sn-networks were first introduced by Lin [12], which are the concept between weak bases and cs-networks. sn-metrizable spaces [6] (i.e., spaces with σ-locally finite sn-networks) are one class of generalized metric spaces, and they play an important role in metrization theory, see [6, 13]. In this paper, we give a mapping theorem on sn-metrizable spaces, discuss relationships among spaces with ...

In this paper, we prove the convergence of a finite-volume scheme for the time-dependent convection–diffusion equation with an L1 right-hand side. To this purpose, we first prove estimates for the discrete solution and for its discrete time and space derivatives. Then we show the convergence of a sequence of discrete solutions obtained with more and more refined discretizations, possibly up to ...

The paper deals with a Markov path-valued process : the reeecting Brownian snake. It is a particular case of the path-valued process former introduced by Le Gall. Here the spatial motion (which is for Le Gall any Markov process) is a reeecting Brownian motion in a domain D of R d. Using this probabilistic tool, we construct an explicit function v solution of an integral equation which is, under...

We develop a general approach to the Policy Improvement Algorithm (PIA) for stochastic control problems for continuous-time processes. The main results assume only that the controls lie in a compact metric space and give general sufficient conditions for the PIA to be well-defined and converge in continuous time (i.e. without time discretisation). It emerges that the natural context for the PIA...

We present a weak formulation for a steady fluid-structure interaction problem using an embedding domain technique with penalization. Except of the penalizing term, the coefficients of the fluid problem are constant and independent of the deformation of the structure, which represents an advantage of this approach. A second advantage of this model is the fact that the continuity of the stress a...

The paper deals with the numerical solution of initial-boundary value problems for diffusion equation with variable coefficients by using a local weak formulation and a meshless approximation of spatial variations of the field variable. The time variation is treated either by the Laplace transform technique or by the linear Lagrange interpolation in the time stepping approach. Advanced formulat...

We present a Hamiltonian formulation for gauged non-anomalous chiral theories on a spatial lattice. The formulation has the desirable properties that it provides exact chiral symmetry in the mass + 0 limit, with a correct fermion spectrum and correct weak coupling perturbation theory for QED. It can be generalized to non-Abelian theories. The disadvantage of the formalism is that it is complica...

Original scientific paper Finite difference procedures for flux determination are not well suited for application to field results obtained from finite element calculations. A novel method for flux calculation has been derived. This method is based on the weak formulation and is suitable for use with finite elements. A matrix formulation for local and global application to finite element formul...

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if K ⊆ L ⊆ L′ are quasivarieties of finite signature, and L′ is finitely generated while K |= WEP, then K is finitely axiomatizable relative to L. We prove for any quasivariety K that K |= RSD(∧) iff...