Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Krätzel Function as a Function of Hypergeometric Type

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

Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15

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.

Asymptotic and structural properties of special cases of the Wright function arising in probability theory

This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymptotic properties of the particular Wright function 1Ψ1(ρ, k; ρ, 0; x) = X∞ n=0 Γ(k + ρn) Γ(ρn) x n n! (|x| < ∞) when the parameter ρ ∈ (−1, 0)∪(0, ∞) and the argument x is real. In the probability theory applications, which are focused on studies of the Poisson-Tweedie mixtures, the parameter k is a non-negative integer. Several representations involving well-known special functions are given for certain particular values of ρ. The asymptotics of 1Ψ1(ρ, k; ρ, 0; x) are obtained under numerous assumptions on the behavior of the arguments k and x when the parameter ρ is both positive and negative. We also provide some integral representations and structural properties involving the ‘reduced’ Wright function 0Ψ1(−−; ρ, 0; x) with ρ ∈ (−1, 0) ∪ (0, ∞), which might be useful for the derivation of new properties of members of the power-variance family of distributions. Some of these imply a reflection principle that connects the functions 0Ψ1(−−;±ρ, 0; ·) and certain Bessel functions. Several asymptotic relationships for both particular cases of this function are also given. A few of these follow under additional constraints from probability theory results which, although previously available, were unknown to analysts.

On Hankel Transform of Generalized Mathieu Series

Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.

CO2-response function of radiation use efficiency in rice for climate change scenarios

The objective of this work was to evaluate a generalized response function to the atmospheric CO2 concentration [f(CO2)] by the radiation use efficiency (RUE) in rice. Experimental data on RUE at different CO2 concentrations were collected from rice trials performed in several locations around the world. RUE data were then normalized, so that all RUE at current CO2 concentration were equal to 1. The response function was obtained by fitting normalized RUE versus CO2 concentration to a Morgan-Mercer-Flodin (MMF) function, and by using Marquardt's method to estimate the model coefficients. Goodness of fit was measured by the standard deviation of the estimated coefficients, the coefficient of determination (R²), and the root mean square error (RMSE). The f(CO2) describes a nonlinear sigmoidal response of RUE in rice, in function of the atmospheric CO2 concentration, which has an ecophysiological background, and, therefore, renders a robust function that can be easily coupled to rice simulation models, besides covering the range of CO2 emissions for the next generation of climate scenarios for the 21st century.

Renewal Processes of Mittag-Leffler and Wright Type

2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.

Generalization of the Modified Bessel Function and Its Generating Function

2000 Mathematics Subject Classification: 33C10, 33-02, 60K25