The Annals of Statistics, ISSN 0090-5364, 10/2010, Volume 38, Issue 5, pp. 2916 - 2957

We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing...

Density estimation | Estimation bias | Sample size | Random variables | Data smoothing | Diffusion coefficient | Estimators | Point estimators | Estimation methods | Bandwidth selection | Heat kernel | Nonparametric density estimation | Diffusion equation | Langevin process | Boundary bias | Data sharpening | Variable bandwidth | Normal reference rules | variable bandwidth | normal reference rules | heat kernel | bandwidth selection | STATISTICS & PROBABILITY | BOUNDARY CORRECTION | VARIABLE LOCATION | diffusion equation | boundary bias | data sharpening | 62G07 | 60J60 | 60J70 | 35K05 | 35K15 | 62G20

Density estimation | Estimation bias | Sample size | Random variables | Data smoothing | Diffusion coefficient | Estimators | Point estimators | Estimation methods | Bandwidth selection | Heat kernel | Nonparametric density estimation | Diffusion equation | Langevin process | Boundary bias | Data sharpening | Variable bandwidth | Normal reference rules | variable bandwidth | normal reference rules | heat kernel | bandwidth selection | STATISTICS & PROBABILITY | BOUNDARY CORRECTION | VARIABLE LOCATION | diffusion equation | boundary bias | data sharpening | 62G07 | 60J60 | 60J70 | 35K05 | 35K15 | 62G20

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2014, Volume 163, Issue 7, pp. 1405 - 1490

In this paper, we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X, d, m) which is stable under measured...

MATHEMATICS | SOBOLEV SPACES | TRANSPORT | INEQUALITIES | STABILITY | COMPACT ALEXANDROV SPACES | FINSLER MANIFOLDS | WASSERSTEIN SPACES | HEAT-FLOW | GRADIENT FLOWS | GEOMETRY | 60J65 | 35K05

MATHEMATICS | SOBOLEV SPACES | TRANSPORT | INEQUALITIES | STABILITY | COMPACT ALEXANDROV SPACES | FINSLER MANIFOLDS | WASSERSTEIN SPACES | HEAT-FLOW | GRADIENT FLOWS | GEOMETRY | 60J65 | 35K05

Journal Article

Journal of Physics: Conference Series, ISSN 1742-6588, 06/2015, Volume 621, Issue 1

J. Phys.: Conf. Ser. 621 (2015), 012011 We find the equivalence groupoid of a~class of $(1+1)$-dimensional second-order evolution equations, which are called...

Conference Proceeding

The Annals of probability, ISSN 0091-1798, 11/2015, Volume 43, Issue 6, pp. 3359 - 3467

We prove pathwise nonuniqueness in the stochastic partial differential equations (SPDEs) for some one-dimensional super-Brownian motions with immigration. In...

Immigration | Continuous decomposition | Stochastic partial differential equations | Super-Brownian motion | super-Brownian motion | immigration | PARTIAL-DIFFERENTIAL EQUATIONS | STATISTICS & PROBABILITY | continuous decomposition | UNIQUENESS | Mathematics - Probability | 35R60 | 35K05 | 60H15 | 60J68

Immigration | Continuous decomposition | Stochastic partial differential equations | Super-Brownian motion | super-Brownian motion | immigration | PARTIAL-DIFFERENTIAL EQUATIONS | STATISTICS & PROBABILITY | continuous decomposition | UNIQUENESS | Mathematics - Probability | 35R60 | 35K05 | 60H15 | 60J68

Journal Article

Acta Mathematica Scientia, ISSN 0252-9602, 7/2019, Volume 39, Issue 4, pp. 1185 - 1194

In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the...

Heat equation | Analysis | heat kernel | 53C44 | Li-Yau-type gradient estimate | Mathematics, general | 35K05 | Mathematics

Heat equation | Analysis | heat kernel | 53C44 | Li-Yau-type gradient estimate | Mathematics, general | 35K05 | Mathematics

Journal Article

Acta Mathematica Scientia, ISSN 0252-9602, 3/2019, Volume 39, Issue 2, pp. 618 - 626

We consider a quasilinear heat system in the presence of an integral term and establish a general and optimal decay result from which improves and generalizes...

heat equation | optimal | Analysis | general decay | Mathematics, general | 35K05 | Mathematics | viscoelastic

heat equation | optimal | Analysis | general decay | Mathematics, general | 35K05 | Mathematics | viscoelastic

Journal Article

Experimental Thermal and Fluid Science, ISSN 0894-1777, 2018, Volume 90, pp. 246 - 259

This paper presents a practical application of the concept of Optimal Experiment Design (OED) for the determination of properties of porous materials with in...

Parameter estimation | Sensitivity functions | Convective moisture transport | Optimal experiment design (OED) | Model identification | Inverse problem | COUPLED HEAT | PHYSICS, FLUIDS & PLASMAS | SENSITIVITY | AIR | MODEL | SIMULATION | ENGINEERING, MECHANICAL | THERMODYNAMICS | DIFFUSION | Usage | Permeability | Sensors | Analysis | Mathematics - Optimization and Control | Computational Physics | Operations Research | Civil Engineering | Construction durable | Mathematics | Classical Physics | Physics | Matériaux composites et construction | Thermics | Numerical Analysis | Computer Science | Mechanics | Optimization and Control | Engineering Sciences

Parameter estimation | Sensitivity functions | Convective moisture transport | Optimal experiment design (OED) | Model identification | Inverse problem | COUPLED HEAT | PHYSICS, FLUIDS & PLASMAS | SENSITIVITY | AIR | MODEL | SIMULATION | ENGINEERING, MECHANICAL | THERMODYNAMICS | DIFFUSION | Usage | Permeability | Sensors | Analysis | Mathematics - Optimization and Control | Computational Physics | Operations Research | Civil Engineering | Construction durable | Mathematics | Classical Physics | Physics | Matériaux composites et construction | Thermics | Numerical Analysis | Computer Science | Mechanics | Optimization and Control | Engineering Sciences

Journal Article

Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 4/2018, Volume 24, Issue 1, pp. 203 - 217

In this work we find a sequence of functions $$f_n$$ fn at which the integral 1$$\begin{aligned} v(t,x)=\int _{-\infty }^{\infty }e^{i\lambda x-\lambda...

Heat equation | 35C99 | Rayleigh-type equation | Mathematics, general | Primary: 30E25 | 35K05 | Mathematics | Secondary: 60H30 | Pearcey function | Boundary crossing

Heat equation | 35C99 | Rayleigh-type equation | Mathematics, general | Primary: 30E25 | 35K05 | Mathematics | Secondary: 60H30 | Pearcey function | Boundary crossing

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 08/2018, Volume 63, Issue 7-8, pp. 1142 - 1167

This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far...

35K05 | Primary: 32D15 | inegral formulas | Secondary: 35J56 | Analytic continuation | Cauchy problem | MATHEMATICS | RIEMANN-HYPOTHESIS | SPACES

35K05 | Primary: 32D15 | inegral formulas | Secondary: 35J56 | Analytic continuation | Cauchy problem | MATHEMATICS | RIEMANN-HYPOTHESIS | SPACES

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 2/2017, Volume 56, Issue 1, pp. 1 - 8

We show a connection between the $$CDE'$$ C D E ′ inequality introduced in Horn et al. (Volume doubling, Poincaré inequality and Gaussian heat kernel estimate...

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 53C21 | 35K05 | Mathematics | 05C81 | MATHEMATICS | MATHEMATICS, APPLIED

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 53C21 | 35K05 | Mathematics | 05C81 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 2/2011, Volume 183, Issue 2, pp. 245 - 336

In (0,T)×Ω, Ω open subset of ℝ n , n≥2, we consider a parabolic operator P=∂ t −∇ x δ(t,x)∇ x , where the (scalar) coefficient δ(t,x) is piecewise smooth in...

35K20 | Mathematics, general | 35K05 | Mathematics | 35S15 | MATHEMATICS | EXACT CONTROLLABILITY | DIMENSIONAL HEAT-EQUATION | Projectors | Anisotropy | Analysis of PDEs

35K20 | Mathematics, general | 35K05 | Mathematics | 35S15 | MATHEMATICS | EXACT CONTROLLABILITY | DIMENSIONAL HEAT-EQUATION | Projectors | Anisotropy | Analysis of PDEs

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 04/2019, Volume 292, Issue 4, pp. 805 - 825

In this paper we study the spectral heat content for various Lévy processes. We establish the small time asymptotic behavior of the spectral heat content for...

heat content | 60J75 | infinitesimal generator | Lévy process | 60G51 | spectral heat content | 35K05 | MATHEMATICS | Levy process | SETS | PERIMETER

heat content | 60J75 | infinitesimal generator | Lévy process | 60G51 | spectral heat content | 35K05 | MATHEMATICS | Levy process | SETS | PERIMETER

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2018, Volume 57, Issue 2, pp. 1 - 9

We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery sense. Our first result using only curvature and...

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 53C21 | 35K05 | Mathematics | 05C81 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | RICCI CURVATURE | COMPLEXES | Mathematics - Differential Geometry

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 53C21 | 35K05 | Mathematics | 05C81 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | RICCI CURVATURE | COMPLEXES | Mathematics - Differential Geometry

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 01/2012, Volume 252, Issue 2, pp. 1403 - 1420

In this paper, we first prove a localized Hamilton-type gradient estimate for the positive solutions of Porous Media type equations:ut=δF(u), with F (u)>0, on...

Fast Diffusion Equation | Liouville-type theorem | 35K05 | Porous Media Equation | 53C21 | Localized Hamilton-type gradient estimate

Fast Diffusion Equation | Liouville-type theorem | 35K05 | Porous Media Equation | 53C21 | Localized Hamilton-type gradient estimate

Journal Article

The Annals of Statistics, ISSN 0090-5364, 2/2009, Volume 37, Issue 1, pp. 73 - 104

We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a...

Minimax | Observational research | Inverse problems | Partial differential equations | Threshing | Boundary conditions | LIDAR | Mathematical functions | Fourier coefficients | Estimators | Adaptivity | Deconvolution | Meyer wavelets | Minimax estimators | Block thresholding | Functional data | Fourier analysis | Wavelet analysis | Multichannel deconvolution | Besov spaces | WAVELET DECONVOLUTION | minimax estimators | STATISTICS & PROBABILITY | block thresholding | deconvolution | multichannel deconvolution | wavelet analysis | functional data | partial differential equations | 62G05 | 62G08 | 35L05 | 35K05 | 35J05

Minimax | Observational research | Inverse problems | Partial differential equations | Threshing | Boundary conditions | LIDAR | Mathematical functions | Fourier coefficients | Estimators | Adaptivity | Deconvolution | Meyer wavelets | Minimax estimators | Block thresholding | Functional data | Fourier analysis | Wavelet analysis | Multichannel deconvolution | Besov spaces | WAVELET DECONVOLUTION | minimax estimators | STATISTICS & PROBABILITY | block thresholding | deconvolution | multichannel deconvolution | wavelet analysis | functional data | partial differential equations | 62G05 | 62G08 | 35L05 | 35K05 | 35J05

Journal Article

Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 24

In this paper, we consider the initial inverse problem for a diffusion equation with a conformable derivative in a general bounded domain. We show that the...

35K05 | Mathematics | Conformable derivative | 35K99 | Inverse problem | 47H10 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Diffusion equation | 47J06 | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Regularization methods | Inverse problems | Ill-posed problems (mathematics) | Regularization

35K05 | Mathematics | Conformable derivative | 35K99 | Inverse problem | 47H10 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Diffusion equation | 47J06 | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Regularization methods | Inverse problems | Ill-posed problems (mathematics) | Regularization

Journal Article

Numerische Mathematik, ISSN 0029-599X, 6/2018, Volume 139, Issue 2, pp. 315 - 348

In this article, we study theoretically and numerically the heat equation coupled with Darcy’s law by a nonlinear viscosity depending on the temperature. We...

Mathematical Methods in Physics | 74S05 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | 35K05 | 25B45 | Mathematics | Numerical and Computational Physics, Simulation | APPROXIMATION | NAVIER-STOKES | MATHEMATICS, APPLIED | Finite element method | Analysis | Methods

Mathematical Methods in Physics | 74S05 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | 35K05 | 25B45 | Mathematics | Numerical and Computational Physics, Simulation | APPROXIMATION | NAVIER-STOKES | MATHEMATICS, APPLIED | Finite element method | Analysis | Methods

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 6/2014, Volume 14, Issue 2, pp. 477 - 497

For a finite not necessarily compact metric graph, one considers the differential expression $${-\frac{d^2}{d x^2}}$$ - d 2 d x 2 on each edge. The boundary...

47D06 | Secondary 35J05 | Analysis | Differential operators on metric graphs | 35K05 | Mathematics | Primary 34B45 | Quasi-contractive semigroups | Quasi-m-accretive Laplacians | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED

47D06 | Secondary 35J05 | Analysis | Differential operators on metric graphs | 35K05 | Mathematics | Primary 34B45 | Quasi-contractive semigroups | Quasi-m-accretive Laplacians | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED

Journal Article

The Annals of probability, ISSN 0091-1798, 09/2014, Volume 42, Issue 5, pp. 2032 - 2112

Motivated by Girsanov’s nonuniqueness examples for SDEs, we prove nonuniqueness for the parabolic stochastic partial differential equation (SPDE)...

35K05 | white noise | 35R60 | Heat equation | 60H15 | stochastic partial differential equations

35K05 | white noise | 35R60 | Heat equation | 60H15 | stochastic partial differential equations

Journal Article

Journal of Inverse and Ill-posed Problems, ISSN 0928-0219, 06/2020, Volume 28, Issue 3, pp. 349 - 366

A simple idea of finding a domain that encloses an unknown discontinuity embedded in a body is introduced by considering an inverse boundary value problem for...

80A23 | heat equation | 35R30 | wave equation | 35L05 | 35K05 | 35J05 | cavity | non-destructive testing | 74J25 | inclusion | 74F05 | 35Q79 | Enclosure method | 35B40 | inverse obstacle problem | displacement-temperature equation of motion | 35R05 | Thermodynamics | Temperature distribution | Boundary value problems | Elastic waves | Inclusions | Heat flux

80A23 | heat equation | 35R30 | wave equation | 35L05 | 35K05 | 35J05 | cavity | non-destructive testing | 74J25 | inclusion | 74F05 | 35Q79 | Enclosure method | 35B40 | inverse obstacle problem | displacement-temperature equation of motion | 35R05 | Thermodynamics | Temperature distribution | Boundary value problems | Elastic waves | Inclusions | Heat flux

Journal Article

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