IEEE Transactions on Electromagnetic Compatibility, ISSN 0018-9375, 12/2015, Volume 57, Issue 6, pp. 1698 - 1704

A fast and stable algorithm for approximation of sine and cosine hyperbolic functions is presented in this paper. The algorithm can be used for S-parameter...

Geometry | Accuracy | ABCD parameters | Estimation | RLGC parameters | Approximation algorithms | Scattering parameters | Approximation methods | MATLAB | sine and cosine hyperbolic functions | transmission lines | scattering parameters | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Functions, Exponential | Research | Accuracy and precision | Analysis | Algorithms | Approximation | Mathematical analysis | Electromagnetic compatibility | Mathematical models | Hyperbolic functions | Trigonometric functions | Convergence

Geometry | Accuracy | ABCD parameters | Estimation | RLGC parameters | Approximation algorithms | Scattering parameters | Approximation methods | MATLAB | sine and cosine hyperbolic functions | transmission lines | scattering parameters | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Functions, Exponential | Research | Accuracy and precision | Analysis | Algorithms | Approximation | Mathematical analysis | Electromagnetic compatibility | Mathematical models | Hyperbolic functions | Trigonometric functions | Convergence

Journal Article

Pakistan Journal of Statistics, ISSN 1012-9367, 05/2013, Volume 29, Issue 3, pp. 315 - 321

In the paper, the authors establish two sharp double inequalities between the hyperbolic cosine function and the sine and cosine functions.

Sharp inequality | Hyperbolic cosine | Sine | Cosine | WILKER | MONOTONICITY | STATISTICS & PROBABILITY | JORDANS INEQUALITY | RULES

Sharp inequality | Hyperbolic cosine | Sine | Cosine | WILKER | MONOTONICITY | STATISTICS & PROBABILITY | JORDANS INEQUALITY | RULES

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2001, Volume 47, Issue 2, pp. 861 - 872

The hyperbolic sine and cosine functions on measure chains were defined and their basic properties were established. The so-called calculus on measure chains...

Focal point | Hyperbolic sine and cosine functions | Measure chain | MATHEMATICS | MATHEMATICS, APPLIED | measure chain | hyperbolic sine and cosine functions | focal point

Focal point | Hyperbolic sine and cosine functions | Measure chain | MATHEMATICS | MATHEMATICS, APPLIED | measure chain | hyperbolic sine and cosine functions | focal point

Journal Article

International Journal of Modern Physics B, ISSN 0217-9792, 11/2014, Volume 28, Issue 28, pp. 1450194 - 1-1450194-10

In this paper, the even and odd truncated coherent states are considered. In this process, the incomplete hyperbolic cosine and sine function are proposed. For...

Even and odd truncated coherent state | incomplete hyperbolic cosine and sine function | nonclassical property | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | ELECTROMAGNETIC-FIELD | PHYSICS, MATHEMATICAL | OSCILLATOR | MECHANICS | DISTINGUISHABLE QUANTUM STATES | GENERATION | DIMENSIONAL HILBERT-SPACE | SUPERPOSITIONS | Trigonometric functions | Coherence

Even and odd truncated coherent state | incomplete hyperbolic cosine and sine function | nonclassical property | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | ELECTROMAGNETIC-FIELD | PHYSICS, MATHEMATICAL | OSCILLATOR | MECHANICS | DISTINGUISHABLE QUANTUM STATES | GENERATION | DIMENSIONAL HILBERT-SPACE | SUPERPOSITIONS | Trigonometric functions | Coherence

Journal Article

Nonlinear Studies, ISSN 1359-8678, 2013, Volume 20, Issue 3, pp. 331 - 348

Journal Article

04/2014, ISBN 9781631173356

Book Chapter

Journal of Mathematical Inequalities, ISSN 1846-579X, 2017, Volume 11, Issue 3, pp. 817 - 829

In this article we present a method for proving inequalities of the form f(x) = Sigma(n)(i=1) alpha(i)x(pi) sinh(qi) x cosh(ri) x > 0, for x. (delta(1),...

Approximations of the hyperbolic sine and hyperbolic cosine | Hyperbolic inequalities | Trigonometric inequalities | MATHEMATICS | MATHEMATICS, APPLIED | trigonometric inequalities | approximations of the hyperbolic sine and hyperbolic cosine

Approximations of the hyperbolic sine and hyperbolic cosine | Hyperbolic inequalities | Trigonometric inequalities | MATHEMATICS | MATHEMATICS, APPLIED | trigonometric inequalities | approximations of the hyperbolic sine and hyperbolic cosine

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 3, pp. A1696 - A1713

A new algorithm is derived for computing the action f(tA)B, where A is an n x n matrix, B is n x n(0) with n(0) x n, and f is cosine, sinc, sine, hyperbolic...

Trigonometric integrators | Hyperbolic cosine | Taylor series | Hyperbolic sine | Variation of the constants formula | Ordinary differential equation | MATLAB | Matrix cosine | Sinc function | Chebyshev polynomials | Matrix sine | MATHEMATICS, APPLIED | variation of the constants formula | matrix sine | ordinary differential equation | trigonometric integrators | sinc function | hyperbolic cosine | COSINE | matrix cosine | hyperbolic sine

Trigonometric integrators | Hyperbolic cosine | Taylor series | Hyperbolic sine | Variation of the constants formula | Ordinary differential equation | MATLAB | Matrix cosine | Sinc function | Chebyshev polynomials | Matrix sine | MATHEMATICS, APPLIED | variation of the constants formula | matrix sine | ordinary differential equation | trigonometric integrators | sinc function | hyperbolic cosine | COSINE | matrix cosine | hyperbolic sine

Journal Article

SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2016, Volume 37, Issue 4, pp. 1453 - 1477

Theoretical and computational aspects of matrix inverse trigonometric and inverse hyperbolic functions are studied. Conditions for existence are given, all...

Inverse trigonometric functions | Rational approximation | Matrix inverse cosine | Fréchet derivative | MATLAB | Matrix function | Matrix inverse hyperbolic cosine | Matrix exponential | Matrix inverse sine | Matrix inverse hyperbolic sine | Matrix sign function | Condition number | GNU Octave | Inverse hyperbolic functions | Matrix logarithm | Padé approximation | MATHEMATICS, APPLIED | matrix inverse cosine | matrix exponential | Pade approximation | matrix inverse hyperbolic cosine | ELEMENTARY-FUNCTIONS | inverse trigonometric functions | Frechet derivative | matrix inverse sine | matrix inverse hyperbolic sine | matrix function | matrix logarithm | rational approximation | matrix sign function | LOGARITHM | inverse hyperbolic functions | condition number

Inverse trigonometric functions | Rational approximation | Matrix inverse cosine | Fréchet derivative | MATLAB | Matrix function | Matrix inverse hyperbolic cosine | Matrix exponential | Matrix inverse sine | Matrix inverse hyperbolic sine | Matrix sign function | Condition number | GNU Octave | Inverse hyperbolic functions | Matrix logarithm | Padé approximation | MATHEMATICS, APPLIED | matrix inverse cosine | matrix exponential | Pade approximation | matrix inverse hyperbolic cosine | ELEMENTARY-FUNCTIONS | inverse trigonometric functions | Frechet derivative | matrix inverse sine | matrix inverse hyperbolic sine | matrix function | matrix logarithm | rational approximation | matrix sign function | LOGARITHM | inverse hyperbolic functions | condition number

Journal Article

Physics Letters A, ISSN 0375-9601, 2007, Volume 360, Issue 4, pp. 588 - 592

In this work we use the sine–cosine method, the tanh method, the extended tanh method, and ansatze of hyperbolic functions for analytic treatment for the...

The sine–cosine method | Extended tanh method | Modified Kawahara equation | Solitons | The tanh method | Hyperbolic functions ansatze | Periodic wave solutions | The sine-cosine method | periodic wave solutions | TANH METHOD | NONCOMPACT STRUCTURES | VARIANTS | PHYSICS, MULTIDISCIPLINARY | NONLINEAR EVOLUTION | hyperbolic functions ansatze | COMPACT | extended tanh method | SYMBOLIC COMPUTATION | SYSTEMS | KDV EQUATION | modified Kawahara equation | the tanh method | the sine-cosine method | solitons

The sine–cosine method | Extended tanh method | Modified Kawahara equation | Solitons | The tanh method | Hyperbolic functions ansatze | Periodic wave solutions | The sine-cosine method | periodic wave solutions | TANH METHOD | NONCOMPACT STRUCTURES | VARIANTS | PHYSICS, MULTIDISCIPLINARY | NONLINEAR EVOLUTION | hyperbolic functions ansatze | COMPACT | extended tanh method | SYMBOLIC COMPUTATION | SYSTEMS | KDV EQUATION | modified Kawahara equation | the tanh method | the sine-cosine method | solitons

Journal Article

11.
Full Text
Teaching and Learning Hyperbolic Functions (I); Definitions and Fundamental Properties

PedActa, 07/2016, Volume 6, Issue 2, pp. 1 - 21

We propose that in some papers (4 maybe 5 !) to present a model of teaching and learning in secondary education of hyperbolic functions, giving many properties...

hyperbolic tangent | hyperbolic secant | hyperbolic functions | hyperbolic cotangent | hyperbolic sine | hyperbolic cosine

hyperbolic tangent | hyperbolic secant | hyperbolic functions | hyperbolic cotangent | hyperbolic sine | hyperbolic cosine

Journal Article

The American Mathematical Monthly, ISSN 0002-9890, 05/2016, Volume 123, Issue 6, pp. 574 - 582

In this article, we review the basics of the phasor formalism in a rigorous way, highlighting the physical motivation behind it and presenting a hyperbolic...

Addition | Banach algebra | Algebra | Cosine function | Sine function | Particle mass | Mathematical vectors | Mathematical functions | ARTICLES | Physics | Arithmetic | MATHEMATICS

Addition | Banach algebra | Algebra | Cosine function | Sine function | Particle mass | Mathematical vectors | Mathematical functions | ARTICLES | Physics | Arithmetic | MATHEMATICS

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 2008, Volume 1048, pp. 454 - 457

In the present work, on the basis of rational splitting of cosine operator-function, there is constructed fourth order of accuracy decomposition scheme for...

Operator splitting | Sine and cosine operator function | Decomposition method | Hyperbolic equation

Operator splitting | Sine and cosine operator function | Decomposition method | Hyperbolic equation

Conference Proceeding

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 6

In the paper, the authors present monotonicity results of a function involving the inverse hyperbolic sine. From these, the authors derive some inequalities...

Analysis | bound | inverse hyperbolic sine | Mathematics, general | Mathematics | monotonicity | Applications of Mathematics | minimum | Bound | Minimum | Inverse hyperbolic sine | Monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | COSINE

Analysis | bound | inverse hyperbolic sine | Mathematics, general | Mathematics | monotonicity | Applications of Mathematics | minimum | Bound | Minimum | Inverse hyperbolic sine | Monotonicity | MATHEMATICS | MATHEMATICS, APPLIED | COSINE

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2012, Volume 2012, Issue 1, pp. 1 - 9

In this paper, we obtain some new inequalities in the exponential form for the whole of the triples about the four functions . Then we generalize some...

Analysis | hyperbolic cotangent | arithmetic mean | hyperbolic sine | Mathematics, general | logarithmic mean | Mathematics | best constants | Applications of Mathematics | hyperbolic cosine | geometric mean | identric mean | Logarithmic mean | Best constants | Hyperbolic cotangent | Geometric mean | Hyperbolic cosine | Hyperbolic sine | Arithmetic mean | Identric mean | MATHEMATICS | MATHEMATICS, APPLIED | VALUES | 2 VARIABLES

Analysis | hyperbolic cotangent | arithmetic mean | hyperbolic sine | Mathematics, general | logarithmic mean | Mathematics | best constants | Applications of Mathematics | hyperbolic cosine | geometric mean | identric mean | Logarithmic mean | Best constants | Hyperbolic cotangent | Geometric mean | Hyperbolic cosine | Hyperbolic sine | Arithmetic mean | Identric mean | MATHEMATICS | MATHEMATICS, APPLIED | VALUES | 2 VARIABLES

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 06/2017, Volume 139, pp. 123 - 144

In this paper, we apply four mathematical methods, namely, the sine–cosine method, the Jacobi elliptic equation method, the generalized Kudryashov method and...

Jacobi elliptic equation method | 37 K10 | Bright, dark, singular soliton solutions | Exact solutions | 35Q55 | Sine–cosine method | Generalized Kudryashov method | Riccati equation method | 78A60 | Nonlinear Schrödinger equation | 35Q51 | Hyperbolic and trigonometric function solutions | SYSTEM | Sine-cosine method | TANH METHOD | Nonlinear Schrodinger equation | WAVE SOLUTIONS | OPTICAL SOLITONS | EXP-FUNCTION METHOD | KERR | OPTICS | BRIGHT

Jacobi elliptic equation method | 37 K10 | Bright, dark, singular soliton solutions | Exact solutions | 35Q55 | Sine–cosine method | Generalized Kudryashov method | Riccati equation method | 78A60 | Nonlinear Schrödinger equation | 35Q51 | Hyperbolic and trigonometric function solutions | SYSTEM | Sine-cosine method | TANH METHOD | Nonlinear Schrodinger equation | WAVE SOLUTIONS | OPTICAL SOLITONS | EXP-FUNCTION METHOD | KERR | OPTICS | BRIGHT

Journal Article

Journal of Applied Mathematics, ISSN 1110-757X, 2012, Volume 2012, pp. 1 - 16

The extended hyperbolic function method is used to derive abundant exact solutions for generalized forms of nonlinear heat conduction and Huxley equations. The...

MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | SOLITARY WAVE | SOLITONS | TANH METHOD | SINE-COSINE METHOD | ELLIPTIC FUNCTION-METHOD | EVOLUTION-EQUATIONS | VARIANT BOUSSINESQ EQUATIONS | TASSO-OLVER EQUATION | Studies | Queuing theory | Decomposition | Mathematical models | Mathematical programming | Heat conduction | Conduction | Mathematical analysis | Exact solutions | Nonlinearity | Hyperbolic functions | Heat transfer

MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | SOLITARY WAVE | SOLITONS | TANH METHOD | SINE-COSINE METHOD | ELLIPTIC FUNCTION-METHOD | EVOLUTION-EQUATIONS | VARIANT BOUSSINESQ EQUATIONS | TASSO-OLVER EQUATION | Studies | Queuing theory | Decomposition | Mathematical models | Mathematical programming | Heat conduction | Conduction | Mathematical analysis | Exact solutions | Nonlinearity | Hyperbolic functions | Heat transfer

Journal Article

ADVANCES IN MATHEMATICAL PHYSICS, ISSN 1687-9120, 08/2019, Volume 2019, pp. 1 - 15

The Davey-Stewartson Equation (DSE) is an equation system that reflects the evolution in finite depth of soft nonlinear packets of water waves that move in one...

PERIODIC-SOLUTIONS | BROER-KAUP | SOLITONS | STABILITY ANALYSIS | SINE-COSINE METHOD | DYNAMICAL EQUATION | SCHRODINGER-EQUATION | SOLITARY WAVE SOLUTIONS | ZAKHAROV-KUZNETSOV EQUATION | TRANSFORM | PHYSICS, MATHEMATICAL | Stability | Propagation | Partial differential equations | Exact solutions | Stability analysis | Hyperbolic functions | Physical properties | Physics | Water waves | Algebra | Applied mathematics | Modulation | Rational functions

PERIODIC-SOLUTIONS | BROER-KAUP | SOLITONS | STABILITY ANALYSIS | SINE-COSINE METHOD | DYNAMICAL EQUATION | SCHRODINGER-EQUATION | SOLITARY WAVE SOLUTIONS | ZAKHAROV-KUZNETSOV EQUATION | TRANSFORM | PHYSICS, MATHEMATICAL | Stability | Propagation | Partial differential equations | Exact solutions | Stability analysis | Hyperbolic functions | Physical properties | Physics | Water waves | Algebra | Applied mathematics | Modulation | Rational functions

Journal Article

Advances in Mathematical Physics, ISSN 1687-9120, 2018, Volume 2018, pp. 1 - 8

We employ the (G'/G)-expansion method to seek exact traveling wave solutions of two nonlinear wave equations-Pade-II equation and Drinfel'd-Sokolov-Wilson...

MATHEMATICAL PHYSICS | PERIODIC-SOLUTIONS | COMPACT | CAMASSA-HOLM | BROER-KAUP | SOKOLOV-WILSON EQUATION | SINE-COSINE METHOD | EXP-FUNCTION METHOD | EVOLUTION-EQUATIONS | PHYSICS, MATHEMATICAL | TANH-FUNCTION METHOD | Water waves | Nonlinear equations | Numerical analysis | Algebra | Parameters | Partial differential equations | Applied mathematics | Mathematical analysis | Wave equations | Hyperbolic functions | Trigonometric functions | Physics

MATHEMATICAL PHYSICS | PERIODIC-SOLUTIONS | COMPACT | CAMASSA-HOLM | BROER-KAUP | SOKOLOV-WILSON EQUATION | SINE-COSINE METHOD | EXP-FUNCTION METHOD | EVOLUTION-EQUATIONS | PHYSICS, MATHEMATICAL | TANH-FUNCTION METHOD | Water waves | Nonlinear equations | Numerical analysis | Algebra | Parameters | Partial differential equations | Applied mathematics | Mathematical analysis | Wave equations | Hyperbolic functions | Trigonometric functions | Physics

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2002, Volume 170, Issue 2, pp. 206 - 223

New pointwise inversion formulae are obtained for the d-dimensional totally geodesic Radon transform on the n-dimensional real hyperbolic space, 1dn-1, in...

Radon transform | hyperbolic space | hyperbolic cosine and sine transforms | inversion formulas | MATHEMATICS | radon transform | RANGE

Radon transform | hyperbolic space | hyperbolic cosine and sine transforms | inversion formulas | MATHEMATICS | radon transform | RANGE

Journal Article

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