). We will show that the geometric unitaries of a JB algebra are precisely those central algebraic unitaries (or central symmetries). We will also show that the group of surjective isometries on a JB-algebra A (with point-norm topology) is the semi-direct product of the canonical action...

This paper discusses some serious difficulties for what we shall call the standard account of various kinds of relative necessity, according to which any given kind of relative necessity may be defined by a strict conditional necessarily, if C then p where C is a suitable constant proposition, such as a conjunction of physical laws. We argue, with the help of Humberstone (Reports on Mathematica...

Given a bounded open set Ω ⊂ ℝ 2 , we study the relaxation of nonparametric area functional in strict topology BV (Ω; ). and compute it for vortex-type maps, more generally maps W 1,1 (Ω;S 1 ) having finite number topological singularities. We also extend analysis to some specific piecewise constant ), including symmetric triple junction map.