Basic Exponential Functions on a q-Quadratic Grid

2001 ◽  
pp. 411-456 ◽  
Author(s):  
Sergei K. Suslov
Keyword(s):  
Exponential Functions

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales

2020 ◽  
Vol 18 (1) ◽  
pp. 353-377 ◽  
Author(s):  
Zhien Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Quaternion Algebra ◽  
Matrix Exponential ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Quaternion Matrix ◽  
Exponential Functions ◽  
Cauchy Matrix ◽  
Adjoint Matrix ◽  
Sufficient And Necessary Condition

Abstract In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex adjoint matrix of a quaternion matrix. Moreover, the Cauchy matrices and Liouville formulas for the quaternion homogeneous and nonhomogeneous impulsive dynamic equations are given and proved. Based on it, the existence, uniqueness, and expressions of their solutions are also obtained, including their scalar and matrix forms. Since the quaternion algebra is noncommutative, many concepts and properties of the non-quaternion impulsive dynamic equations are ineffective, we provide several examples and counterexamples on various time scales to illustrate the effectiveness of our results.

scholarly journals Simultaneous Contour Method of a Trigonometric Integral by Prudnikov et al.

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1453
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Closed Form ◽  
Contour Method ◽  
Substantial Part ◽  
Exponential Functions ◽  
Closed Form Solutions ◽  
Definite Integrals ◽  
Transcendental Functions ◽  
Trigonometric Integral

In this present work we derive, evaluate and produce a table of definite integrals involving logarithmic and exponential functions. Some of the closed form solutions derived are expressed in terms of elementary or transcendental functions. A substantial part of this work is new.

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

scholarly journals Energy Minimization Scheme for Split Potential Systems Using Exponential Variational Integrators

2021 ◽  
Vol 2 (3) ◽  
pp. 431-441
Author(s):  
Odysseas Kosmas
Keyword(s):  
Numerical Solutions ◽  
Oscillatory Behavior ◽  
Lagrangian Function ◽  
Computational Time ◽  
Variational Integrators ◽  
Weighted Sum ◽  
Lagrange Equations ◽  
Exponential Functions ◽  
Intermediate Time ◽  
Definition Of

In previous works we developed a methodology of deriving variational integrators to provide numerical solutions of systems having oscillatory behavior. These schemes use exponential functions to approximate the intermediate configurations and velocities, which are then placed into the discrete Lagrangian function characterizing the physical system. We afterwards proved that, higher order schemes can be obtained through the corresponding discrete Euler–Lagrange equations and the definition of a weighted sum of “continuous intermediate Lagrangians” each of them evaluated at an intermediate time node. In the present article, we extend these methods so as to include Lagrangians of split potential systems, namely, to address cases when the potential function can be decomposed into several components. Rather than using many intermediate points for the complete Lagrangian, in this work we introduce different numbers of intermediate points, resulting within the context of various reliable quadrature rules, for the various potentials. Finally, we assess the accuracy, convergence and computational time of the proposed technique by testing and comparing them with well known standards.

An elastic phenomenological material law of technical textile with a nonlinear shear behaviour

2021 ◽  
pp. 073168442110058
Author(s):  
Dániel T Karádi ◽  
András A Sipos ◽  
Marianna Halász ◽  
Viktor Hliva ◽  
Dezső Hegyi
Keyword(s):  
Service Level ◽  
Shear Behaviour ◽  
Nonlinear Behaviour ◽  
Exponential Functions ◽  
Normal Stiffness ◽  
Material Parameters ◽  
Fitting Method ◽  
Highly Nonlinear ◽  
Nonlinear Shear ◽  
Magnitude Difference

In technical textile engineering, macro-level phenomenological modelling effectively describes the material’s highly nonlinear behaviour. However, existing material laws concentrate on the normal stiffness in the orthotropic yarns and simplify the shear effect because of the two orders of magnitude difference between shear and normal stiffness. This article introduces an improved phenomenological model that includes nonlinear shear behaviour, and it determines the material parameters with a previously applied data fitting method for exponential functions. The nonlinear shear behaviour is valid for the elastic state, that is, at the service level of the loads. Time-dependent, cyclic loading or plastic behaviour is not considered.

An Advanced Strategy for Detecting Impulses in Mechanical Signals

2005 ◽  
Vol 127 (3) ◽  
pp. 280-284 ◽  
Author(s):  
Wen-xian Yang ◽  
Peter W. Tse
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Spectral Features ◽  
Continuous Wavelet ◽  
Exponential Functions ◽  
Soft Thresholding ◽  
Thresholding Method ◽  
Mechanical Signals ◽  
Soft Threshold

The appearance of overlapping in the results derived by continuous wavelet transform (CWT) smears the spectral features and makes the results difficult to interpret. This will significantly affect the accuracy of analysis of anomalous signals. Aiming at minimizing the undesired effect of overlapping, a new soft-thresholding method in terms of exponential functions is proposed. Using the proposed soft-threshold and combining with Donoho’s approach for reducing the structures induced by noise, a strategy for purifying the results derived by the CWT is designed. A series of simulated and practical experiments show that, after adopting the proposed strategy, the results of CWT are further purified and thereby the spectral features of the inspected signal become more explicit and much more easily identified.

ELIMINATION OF INFUSED ARGININE-VASOPRESSIN AND ITS LONG-ACTING DEAMINATED ANALOGUE IN RATS

1978 ◽  
Vol 78 (2) ◽  
pp. 179-186 ◽  
Author(s):  
DIANA GAZIS ◽  
W. H. SAWYER
Keyword(s):  
Arginine Vasopressin ◽  
Plasma Concentrations ◽  
Metabolic Clearance ◽  
Prolonged Infusion ◽  
Exponential Functions ◽  
Antidiuretic Effect ◽  
Long Acting ◽  
Deamino Arginine Vasopressin

SUMMARY Arginine-vasopressin (AVP) and deamino-arginine-vasopressin (dAVP) were infused into rats. When the concentrations of the two peptides were steady, the rate of clearance of AVP from the plasma was six times the rate of clearance of dAVP. Only 6% of the infused AVP was excreted unchanged in the urine, whereas approximately 100% of the dAVP was excreted. When the infusions were stopped, AVP disappeared from the plasma much more rapidly than dAVP. The plasma concentrations of the two peptides did not decay as simple exponential functions, suggesting that both AVP and dAVP entered a slowly exchanging compartment or compartments during prolonged infusion. These differences in the metabolic clearance of AVP and dAVP may well explain the prolonged antidiuretic effect of dAVP in rats.

An Explanation of the Removal of Metastability in Some Hydroacid Salts by Water Adsorption

2001 ◽  
Vol 56 (12) ◽  
pp. 869-872
Author(s):  
B. Baranowski ◽  
A. Lundén
Keyword(s):  
Phase Transition ◽  
Surface Layer ◽  
Water Activity ◽  
Induction Time ◽  
Lattice Spacing ◽  
Water Adsorption ◽  
Zeroth Order ◽  
Exponential Functions ◽  
Kinetics Of ◽  
Volume Decrease

Abstract The metastability of some phases of CsHSO4 and RbH2PO4 is due to the volume decrease at an endothermic phase transition which "locks in" the metastability in question. Water adsorption, which removes these metastabilities, probably exerts a "wedge-like" force which expands the lattice spacing in the surface layer, thus facilitating the start of the phase transition. The induction time and the zeroth order kinetics of the transition in RbH2PO4 are exponential functions of the water activity applied.

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