Acta Mathematica Sinica, English Series, ISSN 1439-8516, 2/2009, Volume 25, Issue 2, pp. 279 - 286

Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the L p metrics and gave the upper estimates of the...

41A46 | 42A15 | 42A10 | 47A58 | Mathematics, general | Mathematics | optimal recovery | standard information | class of functions with bounded mixed derivative | Optimal recovery | Standard information | Class of functions with bounded mixed derivative | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | SMOOTHNESS | INTEGRAL-EQUATIONS | APPROXIMATE SOLUTION | VALUES | POINTS | Mathematical optimization | Algorithms | Universities and colleges | Studies | Mathematical functions

41A46 | 42A15 | 42A10 | 47A58 | Mathematics, general | Mathematics | optimal recovery | standard information | class of functions with bounded mixed derivative | Optimal recovery | Standard information | Class of functions with bounded mixed derivative | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | SMOOTHNESS | INTEGRAL-EQUATIONS | APPROXIMATE SOLUTION | VALUES | POINTS | Mathematical optimization | Algorithms | Universities and colleges | Studies | Mathematical functions

Journal Article

2.
Full Text
Quadrature formulas for classes of functions with bounded mixed derivative or difference

中国科学：数学英文版, ISSN 1674-7283, 1997, Issue 5, pp. 449 - 458

Quadrature formulas are considered for classes of smooth functions Wpr, Bpr,(?) with bounded mixed derivative or difference. For the classes of functions...

quadrature | optimal | Besov | methods | formula | class | number-theoretic

quadrature | optimal | Besov | methods | formula | class | number-theoretic

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 20

The present paper introduces the Szasz-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials...

Ditzian-Totik modulus of smoothness | weighted modulus of continuity | Lipschitz class function | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | CONVERGENCE | DERIVATIVES | POLYA-EGGENBERGER DISTRIBUTION | BOUNDED VARIATION | Functions (mathematics) | Operators (mathematics) | Theorems | Approximation | Mathematical analysis | Polynomials | Smoothness | 41A25 | 41A36 | 41A10 | Research

Ditzian-Totik modulus of smoothness | weighted modulus of continuity | Lipschitz class function | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | CONVERGENCE | DERIVATIVES | POLYA-EGGENBERGER DISTRIBUTION | BOUNDED VARIATION | Functions (mathematics) | Operators (mathematics) | Theorems | Approximation | Mathematical analysis | Polynomials | Smoothness | 41A25 | 41A36 | 41A10 | Research

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 12/2013, Volume 13, Issue 6, pp. 965 - 1003

In this paper, we study linear trigonometric hyperbolic cross approximations, Kolmogorov n-widths d n (W,H γ ), and ε-dimensions n ε (W,H γ ) of periodic...

Economics general | Sobolev space | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Kolmogorov n -widths | 41A25 | 41A63 | Numerical Analysis | Trigonometric hyperbolic cross space | 42A10 | High-dimensional approximation | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Function classes with anisotropic smoothness | ε -dimensions | ε-dimensions | Kolmogorov n-widths | MATHEMATICS, APPLIED | GRIDS | SPACES | ELECTRONIC SCHRODINGER-EQUATION | SPARSE FINITE-ELEMENTS | epsilon-dimensions | INTERPOLATION | MATHEMATICS | ELLIPTIC PROBLEMS | VARIABLES | COMPUTER SCIENCE, THEORY & METHODS | BOUNDED MIXED DERIVATIVES

Economics general | Sobolev space | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Kolmogorov n -widths | 41A25 | 41A63 | Numerical Analysis | Trigonometric hyperbolic cross space | 42A10 | High-dimensional approximation | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Function classes with anisotropic smoothness | ε -dimensions | ε-dimensions | Kolmogorov n-widths | MATHEMATICS, APPLIED | GRIDS | SPACES | ELECTRONIC SCHRODINGER-EQUATION | SPARSE FINITE-ELEMENTS | epsilon-dimensions | INTERPOLATION | MATHEMATICS | ELLIPTIC PROBLEMS | VARIABLES | COMPUTER SCIENCE, THEORY & METHODS | BOUNDED MIXED DERIVATIVES

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2018, Volume 370, Issue 12, pp. 8581 - 8612

We prove that bilinear fractional integral operators and similar multipliers are smoothing in the sense that they improve the regularity of functions. We also...

SYMBOLIC-CALCULUS | mixed Lebesgue spaces | KATO-PONCE INEQUALITY | Bilinear operators | WEIGHTED NORM INEQUALITIES | SINGULAR INTEGRAL-OPERATORS | PSEUDODIFFERENTIAL-OPERATORS | Leibniz rule | KORTEWEG-DEVRIES EQUATION | MATHEMATICS | maximal function | fractional derivatives | MULTILINEAR FOURIER MULTIPLIERS | multipliers | VALUED INEQUALITIES | smoothing properties | HORMANDER CLASSES | HELICOIDAL METHOD

SYMBOLIC-CALCULUS | mixed Lebesgue spaces | KATO-PONCE INEQUALITY | Bilinear operators | WEIGHTED NORM INEQUALITIES | SINGULAR INTEGRAL-OPERATORS | PSEUDODIFFERENTIAL-OPERATORS | Leibniz rule | KORTEWEG-DEVRIES EQUATION | MATHEMATICS | maximal function | fractional derivatives | MULTILINEAR FOURIER MULTIPLIERS | multipliers | VALUED INEQUALITIES | smoothing properties | HORMANDER CLASSES | HELICOIDAL METHOD

Journal Article

6.
Full Text
Quadrature formulas for classes of functions with bounded mixed derivative or difference

Science in China Series A: Mathematics, ISSN 1006-9283, 5/1997, Volume 40, Issue 5, pp. 449 - 458

Quadrature formulas are considered for classes of smooth functions W p r , B p r , θ with bounded mixed derivative or difference. For the classes of functions...

number-theoretic methods | Mathematics | Applications of Mathematics | optimal quadrature formula | Besov class | K RO MULTIDISCIPLINARY SCIENCES | MULTIDISCIPLINARY SCIENCES

number-theoretic methods | Mathematics | Applications of Mathematics | optimal quadrature formula | Besov class | K RO MULTIDISCIPLINARY SCIENCES | MULTIDISCIPLINARY SCIENCES

Journal Article

7.
Full Text
Quadrature formulas for classes of functions with bounded mixed derivative or difference

Science in China, Series A: Mathematics, Physics, Astronomy, ISSN 1006-9283, 1997, Volume 40, Issue 5, pp. x1 - 458

Journal Article

Sbornik Mathematics, ISSN 1064-5616, 2010, Volume 201, Issue 11, pp. 1689 - 1713

The problem under consideration is that of approximating classes of smooth functions by algebraic-trigonometric polynomials of the form p(n)(t)+ tau(m)(t),...

Classes of smooth functions | Simultaneous approximation of functions and derivatives | Mixed series in Legendre polynomials | Algebraic-trigonometric polynomials | MATHEMATICS | classes of smooth functions | mixed series in Legendre polynomials | simultaneous approximation of functions and derivatives | MIXED SERIES | algebraic-trigonometric polynomials

Classes of smooth functions | Simultaneous approximation of functions and derivatives | Mixed series in Legendre polynomials | Algebraic-trigonometric polynomials | MATHEMATICS | classes of smooth functions | mixed series in Legendre polynomials | simultaneous approximation of functions and derivatives | MIXED SERIES | algebraic-trigonometric polynomials

Journal Article

Information, ISSN 1343-4500, 01/2012, Volume 15, Issue 1, pp. 83 - 90

In this paper, we investigate information complexity of integration of the Sobolev classes with bounded mixed derivative in the Monte Carlo setting. We develop...

Integration problem | Monte Carlo algorithm | Sobolev class with mixed derivative | Information complexity | ENGINEERING, MULTIDISCIPLINARY | APPROXIMATION

Integration problem | Monte Carlo algorithm | Sobolev class with mixed derivative | Information complexity | ENGINEERING, MULTIDISCIPLINARY | APPROXIMATION

Journal Article

2012, Universitext, ISBN 1447128060, 480

The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is...

Differential equations, Elliptic | Functional analysis | Function spaces | Differential equations, Partial | Mathematics

Differential equations, Elliptic | Functional analysis | Function spaces | Differential equations, Partial | Mathematics

eBook

Monatshefte für Mathematik, ISSN 0026-9255, 7/2018, Volume 186, Issue 3, pp. 407 - 438

We construct embeddings of spaces of non-quasianalytic ultradistributions into differential algebras enjoying optimal properties in view of a Schwartz type...

Denjoy–Carleman classes | Generalized functions | 46F30 | Mathematics, general | Mathematics | Ultradifferentiable functions | Wave front sets | Primary 46F05 | Secondary 35A18 | Colombeau algebras | Multiplication of ultradistributions | SPACES | GENERALIZED-FUNCTIONS | DISTRIBUTIONS | MATHEMATICS | MICROLOCAL ANALYSIS | Denjoy-Carleman classes | SETS | COEFFICIENTS | REGULARITY PROPERTIES | OPERATORS | Analysis | Algebra

Denjoy–Carleman classes | Generalized functions | 46F30 | Mathematics, general | Mathematics | Ultradifferentiable functions | Wave front sets | Primary 46F05 | Secondary 35A18 | Colombeau algebras | Multiplication of ultradistributions | SPACES | GENERALIZED-FUNCTIONS | DISTRIBUTIONS | MATHEMATICS | MICROLOCAL ANALYSIS | Denjoy-Carleman classes | SETS | COEFFICIENTS | REGULARITY PROPERTIES | OPERATORS | Analysis | Algebra

Journal Article

Turkish Journal of Mathematics, ISSN 1300-0098, 2009, Volume 33, Issue 2, pp. 151 - 158

In this paper, we introduce a modification of the Szasz-Mirakjan-Kantorovich operators, which preserve the linear functions. This type of operator modification...

Szász-mirakjan operators | The korovkin-type approximation theorem | Lipschitz class functionals | Voronovskaya type theorem | Modulus of continuity | Szász-mirakjan-kantorovich operators | MATHEMATICS | Szasz-Mirakjan operators | the Korovkin-type approximation theorem | BETA OPERATORS | APPROXIMATION | ERROR ESTIMATION | Szasz-Mirakjan-Kantorovich operators | modulus of continuity

Szász-mirakjan operators | The korovkin-type approximation theorem | Lipschitz class functionals | Voronovskaya type theorem | Modulus of continuity | Szász-mirakjan-kantorovich operators | MATHEMATICS | Szasz-Mirakjan operators | the Korovkin-type approximation theorem | BETA OPERATORS | APPROXIMATION | ERROR ESTIMATION | Szasz-Mirakjan-Kantorovich operators | modulus of continuity

Journal Article

13.
Full Text
Approximation by polynomials and ridge functions of classes of s-monotone radial functions

Journal of Approximation Theory, ISSN 0021-9045, 2008, Volume 152, Issue 1, pp. 20 - 51

We obtain estimates on the order of best approximation by polynomials and ridge functions in the spaces L q of classes of s-monotone radial functions which...

[formula omitted]-Monotone functions | Ridge functions | Polynomials | Radial functions | s-Monotone functions | MATHEMATICS | polynomials | WIDTHS | radial functions | ridge functions | SOBOLEV-TYPE CLASSES | s-monotone functions

[formula omitted]-Monotone functions | Ridge functions | Polynomials | Radial functions | s-Monotone functions | MATHEMATICS | polynomials | WIDTHS | radial functions | ridge functions | SOBOLEV-TYPE CLASSES | s-monotone functions

Journal Article

Statistics in Medicine, ISSN 0277-6715, 02/2016, Volume 35, Issue 3, pp. 382 - 398

Joint models initially dedicated to a single longitudinal marker and a single time‐to‐event need to be extended to account for the rich longitudinal data of...

conditional independence | multivariate longitudinal data | latent class | competing risk | joint model | curvilinearity | Conditional independence | Joint model | Latent class | Competing risk | Curvilinearity | Multivariate longitudinal data | VARIABLE MODELS | MEDICINE, RESEARCH & EXPERIMENTAL | MEDICAL INFORMATICS | STATISTICS & PROBABILITY | LONGITUDINAL DATA | RECURRENT EVENTS | SURVIVAL TIMES | PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH | MATHEMATICAL & COMPUTATIONAL BIOLOGY | TIME-TO-EVENT | OUTCOMES | Multivariate Analysis | Predictive Value of Tests | Risk Assessment - methods | Prospective Studies | Humans | Biomedical Research - statistics & numerical data | Dementia - diagnosis | Male | Risk Assessment - statistics & numerical data | Likelihood Functions | Time Factors | Computer Simulation | Aged, 80 and over | Biomedical Research - methods | Female | France | Cognition - classification | Psychometrics | Apolipoprotein E4 - analysis | Genetic Markers | Models, Statistical | Disease Progression | Bayes Theorem | Aged | Longitudinal Studies | Measurement | Models | Risk factors | Dementia | Statistics - Applications

conditional independence | multivariate longitudinal data | latent class | competing risk | joint model | curvilinearity | Conditional independence | Joint model | Latent class | Competing risk | Curvilinearity | Multivariate longitudinal data | VARIABLE MODELS | MEDICINE, RESEARCH & EXPERIMENTAL | MEDICAL INFORMATICS | STATISTICS & PROBABILITY | LONGITUDINAL DATA | RECURRENT EVENTS | SURVIVAL TIMES | PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH | MATHEMATICAL & COMPUTATIONAL BIOLOGY | TIME-TO-EVENT | OUTCOMES | Multivariate Analysis | Predictive Value of Tests | Risk Assessment - methods | Prospective Studies | Humans | Biomedical Research - statistics & numerical data | Dementia - diagnosis | Male | Risk Assessment - statistics & numerical data | Likelihood Functions | Time Factors | Computer Simulation | Aged, 80 and over | Biomedical Research - methods | Female | France | Cognition - classification | Psychometrics | Apolipoprotein E4 - analysis | Genetic Markers | Models, Statistical | Disease Progression | Bayes Theorem | Aged | Longitudinal Studies | Measurement | Models | Risk factors | Dementia | Statistics - Applications

Journal Article

Boundary Value Problems, ISSN 2211-3037, 12/2014, Volume 2014, Issue 1, pp. 1 - 21

In this paper it is established that in an infinite angular domain for Dirichlet problem of the heat conduction equation the unique (up to a constant factor)...

35D05 | 35K20 | angular domain | unique classes | Mathematics | non-trivial solution | heat conductivity | Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | boundary value problem | Volterra integral equation | 45D05 | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Heat conduction | Conduction | Operators | Boundary value problems | Mathematical analysis | Dirichlet problem | Thermal conductivity | Constants | Heat equations

35D05 | 35K20 | angular domain | unique classes | Mathematics | non-trivial solution | heat conductivity | Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | boundary value problem | Volterra integral equation | 45D05 | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Heat conduction | Conduction | Operators | Boundary value problems | Mathematical analysis | Dirichlet problem | Thermal conductivity | Constants | Heat equations

Journal Article

Statistics, ISSN 0233-1888, 11/2019, Volume 53, Issue 6, pp. 1251 - 1268

In deconvolution in with mixing density and kernel h, the mixture density is estimated with MDE having upper -error rate, in probability or in risk; . In one...

Deconvolution | Vapnik-Chervonenkis classes | plug-in upper error/risk bounds | minimum distance estimation | totally positive kernels

Deconvolution | Vapnik-Chervonenkis classes | plug-in upper error/risk bounds | minimum distance estimation | totally positive kernels

Journal Article

Social Choice and Welfare, ISSN 0176-1714, 9/2007, Volume 29, Issue 2, pp. 271 - 293

The Moulin-Shenker rule is a non-linear solution concept for solving heterogeneous cost sharing problems. It is the unique continuous rule with the properties...

Capital costs | Marginal costs | Linear transformations | Cost allocation | Economic costs | Game theory | Partial derivatives | Cost functions | Production costs | class eco B | Economic Theory | Economics general | Economics / Management Science | JOINT COSTS | CONSISTENCY | SITUATIONS | PRICES | AXIOMS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | ALLOCATION | Studies | Social sciences | Theory | Cost sharing

Capital costs | Marginal costs | Linear transformations | Cost allocation | Economic costs | Game theory | Partial derivatives | Cost functions | Production costs | class eco B | Economic Theory | Economics general | Economics / Management Science | JOINT COSTS | CONSISTENCY | SITUATIONS | PRICES | AXIOMS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | ALLOCATION | Studies | Social sciences | Theory | Cost sharing

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2020, Volume 373, Issue 5, pp. 3375 - 3422

We consider the Stokes and Navier-Stokes equations in a bounded domain with analytic boundary. We present a direct, robust, energy-type approach for...

EXISTENCE | GEVREY-CLASS REGULARITY | DISSIPATION | Stokes equation | SPACE ANALYTICITY | Gevrey regularity | EQUATIONS | bounded domain | INVISCID LIMIT | MATHEMATICS | Real analyticity | ZERO-VISCOSITY LIMIT | SPATIAL ANALYTICITY | HALF-SPACE | EULER

EXISTENCE | GEVREY-CLASS REGULARITY | DISSIPATION | Stokes equation | SPACE ANALYTICITY | Gevrey regularity | EQUATIONS | bounded domain | INVISCID LIMIT | MATHEMATICS | Real analyticity | ZERO-VISCOSITY LIMIT | SPATIAL ANALYTICITY | HALF-SPACE | EULER

Journal Article

Computational Economics, ISSN 0927-7099, 2011, Volume 37, Issue 3, pp. 267 - 300

We introduce a framework to analyze the interaction of boundedly rational heterogeneous agents repeatedly playing a participation game with negative feedback....

class eco B | Nonlinear dynamics | Participation games | Heterogeneous behavioral rules | Replicator dynamics | Revision protocol | Economic Theory | C73 | Economics / Management Science | Logit dynamics | C72 | ROUTE | MANAGEMENT | COORDINATION | MARKET ENTRY GAMES | ENDOGENOUS FLUCTUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EQUILIBRIUM | ECONOMICS | EXPECTATIONS | Participation games; Heterogeneous behavioral rules; Revision protocol; Replicator dynamics; Logit dynamics; Nonlinear dynamics; C72; C73 | Studies | Behavioral decision theory | Economic theory | Game theory | Equilibrium

class eco B | Nonlinear dynamics | Participation games | Heterogeneous behavioral rules | Replicator dynamics | Revision protocol | Economic Theory | C73 | Economics / Management Science | Logit dynamics | C72 | ROUTE | MANAGEMENT | COORDINATION | MARKET ENTRY GAMES | ENDOGENOUS FLUCTUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EQUILIBRIUM | ECONOMICS | EXPECTATIONS | Participation games; Heterogeneous behavioral rules; Revision protocol; Replicator dynamics; Logit dynamics; Nonlinear dynamics; C72; C73 | Studies | Behavioral decision theory | Economic theory | Game theory | Equilibrium

Journal Article

PLoS ONE, ISSN 1932-6203, 04/2013, Volume 8, Issue 4, p. e59483

Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to...

MULTIDISCIPLINARY SCIENCES | DIELECTRIC RESPONSE | Models, Theoretical | Skin | Electric Impedance | Nonlinear Dynamics | Humans | Usage | Information management | Analysis | Electric properties | Biological properties | Bioengineering | Viscoelasticity | Neurosciences | MacLaurin series | Parameter estimation | Electrical properties | Data processing | Calculus | Biology | Test systems | Complex systems | Mechanical engineering | Fractional calculus | Operators (mathematics) | New classes | Mathematical models | Impedance | Electrical impedance | Biomedical engineering

MULTIDISCIPLINARY SCIENCES | DIELECTRIC RESPONSE | Models, Theoretical | Skin | Electric Impedance | Nonlinear Dynamics | Humans | Usage | Information management | Analysis | Electric properties | Biological properties | Bioengineering | Viscoelasticity | Neurosciences | MacLaurin series | Parameter estimation | Electrical properties | Data processing | Calculus | Biology | Test systems | Complex systems | Mechanical engineering | Fractional calculus | Operators (mathematics) | New classes | Mathematical models | Impedance | Electrical impedance | Biomedical engineering

Journal Article

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