On a 3D-Hypersingular Equation of a Problem for a Crack

MSC 2010: 45DB05, 45E05, 78A45

Direct and Converse Theorems for Generalized Bernstein-Type Operators

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.

Best Approximation and Moduli of Smoothness

2010 Mathematics Subject Classification: 41A25, 41A10.

On generalized orlicz sequence spaces of Fourier coefficients for trigonometric gap series. I.

We investigate the operator associating with a function fєLp2π, 1operator from a modular space X ρs(ϕ) to the generalized Orlicz sequence space lϕ.

A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.

Solvability of an Infinite System of Singular Integral Equations

2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.

Generalized Backscattering and the Lax-Phillips Transform

2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.

An Iterative Procedure for Solving Nonsmooth Generalized Equation

2000 Mathematics Subject Classification: 47H04, 65K10.

On Some Generalizations of Classical Integral Transforms

MSC 2010: 44A15, 44A20, 33C60

Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.

Generalized Derivations and Norm Equality in Normed Ideals

2000 Mathematics Subject Classification: 47A10, 47A12, 47A30, 47B10, 47B20, 47B37, 47B47, 47D50.

Topologies on groups related to the theory of shape and generalized coverings

El presente trabajo consiste en dos partes diferenciadas: la principal de ellas (Cap tulos 1 y 2) est a dedicada a introducir estructura adicional en grupos que aparecen de manera natural en el contexto de la teor a de la forma. En la segunda parte (Cap tulo 3), se plantea c omo generalizar la teor a de espacios recubridores y, en particular, se propone una l nea de trabajo relacionada con la teor a de la forma. El punto de partida de esta tesis doctoral son los trabajos [25, 26, 68, 69, 70] en los que los autores introducen y utilizan algunas ultram etricas en el conjunto de los mor smos shape entre dos espacios topol ogicos punteados. En particular, si el dominio es (S1; 1); la construcci on realizada en [68] permite explicitar una ultram etrica en el grupo shape 1(X; x0) de un espacio m etrico compacto X; como ya fue observado en [69] y [80]. Si el espacio no es m etrico compacto, la construcci on nos lleva a utilizar el concepto de ultram etrica generalizada, en el sentido de Priess-Crampe y Ribenboim [78, 79]. En [7], D. K. Biss introduce la idea de topologizar el grupo fundamental de un espacio, de forma que la topolog a en 1(X; x0) sea una topolog a de grupo que permita detectar la (no) existencia de un recubridor universal para X: La forma de proceder sugerida es tomar en 1(X; x0)la toplog a cociente inducida por la topolog a compacto-abierta en el espacio de lazos (X; x0): Sin embargo, hay algunos errores en el art culo mencionado: en concreto, el error relacionado con el presente trabajo fue puesto de mani esto por P. Fabel en [33], mostrando que, en general, la operaci on de grupo en 1(X; x0)con la topolog a cociente no es continua. Utilizando un punto de vista similar, varios autores han tratado de dotar al grupo fundamental con una topolog a, de forma que 1(X; x0) sea un grupo topol ogico y la proyecci on q (X; x0){u100000} 1(X; x0)sea continua...

Secure Transmission in Spectrum Sharing MIMO Networks with Generalized Antenna Selection over Nakagami-m Channels

In this paper, we investigate the secrecy outage performance of spectrum sharing multiple-input multiple-output networks using generalized transmit antenna selection with maximal ratio combining over Nakagami-m channels. In particular, the outdated channel state information is considered at the process of antenna selection due to feedback delay. Considering a practical passive eavesdropper scenario, we derive the exact and asymptotic closed-form expressions of secrecy outage probability, which enable us to evaluate the secrecy performance with high efficiency and present a new design insight into the impact of key parameters on the secrecy performance. In addition, the analytical results demonstrate that the achievable secrecy diversity order is only determined by the parameters of the secondary network, while other parameters related to primary or eavesdropper’s channels have a significantly impact on the secrecy coding gain. 

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.