This paper sets out a theoretical framework for approximating the attractor A of a semigroup S(t) deened on a Banach space X by a q{step semi{discretization in time with constant step{length k. Using the one{step theory of Hale, Lin and Raugel, suucient conditions are established for the existence of a family of attractors fA k g X q , for the discrete semigroups S n k deened by the numerical m...

The Arnoldi process is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a general square matrix. Numerical difficulties such as loss of orthogonality and assessment of the numerical quality of the approximations as well as a potential for unbounded growth in storage have limited the applicability of the method. These issues are addressed by fixing the...

with the increasing number of keratorefractive surgical procedures in the past years, an increasing number of cataract operations in eyes with previous keratorefractive surgery is anticipated. although cataract extraction seems to be feasible without major technical obstacles, intraocular lens (iol) power calculation remains problematic. insertion of measured k-readings after myopic photorefrac...

We examine the formation of giant elliptical galaxies using their globular cluster (GC) systems as probes of their evolutionary history. The bimodal distributions of GC metallicities in such galaxies are often cited as evidence for the formation of giant elliptical galaxies through mergers involving gas-rich spirals, with the metal-rich GCs forming during the merger process. We explore an alter...

We study the stability of the giant gravitons in the string theory background with NSNS B field. We consider the perturbation of giant gravitons formed by a probe D(8− p) brane in the background generated by D(p− 2)D(p) branes for 2 ≤ p ≤ 5. We use the quadratic approximation to the brane action to find the equations of motion. The vibration modes for ρ , φ and r are coupled, while those of xk’...

The notion of return probability – explored most famously by George Pólya on d-dimensional lattices – has potential as a measure for the analysis of networks. We present an efficient method for finding return probability distributions for connected undirected graphs. We argue that return probability has the same discriminatory power as existing k-step measures – in particular, beta centrality (...

Paying off the mortgage, once a widespread rite of passage for homeowners approaching retirement, has become less common in recent years. Concerns are mounting that the increased prevalence of housing debt among older homeowners could compromise financial security in retirement by expanding housing affordability problems, crimping essential nonhousing spending, increasing vulnerability to home ...