Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 374, Issue 1, pp. 118 - 132

In this paper, we introduce the notion of a weak sharp set of solutions to a variational inequality problem (VIP) in a reflexive, strictly convex and smooth...

Error bound | Proximal point algorithms | Finite convergence | Weakly sharp | Variational inequalities | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | PROXIMAL POINT ALGORITHM | Algorithms

Error bound | Proximal point algorithms | Finite convergence | Weakly sharp | Variational inequalities | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | PROXIMAL POINT ALGORITHM | Algorithms

Journal Article

Optimization Letters, ISSN 1862-4472, 3/2016, Volume 10, Issue 3, pp. 563 - 576

Our aim is to study weakly sharp solutions of a variational inequality in terms of its primal gap function $$g$$ g . We discuss sufficient conditions for the...

Gap functions | Computational Intelligence | Variational inequality | 49J52 | 90C33 | Numerical and Computational Physics | Error bound | Mathematics | Operation Research/Decision Theory | Convergence of algorithm | Weakly sharp solution | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EQUILIBRIA

Gap functions | Computational Intelligence | Variational inequality | 49J52 | 90C33 | Numerical and Computational Physics | Error bound | Mathematics | Operation Research/Decision Theory | Convergence of algorithm | Weakly sharp solution | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EQUILIBRIA

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2011, Volume 235, Issue 14, pp. 4283 - 4301

Collocation methods are a well-developed approach for the numerical solution of smooth and weakly singular Volterra integral equations. In this paper, we...

Linear Volterra integral equation | Qualocation | Collocation | Partitioned quadrature | MATHEMATICS, APPLIED | INTEGRODIFFERENTIAL EQUATIONS | WEAKLY SINGULAR KERNELS | COLLOCATION METHODS | EXPLICIT BELTYUKOV PAIRS | DOUBLE-EXPONENTIAL TRANSFORMATION | QUADRATURE | CONVERGENCE | DIFFUSION | Employee motivation | Kernels | Approximation | Computation | Collocation methods | Performance enhancement | Mathematical models | Volterra integral equations | Quadratures

Linear Volterra integral equation | Qualocation | Collocation | Partitioned quadrature | MATHEMATICS, APPLIED | INTEGRODIFFERENTIAL EQUATIONS | WEAKLY SINGULAR KERNELS | COLLOCATION METHODS | EXPLICIT BELTYUKOV PAIRS | DOUBLE-EXPONENTIAL TRANSFORMATION | QUADRATURE | CONVERGENCE | DIFFUSION | Employee motivation | Kernels | Approximation | Computation | Collocation methods | Performance enhancement | Mathematical models | Volterra integral equations | Quadratures

Journal Article

Optimization, ISSN 0233-1934, 02/2018, Volume 67, Issue 2, pp. 329 - 340

The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using...

convergence of an algorithm | gap functions | gâteaux differentiable | error bound | Variational inequality | locally Lipschitz property | weakly sharp solution | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | gateaux differentiable | TERMINATION | GAP FUNCTION | Optimization algorithms | Algorithms | Sharpness | Portfolio management | Inequality

convergence of an algorithm | gap functions | gâteaux differentiable | error bound | Variational inequality | locally Lipschitz property | weakly sharp solution | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | gateaux differentiable | TERMINATION | GAP FUNCTION | Optimization algorithms | Algorithms | Sharpness | Portfolio management | Inequality

Journal Article

5.
Characterization of weak sharp solutions for generalized variational inequalities in Banach spaces

Journal of Computational Analysis and Applications, ISSN 1521-1398, 2018, Volume 25, Issue 4, pp. 738 - 750

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 12/2018, Volume 179, Issue 3, pp. 962 - 982

Subgradient methods converge linearly on a convex function that grows sharply away from its solution set. In this work, we show that the same is true for sharp...

65K05 | Sharp | Weakly convex | Error bound | Mathematics | Theory of Computation | Optimization | Subgradient | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | 65K10 | Applications of Mathematics | Engineering, general | Linear rate | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Signal processing | Methods | Management science | Formulations | Covariance | Phase retrieval

65K05 | Sharp | Weakly convex | Error bound | Mathematics | Theory of Computation | Optimization | Subgradient | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | 65K10 | Applications of Mathematics | Engineering, general | Linear rate | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Signal processing | Methods | Management science | Formulations | Covariance | Phase retrieval

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2016, Volume 325, pp. 338 - 357

We present Gauss–Jacobi quadrature rules in terms of hypergeometric functions for the discretization of weakly singular, strongly singular, hypersingular, and...

Nyström method | Gauss–Jacobi quadrature rules | Nearly singular integrals | Weakly singular integrals | Hypersingular integrals | Strongly singular integrals | Analysis | Methods | Electromagnetism

Nyström method | Gauss–Jacobi quadrature rules | Nearly singular integrals | Weakly singular integrals | Hypersingular integrals | Strongly singular integrals | Analysis | Methods | Electromagnetism

Journal Article

PACIFIC JOURNAL OF OPTIMIZATION, ISSN 1348-9151, 01/2016, Volume 12, Issue 1, pp. 207 - 220

We discuss relations between the Gateaux differentiability of two gap functions of a variational inequality problem and its dual problem and present sufficient...

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | gap functions | error bound | EQUILIBRIUM | variational inequality | locally Lipschitz property | Gateaux differentiability | GAP FUNCTION | weakly sharp solution

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | gap functions | error bound | EQUILIBRIUM | variational inequality | locally Lipschitz property | Gateaux differentiability | GAP FUNCTION | weakly sharp solution

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 2/2017, Volume 43, Issue 1, pp. 77 - 99

A two-point boundary value problem is considered on the interval [0, 1], where the leading term in the differential operator is a Riemann-Liouville fractional...

Fractional differential equation | Visualization | Computational Mathematics and Numerical Analysis | Boundary value problem | Mathematical and Computational Biology | Riemann-Liouville fractional derivative | Weakly singular Volterra integral equation | Mathematics | Mathematical Modeling and Industrial Mathematics | Computational Science and Engineering | Collocation method | 65L10 | MATHEMATICS, APPLIED | Boundary value problems | Analysis | Differential equations

Fractional differential equation | Visualization | Computational Mathematics and Numerical Analysis | Boundary value problem | Mathematical and Computational Biology | Riemann-Liouville fractional derivative | Weakly singular Volterra integral equation | Mathematics | Mathematical Modeling and Industrial Mathematics | Computational Science and Engineering | Collocation method | 65L10 | MATHEMATICS, APPLIED | Boundary value problems | Analysis | Differential equations

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 10/2019, Volume 267, Issue 9, pp. 5165 - 5201

In this paper we consider the wave equations with power type nonlinearities including time-derivatives of unknown functions and their weakly coupled systems....

Weakly coupled system | Upper bounds of lifespan | Blowup | Test function methods | Semilinear wave equations | LIFE-SPAN | NONEXISTENCE | GLOBAL EXISTENCE | CAUCHY-PROBLEM | MATHEMATICS | U=/U/P | CRITICAL EXPONENT | NONLINEAR-SYSTEMS | LARGE TIME BEHAVIOR | CLASSICAL-SOLUTIONS

Weakly coupled system | Upper bounds of lifespan | Blowup | Test function methods | Semilinear wave equations | LIFE-SPAN | NONEXISTENCE | GLOBAL EXISTENCE | CAUCHY-PROBLEM | MATHEMATICS | U=/U/P | CRITICAL EXPONENT | NONLINEAR-SYSTEMS | LARGE TIME BEHAVIOR | CLASSICAL-SOLUTIONS

Journal Article

混相流, ISSN 0914-2843, 2018, Volume 32, Issue 4, pp. 416 - 423

Incompressible flows have much lower flow speeds to compare with the sound speed and called low Mach number flows. So far, we have simulated incompressible...

AMR method | Gas-liquid two-phase flow | Conservative phase-field model | Weakly compressible flow computation | Fully-explicit solver

AMR method | Gas-liquid two-phase flow | Conservative phase-field model | Weakly compressible flow computation | Fully-explicit solver

Journal Article

Electrochimica Acta, ISSN 0013-4686, 2010, Volume 55, Issue 3, pp. 721 - 728

Considering modern trends of laboratory automation in electroanalysis, the development of adaptive methods for automatic simulation of electrochemical...

Cyclic voltammetry | Laboratory automation | Computational electrochemistry | Digital simulation | Second kind Volterra integral equations | Weakly singular kernels | ELECTROCHEMISTRY | NUMERICAL-SOLUTION | STATIONARY ELECTRODE POLAROGRAPHY | VOLTAMMETRY

Cyclic voltammetry | Laboratory automation | Computational electrochemistry | Digital simulation | Second kind Volterra integral equations | Weakly singular kernels | ELECTROCHEMISTRY | NUMERICAL-SOLUTION | STATIONARY ELECTRODE POLAROGRAPHY | VOLTAMMETRY

Journal Article

Chinese Annals of Mathematics. Series B, ISSN 0252-9599, 2003, Volume 24, Issue 4, pp. 457 - 468

This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilinear hyperbolic systems, which bases on the existence of the...

Matching condition | Weakly linearly degenerate | Normalize translation and normalize coordinate | MATHEMATICS | WAVES | normalize translation and normalize coordinate | weakly linearly degenerate | SINGULARITIES | GLOBAL CLASSICAL-SOLUTIONS | matching condition | DECAY INITIAL DATA

Matching condition | Weakly linearly degenerate | Normalize translation and normalize coordinate | MATHEMATICS | WAVES | normalize translation and normalize coordinate | weakly linearly degenerate | SINGULARITIES | GLOBAL CLASSICAL-SOLUTIONS | matching condition | DECAY INITIAL DATA

Journal Article

14.
Full Text
Stability of Numerical Solutions for Abel–Volterra Integral Equations of the Second Kind

Mediterranean Journal of Mathematics, ISSN 1660-5446, 6/2018, Volume 15, Issue 3, pp. 1 - 14

We analyze the stability of convolution quadrature methods for weakly singular Volterra integral equations with respect to a linear test equation. We prove...

Convolution quadrature | 65L06 | Primary 34A08 | Weakly singular integral equations | Mathematics, general | Mathematics | Secondary 65R20 | Numerical stability | MATHEMATICS | MATHEMATICS, APPLIED

Convolution quadrature | 65L06 | Primary 34A08 | Weakly singular integral equations | Mathematics, general | Mathematics | Secondary 65R20 | Numerical stability | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 21

We provide the numerical solution of a Volterra integro-differential equation of parabolic type with memory term subject to initial boundary value conditions....

65R99 | Mathematics | partial integro-differential equation | finite difference method | product trapezoidal integration rule | Ordinary Differential Equations | Functional Analysis | 45A99 | Analysis | Difference and Functional Equations | Mathematics, general | 45K05 | Partial Differential Equations | sinc-collocation method | DIFFERENTIAL EQUATIONS | MATHEMATICS, APPLIED | MEMORY TERM | WEAKLY SINGULAR KERNEL | GALERKIN METHOD | MATHEMATICS | SCHEME | POSITIVE-TYPE | EVOLUTION EQUATION | DIFFUSION | Finite element method | Usage | Boundary value problems | Differential equations | Collocation methods | Convergence | Finite difference method

65R99 | Mathematics | partial integro-differential equation | finite difference method | product trapezoidal integration rule | Ordinary Differential Equations | Functional Analysis | 45A99 | Analysis | Difference and Functional Equations | Mathematics, general | 45K05 | Partial Differential Equations | sinc-collocation method | DIFFERENTIAL EQUATIONS | MATHEMATICS, APPLIED | MEMORY TERM | WEAKLY SINGULAR KERNEL | GALERKIN METHOD | MATHEMATICS | SCHEME | POSITIVE-TYPE | EVOLUTION EQUATION | DIFFUSION | Finite element method | Usage | Boundary value problems | Differential equations | Collocation methods | Convergence | Finite difference method

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 8/2018, Volume 229, Issue 2, pp. 709 - 788

We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | MATHEMATICS, APPLIED | MECHANICS | MEAN-CURVATURE | HARDY-SPACES | 1/2-HARMONIC MAPS | COMMUTATORS | CONSERVATION-LAWS | WEAKLY HARMONIC MAPS | COMPACTNESS | SURFACES

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | MATHEMATICS, APPLIED | MECHANICS | MEAN-CURVATURE | HARDY-SPACES | 1/2-HARMONIC MAPS | COMMUTATORS | CONSERVATION-LAWS | WEAKLY HARMONIC MAPS | COMPACTNESS | SURFACES

Journal Article

Neurocomputing, ISSN 0925-2312, 04/2019, Volume 338, pp. 321 - 348

•Extensive survey on deep neural networks for semantic segmentation.•110 neural network models are categorized into 10 different concepts.•Review of...

Deep learning | Semantic segmentation | Recurrent neural network | Semi-weakly supervised networks | SALIENT OBJECT DETECTION | NEURAL-NETWORKS | DATABASE | VIDEO | SCENES | FRAMEWORK | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Surveys | Machine vision | Neural networks | Driverless cars | Methods | Robotics

Deep learning | Semantic segmentation | Recurrent neural network | Semi-weakly supervised networks | SALIENT OBJECT DETECTION | NEURAL-NETWORKS | DATABASE | VIDEO | SCENES | FRAMEWORK | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Surveys | Machine vision | Neural networks | Driverless cars | Methods | Robotics

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2009, Volume 41, Issue 3, pp. 1190 - 1205

We construct global BV solutions to the Cauchy problem for the damped p-system, under initial data with distinct end-states. The solution will be realized as a...

Darcy law | Porous medium flow | BV estimates | Entropy estimates | Weakly dissipative | Frictional damping | EXISTENCE | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | EQUATIONS | weakly dissipative | porous medium flow | UNIQUENESS | ENTROPY SOLUTIONS | NONLINEAR DIFFUSION WAVES | BALANCE LAWS | entropy estimates | frictional damping | LAX-FRIEDRICHS SCHEME | HYPERBOLIC CONSERVATION-LAWS | CONVERGENCE-RATES | Damping | Law | Perturbation methods | Asymptotic properties | Gas flow | Mathematical analysis | Density | Cauchy problem

Darcy law | Porous medium flow | BV estimates | Entropy estimates | Weakly dissipative | Frictional damping | EXISTENCE | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | EQUATIONS | weakly dissipative | porous medium flow | UNIQUENESS | ENTROPY SOLUTIONS | NONLINEAR DIFFUSION WAVES | BALANCE LAWS | entropy estimates | frictional damping | LAX-FRIEDRICHS SCHEME | HYPERBOLIC CONSERVATION-LAWS | CONVERGENCE-RATES | Damping | Law | Perturbation methods | Asymptotic properties | Gas flow | Mathematical analysis | Density | Cauchy problem

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 6/2012, Volume 153, Issue 3, pp. 619 - 632

In this paper, we refine and improve the results established in a 2003 paper by Deng in a number of directions. Specifically, we establish a well-posedness...

Weakly efficient solution | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Hausdorff distance | Engineering, general | Applications of Mathematics | Convexity | Optimization | Well-posedness | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Paper | Vectors (mathematics) | Mathematical analysis | Convergence

Weakly efficient solution | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Hausdorff distance | Engineering, general | Applications of Mathematics | Convexity | Optimization | Well-posedness | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Paper | Vectors (mathematics) | Mathematical analysis | Convergence

Journal Article

European Journal of Inorganic Chemistry, ISSN 1434-1948, 07/2015, Volume 2015, Issue 19, pp. 3128 - 3138

Lithium chloro‐ and bromoaluminates were prepared, fully characterized, and investigated as conducting salts for battery applications. In addition,...

Lewis acids | Electrolytes | Lithium batteries | Lattice energies | Density functional calculations | Batteries | Weakly coordinating anions | ENERGY | ACID-BASE PROPERTIES | PASSIVE FILMS | NONAQUEOUS ELECTROLYTES | ALUMINUM CORROSION | CHEMISTRY, INORGANIC & NUCLEAR | LIPF6 | LITHIUM-OXYGEN BATTERIES | AIR BATTERIES | LI-ION BATTERY | LIQUIDS | Thermodynamics | Sulfur compounds | Crystals | Chemical properties | Carbonates | Structure | Investigations | Electric properties | Lithium | Solvents | Conduction | Enthalpy | Lattices | Conductivity | Electric batteries

Lewis acids | Electrolytes | Lithium batteries | Lattice energies | Density functional calculations | Batteries | Weakly coordinating anions | ENERGY | ACID-BASE PROPERTIES | PASSIVE FILMS | NONAQUEOUS ELECTROLYTES | ALUMINUM CORROSION | CHEMISTRY, INORGANIC & NUCLEAR | LIPF6 | LITHIUM-OXYGEN BATTERIES | AIR BATTERIES | LI-ION BATTERY | LIQUIDS | Thermodynamics | Sulfur compounds | Crystals | Chemical properties | Carbonates | Structure | Investigations | Electric properties | Lithium | Solvents | Conduction | Enthalpy | Lattices | Conductivity | Electric batteries

Journal Article