Hyperbolic cosine ratio and hyperbolic sine ratio random fields

2021 ◽  
pp. 109212
Author(s):  
Chunsheng Ma
Keyword(s):  
Random Fields ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine

scholarly journals Modelling of Nonuniform RC Structures for Computer Aided Design

1994 ◽  
Vol 16 (2) ◽  
pp. 89-95
Author(s):  
Muhammad Taher Abuelma'atti
Keyword(s):  
Simple Model ◽  
Computer Aided Design ◽  
Rc Structures ◽  
Analysis And Design ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Computer Aided Analysis ◽  
Computer Aided ◽  
Aided Design

A simple model for nonuniform distributed RC structures is presented. The model consists of three passive elements only and can be used for modelling nonuniform distributed RC structures involving exponential, hyperbolic sine squared, hyperbolic cosine squared and square taper geometries. The model can be easily implemented for computer-aided analysis and design of circuits and systems comprising nonuniform distributed RC structures.

scholarly journals Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution

2017 ◽  
Vol 8 ◽  
pp. 117959721773030 ◽  
Author(s):  
Glen Atlas ◽  
John K-J Li ◽  
Shawn Amin ◽  
Robert G Hahn
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Human Study ◽  
Patient Specific ◽  
Sine Function ◽  
Integro Differential Equation ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Group 2 ◽  
Group 1

A closed-form integro-differential equation (IDE) model of plasma dilution (PD) has been derived which represents both the intravenous (IV) infusion of crystalloid and the postinfusion period. Specifically, PD is mathematically represented using a combination of constant ratio, differential, and integral components. Furthermore, this model has successfully been applied to preexisting data, from a prior human study, in which crystalloid was infused for a period of 30 minutes at the beginning of thyroid surgery. Using Euler’s formula and a Laplace transform solution to the IDE, patients could be divided into two distinct groups based on their response to PD during the infusion period. Explicitly, Group 1 patients had an infusion-based PD response which was modeled using an exponentially decaying hyperbolic sine function, whereas Group 2 patients had an infusion-based PD response which was modeled using an exponentially decaying trigonometric sine function. Both Group 1 and Group 2 patients had postinfusion PD responses which were modeled using the same combination of hyperbolic sine and hyperbolic cosine functions. Statistically significant differences, between Groups 1 and 2, were noted with respect to the area under their PD curves during both the infusion and postinfusion periods. Specifically, Group 2 patients exhibited a response to PD which was most likely consistent with a preoperative hypovolemia. Overall, this IDE model of PD appears to be highly “adaptable” and successfully fits clinically-obtained human data on a patient-specific basis, during both the infusion and postinfusion periods. In addition, patient-specific IDE modeling of PD may be a useful adjunct in perioperative fluid management and in assessing clinical volume kinetics, of crystalloid solutions, in real time.

scholarly journals Generalized bounds for hyperbolic sine and hyperbolic cosine functions

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Ramkrishna M. Dhaigude ◽  
Yogesh J. Bagul ◽  
Vinay M. Raut
Keyword(s):  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Cosine Functions

scholarly journals A Kind of Infinite-Dimensional Novikov Algebras and Its Realizations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Liangyun Chen
Keyword(s):  
Infinite Dimensional ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Novikov Algebras ◽  
Sine Functions ◽  
Cosine Functions

We construct a kind of infinite-dimensional Novikov algebras and give its realization by hyperbolic sine functions and hyperbolic cosine functions.

scholarly journals EXCEL-orientated procedure for calculating the values of special functions with interval argument assigned on the hyperbolic form

2021 ◽  
Vol 5 (4) ◽  
pp. 116-123
Author(s):  
Valeriy Dubnitskiy ◽  
Anatolii Kobylin ◽  
Oleg Kobylin ◽  
Yuriy Kushneruk
Keyword(s):  
Exponential Function ◽  
Gamma Function ◽  
Special Functions ◽  
Beta Function ◽  
Digamma Function ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Hyperbolic Form ◽  
Hyperbolic Trigonometry ◽  
Integral Exponential Function

Aim of the work is to propose the main terms of the EXCEL-orientated procedures for calculating the values of elementary and special functions with interval argument that is assigned on the hyperbolic form. The results of the work. The methods of presenting the interval values in the hyperbolic form and the rules of addition, subtraction, multiplication, and division of this values were considered. The procedures of calculating the function values, whose arguments can be degenerate or interval values were described. Namely, the direct and the reverse functions of the linear trigonometry, the direct and the reverse functions of the hyperbolic trigonometry, exponential function, arbitrary exponential function and power function, Gamma-function, incomplete Gamma-function, digamma-function, trigamma-function, tetragamma-function, pentagamma-function, Beta-function and its partial derivatives, integral exponential function, integral logarithm, dilogarithm, Frenel integrals, sine integral, cosine integral, hyperbolic sine integral, hyperbolic cosine integral. The basic terms of the EXCEL-orientated procedures for calculating the values of elementary and special functions with interval argument that is assigned on the hyperbolic form were proposed. The numerical examples were provided, that illustrate the application of the proposed methods.

Fractional Integration of Generalized Bessel Function of the First Kind

2011 ◽  
Author(s):  
Pradeep Malik ◽  
Saiful R. Mondal ◽  
A. Swaminathan
Keyword(s):  
Bessel Function ◽  
Hypergeometric Functions ◽  
Fractional Integration ◽  
Integral Transforms ◽  
Generalized Hypergeometric Functions ◽  
Fractional Integral Operators ◽  
Generalized Bessel Function ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Special Cases

Generalizing the classical Riemann-Liouville and Erde´yi-Kober fractional integral operators two integral transforms involving Gaussian hypergeometric functions in the kernel are considered. Formulas for composition of such integrals with generalized Bessel function of the first kind are obtained. Special cases involving trigonometric functions such as sine, cosine, hyperbolic sine and hyperbolic cosine are deduced. These results are established in terms of generalized Wright function and generalized hypergeometric functions.

scholarly journals EXACT ROLLING TACHYON IN NONCOMMUTATIVE FIELD THEORY

2006 ◽  
Vol 21 (05) ◽  
pp. 421-431 ◽  
Author(s):  
YOONBAI KIM ◽  
O-KAB KWON
Keyword(s):  
Field Theory ◽  
Electric Field ◽  
Constant Electric Field ◽  
Equations Of Motion ◽  
Open String ◽  
Noncommutative Field Theory ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Noncommutative Parameter

We find exact rolling tachyon solutions in DBI type noncommutative field theory with constant open string metric and noncommutative parameter on an unstable D p-brane. Their functional shapes span all possible homogeneous rolling tachyon solutions, i.e. they are hyperbolic-cosine, hyperbolic-sine, and exponential under 1/cosh runaway NC tachyon potential. Even if general DBI type NC electric field is turned on, only constant electric field satisfies equations of motion and again exact homogeneous rolling tachyon solutions are obtained.

scholarly journals Modified Sumudu Transform and Its Properties

2020 ◽  
Author(s):  
Ugur Duran
Keyword(s):  
Laplace Transform ◽  
Power Function ◽  
Exponential Function ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Sumudu Transform ◽  
And Function ◽  
Sumudu Transforms ◽  
Dual Transform

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

scholarly journals Degenerate Sumudu Transform and Its Properties

2020 ◽  
Author(s):  
Ugur Duran
Keyword(s):  
Laplace Transform ◽  
Gamma Function ◽  
Power Functions ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Sumudu Transform ◽  
And Function ◽  
Sumudu Transforms ◽  
Dual Transform ◽  
Math Phys

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

scholarly journals On solutions of PDEs by using algebras

2021 ◽  
Author(s):  
ELIFALET LÓPEZ-GONZÁLEZ
Keyword(s):  
Vector Field ◽  
Exponential Function ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Differentiable Functions ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Dependent Variables ◽  
Planar Vector ◽  
Cosine Functions

The components of complex differentiable functions define solutions for the Laplace’s equation. In this paper we generalize this result; for each PDE of the form $Au_{xx}+Bu_{xy}+Cu_{yy}=0$ we give an affine planar vector field $\varphi$ and an associative and commutative 2D algebra with unit $\mathbb A$, with respect to which the components of all functions of the form $\mathcal L\circ\varphi$ define solutions for this PDE, where $\mathcal L$ is differentiable in the sense of Lorch with respect to $\mathbb A$. In the same way, for each PDE of the form $Au_{xx}+Bu_{xy}+Cu_{yy}+Du_x+Eu_y+Fu=0$, the components of the exponential function $e^{\varphi}$ defined with respect to $\mathbb A$, define solutions for this PDE. In the case of PDEs of the form $Au_{xx}+Bu_{xy}+Cu_{yy}+Fu=0$, sine, cosine, hyperbolic sine, and hyperbolic cosine functions can be used instead of the exponential function. Also, solutions for two dependent variables $3^{\text{th}}$ order PDEs and a $4^{\text{th}}$ order PDE are constructed.

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