It is known (for details see, Traub, Wasilkowski, and Wofniakowski, 1988, “Information-Based Complexity,” Academic Press, New York) that a linear problem with solution operator S: X --f Y in the probabilistic or average case setting has finite e-complexity with respect to a probability measure k iff S E L2(X, CL; Y) or, equivalently, iff I E L2( Y, h 0 S-i; Y) where I denotes the identity opera...

We study connections between diagonal Pad e approximants and spectral properties of second order diierence operators with complex coeecients. In a rst part, we identify the diagonal of the Pad e table with a particular diierence operator which is shown to have maximal resolvent set. The spectrum of an asymptotically periodic complex diierence operator is given, and we prove convergence on the r...

|This paper presents a new operator called adaptive operator for the Pseudo-Bacterial Genetic Algorithm (PBGA). The PBGA was proposed by the authors as a new approach combining a genetic algorithm (GA) with a local improvement mechanism inspired by a process in bacterial genetics. The PBGA was applied for the discovery of fuzzy rules. The aim of the newly introduced adaptive operator is to impr...

Let T be a positive operator on a Banach lattice E. Some properties of Weyl essential spectrum σew(T ), in particular, the equality σew(T ) = ⋂ 0≤K∈K(E) σ(T +K), where K(E) is the set of all compact operators on E, are established. If r(T ) does not belong to Fredholm essential spectrum σef(T ), then r(T ) 6∈ σ(T +a|T−1|) for every a 6= 0, where T−1 is a residue of the resolvent R(., T ) at r(T...

this research presents a numerical tool to estimate the green's function operator matrix of intraplate faults. having this matrix and its inverse, spatial distribution of fault slippage could be investigated through the inverse analysis of geodetic data. this information could be employed to predict the location of future powerful earthquakes. to implement fault sliding in fe calculations,...

We construct the commutative current operator x̄+(z) inside Uq(ŝl(2)). With this operator and the condition of quantum integrability on the quantum currents of Uq(ŝl(2)), we derive the quantization of the semiinfinite construction of integrable modules of ŝl(2) which has been previously obtained by means of the current operator e(z) of ŝl(2). The quantization of the functional models for ŝl(2) i...

In general, a symmetric operator does not have a unique spectral function. If T is a symmetric operator and F(t) is a spectral function for T, by the theory of Naimark (see Akhiezer and Glazman [1]) there exists a Hilbert space H of which H is a subspace and a self-adjoint operator T onif with resolution of the identity E(t) such that T + is an extension of T and F(t) = P£(<) where P is the pro...

where 0 < α≤ 1, Γ(α) is the gamma function, {A(t) : t ∈ [0,T]} is a family of linear closed operators defined on dense set D(A) in a Banach space E into E, u is the unknown Evalued function, u0 ∈ D(A), and f is a given E-valued function defined on [0,T]. It is assumed that D(A) is independent of t. Let B(E) denote the Banach space of all linear bounded operators in E endowed with the topology d...

Letting E, F be Banach spaces, the main two results of this paper are the following: (1) If every (linear bounded) operator E → F is unconditionally converging, then every polynomial from E to F is unconditionally converging (definition as in the linear case). (2) If E has the Dunford-Pettis property and every operator E → F is weakly compact, then every k-linear mapping from E into F takes wea...

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.