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 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 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.

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 Periodic solution to general conduction problems

2013 ◽  
Vol 17 (5) ◽  
pp. 1494-1496
Author(s):  
Gui Mu ◽  
Zhengde Dai ◽  
Jun Liu ◽  
Jie Fu
Keyword(s):  
Periodic Solution ◽  
Function Method ◽  
Solution Process ◽  
Energy Localization ◽  
Periodic Effect ◽  
Hyperbolic Cosine ◽  
Cosine Functions

In this paper, we present a modified exp-function method, where hyperbolic cosine and cosine functions are used. The hyperbolic cosine functions are responsible for energy localization while cosine functions reveal the periodic effect. A general conduction problem is used as an example to illustrate the solution process.

scholarly journals Circuit Implementation of a Modified Chaotic System with Hyperbolic Sine Nonlinearities Using Bi-Color LED

Technologies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 15
Author(s):  
Christos K. Volos ◽  
Lazaros Moysis ◽  
George D. Roumelas ◽  
Aggelos Giakoumis ◽  
Hector E. Nistazakis ◽  
...  
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Original System ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
Circuit Realization ◽  
Hyperbolic Sine ◽  
Route To Chaos ◽  
Sine Functions

In this paper, a chaotic three dimansional dynamical system is proposed, that is a modification of the system in Volos et al. (2017). The new system has two hyperbolic sine nonlinear terms, as opposed to the original system that only included one, in order to optimize system’s chaotic behavior, which is confirmed by the calculation of the maximal Lyapunov exponents and Kaplan-Yorke dimension. The system is experimentally realized, using Bi-color LEDs to emulate the hyperbolic sine functions. An extended dynamical analysis is then performed, by computing numerically the system’s bifurcation and continuation diagrams, Lyapunov exponents and phase portraits, and comparing the numerical simulations with the circuit simulations. A series of interesting phenomena are unmasked, like period doubling route to chaos, coexisting attractors and antimonotonicity, which are all verified from the circuit realization of the system. Hence, the circuit setup accurately emulates the chaotic dynamics of the proposed system.

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.

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