Approximation by exponentials. III. The use of the product of a polynomial and an exponential function

1973 ◽  
Vol 38 (11) ◽  
pp. 3352-3361 ◽  
Author(s):  
E. Slavíček
Keyword(s):  
Exponential Function

Distribution and Correlation of the Coding Sequence Lengths in Bacterial Genomes

2008 ◽  
Vol 59 (11) ◽  
Author(s):  
Vasile V. Morariu
Keyword(s):  
Correlation Analysis ◽  
Exponential Function ◽  
Short Range ◽  
Statistical Physics ◽  
Bacterial Genomes ◽  
Coding Sequence ◽  
Correlation Properties ◽  
Short Range Correlations ◽  
Fluctuating System

The length of coding sequence (CDS) series in bacterial genomes were regarded as a fluctuating system and characterized by the methods of statistical physics. The distribution and the correlation properties of CDS for 47 genomes were investigated. The distribution was found to be approximated by an exponential function while the correlation analysis revealed short range correlations.

Myocardial blood flow determined with krypton 85 in unanesthetized dogs

1962 ◽  
Vol 203 (1) ◽  
pp. 122-124 ◽  
Author(s):  
J. A. Herd ◽  
M. Hollenberg ◽  
G. D. Thorburn ◽  
H. H. Kopald ◽  
A. C. Barger
Keyword(s):  
Blood Flow ◽  
Coronary Artery ◽  
Myocardial Blood Flow ◽  
Exponential Function ◽  
Scintillation Detector ◽  
Left Ventricular ◽  
Blood Flows ◽  
Single Exponential Function ◽  
Single Exponential ◽  
Rapid Measurements

Serial, rapid measurements of left ventricular myocardial blood flow in trained, unanesthetized dogs have been made by injecting krypton 85 through chronically implanted coronary artery catheters and counting with an external scintillation detector. Precordial radioactivity declined as a single exponential function during the first 2 min after injection, suggesting a single rate of myocardial blood flow. Simultaneous estimations with Kr85 and blood flowmeters in acute experiments established the accuracy and reproducibility of the technique. Myocardial blood flows between 40 and 55 ml/100 g/min were observed repeatedly in three well-trained, unanesthetized dogs in the basal state.

An FPGA-based Application-Specific Processor for Implementing the Exponential Function

2020 ◽  
Author(s):  
Shrikant S. Jadhav ◽  
Clay Gloster ◽  
Jannatun Naher ◽  
Christopher Doss ◽  
Youngsoo Kim
Keyword(s):  
Exponential Function ◽  
Application Specific

scholarly journals The Jacobian of the exponential function

2021 ◽  
Vol 127 ◽  
pp. 104122
Author(s):  
Jan R. Magnus ◽  
Henk G.J. Pijls ◽  
Enrique Sentana
Keyword(s):  
Exponential Function

scholarly journals Some Applications of the Wright Function in Continuum Physics: A Survey

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 198
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Exponential Function ◽  
Nonlocal Elasticity ◽  
Bessel Functions ◽  
Wright Function ◽  
Mainardi Function ◽  
Integral Relations

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

scholarly journals Multidimensional van der Corput-Type estimates involving Mittag-Leffler functions

2020 ◽  
Vol 23 (6) ◽  
pp. 1663-1677
Author(s):  
Michael Ruzhansky ◽  
Berikbol T. Torebek
Keyword(s):  
Cauchy Problem ◽  
Exponential Function ◽  
Evolution Equations ◽  
Oscillatory Integrals ◽  
Schrödinger Equations ◽  
Fractional Evolution Equations ◽  
Type Function ◽  
Fractional Schrödinger Equations ◽  
The Cauchy Problem ◽  
Klein Gordon

Abstract The paper is devoted to study multidimensional van der Corput-type estimates for the intergrals involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study multidimensional oscillatory integrals appearing in the analysis of time-fractional evolution equations. More specifically, we study two types of integrals with functions E α, β (i λ ϕ(x)), x ∈ ℝ N and E α, β (i α λ ϕ(x)), x ∈ ℝ N for the various range of α and β. Several generalisations of the van der Corput-type estimates are proved. As an application of the above results, the Cauchy problem for the multidimensional time-fractional Klein-Gordon and time-fractional Schrödinger equations are considered.

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