Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

Generalized Fractional Evolution Equation

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20

Generalized partition function zeros of 1D spin models and their critical behavior at edge singularities

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimating and forecasting generalized fractional Long memory stochastic volatility models

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model.

Minimization of logic networks under a generalized cost function /

Includes bibliographical references.

Validation of a generalized transfer function to noninvasively derive central blood pressure during exercise

Exercise brachial blood pressure ( BP) predicts mortality, but because of wave reflection, central ( ascending aortic) pressure differs from brachial pressure. Exercise central BP may be clinically important, and a noninvasive means to derive it would be useful. The purpose of this study was to test the validity of a noninvasive technique to derive exercise central BP. Ascending aortic pressure waveforms were recorded using a micromanometer-tipped 6F Millar catheter in 30 patients (56 +/- 9 years; 21 men) undergoing diagnostic coronary angiography. Simultaneous recordings of the derived central pressure waveform were acquired using servocontrolled radial tonometry at rest and during supine cycling. Pulse wave analysis of the direct and derived pressure signals was performed offline (SphygmoCor 7.01). From rest to exercise, mean arterial pressure and heart rate were increased by 20 +/- 10 mm Hg and 15 +/- 7 bpm, respectively, and central systolic BP ranged from 77 to 229 mm Hg. There was good agreement and high correlation between invasive and noninvasive techniques with a mean difference (+/- SD) for central systolic BP of -1.3 +/- 3.2 mm Hg at rest and -4.7 +/- 3.3 mm Hg at peak exercise ( for both r=0.995; P < 0.001). Conversely, systolic BP was significantly higher peripherally than centrally at rest (155 +/- 33 versus 138 +/- 32mm Hg; mean difference, -16.3 +/- 9.4mm Hg) and during exercise (180 +/- 34 versus 164 +/- 33 mm Hg; mean difference, -15.5 +/- 10.4 mm Hg; for both P < 0.001). True myocardial afterload is not reliably estimated by peripheral systolic BP. Radial tonometry and pulse wave analysis is an accurate technique for the noninvasive determination of central BP at rest and during exercise.

A Brief Story about the Operators of the Generalized Fractional Calculus

2000 Mathematics Subject Classification: 26A33, 33C60, 44A20

Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата.

Generalized Discernibility Function Based Attribute Reduction in Incomplete Decision Systems

A rough set approach for attribute reduction is an important research subject in data mining and machine learning. However, most attribute reduction methods are performed on a complete decision system table. In this paper, we propose methods for attribute reduction in static incomplete decision systems and dynamic incomplete decision systems with dynamically-increasing and decreasing conditional attributes. Our methods use generalized discernibility matrix and function in tolerance-based rough sets.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Krätzel Function as a Function of Hypergeometric Type

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15

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

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