We consider regularization methods for numerical solution of linear illposed problems, in particular, image deblurring, when the singular value decomposition (SVD) of the operator is available. We assume that the noise-free problem satisfies the discrete Picard condition and define the Picard parameter, the index beyond which the data, expressed in the coordinate system of the SVD, are dominate...

Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral operators. It is shown that this series is an asymptotic expansion with respect to smoothness under quite general geometric conditions. Propagation of singularitie...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

the main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by özkoç and aslım cite{10} called weakly $er$-open functions and $e$-$theta$-open functions. moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing to...

We present a method for numerical computation of period integrals rigid Calabi-Yau threefold using Picard-Fuchs operator one-parameter smoothing. Our gives possibility computing the lattice double octic without any explicit knowledge its geometric properties, employing only simple facts from theory Fuchsian equations and computations in MAPLE with library differential equations. As surprising c...

An alternative approach is proposed for constructing a strongly continuous semigroup based on the classical method of successive approximations, or Picard iterations, together with generating functions. application to Black–Scholes integro-differential operator which arises in pricing European options under jump-diffusion dynamics provided. The expressed as Mellin convolution time-inhomogeneous...

In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures Mba(Σ,L(X,Y )). This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures Mba(Σ,L1(X,Y )). This result has interesting applications in optim...

In this paper we begin a systematic study of equivariant compactifications of Ga . The question of classifying non-equivariant compactifications was raised by F. Hirzebruch ([10]) and has attracted considerable attention since (see [5], [15], [12] and the references therein). While there are classification results for surfaces and non-singular threefolds with small Picard groups, the general pe...

In this paper we begin a systematic study of equivariant compactifications of Ga . The question of classifying non-equivariant compactifications was raised by F. Hirzebruch ([10]) and has attracted considerable attention since (see [5], [15], [12] and the references therein). While there are classification results for surfaces and non-singular threefolds with small Picard groups, the general pe...