Advances in Mathematics, ISSN 0001-8708, 05/2018, Volume 330, pp. 946 - 996

We show that for every ergodic system (X,μ,T1,…,Td) with commuting transformations, the...

Topological models | Pointwise convergence | Cubic averages | MATHEMATICS | EXTENSIONS | SYSTEMS | CUBES | NORM CONVERGENCE | RECURRENCE | 2 COMMUTING TRANSFORMATIONS

Topological models | Pointwise convergence | Cubic averages | MATHEMATICS | EXTENSIONS | SYSTEMS | CUBES | NORM CONVERGENCE | RECURRENCE | 2 COMMUTING TRANSFORMATIONS

Journal Article

Real Analysis Exchange, ISSN 0147-1937, 1/2019, Volume 44, Issue 1, pp. 167 - 180

For a compact set , we have two indexes given under simple parameters of the set (these parameters go back to Besicovitch and Taylor in the late 50's). In the...

Open intervals | Mathematical theorems | Mathematical sets | RESEARCH ARTICLES | Lebesgue measures | Cubes | Ratio test | Mathematics | Mathematical functions | Density

Open intervals | Mathematical theorems | Mathematical sets | RESEARCH ARTICLES | Lebesgue measures | Cubes | Ratio test | Mathematics | Mathematical functions | Density

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 6/2014, Volume 64, Issue 2, pp. 519 - 537

We compare the forcing-related properties of a complete Boolean algebra B with the properties of the convergences λs (the algebraic convergence) and λls on B...

Cantor cube | 03E40 | 06E10 | 54A20 | complete Boolean algebra | 54D55 | Mathematics | convergence structure | algebraic convergence | forcing | small cardinal | Ordinary Differential Equations | 03E17 | Aleksandrov cube | Analysis | Convex and Discrete Geometry | Mathematics, general | Mathematical Modeling and Industrial Mathematics | SEQUENTIAL TOPOLOGY | SUBMEASURES | MATHEMATICS | REALS | VON-NEUMANN | MAHARAMS PROBLEM | Sects | Algebra

Cantor cube | 03E40 | 06E10 | 54A20 | complete Boolean algebra | 54D55 | Mathematics | convergence structure | algebraic convergence | forcing | small cardinal | Ordinary Differential Equations | 03E17 | Aleksandrov cube | Analysis | Convex and Discrete Geometry | Mathematics, general | Mathematical Modeling and Industrial Mathematics | SEQUENTIAL TOPOLOGY | SUBMEASURES | MATHEMATICS | REALS | VON-NEUMANN | MAHARAMS PROBLEM | Sects | Algebra

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2012, Volume 50, Issue 3, pp. 1433 - 1455

Galerkin discretizations of integral operators in R d require the evaluation of integrals ∫s⁽¹⁾∫s⁽²⁾ f(x,y) dydx, where S⁽¹⁾,S⁽²⁾ are d-dimensional simplices...

Numerical quadratures | Tensors | Integrands | Mathematical integrals | Cubes | Coordinate systems | Polynomials | Mathematical functions | Gaussian quadratures | Exponential convergence | Gauss-Jacobi quadrature | High dimensional integrands | Numerical integration | Hypersingular integrals | Integral equations | Gevrey regularity | high dimensional integrands | integral equations | MATHEMATICS, APPLIED | numerical integration | hypersingular integrals | exponential convergence | OPERATORS

Numerical quadratures | Tensors | Integrands | Mathematical integrals | Cubes | Coordinate systems | Polynomials | Mathematical functions | Gaussian quadratures | Exponential convergence | Gauss-Jacobi quadrature | High dimensional integrands | Numerical integration | Hypersingular integrals | Integral equations | Gevrey regularity | high dimensional integrands | integral equations | MATHEMATICS, APPLIED | numerical integration | hypersingular integrals | exponential convergence | OPERATORS

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 2/2018, Volume 288, Issue 1, pp. 333 - 360

We study threshold functions for the existence of solutions to linear systems of equations in random sets and present a unified framework which includes...

Mathematics, general | Mathematics | MATHEMATICS | PROOF | LINEAR-EQUATION | THEOREM | VOLUME | Random sets | Matemàtiques i estadística | Geometria | Àrees temàtiques de la UPC | Random, variables de

Mathematics, general | Mathematics | MATHEMATICS | PROOF | LINEAR-EQUATION | THEOREM | VOLUME | Random sets | Matemàtiques i estadística | Geometria | Àrees temàtiques de la UPC | Random, variables de

Journal Article

The Econometrics Journal, ISSN 1368-4221, 06/2015, Volume 18, Issue 2, pp. 172 - 199

Summary This paper establishes consistency and non‐standard rates of convergence for set estimators based on contour sets of criterion functions for a...

Cube‐root asymptotics | Partial identification | Maximum score estimator | Binary response model | Transformation model | Limited support regressors | Semi‐parametric models | Cube-root asymptotics | Semi-parametric models | CONFIDENCE-INTERVALS | PARTIALLY IDENTIFIED PARAMETERS | ASYMPTOTIC PROPERTIES | INTERVAL DATA | STATISTICS & PROBABILITY | CHOICE MODELS | ECONOMETRIC-MODELS | MOMENT INEQUALITIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | CONSISTENT ESTIMATION | ECONOMICS | REGRESSION-MODEL | Studies | Economic models | Estimating techniques | Economic theory | Convergence

Cube‐root asymptotics | Partial identification | Maximum score estimator | Binary response model | Transformation model | Limited support regressors | Semi‐parametric models | Cube-root asymptotics | Semi-parametric models | CONFIDENCE-INTERVALS | PARTIALLY IDENTIFIED PARAMETERS | ASYMPTOTIC PROPERTIES | INTERVAL DATA | STATISTICS & PROBABILITY | CHOICE MODELS | ECONOMETRIC-MODELS | MOMENT INEQUALITIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | CONSISTENT ESTIMATION | ECONOMICS | REGRESSION-MODEL | Studies | Economic models | Estimating techniques | Economic theory | Convergence

Journal Article

Advanced Science Letters, ISSN 1936-6612, 10/2015, Volume 21, Issue 10, pp. 2974 - 2978

This study designs and proposes a Quality-of-Experience-based Digital-convergence iHome caregiving service platform with adaptive event construction and...

Digital convergence | Integrated social network | Open services gateway initiative (OSGi) | Situation confliction | Quality of experience (QoE) | Remote sensors | Construction | Wireless networks | Cubes | Servers | Engines | Application servers | Convergence

Digital convergence | Integrated social network | Open services gateway initiative (OSGi) | Situation confliction | Quality of experience (QoE) | Remote sensors | Construction | Wireless networks | Cubes | Servers | Engines | Application servers | Convergence

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2011, Volume 139, Issue 4, pp. 1445 - 1454

We prove a multiparameter version of a classical theorem of Jones and Journé on weak-star convergence in the Hardy space H^1

Mathematical theorems | Rectangles | Cubes | Dyadics | Mathematical functions | Mathematical inequalities | Mathematical duality | Commutators | Perceptron convergence procedure | Multiparameter Hardy space | VMO | Weak-star convergence | MATHEMATICS, APPLIED | MEAN-OSCILLATION | multiparameter Hardy space | DYADIC BMO | HANKEL-OPERATORS | COMMUTATORS | H-1 | MATHEMATICS | PRODUCT BMO | BIDISC | DUALITY | VARIABLES

Mathematical theorems | Rectangles | Cubes | Dyadics | Mathematical functions | Mathematical inequalities | Mathematical duality | Commutators | Perceptron convergence procedure | Multiparameter Hardy space | VMO | Weak-star convergence | MATHEMATICS, APPLIED | MEAN-OSCILLATION | multiparameter Hardy space | DYADIC BMO | HANKEL-OPERATORS | COMMUTATORS | H-1 | MATHEMATICS | PRODUCT BMO | BIDISC | DUALITY | VARIABLES

Journal Article

The Annals of Statistics, ISSN 0090-5364, 6/1994, Volume 22, Issue 2, pp. 580 - 615

In this paper, we develop a general theory for the convergence rate of sieve estimates, maximum likelihood estimates (MLE's) and related estimates obtained by...

Asymptotic Theory | Maximum likelihood estimation | Density estimation | Approximation | Estimation theory | Cubes | Maximum likelihood estimators | Mathematical independent variables | Entropy | Truncation | Perceptron convergence procedure | REGRESSION | MAXIMUM-LIKELIHOOD-ESTIMATION | SPACES | STATISTICS & PROBABILITY | METRIC ENTROPY FUNCTION | CONVERGENCE RATE | METHOD OF SIEVES | MAXIMUM LIKELIHOOD AND RELATED ESTIMATES | ENTROPY | maximum likelihood and related estimates | 62A10 | Convergence rate | metric entropy function | 62G20 | 62F12 | method of sieves

Asymptotic Theory | Maximum likelihood estimation | Density estimation | Approximation | Estimation theory | Cubes | Maximum likelihood estimators | Mathematical independent variables | Entropy | Truncation | Perceptron convergence procedure | REGRESSION | MAXIMUM-LIKELIHOOD-ESTIMATION | SPACES | STATISTICS & PROBABILITY | METRIC ENTROPY FUNCTION | CONVERGENCE RATE | METHOD OF SIEVES | MAXIMUM LIKELIHOOD AND RELATED ESTIMATES | ENTROPY | maximum likelihood and related estimates | 62A10 | Convergence rate | metric entropy function | 62G20 | 62F12 | method of sieves

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2010, Volume 59, Issue 2, pp. 427 - 457

Two-scale techniques are developed for sequences of maps {uk} ⊂ Lp(Ω;ℝM) satisfying a linear differential constraint 𝒜uk = 0. These, together with...

Integers | Mathematical integrals | Homogenization | Cubes | Mathematical constants | Fourier transformations | Mathematical functions | Perceptron convergence procedure | College mathematics | Equiintegrability | Γ | Two-scale convergence | Convergence | MATHEMATICS | homogenization | REITERATED HOMOGENIZATION | CALCULUS | RELAXATION | Gamma-convergence | equiintegrability | A-QUASICONVEXITY | FUNCTIONALS | two-scale convergence | PERIODIC UNFOLDING METHOD

Integers | Mathematical integrals | Homogenization | Cubes | Mathematical constants | Fourier transformations | Mathematical functions | Perceptron convergence procedure | College mathematics | Equiintegrability | Γ | Two-scale convergence | Convergence | MATHEMATICS | homogenization | REITERATED HOMOGENIZATION | CALCULUS | RELAXATION | Gamma-convergence | equiintegrability | A-QUASICONVEXITY | FUNCTIONALS | two-scale convergence | PERIODIC UNFOLDING METHOD

Journal Article

Russian Mathematical Surveys, ISSN 0036-0279, 2016, Volume 71, Issue 2, pp. 379 - 381

Let [dbl-struck I] super(n)= [0,1] super(n) be the n-dimensional cube, [dbl-struck T] super(i) [0,2[pi]) super(n) the n-dimensional torus, and C([dbl-struck I]...

MATHEMATICS | Functions (mathematics) | Mathematical analysis | Cubes | Texts | Fourier series | Formulas (mathematics) | Continuity (mathematics) | Convergence

MATHEMATICS | Functions (mathematics) | Mathematical analysis | Cubes | Texts | Fourier series | Formulas (mathematics) | Continuity (mathematics) | Convergence

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 3/2012, Volume 32, Issue 3, pp. 1 - 21

We study the limiting behavior of multiple ergodic averages involving several, not necessarily commuting, measure-preserving transformations. We work on two...

MATHEMATICS | MATHEMATICS, APPLIED | CUBES | RECURRENCE | THEOREM | Dynamical systems | Polynomials | Mathematics | Variability | Transformations | Combinatorial analysis | Constraining | Ergodic processes | Convergence

MATHEMATICS | MATHEMATICS, APPLIED | CUBES | RECURRENCE | THEOREM | Dynamical systems | Polynomials | Mathematics | Variability | Transformations | Combinatorial analysis | Constraining | Ergodic processes | Convergence

Journal Article

Neural Network World, ISSN 1210-0552, 2012, Volume 22, Issue 4, pp. 343 - 355

After sigmoid activation function is replaced with piecewise linear activation function, the adding decaying self-feedback continuous Hopfield neural network...

Piecewise linear function | Adding decaying self-feedback continuous Hopfield neural network | Hyper-cube | Convergence analysis | convergence analysis | piecewise linear function | hyper-cube | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | GLOBAL CONVERGENCE

Piecewise linear function | Adding decaying self-feedback continuous Hopfield neural network | Hyper-cube | Convergence analysis | convergence analysis | piecewise linear function | hyper-cube | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | GLOBAL CONVERGENCE

Journal Article

The Annals of Statistics, ISSN 0090-5364, 8/2000, Volume 28, Issue 4, pp. 1105 - 1127

Gaussian mixtures provide a convenient method of density estimation that lies somewhere between parametric models and kernel density estimators. When the...

Density estimation | Maximum likelihood estimation | Lebesgue measures | Cubes | Maximum likelihood estimators | Inference | Entropy | Density | Parametric models | Estimators | Mixtures | Sieves | Rates of convergence | sieves | STATISTICS & PROBABILITY | BAYESIAN DENSITY-ESTIMATION | density estimation | mixtures | rates of convergence | none

Density estimation | Maximum likelihood estimation | Lebesgue measures | Cubes | Maximum likelihood estimators | Inference | Entropy | Density | Parametric models | Estimators | Mixtures | Sieves | Rates of convergence | sieves | STATISTICS & PROBABILITY | BAYESIAN DENSITY-ESTIMATION | density estimation | mixtures | rates of convergence | none

Journal Article

Journal of Complexity, ISSN 0885-064X, 08/2014, Volume 30, Issue 4, pp. 444 - 468

This paper provides the theoretical foundation for the component-by-component (CBC) construction of randomly shifted lattice rules that are tailored to...

Monte Carlo methods | Construction | Function space | Integrals | Lattices | Cubes | Strategy | Density

Monte Carlo methods | Construction | Function space | Integrals | Lattices | Cubes | Strategy | Density

Journal Article

16.
Full Text
Convergence of Minimizers with Local Energy Bounds for the Ginzburg-Landau Functionals

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2009, Volume 58, Issue 5, pp. 2369 - 2407

We study the asymptotic behaviour, as ε → 0, of a sequence {uε} of minimizers for the Ginzburg-Landau functional which satisfies local energy bounds of order |...

Topological compactness | Interpolation | Mathematical sequences | Integral currents | Minimal surfaces | Cubes | Mathematical constants | Mathematical functions | Jacobians | Γ-convergence | Ginzburg-landau | Vortices | MATHEMATICS | FIELD | vortices | minimal surfaces | Gamma-convergence | Ginzburg-Landau | 3 DIMENSIONS | EQUATION

Topological compactness | Interpolation | Mathematical sequences | Integral currents | Minimal surfaces | Cubes | Mathematical constants | Mathematical functions | Jacobians | Γ-convergence | Ginzburg-landau | Vortices | MATHEMATICS | FIELD | vortices | minimal surfaces | Gamma-convergence | Ginzburg-Landau | 3 DIMENSIONS | EQUATION

Journal Article

Studia Mathematica, ISSN 0039-3223, 2010, Volume 196, Issue 1, pp. 13 - 22

We prove the norm convergence of multiple ergodic averages along cubes for several commuting transformations, and derive corresponding combinatorial results....

Averages along cubes | Commuting transformations | Magic system | Ergodic seminorms | MATHEMATICS | commuting transformations | averages along cubes | magic system | ergodic seminorms

Averages along cubes | Commuting transformations | Magic system | Ergodic seminorms | MATHEMATICS | commuting transformations | averages along cubes | magic system | ergodic seminorms

Journal Article

Applied Physics Letters, ISSN 0003-6951, 07/2018, Volume 113, Issue 5

We demonstrate acoustic trapping in both position and orientation of a non-spherical particle of sub-wavelength size in mid-air. To do so, we multiplex in time...

Multiplexing | Pyramids | Torque | Acoustic levitation | Crickets | Levitation | Locks | Acoustics | Orientation | Convergence | Standing waves | Trapping | Insects | Cubes | Stiffness | Containment | Cylinders

Multiplexing | Pyramids | Torque | Acoustic levitation | Crickets | Levitation | Locks | Acoustics | Orientation | Convergence | Standing waves | Trapping | Insects | Cubes | Stiffness | Containment | Cylinders

Journal Article

Scandinavian Journal of Statistics, ISSN 0303-6898, 12/2005, Volume 32, Issue 4, pp. 639 - 660

We are interested in estimating level sets using a Bayesian non-parametric approach, from an independent and identically distributed sample drawn from an...

Density estimation | Minimax | Statistical theories | Pavements | Cubes | Entropy | Density | Frequentism | Estimators | Point estimators | convergence rates of the posterior distribution | level set | Bayesian non‐parametric estimation | Level set | Convergence rates of the posterior distribution | Bayesian non-parametric estimation | CONSISTENCY | DIMENSIONS | NONPARAMETRIC-ESTIMATION | DENSITY CONTOUR | STATISTICS & PROBABILITY | POSTERIOR DISTRIBUTIONS

Density estimation | Minimax | Statistical theories | Pavements | Cubes | Entropy | Density | Frequentism | Estimators | Point estimators | convergence rates of the posterior distribution | level set | Bayesian non‐parametric estimation | Level set | Convergence rates of the posterior distribution | Bayesian non-parametric estimation | CONSISTENCY | DIMENSIONS | NONPARAMETRIC-ESTIMATION | DENSITY CONTOUR | STATISTICS & PROBABILITY | POSTERIOR DISTRIBUTIONS

Journal Article

The Annals of Statistics, ISSN 0090-5364, 8/2010, Volume 38, Issue 4, pp. 1953 - 1977

In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that...

Density estimation | Conditional probabilities | Conditional convergence | Random variables | Estimators | Consistent estimators | Bootstrap resampling | Perceptron convergence procedure | Distribution functions | Estimation methods | Empirical distribution function | Nonparametric maximum likelihood estimate | Least concave majorant | M out of n bootstrap | Smoothed bootstrap | Decreasing density | m out of n bootstrap | smoothed bootstrap | CUBE ROOT ASYMPTOTICS | empirical distribution function | STATISTICS & PROBABILITY | nonparametric maximum likelihood estimate | least concave majorant | 62G07 | 62G09 | 62G20

Density estimation | Conditional probabilities | Conditional convergence | Random variables | Estimators | Consistent estimators | Bootstrap resampling | Perceptron convergence procedure | Distribution functions | Estimation methods | Empirical distribution function | Nonparametric maximum likelihood estimate | Least concave majorant | M out of n bootstrap | Smoothed bootstrap | Decreasing density | m out of n bootstrap | smoothed bootstrap | CUBE ROOT ASYMPTOTICS | empirical distribution function | STATISTICS & PROBABILITY | nonparametric maximum likelihood estimate | least concave majorant | 62G07 | 62G09 | 62G20

Journal Article

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