Canadian Journal of Physics, ISSN 0008-4204, 2016, Volume 94, Issue 3, pp. 249 - 253

The 1/Z expansion for the ground state energy of the Coulomb system of an infinitely massive center of charge Z and two electrons...

32.60.+i | charge critique | 31.15.Pf | théorème de Kato | two-electron ion | Puiseux expansion | critical charge | 97.10.Ld | ion à deux électrons | expansion en 1/Z | série de Puiseux | Kato theorem | 31.10.+z | 1/Z-expansion | Critical charge | Two-electron ion | 1/ Z -expansion | GROUND-STATE | PHYSICS, MULTIDISCIPLINARY | IONS | PERTURBATION-THEORY | RADIUS | CONVERGENCE | ATOMS | ANHARMONIC-OSCILLATOR | Ground state | Analysis | Electrons | Accuracy | Theorems | Mathematical analysis | Digits | Charge | Mathematical models | Decimals

32.60.+i | charge critique | 31.15.Pf | théorème de Kato | two-electron ion | Puiseux expansion | critical charge | 97.10.Ld | ion à deux électrons | expansion en 1/Z | série de Puiseux | Kato theorem | 31.10.+z | 1/Z-expansion | Critical charge | Two-electron ion | 1/ Z -expansion | GROUND-STATE | PHYSICS, MULTIDISCIPLINARY | IONS | PERTURBATION-THEORY | RADIUS | CONVERGENCE | ATOMS | ANHARMONIC-OSCILLATOR | Ground state | Analysis | Electrons | Accuracy | Theorems | Mathematical analysis | Digits | Charge | Mathematical models | Decimals

Journal Article

2.
Full Text
The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions

Advances in Computational Mathematics, ISSN 1019-7168, 4/2017, Volume 43, Issue 2, pp. 319 - 350

.... Firstly, the integrands are assumed to have the Puiseux expansions at the endpoints with arbitrary algebraic and logarithmic singularities...

Visualization | MSC 65B15 | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Composite Gauss-Legendre rule | Mathematics | Error asymptotic expansion | Computational Science and Engineering | Hadamard finite-part integral | Roundoff error analysis | MSC 65D30 | Mathematical Modeling and Industrial Mathematics | Algebraic and logarithmic singularity | Gauss-Kronrod rule | Puiseux series | MATHEMATICS, APPLIED | CAUCHY PRINCIPAL VALUE | NUMERICAL EVALUATION | END-POINT SINGULARITIES | HYPERSINGULAR INTEGRALS | LEGENDRE QUADRATURE | TRAPEZOIDAL RULE | ASYMPTOTIC EXPANSIONS | KRONROD QUADRATURE-RULES | EULER-MACLAURIN EXPANSIONS | HURWITZ ZETA-FUNCTION | Integrals | Analysis | Numerical integration

Visualization | MSC 65B15 | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Composite Gauss-Legendre rule | Mathematics | Error asymptotic expansion | Computational Science and Engineering | Hadamard finite-part integral | Roundoff error analysis | MSC 65D30 | Mathematical Modeling and Industrial Mathematics | Algebraic and logarithmic singularity | Gauss-Kronrod rule | Puiseux series | MATHEMATICS, APPLIED | CAUCHY PRINCIPAL VALUE | NUMERICAL EVALUATION | END-POINT SINGULARITIES | HYPERSINGULAR INTEGRALS | LEGENDRE QUADRATURE | TRAPEZOIDAL RULE | ASYMPTOTIC EXPANSIONS | KRONROD QUADRATURE-RULES | EULER-MACLAURIN EXPANSIONS | HURWITZ ZETA-FUNCTION | Integrals | Analysis | Numerical integration

Journal Article

Michigan Mathematical Journal, ISSN 0026-2285, 2017, Volume 66, Issue 1, pp. 155 - 174

Using the theory of jet schemes, we give a new approach to the description of a minimal generating sequence of a divisorial valuations on A(2). For this...

MATHEMATICS | BRANCHES | NEWTON-PUISEUX EXPANSION

MATHEMATICS | BRANCHES | NEWTON-PUISEUX EXPANSION

Journal Article

JOURNAL OF SCIENTIFIC COMPUTING, ISSN 0885-7474, 02/2020, Volume 82, Issue 3

... truncation of the asymptotic expansion by Picard iteration. This asymptotic expansion can easily yield a more accurate Pade approximation...

MATHEMATICS, APPLIED | SPLINE COLLOCATION | Trapezoidal rule | Puiseux expansion | ASYMPTOTIC SOLUTION | Convergence analysis | COLLOCATION METHODS | EXTRAPOLATION | SPECTRAL-COLLOCATION | Nonlinear Volterra integral equation of the second kind | Weakly singular convolution kernel | EULER-MACLAURIN EXPANSIONS | CONVERGENCE | Lighthill integral equation | PRODUCT INTEGRATION

MATHEMATICS, APPLIED | SPLINE COLLOCATION | Trapezoidal rule | Puiseux expansion | ASYMPTOTIC SOLUTION | Convergence analysis | COLLOCATION METHODS | EXTRAPOLATION | SPECTRAL-COLLOCATION | Nonlinear Volterra integral equation of the second kind | Weakly singular convolution kernel | EULER-MACLAURIN EXPANSIONS | CONVERGENCE | Lighthill integral equation | PRODUCT INTEGRATION

Journal Article

5.
Full Text
The modified composite Gauss type rules for singular integrals using Puiseux expansions

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2017, Volume 86, Issue 303, pp. 345 - 29

This paper is devoted to designing some modified composite Gauss type rules for the integrals involving algebraic and logarithmic endpoint singularities, at which the integrands possess the Puiseux expansions in series...

Integral with algebraic and logarithmic singularity | Oscillatory Fourier transform | Cauchy principal value integral | Modified composite Gauss-Legendre rule | Error asymptotic expansion | Gauss-Kronrod rule | Puiseux series | MATHEMATICS, APPLIED | oscillatory Fourier transform | modified composite Gauss-Legendre rule | END-POINT SINGULARITIES | HIGHLY OSCILLATORY INTEGRALS | FORMULA | LEGENDRE QUADRATURE | error asymptotic expansion | ASYMPTOTIC EXPANSIONS | KRONROD QUADRATURE-RULES | EULER-MACLAURIN EXPANSIONS | POWER-SERIES SOLUTIONS | NUMERICAL-INTEGRATION | HURWITZ ZETA-FUNCTION

Integral with algebraic and logarithmic singularity | Oscillatory Fourier transform | Cauchy principal value integral | Modified composite Gauss-Legendre rule | Error asymptotic expansion | Gauss-Kronrod rule | Puiseux series | MATHEMATICS, APPLIED | oscillatory Fourier transform | modified composite Gauss-Legendre rule | END-POINT SINGULARITIES | HIGHLY OSCILLATORY INTEGRALS | FORMULA | LEGENDRE QUADRATURE | error asymptotic expansion | ASYMPTOTIC EXPANSIONS | KRONROD QUADRATURE-RULES | EULER-MACLAURIN EXPANSIONS | POWER-SERIES SOLUTIONS | NUMERICAL-INTEGRATION | HURWITZ ZETA-FUNCTION

Journal Article

Annals of Operations Research, ISSN 0254-5330, 6/2016, Volume 241, Issue 1, pp. 515 - 573

Built upon a ground field is the parametric field, the Puiseux field, of semi-terminating formal fractional power series. A parametric polynomial is a...

Sensitivity | Business and Management | Approximate parametric roots | Puiseux fields | Theory of Computation | Algebraic plane curves | Operation Research/Decision Theory | Combinatorics | Parametric polynomials | Newton Polygon process | Complexity | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PUISEUX EXPANSION | SYSTEMS | POLYTOPES | Studies | Operations research | Polynomials | Approximation | Preprocessing | Meetings | Roots | Grounds | Polygons

Sensitivity | Business and Management | Approximate parametric roots | Puiseux fields | Theory of Computation | Algebraic plane curves | Operation Research/Decision Theory | Combinatorics | Parametric polynomials | Newton Polygon process | Complexity | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PUISEUX EXPANSION | SYSTEMS | POLYTOPES | Studies | Operations research | Polynomials | Approximation | Preprocessing | Meetings | Roots | Grounds | Polygons

Journal Article

Numerical Algorithms, ISSN 1017-1398, 05/2018, Volume 78, Issue 1, pp. 107 - 132

This paper is devoted to designing a practical algorithm to invert the Laplace transform by assuming that the transform possesses the Puiseux expansion at infinity...

Bromwich integral | Gauss–Kronrod rule | Puiseux expansion | Inverse Laplace transform | Gauss–Legendre rule | Error estimate | MATHEMATICS, APPLIED | SERIES | Gauss-Legendre rule | TALBOTS METHOD | IMPLEMENTATION | EQUATIONS | NUMERICAL INVERSION | PRECISION | INTEGRALS | KRONROD QUADRATURE-RULES | GAUSS-LEGENDRE QUADRATURE | COMPUTATION | Gauss-Kronrod rule | Usage | Algorithms

Bromwich integral | Gauss–Kronrod rule | Puiseux expansion | Inverse Laplace transform | Gauss–Legendre rule | Error estimate | MATHEMATICS, APPLIED | SERIES | Gauss-Legendre rule | TALBOTS METHOD | IMPLEMENTATION | EQUATIONS | NUMERICAL INVERSION | PRECISION | INTEGRALS | KRONROD QUADRATURE-RULES | GAUSS-LEGENDRE QUADRATURE | COMPUTATION | Gauss-Kronrod rule | Usage | Algorithms

Journal Article

Algebraic & geometric topology, ISSN 1472-2739, 2016, Volume 16, Issue 2, pp. 843 - 898

...; the Puiseux expansion naturally emerges. The corresponding DAHA superpolynomials are expected to coincide with the reduced ones in the Oblomkov-Shende-Rasmussen conjecture upon its generalization to arbitrary dominant weights...

HOMFLY-PT polynomial | Iterated torus knot | Cabling | Khovanov-Rozansky homology | Double affine Hecke algebra | Jones polynomials | Macdonald polynomial | Generalized Jacobian | Puiseux expansion | Betti numbers | Plane curve singularity | SPRINGER | POLYNOMIALS | MATHEMATICS | STABLE PAIRS | FIBERS | COMPACTIFIED JACOBIANS | MATRIX FACTORIZATIONS | LINK HOMOLOGY | INVARIANTS | RATIONAL CURVES | SURFACES

HOMFLY-PT polynomial | Iterated torus knot | Cabling | Khovanov-Rozansky homology | Double affine Hecke algebra | Jones polynomials | Macdonald polynomial | Generalized Jacobian | Puiseux expansion | Betti numbers | Plane curve singularity | SPRINGER | POLYNOMIALS | MATHEMATICS | STABLE PAIRS | FIBERS | COMPACTIFIED JACOBIANS | MATRIX FACTORIZATIONS | LINK HOMOLOGY | INVARIANTS | RATIONAL CURVES | SURFACES

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2016, Volume 44, Issue 5, pp. 2100 - 2109

We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is isolated or not. We present conditions on a given...

Algebraic varieties | Isolated points | Puiseux series | Curves | SYSTEM | MATHEMATICS | SET | DIMENSION | EQUIDIMENSIONAL DECOMPOSITION | Parametrization | Polynomials | Algebra | Vectors (mathematics) | Mathematical analysis

Algebraic varieties | Isolated points | Puiseux series | Curves | SYSTEM | MATHEMATICS | SET | DIMENSION | EQUIDIMENSIONAL DECOMPOSITION | Parametrization | Polynomials | Algebra | Vectors (mathematics) | Mathematical analysis

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 1/2015, Volume 28, Issue 1, pp. 227 - 252

... of arbitrary characteristic. We do not use the Hamburger-Noether expansions. Our basic tool is the logarithmic distance on the set of branches satisfying the strong...

Secondary 14H20 | Semigroup associated with a branch | Logarithmic distance | Mathematics | Topology | Plane algebroid curve | Geometry | Algebra | Analysis | Branch | Mathematics, general | Key polynomials | Applications of Mathematics | Abhyankar-Moh theory | Primary 32S05 | CRITERIA | MATHEMATICS, APPLIED | IRREDUCIBILITY | RINGS | NEWTON-PUISEUX EXPANSION | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | CURVES | HAMBURGER-NOETHER EXPANSIONS | MATHEMATICS | SEMIGROUPS | VALUATIONS

Secondary 14H20 | Semigroup associated with a branch | Logarithmic distance | Mathematics | Topology | Plane algebroid curve | Geometry | Algebra | Analysis | Branch | Mathematics, general | Key polynomials | Applications of Mathematics | Abhyankar-Moh theory | Primary 32S05 | CRITERIA | MATHEMATICS, APPLIED | IRREDUCIBILITY | RINGS | NEWTON-PUISEUX EXPANSION | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | CURVES | HAMBURGER-NOETHER EXPANSIONS | MATHEMATICS | SEMIGROUPS | VALUATIONS

Journal Article

Algebraic and Geometric Topology, ISSN 1472-2747, 01/2018, Volume 18, Issue 1, pp. 333 - 385

We suggest a relatively simple and totally geometric conjectural description of uncolored DAHA superpolynomials of arbitrary algebraic knots (conjecturally...

Algebraic knot | Khovanov-rozansky homology | Hecke algebra | Compactified jacobian | Macdonald polynomial | Puiseux expansion | HOMFLYPT polynomial | Jones polynomial | Orbital integral | Plane curve singularity | T-CATALAN NUMBERS | SPRINGER | POLYNOMIALS | MATHEMATICS | ALGEBRAS | COMPACTIFIED JACOBIANS | MATRIX FACTORIZATIONS | REPRESENTATIONS | LINK HOMOLOGY | TORUS KNOTS | FIXED-POINT VARIETIES

Algebraic knot | Khovanov-rozansky homology | Hecke algebra | Compactified jacobian | Macdonald polynomial | Puiseux expansion | HOMFLYPT polynomial | Jones polynomial | Orbital integral | Plane curve singularity | T-CATALAN NUMBERS | SPRINGER | POLYNOMIALS | MATHEMATICS | ALGEBRAS | COMPACTIFIED JACOBIANS | MATRIX FACTORIZATIONS | REPRESENTATIONS | LINK HOMOLOGY | TORUS KNOTS | FIXED-POINT VARIETIES

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2016, Volume 44, Issue 5, pp. 2118 - 2151

.... Each member of the family can be expressed via the Puiseux expansion. Studying the limits of suitably renormalized coefficients of the Puiseux expansions, we obtain...

Parametric deformation | Primary: 14B07 | Puiseux expansion | Plane curve singularity | Secondary: 14H20 | MATHEMATICS | Parametrization | Obstructions | Algebra | Deformation | Singularities | Curves (geometry)

Parametric deformation | Primary: 14B07 | Puiseux expansion | Plane curve singularity | Secondary: 14H20 | MATHEMATICS | Parametrization | Obstructions | Algebra | Deformation | Singularities | Curves (geometry)

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 11/2015, Volume 14, Issue 9

The celebrated "Epimorphism Theorem" opened up several directions of research. In this survey article we highlight the known partial results and open questions...

Epimorphism theorem | affine fibrations | cancellation problem | Polynomial rings | linearization problem | embedding problem | MATHEMATICS, APPLIED | TOPOLOGICAL PROOF | AFFINE RATIONAL DOMAINS | CANCELLATION THEOREM | NEWTON-PUISEUX EXPANSION | CODIMENSION-ONE | MATHEMATICS | LINEAR PLANES | VARIABLES | EMBEDDINGS | POLYNOMIAL ALGEBRAS | TSCHIRNHAUSEN TRANSFORMATION

Epimorphism theorem | affine fibrations | cancellation problem | Polynomial rings | linearization problem | embedding problem | MATHEMATICS, APPLIED | TOPOLOGICAL PROOF | AFFINE RATIONAL DOMAINS | CANCELLATION THEOREM | NEWTON-PUISEUX EXPANSION | CODIMENSION-ONE | MATHEMATICS | LINEAR PLANES | VARIABLES | EMBEDDINGS | POLYNOMIAL ALGEBRAS | TSCHIRNHAUSEN TRANSFORMATION

Journal Article

Journal of Algebra, ISSN 0021-8693, 2011, Volume 343, Issue 1, pp. 143 - 159

We generalize Abhyankar–Mohʼs theory of approximate roots of polynomials to the case of approximate roots of non-characteristic degrees of an irreducible...

Approximate roots of polynomials | Characteristic sequences | MATHEMATICS | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | NEWTON-PUISEUX EXPANSION

Approximate roots of polynomials | Characteristic sequences | MATHEMATICS | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | NEWTON-PUISEUX EXPANSION

Journal Article

15.
A new proof of the Abhyankar-Moh-Suzuki theorem via a new algorithm for the polynomial dependence

Journal of Algebra and its Applications, ISSN 0219-4988, 11/2015, Volume 14, Issue 9

This paper contains a complete and self-contained proof of the AMS theorem. The main tool is a new algorithm producing an irreducible dependence for a pair of...

degree semigroup | Abhyankar-Moh-Suzuki theorem | minimal polynomial dependence | MATHEMATICS, APPLIED | NEWTON-PUISEUX EXPANSION | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | MINIMAL POLYNOMIALS | CURVES | MATHEMATICS | AFFINE PLANE | LINE | ROOTS | EMBEDDINGS

degree semigroup | Abhyankar-Moh-Suzuki theorem | minimal polynomial dependence | MATHEMATICS, APPLIED | NEWTON-PUISEUX EXPANSION | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | MINIMAL POLYNOMIALS | CURVES | MATHEMATICS | AFFINE PLANE | LINE | ROOTS | EMBEDDINGS

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2000, Volume 69, Issue 231, pp. 1167 - 1182

In this paper we present a refined version of the Newton polygon process to compute the Puiseux expansions of an algebraic function defined over the rational function field...

Integers | Algebra | Mathematical theorems | Algorithms | Polynomials | Algebraic functions | Logarithms | Coefficients | Power series | Polygons | Algebraic function | Puiseux expansion | Newton polygon complexity | Newton polygon | complexity | MATHEMATICS, APPLIED | algebraic function | THEOREM | FACTORING POLYNOMIALS | ALGORITHM | NUMBER-FIELDS

Integers | Algebra | Mathematical theorems | Algorithms | Polynomials | Algebraic functions | Logarithms | Coefficients | Power series | Polygons | Algebraic function | Puiseux expansion | Newton polygon complexity | Newton polygon | complexity | MATHEMATICS, APPLIED | algebraic function | THEOREM | FACTORING POLYNOMIALS | ALGORITHM | NUMBER-FIELDS

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 11/2015, Volume 14, Issue 9

In this work we deal with dicritical divisors, curvettes and polynomials. These objects have been one of the main research interests of Abhyankar during his...

Dicritical divisor | special pencil | INFINITY | MATHEMATICS | MATHEMATICS, APPLIED | GENERIC INCARNATIONS | NEWTON-PUISEUX EXPANSION | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | JACOBIAN PROBLEM | CURVES | QUADRATIC TRANSFORMS | Mathematics - Algebraic Geometry

Dicritical divisor | special pencil | INFINITY | MATHEMATICS | MATHEMATICS, APPLIED | GENERIC INCARNATIONS | NEWTON-PUISEUX EXPANSION | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | JACOBIAN PROBLEM | CURVES | QUADRATIC TRANSFORMS | Mathematics - Algebraic Geometry

Journal Article

Designs, codes, and cryptography, ISSN 0925-1022, 2012, Volume 70, Issue 1-2, pp. 189 - 213

We construct evaluation codes given by weight functions defined over polynomial rings in m ≥ 2 indeterminates. These weight functions are determined by sets of...

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | 11T71 | Discrete Mathematics in Computer Science | Data Encryption | 94B27 | Error-correcting codes | Coding and Information Theory | Algebraic Geometric Codes | Mathematics | Combinatorics | 14B05 | ONE PLACE | MATHEMATICS, APPLIED | NEWTON-PUISEUX EXPANSION | ALGORITHM | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | CURVES | ALGEBRAIC-GEOMETRIC CODES | LOCAL UNIFORMIZATION | CONSTRUCTION | COMPUTER SCIENCE, THEORY & METHODS | DESIGNED MINIMUM DISTANCE | SURFACES | Valuation

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | 11T71 | Discrete Mathematics in Computer Science | Data Encryption | 94B27 | Error-correcting codes | Coding and Information Theory | Algebraic Geometric Codes | Mathematics | Combinatorics | 14B05 | ONE PLACE | MATHEMATICS, APPLIED | NEWTON-PUISEUX EXPANSION | ALGORITHM | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | CURVES | ALGEBRAIC-GEOMETRIC CODES | LOCAL UNIFORMIZATION | CONSTRUCTION | COMPUTER SCIENCE, THEORY & METHODS | DESIGNED MINIMUM DISTANCE | SURFACES | Valuation

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 10/2010, Volume 266, Issue 2, pp. 243 - 264

... at in nity · ojasiewicz exponent at in nity · Puiseux expansion at in nity · Real approximation of complex curves Mathematics Subject Classi cation (2000) Primary 32C99...

Łojasiewicz inequality at infinity | Primary 32C99 | Secondary 14R25 | 32A20 | Łojasiewicz exponent at infinity | Mathematics, general | Mathematics | Puiseux expansion at infinity | Real approximation of complex curves | 32S05 | MATHEMATICS | EXPONENT | Lojasiewicz inequality at infinity | Lojasiewicz exponent at infinity

Łojasiewicz inequality at infinity | Primary 32C99 | Secondary 14R25 | 32A20 | Łojasiewicz exponent at infinity | Mathematics, general | Mathematics | Puiseux expansion at infinity | Real approximation of complex curves | 32S05 | MATHEMATICS | EXPONENT | Lojasiewicz inequality at infinity | Lojasiewicz exponent at infinity

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2013, Volume 65, Issue 1, pp. 169 - 182

We introduce the notion of an approximate Jacobian Newton diagram which is the Jacobian Newton diagram of the morphism (f((k)), f), where f is a branch and...

Jacobian Newton diagram | Approximate root | Irreducible plane curve | MATHEMATICS | DISCRIMINANT | SINGULARITIES | approximate root | PUISEUX EXPANSION | irreducible plane curve | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | POLAR INVARIANTS | Mathematics - Algebraic Geometry

Jacobian Newton diagram | Approximate root | Irreducible plane curve | MATHEMATICS | DISCRIMINANT | SINGULARITIES | approximate root | PUISEUX EXPANSION | irreducible plane curve | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | POLAR INVARIANTS | Mathematics - Algebraic Geometry

Journal Article

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