In this paper we describe an extension of a recently developed lattice Boltzmann method for solving the advection–diffusion equation. Our proposed approach allows to couple grids of different grid resolutions and includes a staggered timestepping scheme, interpolations in space and time and finally a scaling step ensuring the continuity of the desired macroscopic quantities across the grid inte...

By introducing lattice-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L an integral commutative quantale). By showing, via an intermediate L-valued structure of uniformity, how filters of covers may describe the uniform operators of Hutton, we prove that, when restricted to Girard quantales, this general framework captures Hutt...

Let I ⊂ P(N) stand for an ideal containing finite sets. We discuss various kinds of statistical convergence and I-convergence for sequences of functions with values in R or in a metric space. For real valued measurable functions defined on a measure space (X,M, μ), we obtain a statistical version of the Egorov theorem (when μ(X) < ∞). We show that, in its assertion, equi-statistical convergence...

Abstract We characterize the uniform convergence points set of a pointwisely convergent sequence real-valued functions defined on perfectly normal space. prove that if X is space which can be covered by disjoint dense subsets and A ⊆ , then for some ( f n ) ∈ ω : → ℝ only G δ -set contains all isolated . This result generalizes theorem Ján Borsík published in 2019.

Investigated are possibilistic distributions taking as their values sequences from the infinite Cartesian product of identical copies of a fixed finite subset of the unit interval of real numbers. Uniform and lexicographic partial orderings on the space of these sequences are defined and the related complete lattices introduced. Lattice-valued entropy function is defined in the common pattern f...

The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications c space. first one produces sequential sc. second makes absolute c-convergence generalizes weak convergence. third modification unbounded various convergences recently studied in literature. last applicable whenever commu...

In this paper, we study some basic properties of bicomplex numbers. We introduce two different types partial order relations on numbers, discuss valued metric spaces with respect to orders, and compare them. also define a hyperbolic space, the density natural statistical convergence, Cauchy property sequence numbers investigate in space prove that is complete if only complex are complete.

In this paper, using the concept of A-statistical convergence for double sequences, we provide a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued uniform continuous functions on [0,∞) × [0,∞) with the property that have a finite limit at the infinity. Then, we display an application which shows that our new result is stronger than its classical v...