An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

Indirect ties in knowledge networks:a social network analysis with ordered weighted averaging operators

This PhD thesis analyses networks of knowledge flows, focusing on the role of indirect ties in the knowledge transfer, knowledge accumulation and knowledge creation process. It extends and improves existing methods for mapping networks of knowledge flows in two different applications and contributes to two stream of research. To support the underlying idea of this thesis, which is finding an alternative method to rank indirect network ties to shed a new light on the dynamics of knowledge transfer, we apply Ordered Weighted Averaging (OWA) to two different network contexts. Knowledge flows in patent citation networks and a company supply chain network are analysed using Social Network Analysis (SNA) and the OWA operator. The OWA is used here for the first time (i) to rank indirect citations in patent networks, providing new insight into their role in transferring knowledge among network nodes; and to analyse a long chain of patent generations along 13 years; (ii) to rank indirect relations in a company supply chain network, to shed light on the role of indirectly connected individuals involved in the knowledge transfer and creation processes and to contribute to the literature on knowledge management in a supply chain. In doing so, indirect ties are measured and their role as means of knowledge transfer is shown. Thus, this thesis represents a first attempt to bridge the OWA and SNA fields and to show that the two methods can be used together to enrich the understanding of the role of indirectly connected nodes in a network. More specifically, the OWA scores enrich our understanding of knowledge evolution over time within complex networks. Future research can show the usefulness of OWA operator in different complex networks, such as the on-line social networks that consists of thousand of nodes.

A Remark On S.M. Bates' Theorem

In his paper [1], Bates investigates the existence of nonlinear, but highly smooth, surjective operators between various classes of Banach spaces. Modifying his basic method, he obtains the following striking results.

Continuity of Pseudo-differential Operators on Bessel And Besov Spaces

We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

On an Extremal Problem concerning Bernstein Operators

* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.

Self Evolving Character Recognition Using Genetic Operators

In this paper, a novel approach for character recognition has been presented with the help of genetic operators which have evolved from biological genetics and help us to achieve highly accurate results. A genetic algorithm approach has been described in which the biological haploid chromosomes have been implemented using a single row bit pattern of 315 values which have been operated upon by various genetic operators. A set of characters are taken as an initial population from which various new generations of characters are generated with the help of selection, crossover and mutation. Variations of population of characters are evolved from which the fittest solution is found by subjecting the various populations to a new fitness function developed. The methodology works and reduces the dissimilarity coefficient found by the fitness function between the character to be recognized and members of the populations and on reaching threshold limit of the error found from dissimilarity, it recognizes the character. As the new population is being generated from the older population, traits are passed on from one generation to another. We present a methodology with the help of which we are able to achieve highly efficient character recognition.

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function

Mathematics Subject Classification: 26A33, 33E12, 33C20.

LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators

Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15.

Rough Maximal Oscillatory Singular Integral Operators

2000 Mathematics Subject Classification: Primary 42B20; Secondary 42B15, 42B25

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

2000 Mathematics Subject Classification: 42B10, 43A32.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

On Integral Means for Fractional Calculus Operators of Multivalent Functions

2000 Mathematics Subject Classification: Primary 30C45, Secondary 26A33, 30C80

Commutants of the Dunkl Operators in C(R)

2000 Mathematics Subject Classification: 44A35; 42A75; 47A16, 47L10, 47L80