Journal of symbolic computation, ISSN 0747-7171, 11/2020, Volume 101, pp. 61 - 72

An algorithm is designed to decompose a tropical univariate rational function into a composition of tropical binomials and trinomials...

Decomposing a univariate tropical rational function | Commuting composition of tropical polynomials | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Decomposing a univariate tropical rational function | Commuting composition of tropical polynomials | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Mathematische Annalen, ISSN 0025-5831, 2/2018, Volume 370, Issue 1, pp. 39 - 69

Let W be a subset of the set of real points of a real algebraic variety X. We investigate which functions
$$f: W \rightarrow \mathbb {R}$$
f
:
W...

Mathematics, general | 14P05 | 26C15 | Mathematics | 14P10 | MATHEMATICS | MAPS | TOPOLOGICAL VECTOR-SPACES | Computer science | Mathematics - Algebraic Geometry

Mathematics, general | 14P05 | 26C15 | Mathematics | 14P10 | MATHEMATICS | MAPS | TOPOLOGICAL VECTOR-SPACES | Computer science | Mathematics - Algebraic Geometry

Journal Article

Dalton transactions : an international journal of inorganic chemistry, ISSN 1477-9234, 2015, Volume 44, Issue 12, pp. 5258 - 5275

.... A major part of the research and its success are due to the vital role of the concept of mixed organic ligands in the design, tuning and functions...

SINGLE-CRYSTAL | BUILDING-BLOCKS | ELECTRICAL-CONDUCTIVITY | MOLECULAR TECTONICS | POROUS COORDINATION POLYMER | MAGNETIC-PROPERTIES | ADSORPTION PROPERTIES | CATALYTIC-ACTIVITY | SORPTION PROPERTIES | RATIONAL DESIGN | CHEMISTRY, INORGANIC & NUCLEAR | Solvents | Categories | Clusters | Constants | Ligands | Catalysis | Order disorder | Metal-organic frameworks | Tuning | Controlled release

SINGLE-CRYSTAL | BUILDING-BLOCKS | ELECTRICAL-CONDUCTIVITY | MOLECULAR TECTONICS | POROUS COORDINATION POLYMER | MAGNETIC-PROPERTIES | ADSORPTION PROPERTIES | CATALYTIC-ACTIVITY | SORPTION PROPERTIES | RATIONAL DESIGN | CHEMISTRY, INORGANIC & NUCLEAR | Solvents | Categories | Clusters | Constants | Ligands | Catalysis | Order disorder | Metal-organic frameworks | Tuning | Controlled release

Journal Article

Applied Economics, ISSN 0003-6846, 04/2019, Volume 51, Issue 20, pp. 2091 - 2119

This paper shows that asset prices are linear polynomials of various underlying explanatory factors and asset returns being ratios of these polynomials, are rational functions that do not add linearly when averaging...

rational function model | Fama French 3 and 5 factor models | asset volumes | CAPM | Asset pricing | average returns | TESTS | PRICES | PORTFOLIOS | PREMIUM | MARKET VALUE | RISK | MODEL | STOCK RETURNS | EQUILIBRIUM | ECONOMICS | SELECTION | Economic models | Prices | Assets | Pricing | Capital assets | Pricing policies | Change agents | Five factor model | Wealth | Averages

rational function model | Fama French 3 and 5 factor models | asset volumes | CAPM | Asset pricing | average returns | TESTS | PRICES | PORTFOLIOS | PREMIUM | MARKET VALUE | RISK | MODEL | STOCK RETURNS | EQUILIBRIUM | ECONOMICS | SELECTION | Economic models | Prices | Assets | Pricing | Capital assets | Pricing policies | Change agents | Five factor model | Wealth | Averages

Journal Article

Modern physics letters A, ISSN 0217-7323, 2019, Volume 34, Issue 20, p. 1950155

... differential equations, and the reduced equations are solved via the generalized exponential rational function method (GERFM...

FOKAS-LENELLS EQUATION | LUMP SOLUTIONS | PHYSICS, NUCLEAR | Extended Zakharov-Kuzetsov equation | exact solitary wave solution | PHYSICS, MATHEMATICAL | VARIABLE-COEFFICIENTS | ASTRONOMY & ASTROPHYSICS | LIE SYMMETRIES | generalized exponential rational function method | SOLITARY WAVE SOLUTIONS | the conformable derivative | PHYSICS, PARTICLES & FIELDS

FOKAS-LENELLS EQUATION | LUMP SOLUTIONS | PHYSICS, NUCLEAR | Extended Zakharov-Kuzetsov equation | exact solitary wave solution | PHYSICS, MATHEMATICAL | VARIABLE-COEFFICIENTS | ASTRONOMY & ASTROPHYSICS | LIE SYMMETRIES | generalized exponential rational function method | SOLITARY WAVE SOLUTIONS | the conformable derivative | PHYSICS, PARTICLES & FIELDS

Journal Article

Nonlinear dynamics, ISSN 1573-269X, 2018, Volume 92, Issue 4, pp. 2077 - 2092

... functions, trigonometric functions and hyperbolic functions. All solutions have been verified back into its corresponding equation by Maple...

Engineering | Vibration, Dynamical Systems, Control | Lump solutions | Interaction | Classical Mechanics | Hirota bilinear method | Positive quadratic functions, trigonometric functions and hyperbolic functions | Automotive Engineering | Mechanical Engineering | Potential-Yu–Toda–Sasa–Fukuyama equation | trigonometric functions and hyperbolic functions | RATIONAL SOLUTIONS | SCHRODINGER-EQUATION | MODEL | Potential-Yu-Toda-Sasa-Fukuyama equation | OPTICAL SOLITONS | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | Positive quadratic functions | MECHANICS | EVOLUTION | SOLITARY-WAVE SOLUTIONS | DYNAMICS | Mechanical engineering | Quadratic equations | Hyperbolic functions | Trustworthiness | Trigonometric functions

Engineering | Vibration, Dynamical Systems, Control | Lump solutions | Interaction | Classical Mechanics | Hirota bilinear method | Positive quadratic functions, trigonometric functions and hyperbolic functions | Automotive Engineering | Mechanical Engineering | Potential-Yu–Toda–Sasa–Fukuyama equation | trigonometric functions and hyperbolic functions | RATIONAL SOLUTIONS | SCHRODINGER-EQUATION | MODEL | Potential-Yu-Toda-Sasa-Fukuyama equation | OPTICAL SOLITONS | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | Positive quadratic functions | MECHANICS | EVOLUTION | SOLITARY-WAVE SOLUTIONS | DYNAMICS | Mechanical engineering | Quadratic equations | Hyperbolic functions | Trustworthiness | Trigonometric functions

Journal Article

2005, 1. Aufl., ISBN 9781852339562, xxvi, 397

.... The use of rational orthogonal basis functions to represent dynamical systems and stochastic signals can provide such a theory and underpin advanced analysis and efficient modelling...

Linear systems | Functions, Orthogonal | Mathematical models | Control Systems | Electrical Engineering, Electronic Engineering, Information Engineering | Reglerteknik | Teknik och teknologier | Rational Basis Function | System Theory | Signal Processing | Control Theory | Engineering and Technology | Elektroteknik och elektronik | Control | System Identification | Control Engineering

Linear systems | Functions, Orthogonal | Mathematical models | Control Systems | Electrical Engineering, Electronic Engineering, Information Engineering | Reglerteknik | Teknik och teknologier | Rational Basis Function | System Theory | Signal Processing | Control Theory | Engineering and Technology | Elektroteknik och elektronik | Control | System Identification | Control Engineering

Book

Numerische Mathematik, ISSN 0029-599X, 6/2019, Volume 142, Issue 2, pp. 359 - 382

The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals...

Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 30C30 | 41A20 | Mathematical and Computational Engineering | Mathematics, general | 65E05 | Mathematics | Numerical and Computational Physics, Simulation | MATHEMATICS, APPLIED | APPROXIMATION | MAPPING METHODS | PLANE | ALGORITHM

Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 30C30 | 41A20 | Mathematical and Computational Engineering | Mathematics, general | 65E05 | Mathematics | Numerical and Computational Physics, Simulation | MATHEMATICS, APPLIED | APPROXIMATION | MAPPING METHODS | PLANE | ALGORITHM

Journal Article

Chemical Society reviews, ISSN 1460-4744, 2015, Volume 44, Issue 12, pp. 3900 - 3923

.... A periodic table database of programmed primary structures was elaborated and used to facilitate the emergence of a diversity of functions in complex...

CONSTITUTIONAL ISOMERIC AB | LIBRARIES | JANUS DENDRIMERS | MACROMOLECULAR COLUMNS | SIDE-GROUPS | SELF-ASSEMBLING DENDRONS | HELICAL COLUMNS | LIQUID-CRYSTAL | CROWN-ETHERS | CHEMISTRY, MULTIDISCIPLINARY | RATIONAL DESIGN

CONSTITUTIONAL ISOMERIC AB | LIBRARIES | JANUS DENDRIMERS | MACROMOLECULAR COLUMNS | SIDE-GROUPS | SELF-ASSEMBLING DENDRONS | HELICAL COLUMNS | LIQUID-CRYSTAL | CROWN-ETHERS | CHEMISTRY, MULTIDISCIPLINARY | RATIONAL DESIGN

Journal Article

SIAM journal on numerical analysis, ISSN 0036-1429, 1/2008, Volume 46, Issue 5, pp. 2505 - 2523

New methods are proposed for the numerical evaluation of f(A) or f(A)b, where f(A) is a function such as A 1/2 or log...

Approximation | Rectangles | Mathematical integrals | Eigenvalues | Trapezoidal rule | Mathematical functions | Matrices | Elliptic functions | Perceptron convergence procedure | Quadrature | Rational approximation | Trapezoid rule | Conformal map | Contour integral | Cauchy integral | Matrix function

Approximation | Rectangles | Mathematical integrals | Eigenvalues | Trapezoidal rule | Mathematical functions | Matrices | Elliptic functions | Perceptron convergence procedure | Quadrature | Rational approximation | Trapezoid rule | Conformal map | Contour integral | Cauchy integral | Matrix function

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 12/2019, Volume 582, pp. 310 - 326

We introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitely generated...

Linear recurrence | Frobenius algebra | Complexity sequence | CARTIER ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | RINGS | COMPLEXITY | TEST-IDEALS | Algebra | Rational functions | Markov analysis | Commutative algebra | Àlgebra commutativa | Equacions diferencials | Classificació AMS | 39 Difference and functional equations | 13A General commutative ring theory | 39A Difference equations | 13 Commutative rings and algebras | Àlgebra | Differential equations | Matemàtiques i estadística | Àrees temàtiques de la UPC

Linear recurrence | Frobenius algebra | Complexity sequence | CARTIER ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | RINGS | COMPLEXITY | TEST-IDEALS | Algebra | Rational functions | Markov analysis | Commutative algebra | Àlgebra commutativa | Equacions diferencials | Classificació AMS | 39 Difference and functional equations | 13A General commutative ring theory | 39A Difference equations | 13 Commutative rings and algebras | Àlgebra | Differential equations | Matemàtiques i estadística | Àrees temàtiques de la UPC

Journal Article

Annals of mathematics, ISSN 0003-486X, 7/2017, Volume 186, Issue 1, pp. 237 - 275

We consider the structure ℝRE obtained from (ℝ, <, +, ·) by adjoining the restricted exponential and sine functions...

Interpolation | Algebra | Mathematical theorems | Analytic functions | Hypersurfaces | Coordinate systems | Polynomials | Mathematical functions | Degrees of polynomials | Pfaffian functions | Rational points | Metric entropy | Definable sets | MATHEMATICS | definable sets | RATIONAL-POINTS | NUMBER | metric entropy | rational points | FAMILIES | SETS | COMPLEXITY | SUBANALYTIC SURFACE

Interpolation | Algebra | Mathematical theorems | Analytic functions | Hypersurfaces | Coordinate systems | Polynomials | Mathematical functions | Degrees of polynomials | Pfaffian functions | Rational points | Metric entropy | Definable sets | MATHEMATICS | definable sets | RATIONAL-POINTS | NUMBER | metric entropy | rational points | FAMILIES | SETS | COMPLEXITY | SUBANALYTIC SURFACE

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 10/2017, Volume 13, Issue 9, pp. 2299 - 2318

For a field
K
, rational function
ϕ
∈
K
(
z
)
of degree at least two, and
α
∈
ℙ
1
(
K
)
, we study the polynomials in
K...

irreducibility of polynomials | S-integer points in dynamics | Arithmetic dynamical systems | POLYNOMIALS | MATHEMATICS | ORDER | PRIME DIVISORS | GALOIS THEORY | INTEGER POINTS

irreducibility of polynomials | S-integer points in dynamics | Arithmetic dynamical systems | POLYNOMIALS | MATHEMATICS | ORDER | PRIME DIVISORS | GALOIS THEORY | INTEGER POINTS

Journal Article

Applied mathematics and computation, ISSN 0096-3003, 11/2018, Volume 337, pp. 494 - 503

.... Here, we focus on a method to improve the accuracy of the evaluation of rational functions...

Horner scheme | Accuracy | Rounding errors | Error-free transformation | Rational function | floating-point | Homer scheme | MATHEMATICS, APPLIED | Numerical Analysis | Computer Arithmetic | Computer Science

Horner scheme | Accuracy | Rounding errors | Error-free transformation | Rational function | floating-point | Homer scheme | MATHEMATICS, APPLIED | Numerical Analysis | Computer Arithmetic | Computer Science

Journal Article

Journal of number theory, ISSN 0022-314X, 11/2017, Volume 180, pp. 512 - 532

Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials...

Generalized trigonometric functions | Infinite series | Rational functions | MATHEMATICS

Generalized trigonometric functions | Infinite series | Rational functions | MATHEMATICS

Journal Article

ACM Transactions on Mathematical Software (TOMS), ISSN 0098-3500, 03/2017, Volume 43, Issue 4, pp. 1 - 29

We present a numerical procedure to approximate integrals of the form ∫ b a f ( x ) dx , where f is a function with singularities close to, but outside the interval...

numerical integration | quadrature | Orthogonal rational functions | Fejér | rational interpolation | Quadrature | Numerical integration | Rational interpolation | INTERPOLATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Fejer | MATHEMATICS, APPLIED | GAUSS QUADRATURE | INTEGRATION | COMPLEX POLES | FORMULAS | Interpolation | Algorithms | Research | Methods

numerical integration | quadrature | Orthogonal rational functions | Fejér | rational interpolation | Quadrature | Numerical integration | Rational interpolation | INTERPOLATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Fejer | MATHEMATICS, APPLIED | GAUSS QUADRATURE | INTEGRATION | COMPLEX POLES | FORMULAS | Interpolation | Algorithms | Research | Methods

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2015, Volume 280, pp. 121 - 187

We discuss transfer-function realization for multivariable holomorphic functions mapping the unit polydisk or the right polyhalfplane into the operator analogue of either the unit disk or the right halfplane...

Positive-kernel decomposition | Bessmertnyĭ long resolvent representation | Schur–Agler class | Lurking-isometry method | Herglotz–Agler class | Transfer-function realization | Lurking-isotropic-subspace method | Herglotz-Agler class | Schur-Agler class | LINEAR-SYSTEMS | PART I | NEVANLINNA-PICK INTERPOLATION | MATHEMATICS | UNITARY COLLIGATIONS | SCATTERING SYSTEMS | MODELS | Bessmertnyi long resolvent representation | RATIONAL MATRIX FUNCTIONS | STATE-SPACE | COMPLEX-VARIABLES | CONTINUOUS-TIME

Positive-kernel decomposition | Bessmertnyĭ long resolvent representation | Schur–Agler class | Lurking-isometry method | Herglotz–Agler class | Transfer-function realization | Lurking-isotropic-subspace method | Herglotz-Agler class | Schur-Agler class | LINEAR-SYSTEMS | PART I | NEVANLINNA-PICK INTERPOLATION | MATHEMATICS | UNITARY COLLIGATIONS | SCATTERING SYSTEMS | MODELS | Bessmertnyi long resolvent representation | RATIONAL MATRIX FUNCTIONS | STATE-SPACE | COMPLEX-VARIABLES | CONTINUOUS-TIME

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2017, Volume 2017, Issue 1, pp. 1 - 17

...
∗
)
$x\in(0, x^{\ast})$
and
Γ
(
x
+
1
)
<
(
x
2
+
1
/
γ
)
/
(
x
+
1
/
γ
)
$\Gamma(x+1)<(x^{2}+1/\gamma)/(x+1/\gamma )$
for
x
∈
(
x
∗
,
1
)
$x\in(x^{\ast}, 1)$
, where
Γ
(
x
)
$\Gamma(x)$
is the classical gamma function...

33B15 | rational bound | psi function | Analysis | gamma function | Mathematics, general | Mathematics | 41A60 | Applications of Mathematics | 26D07 | completely monotonic function | MATHEMATICS | MATHEMATICS, APPLIED | FUNCTION INEQUALITY | completely monotonicn function | Gamma function | Research

33B15 | rational bound | psi function | Analysis | gamma function | Mathematics, general | Mathematics | 41A60 | Applications of Mathematics | 26D07 | completely monotonic function | MATHEMATICS | MATHEMATICS, APPLIED | FUNCTION INEQUALITY | completely monotonicn function | Gamma function | Research

Journal Article