This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the convolution measure algebra M, (S) of a locally compact semigroup. H. Dzinotyiweyi in [5,7] considers an analogous measure space on a large class of C-distinguished topological semigroups containing all completely regular topological semigroups. In this paper, we extend the definitions to study the weighted semigroup ...

The semi-group of weighted composition operators (Wn)n≥1 whereWnf(z)=(1+z+…+zn−1)f(zn) on the classical Hardy-Hilbert space H2 open unit disk is related to Riemann Hypothesis (RH) (see [16]). semigroup also closely Invariant Subspace Problem (ISP) and Periodic Dilation Completeness (PDCP). We obtain results cyclic vectors, spectra, invariant reducing subspaces. In particular, we show that sever...

On modern large-scale parallel computers, the performance of Krylov subspace iterative methods is limited by global synchronization. This has inspired the development of s-step (or communication-avoiding) Krylov subspace method variants, in which iterations are computed in blocks of s. This reformulation can reduce the number of global synchronizations per iteration by a factor of O(s), and has...

Let (S1,S2) be a bi-isometry, that is, pair of commuting isometries S1 and S2 on complex Hilbert space H. By the von Neumann-Wold decomposition, hyper-range H∞(S1):=∩n=0∞S1nH reduces to unitary operator. Although H∞(S1) is an invariant subspace for S2, in general, not reducing S2. We show isometry if only subspaces S2(ker⁡S1⁎) H are orthogonal. Further, we describe all bi-isometries satisfying ...

It is proved that all discontinuity points of a finite cosmological time function, $$\tau $$ , are on past lightlike rays. As result, it if (M, g) chronological space-time without rays then there representation g such its function regular. In addition, by reducing conditions regularity sufficient for causal simplicity and pseudoconvexity given. also the second condition can be reduced to satisf...

Often, we work with vector spaces which consists of an appropriate. Many concepts concerning vectors in Rn can be extended to other mathematical systems. We can think of a vector space in.of a finite-dimensional nontrivial proper subspace of such a vector space is equivalent to ACA0 over RCA0. This paper is a continuation of 3.Subspaces of Vector Spaces. A subspace W of a vector space V is a su...

Hyperspectral imaging, even when restricted to the visible spectrum range, allows what is indiscriminable to the human visual system to become discriminable. The typical human visual system (HVS) projects the light spectrum, the determinant of color, into a threedimensional subspace. The basis is determined by the spectral response of the three types of cones. The response has been modeled as t...