Computational and Theoretical Chemistry, ISSN 2210-271X, 03/2018, Volume 1127, pp. 37 - 43

Efficient exponential type basis sets constructed from new hyperbolic cosine type B functions have been used in self consistent field calculations for the...

Exponential type orbital | Hyperbolic cosine functions | B functions | Hartree-Fock-Roothaan method | MOLECULAR CALCULATIONS | EXPANSIONS | CHEMISTRY, PHYSICAL | ADDITION THEOREMS | COULOMB INTEGRALS | FOURIER-TRANSFORM | OVERLAP | FOCK WAVE-FUNCTIONS | EXPONENTIAL-TYPE ORBITALS | TRANSLATION METHOD | 2-ELECTRON

Exponential type orbital | Hyperbolic cosine functions | B functions | Hartree-Fock-Roothaan method | MOLECULAR CALCULATIONS | EXPANSIONS | CHEMISTRY, PHYSICAL | ADDITION THEOREMS | COULOMB INTEGRALS | FOURIER-TRANSFORM | OVERLAP | FOCK WAVE-FUNCTIONS | EXPONENTIAL-TYPE ORBITALS | TRANSLATION METHOD | 2-ELECTRON

Journal Article

MISKOLC MATHEMATICAL NOTES, ISSN 1787-2405, 2018, Volume 19, Issue 2, pp. 873 - 881

The generalized convexity of the inverse hyperbolic cosine function related to the hyperbolic metric is investigated in this paper.

MATHEMATICS | COMPLETE ELLIPTIC INTEGRALS | RESPECT | INEQUALITIES | KIND | Holder mean | concavity | convexity | inverse hyperbolic cosine function

MATHEMATICS | COMPLETE ELLIPTIC INTEGRALS | RESPECT | INEQUALITIES | KIND | Holder mean | concavity | convexity | inverse hyperbolic cosine function

Journal Article

3.
Full Text
Exponential type orbitals with generalized hyperbolic cosine functions for atomic systems

Computer Physics Communications, ISSN 0010-4655, 09/2015, Volume 194, pp. 59 - 63

Radial basis functions, constructed from Slater type and generalized exponential type functions with the generalized hyperbolic cosine type functions and ,...

Noninteger principal quantum number | Exponential type orbital | Generalized hyperbolic cosine function | Hartree–Fock–Roothaan calculation | Hartree-Fock-Roothaan calculation | COULOMB STURMIANS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FOCK WAVE-FUNCTIONS | BASIS-SETS | PHYSICS, MATHEMATICAL | Radial basis function | Orbitals | Construction | Computer simulation | Basis functions | Mathematical analysis | Mathematical models | Trigonometric functions

Noninteger principal quantum number | Exponential type orbital | Generalized hyperbolic cosine function | Hartree–Fock–Roothaan calculation | Hartree-Fock-Roothaan calculation | COULOMB STURMIANS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FOCK WAVE-FUNCTIONS | BASIS-SETS | PHYSICS, MATHEMATICAL | Radial basis function | Orbitals | Construction | Computer simulation | Basis functions | Mathematical analysis | Mathematical models | Trigonometric functions

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 10/2017, Volume 55, Issue 9, pp. 1849 - 1856

Unconventional basis functions, constructed from exponential type orbitals (ETOs) with hyperbolic cosine functions, are applied to Roothaan-Hartree-Fock...

Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Exponential type orbital | Hyperbolic cosine function | Math. Applications in Chemistry | Roothaan-Hartree-Fock calculation | MOLECULAR CALCULATIONS | COMPLETE ORTHONORMAL SETS | B FUNCTIONS | HARTREE-FOCK | CHEMISTRY, MULTIDISCIPLINARY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SLATER-TYPE ORBITALS | STANDARD CONVENTION | FOCK WAVE-FUNCTIONS | SYSTEMS | GROUND-STATES | Trigonometrical functions | Usage | Analysis | Atomic orbitals

Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Exponential type orbital | Hyperbolic cosine function | Math. Applications in Chemistry | Roothaan-Hartree-Fock calculation | MOLECULAR CALCULATIONS | COMPLETE ORTHONORMAL SETS | B FUNCTIONS | HARTREE-FOCK | CHEMISTRY, MULTIDISCIPLINARY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SLATER-TYPE ORBITALS | STANDARD CONVENTION | FOCK WAVE-FUNCTIONS | SYSTEMS | GROUND-STATES | Trigonometrical functions | Usage | Analysis | Atomic orbitals

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

Signal Processing, ISSN 0165-1684, 03/2020, Volume 168, p. 107348

In this paper, a least lncosh (Llncosh) algorithm is derived by utilizing the lncosh cost function. The lncosh cost is characterized by the natural logarithm...

Adaptive filtering | LMS algorithm | Hyperbolic cosine function | Lncosh cost function | Sign algorithm

Adaptive filtering | LMS algorithm | Hyperbolic cosine function | Lncosh cost function | Sign algorithm

Journal Article

Advances in Quantum Chemistry, ISSN 0065-3276, 2013, Volume 67, pp. 217 - 230

In the last few years, exponential type orbitals became very important in electronic structure calculations of atoms and molecules. In this work, improvements...

Hartree-Fock-Roothaan equations | Exponential type orbital | Hyperbolic cosine function | Electronic structure calculation

Hartree-Fock-Roothaan equations | Exponential type orbital | Hyperbolic cosine function | Electronic structure calculation

Journal Article

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

Gazi University Journal of Science, ISSN 1303-9709, 2016, Volume 29, Issue 4, pp. 811 - 829

Journal Article

International Journal of Quantum Chemistry, ISSN 0020-7608, 03/2012, Volume 112, Issue 6, pp. 1559 - 1565

The efficiency of noninteger n‐generalized exponential type orbitals (NGETO) rn*−1 e −ζ r μ with hyperbolic cosine (HC) cosh (βrμ) as radial basis functions in...

noninteger principal quantum number | Hartree‐Fock‐Roothaan calculation | hyperbolic cosine function | generalized exponential type function | Hartree-Fock-Roothaan calculation | ISOELECTRONIC SERIES | GROUND-STATE | FOCK-ROOTHAAN THEORY | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | H-2 | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | INCREASE | SYSTEMS | BASIS-SETS | PRINCIPAL QUANTUM NUMBERS | EFFICIENCY

noninteger principal quantum number | Hartree‐Fock‐Roothaan calculation | hyperbolic cosine function | generalized exponential type function | Hartree-Fock-Roothaan calculation | ISOELECTRONIC SERIES | GROUND-STATE | FOCK-ROOTHAAN THEORY | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | H-2 | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | INCREASE | SYSTEMS | BASIS-SETS | PRINCIPAL QUANTUM NUMBERS | EFFICIENCY

Journal Article

2017 IEEE Power & Energy Society General Meeting, ISSN 1944-9925, 07/2017, Volume 2018-, pp. 1 - 2

In this paper, a novel robust state estimator based on hyperbolic cosine function (COSH) is proposed considering the uncertainty in the measurements....

Uncertainty | Measurement uncertainty | Linear programming | Robustness | Power systems | Computational efficiency | State estimation | hyperbolic cosine function | Hyperbolic cosine function

Uncertainty | Measurement uncertainty | Linear programming | Robustness | Power systems | Computational efficiency | State estimation | hyperbolic cosine function | Hyperbolic cosine function

Conference Proceeding

Nonlinear Dynamics, ISSN 0924-090X, 6/2016, Volume 84, Issue 4, pp. 2317 - 2332

In this paper, the threshold dynamics of Morris–Lecar neuron model is firstly analyzed by bifurcation diagram of interspike interval as a function of external...

Engineering | Vibration, Dynamical Systems, Control | Mechanics | Electrical activities | Automotive Engineering | Morris–Lecar neuron model | Hyperbolic tangent function | Mechanical Engineering | Electronic implementation | Hyperbolic cosine function | SYNCHRONIZATION | MECHANICS | SPIKING | FRACTIONAL-ORDER | Morris-Lecar neuron model | ENGINEERING, MECHANICAL | Electrical engineering | Models | Neurons | Neural networks | Analysis | Differential equations | Dynamic tests | Nonlinear equations | Circuit design | Circuits | Two dimensional models | Bifurcations | Hyperbolic functions | Trigonometric functions | Nonlinear dynamics | Thresholds | Mathematical analysis | Electronics | Mathematical models

Engineering | Vibration, Dynamical Systems, Control | Mechanics | Electrical activities | Automotive Engineering | Morris–Lecar neuron model | Hyperbolic tangent function | Mechanical Engineering | Electronic implementation | Hyperbolic cosine function | SYNCHRONIZATION | MECHANICS | SPIKING | FRACTIONAL-ORDER | Morris-Lecar neuron model | ENGINEERING, MECHANICAL | Electrical engineering | Models | Neurons | Neural networks | Analysis | Differential equations | Dynamic tests | Nonlinear equations | Circuit design | Circuits | Two dimensional models | Bifurcations | Hyperbolic functions | Trigonometric functions | Nonlinear dynamics | Thresholds | Mathematical analysis | Electronics | Mathematical models

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

Advances in Applied Probability, ISSN 0001-8678, 6/2012, Volume 44, Issue 2, pp. 373 - 390

Hazard rates play an important role in various areas, e.g. reliability theory, survival analysis, biostatistics, queueing theory, and actuarial studies....

Hypergeometric functions | Integers | Sufficient conditions | Statistical variance | Cosine function | General Applied Probability | Semigroups | Mathematical functions | Laplace transformation | Real lines | Density | REGRESSION | Natural exponential family (NEF) | variance function | FAILURE RATE | quadratic variance function | BATHTUB | STATISTICS & PROBABILITY | cubic variance function | DISTRIBUTIONS | MODELS | mixture | hyperbolic cosine NEF | Kummer type-2 NEF | SYSTEMS | Ressel NEF | VARIANCE FUNCTIONS

Hypergeometric functions | Integers | Sufficient conditions | Statistical variance | Cosine function | General Applied Probability | Semigroups | Mathematical functions | Laplace transformation | Real lines | Density | REGRESSION | Natural exponential family (NEF) | variance function | FAILURE RATE | quadratic variance function | BATHTUB | STATISTICS & PROBABILITY | cubic variance function | DISTRIBUTIONS | MODELS | mixture | hyperbolic cosine NEF | Kummer type-2 NEF | SYSTEMS | Ressel NEF | VARIANCE FUNCTIONS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2013, Volume 141, Issue 10, pp. 3515 - 3527

We prove that strongly continuous groups generated by first order systems on Riemannian manifolds have finite propagation speed. Our procedure provides a new...

Hyperbolic equations | groups | First order systems | Finite propagation speed | Huygens' principle | MATHEMATICS | MATHEMATICS, APPLIED | KATO | C-0 groups | hyperbolic equations | FUNCTIONAL CALCULI | SQUARE-ROOT PROBLEM | COSINE FUNCTIONS | first order systems | OPERATORS

Hyperbolic equations | groups | First order systems | Finite propagation speed | Huygens' principle | MATHEMATICS | MATHEMATICS, APPLIED | KATO | C-0 groups | hyperbolic equations | FUNCTIONAL CALCULI | SQUARE-ROOT PROBLEM | COSINE FUNCTIONS | first order systems | OPERATORS

Journal Article

Bernoulli, ISSN 1350-7265, 11/2013, Volume 19, Issue 5B, pp. 2437 - 2454

We investigate distributions of hyperbolic Bessel processes. We find links between the hyperbolic cosine of hyperbolic Bessel processes and functionals of...

Brownian motion | Mathematical theorems | Cosine function | Uniqueness | Laplace transformation | Random variables | Martingales | Laplace transform | Bessel process | Hyperbolic Bessel process | BROWNIAN-MOTION | hyperbolic Bessel process | ASIAN OPTIONS | STATISTICS & PROBABILITY | EXPONENTIAL FUNCTIONALS

Brownian motion | Mathematical theorems | Cosine function | Uniqueness | Laplace transformation | Random variables | Martingales | Laplace transform | Bessel process | Hyperbolic Bessel process | BROWNIAN-MOTION | hyperbolic Bessel process | ASIAN OPTIONS | STATISTICS & PROBABILITY | EXPONENTIAL FUNCTIONALS

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 2011, Volume 1389, pp. 1679 - 1682

Conference Proceeding

Journal of Complexity, ISSN 0885-064X, 10/2016, Volume 36, pp. 166 - 181

We develop algorithms for multivariate integration and approximation in the weighted half-period cosine space of smooth non-periodic functions. We use...

Cosine series | Hyperbolic crosses | Quasi-Monte Carlo methods | Function approximation | Component-by-component construction | Rank-[formula omitted] lattice rules | Rank-1 lattice rules | MATHEMATICS, APPLIED | TRIGONOMETRIC POLYNOMIALS | ALGORITHMS | MATHEMATICS | ACHIEVE | CONVERGENCE | BY-COMPONENT CONSTRUCTION | Algorithms | Mathematics - Numerical Analysis

Cosine series | Hyperbolic crosses | Quasi-Monte Carlo methods | Function approximation | Component-by-component construction | Rank-[formula omitted] lattice rules | Rank-1 lattice rules | MATHEMATICS, APPLIED | TRIGONOMETRIC POLYNOMIALS | ALGORITHMS | MATHEMATICS | ACHIEVE | CONVERGENCE | BY-COMPONENT CONSTRUCTION | Algorithms | Mathematics - Numerical Analysis

Journal Article

Semigroup Forum, ISSN 0037-1912, 10/2013, Volume 87, Issue 2, pp. 277 - 297

In this paper the existence of solutions of a nonautonomous abstract Cauchy problem of second order is considered. Assuming appropriate conditions on the...

Mathematics | Algebra | Mild solutions | Cosine functions of operators | Abstract Cauchy problem of second order | Exponential vectors | FULLY DISCRETE APPROXIMATIONS | PARABOLIC EQUATIONS | TIME-DEPENDENT PERTURBATION | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | SOLUTION MAPPINGS | MATHEMATICS | HIGHER-ORDER | BANACH-SPACES | COEFFICIENTS | HYPERBOLIC-EQUATIONS

Mathematics | Algebra | Mild solutions | Cosine functions of operators | Abstract Cauchy problem of second order | Exponential vectors | FULLY DISCRETE APPROXIMATIONS | PARABOLIC EQUATIONS | TIME-DEPENDENT PERTURBATION | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | SOLUTION MAPPINGS | MATHEMATICS | HIGHER-ORDER | BANACH-SPACES | COEFFICIENTS | HYPERBOLIC-EQUATIONS

Journal Article

2016 IEEE International Symposium on Phased Array Systems and Technology (PAST), 10/2016, pp. 1 - 6

In this paper a modified class of malleable hyperbolic cosine weighting function is proposed based on decreasing the sidelobes by defining a nonconvex problem....

Cosh weighting function | Kaiser weighting function | Adaptive arrays | Radar antennas | Hyperbolic cosine weighting function | Linear antenna arrays | Impedance | Microstrip | Biomedical imaging | Linear array coefficients | Rectangular antenna array

Cosh weighting function | Kaiser weighting function | Adaptive arrays | Radar antennas | Hyperbolic cosine weighting function | Linear antenna arrays | Impedance | Microstrip | Biomedical imaging | Linear array coefficients | Rectangular antenna array

Conference Proceeding

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