Fractional Calculus and Applied Analysis, ISSN 1311-0454, 08/2015, Volume 18, Issue 4, pp. 1039 - 1073

From the point of view of stochastic analysis the Caputo and Riemann- Liouville derivatives of order α ∈ (0, 2) can be viewed as (regularized) generators of...

Markov processes | boundary value problem | Caputo fractional derivative | crossing a boundary | Riemann-Liouville fractional derivative | MATHEMATICS, APPLIED | DIFFUSION-WAVE EQUATION | DISTRIBUTED ORDER | STABLE PROCESSES | MATHEMATICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CAUCHY-PROBLEMS | RANDOM-WALKS | BOUNDED DOMAINS | DYNAMICS | DUALITY | Analysis | Differential equations

Markov processes | boundary value problem | Caputo fractional derivative | crossing a boundary | Riemann-Liouville fractional derivative | MATHEMATICS, APPLIED | DIFFUSION-WAVE EQUATION | DISTRIBUTED ORDER | STABLE PROCESSES | MATHEMATICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CAUCHY-PROBLEMS | RANDOM-WALKS | BOUNDED DOMAINS | DYNAMICS | DUALITY | Analysis | Differential equations

Journal Article

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A penalty approach to a discretized double obstacle problem with derivative constraints

Journal of Global Optimization, ISSN 0925-5001, 8/2015, Volume 62, Issue 4, pp. 775 - 790

This work presents a penalty approach to a nonlinear optimization problem with linear box constraints arising from the discretization of an...

Double obstacle problem | Mixed nonlinear complementarity problem | Operations Research/Decision Theory | Convergence rates | Mathematics | Global optimizer | Computer Science, general | Optimization | Penalty method | Real Functions | Variational inequalities | Bounded linear constraints | MATHEMATICS, APPLIED | OPTION VALUATION | QUASI-VARIATIONAL INEQUALITY | NONLINEAR COMPLEMENTARITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROPORTIONAL TRANSACTION COSTS | MIXED COMPLEMENTARITY-PROBLEMS | Obstacles | Approximation | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Convergence

Double obstacle problem | Mixed nonlinear complementarity problem | Operations Research/Decision Theory | Convergence rates | Mathematics | Global optimizer | Computer Science, general | Optimization | Penalty method | Real Functions | Variational inequalities | Bounded linear constraints | MATHEMATICS, APPLIED | OPTION VALUATION | QUASI-VARIATIONAL INEQUALITY | NONLINEAR COMPLEMENTARITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROPORTIONAL TRANSACTION COSTS | MIXED COMPLEMENTARITY-PROBLEMS | Obstacles | Approximation | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Convergence

Journal Article

Journal of Computational Information Systems, ISSN 1553-9105, 12/2011, Volume 7, Issue 13, pp. 4660 - 4667

Journal Article

Izvestiya: Mathematics, ISSN 1064-5632, 10/2007, Volume 71, Issue 5, pp. 895 - 938

We obtain upper and lower bounds for the best accuracy of approximation in Stechkin's problem for the differentiation operator and in the problem of the...

BOUNDED OPERATORS | MATHEMATICS | NUMBER | VALUES | FINITELY SMOOTH FUNCTIONS | POINTS

BOUNDED OPERATORS | MATHEMATICS | NUMBER | VALUES | FINITELY SMOOTH FUNCTIONS | POINTS

Journal Article

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

Journal of Complexity, ISSN 0885-064X, 06/2008, Volume 24, Issue 3, pp. 398 - 409

We study the information-based complexity of the approximation problem on the multivariate Sobolev space with bounded mixed derivative MWp,αr in the norm of Lq...

Monte Carlo method | Sobolev space with bounded mixed derivative | Asymptotic order | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | asymptotic order | Analysis | Methods

Monte Carlo method | Sobolev space with bounded mixed derivative | Asymptotic order | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | asymptotic order | Analysis | Methods

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2016, Volume 54, Issue 2, pp. 1056 - 1084

We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann...

Domain derivative | Duality | Shape functionals | Infimum problems | MATHEMATICS, APPLIED | CONVEXITY | domain derivative | POSITIVE SOLUTIONS | infimum problems | EQUATIONS | PRINCIPLE | shape functionals | duality | SOBOLEV SPACES | SYMMETRY | BOUNDED SLOPE CONDITION | REGULARITY | OPTIMIZATION | FUNCTIONALS | AUTOMATION & CONTROL SYSTEMS | Mathematics - Optimization and Control | Mathematics

Domain derivative | Duality | Shape functionals | Infimum problems | MATHEMATICS, APPLIED | CONVEXITY | domain derivative | POSITIVE SOLUTIONS | infimum problems | EQUATIONS | PRINCIPLE | shape functionals | duality | SOBOLEV SPACES | SYMMETRY | BOUNDED SLOPE CONDITION | REGULARITY | OPTIMIZATION | FUNCTIONALS | AUTOMATION & CONTROL SYSTEMS | Mathematics - Optimization and Control | Mathematics

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

Electronic Journal of Differential Equations, 08/2012, Volume 2015

Journal Article

Constructive Approximation, ISSN 0176-4276, 11/2006, Volume 24, Issue 3, pp. 245 - 262

In this paper, we determine the asymptotic values of the probabilistic adaptive widths of the space of multivariate functions with bounded mixed derivative...

Average adaptive width | Sobolev space with bounded mixed derivative | Gaussian measure | Analysis | Numerical Analysis | Probabilistic adaptive width | Mathematics | MATHEMATICS | probabilistic adaptive width | average adaptive width | APPROXIMATION

Average adaptive width | Sobolev space with bounded mixed derivative | Gaussian measure | Analysis | Numerical Analysis | Probabilistic adaptive width | Mathematics | MATHEMATICS | probabilistic adaptive width | average adaptive width | APPROXIMATION

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 04/2019, Volume 22, Issue 2, pp. 271 - 286

Unique solvability and well-posedness issues are studied for linear inverse problems with a constant unknown parameter to fractional order differential...

inverse problem | Primary 35R30 | 35R11 | degenerate evolution equation | Secondary 34G10 | bounded operator | 34A08 | fractional Riemann – Liouville derivative | PREDICTION-CONTROL PROBLEM | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | (L, p)-bounded operator | fractional Riemann - Liouville derivative | DIFFERENTIAL-EQUATION | SYSTEMS | IDENTIFICATION | Operators (mathematics) | Inverse problems | Partial differential equations | Initial conditions | Mathematical analysis | Order parameters | Polynomials | Well posed problems | Banach space

inverse problem | Primary 35R30 | 35R11 | degenerate evolution equation | Secondary 34G10 | bounded operator | 34A08 | fractional Riemann – Liouville derivative | PREDICTION-CONTROL PROBLEM | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | (L, p)-bounded operator | fractional Riemann - Liouville derivative | DIFFERENTIAL-EQUATION | SYSTEMS | IDENTIFICATION | Operators (mathematics) | Inverse problems | Partial differential equations | Initial conditions | Mathematical analysis | Order parameters | Polynomials | Well posed problems | Banach space

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 2005, Volume 132, Issue 1, pp. 77 - 96

We determine the asymptotic values on the linear probabilistic ( N , δ ) -widths and linear p-average N-widths of the space of multivariate functions with...

Probabilistic linear width | Sobolev space with bounded mixed derivative | Gaussian measure | Average linear width | MATHEMATICS | SMOOTH FUNCTIONS | APPROXIMATION | average linear width | probabilistic linear width

Probabilistic linear width | Sobolev space with bounded mixed derivative | Gaussian measure | Average linear width | MATHEMATICS | SMOOTH FUNCTIONS | APPROXIMATION | average linear width | probabilistic linear width

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2017, Volume 345, pp. 74 - 90

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media....

Semi-discrete Kansa method | Spatiotemporal FDE | Vector fractional derivative | Anomalous transport | APPROXIMATION | HETEROGENEOUS MEDIA | DIFFERENTIAL-EQUATIONS | TIME | PHYSICS, MATHEMATICAL | SOLUTE TRANSPORT | ANOMALOUS DIFFUSION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOUNDED DOMAINS | POROUS-MEDIA | ADVECTION-DISPERSION EQUATIONS | FINITE-ELEMENT-METHOD | Hydrology | Local transit | Aquatic resources | Analysis | Methods | Differential equations

Semi-discrete Kansa method | Spatiotemporal FDE | Vector fractional derivative | Anomalous transport | APPROXIMATION | HETEROGENEOUS MEDIA | DIFFERENTIAL-EQUATIONS | TIME | PHYSICS, MATHEMATICAL | SOLUTE TRANSPORT | ANOMALOUS DIFFUSION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOUNDED DOMAINS | POROUS-MEDIA | ADVECTION-DISPERSION EQUATIONS | FINITE-ELEMENT-METHOD | Hydrology | Local transit | Aquatic resources | Analysis | Methods | Differential equations

Journal Article

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 1072-6691, 08/2015, Volume 2015, Issue 201, pp. 1 - 18

We study a class of nonlinear partial differential equations, which can be connected with wave-type equations and Laplace-type equations, by using a...

MATHEMATICS | MATHEMATICS, APPLIED | bounded solution | WAVES | Analytic solution | PDE with mixed derivatives | wave-type PDE | sine-Gordon | series solution | Klein-Gordon | SYSTEMS | Laplace-type PDE

MATHEMATICS | MATHEMATICS, APPLIED | bounded solution | WAVES | Analytic solution | PDE with mixed derivatives | wave-type PDE | sine-Gordon | series solution | Klein-Gordon | SYSTEMS | Laplace-type PDE

Journal Article

Kyushu Journal of Mathematics, ISSN 1340-6116, 2017, Volume 71, Issue 1, pp. 31 - 64

We consider a nonsingular transformation whose Perron-Frobenius operator is quasi-compact on an appropriate Banach algebra. We establish the central limit...

central limit theorem of mixed type | perturbed Perron-Frobenius operator | Central limit theorem of mixed type | Perturbed Perron–Frobenius operator | MATHEMATICS | INVARIANT-MEASURES | PIECEWISE MONOTONIC TRANSFORMATIONS | ERGODIC PROPERTIES | BOUNDED VARIATION

central limit theorem of mixed type | perturbed Perron-Frobenius operator | Central limit theorem of mixed type | Perturbed Perron–Frobenius operator | MATHEMATICS | INVARIANT-MEASURES | PIECEWISE MONOTONIC TRANSFORMATIONS | ERGODIC PROPERTIES | BOUNDED VARIATION

Journal Article

Houston Journal of Mathematics, ISSN 0362-1588, 2007, Volume 33, Issue 3, pp. 927 - 939

We study the continuity of functions u whose mixed derivative partial derivative 1...partial derivative(Nu) is a measure. If u epsilon W-1,W-1(R-N), then we...

Functions whose derivatives are measures | Functions of bounded variation | Sobolev spaces | Embedding theorems | Continuous functions | MATHEMATICS | functions of bounded variation | embedding theorems | continuous functions | functions whose derivatives axe measures

Functions whose derivatives are measures | Functions of bounded variation | Sobolev spaces | Embedding theorems | Continuous functions | MATHEMATICS | functions of bounded variation | embedding theorems | continuous functions | functions whose derivatives axe measures

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2002, Volume 29, Issue 1, pp. 145 - 155

A general solution is given for a fractional diffusion-wave equation defined in a bounded space domain. The fractional time derivative is described in the...

Automotive and Aerospace Engineering, Traffic | Engineering | Vibration, Dynamical Systems, Control | bounded domain solution for fractional diffusion-wave equation | Mechanics | fractional derivative | fractional order diffusion-wave equation | Mechanical Engineering | Laplace transform | Bounded domain solution for fractional diffusion-wave equation | Fractional order diffusion-wave equation | Fractional derivative | MECHANICS | INTEGRODIFFERENTIAL EQUATION | HEAT-EQUATION | ENGINEERING, MECHANICAL | Diffusion rate | Wavelengths | Laplace transforms | Mathematical analysis | Differential equations | Wave equations

Automotive and Aerospace Engineering, Traffic | Engineering | Vibration, Dynamical Systems, Control | bounded domain solution for fractional diffusion-wave equation | Mechanics | fractional derivative | fractional order diffusion-wave equation | Mechanical Engineering | Laplace transform | Bounded domain solution for fractional diffusion-wave equation | Fractional order diffusion-wave equation | Fractional derivative | MECHANICS | INTEGRODIFFERENTIAL EQUATION | HEAT-EQUATION | ENGINEERING, MECHANICAL | Diffusion rate | Wavelengths | Laplace transforms | Mathematical analysis | Differential equations | Wave equations

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2007, Volume 359, Issue 5, pp. 2443 - 2461

We prove that if f:I\subset \mathbb{R}\to \mathbb{R} is of bounded variation, then the uncentered maximal function Mf is absolutely continuous, and its...

Open intervals | Mathematical intervals | Mathematical theorems | Interior points | Eigenfunctions | Mathematical functions | Mathematical inequalities | Sobolev spaces | Continuous functions | Functions of bounded variation | Maximal function | MATHEMATICS | functions of bounded variation | maximal function | SOBOLEV SPACES

Open intervals | Mathematical intervals | Mathematical theorems | Interior points | Eigenfunctions | Mathematical functions | Mathematical inequalities | Sobolev spaces | Continuous functions | Functions of bounded variation | Maximal function | MATHEMATICS | functions of bounded variation | maximal function | SOBOLEV SPACES

Journal Article

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, ISSN 0232-2064, 2007, Volume 26, Issue 4, pp. 473 - 480

In this note we prove that a harmonic function u on the unit ball B subset of R-n belongs to the harmonic mixed norm space A(s)(p,q) (B), when p,q is an...

MATHEMATICS, APPLIED | unit ball | POLYDISK | harmonic function | HL-property | WEIGHTED INTEGRALS | mixed norm space | MATHEMATICS | BOUNDED SYMMETRIC DOMAINS | BLOCH SPACE | HOLOMORPHIC-FUNCTIONS | VARIABLES | DERIVATIVES | BERGMAN SPACES

MATHEMATICS, APPLIED | unit ball | POLYDISK | harmonic function | HL-property | WEIGHTED INTEGRALS | mixed norm space | MATHEMATICS | BOUNDED SYMMETRIC DOMAINS | BLOCH SPACE | HOLOMORPHIC-FUNCTIONS | VARIABLES | DERIVATIVES | BERGMAN SPACES

Journal Article

Mathematical Notes, ISSN 0001-4346, 9/1999, Volume 66, Issue 3, pp. 261 - 270

The paper deals with approximations of functions with bounded mixed difference by Haar polynomials. Approximations of the following two different types are...

Haar polynomial | function with bounded mixed derivative or difference | Mathematics, general | Mathematics | approximation of functions | the best approximation | Banach space | the best m -term approximation

Haar polynomial | function with bounded mixed derivative or difference | Mathematics, general | Mathematics | approximation of functions | the best approximation | Banach space | the best m -term approximation

Journal Article

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