scholarly journals Refinements on Some Classes of Complex Function Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 339 ◽  
Author(s):  
Ahmed El-Sayed Ahmed
Keyword(s):  
Complex Function ◽  
Function Spaces ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Chordal Metric

Some weighted classes of hyperbolic function spaces are defined and studied in this paper. Finally, by using the chordal metric concept, some investigations for a class of general hyperbolic functions are also given.

scholarly journals Certain Classes of Operators on Some Weighted Hyperbolic Function Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
A. El-Sayed Ahmed ◽  
Amnah E. Shammaky
Keyword(s):  
General Class ◽  
Metric Spaces ◽  
Function Spaces ◽  
Multiplication Operators ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Bloch Functions

In this paper, some classes of concerned multiplication operators consisting of analytic and hyperbolic functions are defined and considered. Furthermore, some properties such as boundedness and compactness of the new operators are discussed. Finally, a general class of weighted hyperbolic Bloch functions is characterized by metric spaces.

scholarly journals New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yusuf Pandir ◽  
Halime Ulusoy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Wave Equations ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Partial Differential ◽  
New Exact Solutions

We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE), we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

Evaluation of Prior Experience in Skilled Performance

1974 ◽  
Vol 18 (5) ◽  
pp. 526-532
Author(s):  
Stanley Lippert
Keyword(s):  
Skill Acquisition ◽  
Prior Experience ◽  
Individual Performance ◽  
Hyperbolic Function ◽  
Sample Population ◽  
Hyperbolic Functions ◽  
Skilled Performance ◽  
Standard Deviations ◽  
The Individual ◽  
Mean Function

A review of some studies of skill acquisition indicates that a simple hyperbolic function fits data on individual performance well. The function yields an explicit value of prior experience related to the task. The particular function for an individual can be adjusted to a “hypothetical first” trial which is common to other members of the sample population. The individual constants in the adjusted functions may then be averaged arithmetically to give a mean function, which is also an hyperbola. Standard deviations of the values of the constants may also be computed. These too will be hyperbolic functions.

scholarly journals Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zeid I. A. Al-Muhiameed ◽  
Emad A.-B. Abdel-Salam
Keyword(s):  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Nonlinear Schrödinger ◽  
Function Solution ◽  
Balance Principle ◽  
Hyperbolic Function Solution ◽  
Differential Equation Method

With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are investigated and the exact solutions are derived with the aid of the homogenous balance principle and generalized hyperbolic functions. We study the effect of the generalized hyperbolic function parameterspandqin the obtained solutions by using the computer simulation.

A Hyperbolic Arnold's Cat Map-Based System for Multimedia Data Encryption

2021 ◽  
Vol 12 (2) ◽  
pp. 57-71
Author(s):  
Amine Rahmani
Keyword(s):  
Chaotic Map ◽  
Data Encryption ◽  
Multimedia Data ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Mathematical Concepts ◽  
Asymmetric Cryptography ◽  
Chebyshev Map ◽  
Arnold’S Cat Map ◽  
Encryption And Decryption

Cryptography is one of the most used techniques to secure data since antiquity. It has been largely improved by introducing several mathematical concepts. This paper proposes a new asymmetric cryptography approach using combined Arnold's cat map with hyperbolic function and Chebyshev chaotic map for audio and image encryption. The proposed scheme uses Chebyshev map for public and secrete keys generation and the same equation with Arnold's cat map for encryption and decryption. Hyperbolic functions are also introduced replacing regular integer values in Arnold's map. The results show a good and promising efficiency as well as the theoretical discussion. Several future possible improvements are presented in the conclusion.

A series of complexiton soliton solutions for nonlinear Jaulent—Miodek PDEs using the Riccati equations method

2011 ◽  
Vol 141 (5) ◽  
pp. 1001-1015 ◽  
Author(s):  
E. M. E. Zayed ◽  
Khaled A. Gepreel
Keyword(s):  
Rational Function ◽  
Symbolic Computation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Riccati Equations ◽  
Hyperbolic Function ◽  
Periodic Functions ◽  
Hyperbolic Functions ◽  
Hyperbolic Function Solutions ◽  
Triangular Function

We use the extended multiple Riccati equations expansion method to construct a series of double-soliton-like solutions, double triangular function solutions and complexiton soliton solutions for nonlinear Jaulent-Miodek PDEs. With the help of symbolic computation using Maple and Mathematica, we obtain many new types of complexiton soliton solutions, i.e. various combinations of trigonometric periodic functions and hyperbolic function solutions, various combinations of trigonometric periodic functions and rational function solutions, and various combinations of hyperbolic functions and rational function solutions.

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