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Statistical shape analysis using 3D Poisson equation—A quantitatively validated approach

Medical image analysis, ISSN 1361-8415, 05/2016, Volume 30, pp. 72 - 84

•We proposed a new statistical shape analysis/morphometry technique based on the 3D Poisson Equation...

Statistical shape analysis | Poisson equation | Reproducibility | Quantitative evaluation | ENGINEERING, BIOMEDICAL | VOLUME | REPRESENTATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MORPHOMETRY | SEGMENTATION | MANIFOLDS | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Reproducibility of Results | Humans | Image Interpretation, Computer-Assisted - methods | Imaging, Three-Dimensional - methods | Magnetic Resonance Imaging - methods | Hippocampus - pathology | Schizophrenia - pathology | Models, Statistical | Schizophrenia - diagnostic imaging | Hippocampus - diagnostic imaging | Computer Simulation | Sensitivity and Specificity | Poisson Distribution | Image Enhancement - methods | Pattern Recognition, Automated - methods | Computer science | Analysis | Neurosciences | Algorithms | Paleontology

Statistical shape analysis | Poisson equation | Reproducibility | Quantitative evaluation | ENGINEERING, BIOMEDICAL | VOLUME | REPRESENTATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MORPHOMETRY | SEGMENTATION | MANIFOLDS | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Reproducibility of Results | Humans | Image Interpretation, Computer-Assisted - methods | Imaging, Three-Dimensional - methods | Magnetic Resonance Imaging - methods | Hippocampus - pathology | Schizophrenia - pathology | Models, Statistical | Schizophrenia - diagnostic imaging | Hippocampus - diagnostic imaging | Computer Simulation | Sensitivity and Specificity | Poisson Distribution | Image Enhancement - methods | Pattern Recognition, Automated - methods | Computer science | Analysis | Neurosciences | Algorithms | Paleontology

Journal Article

Compositio mathematica, ISSN 0010-437X, 11/2013, Volume 149, Issue 11, pp. 1856 - 1870

In this paper, we develop a method of solving the Poincaré–Lelong equation, mainly via the study of the large time asymptotics of a global solution to the Hodge...

Hodge-Laplacian heat equation | Kähler manifolds | Poincaré-Lelong equation | Convex exhaustion | MATHEMATICS | Kahler manifolds | CURVATURE | COMPLETE KAHLER-MANIFOLDS | POISSON EQUATION | Poincare-Lelong equation | Studies | Theorems | Topological manifolds | Mathematical analysis | Asymptotic properties

Hodge-Laplacian heat equation | Kähler manifolds | Poincaré-Lelong equation | Convex exhaustion | MATHEMATICS | Kahler manifolds | CURVATURE | COMPLETE KAHLER-MANIFOLDS | POISSON EQUATION | Poincare-Lelong equation | Studies | Theorems | Topological manifolds | Mathematical analysis | Asymptotic properties

Journal Article

Fuzzy sets and systems, ISSN 0165-0114, 2018, Volume 347, pp. 105 - 128

.... In detail, a fuzzy Poisson equation is considered by discussion of fuzzy maximum and minimum principles...

Fuzzy-valued vector function | Fuzzy Green's theorem | Fuzzy Green's identity | Fuzzy Poisson equation | Fuzzy partial differential equation | Fuzzy divergence theorem | INTERVAL | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | PARTIAL-DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | VALUED FUNCTIONS | GENERALIZED HUKUHARA DIFFERENTIABILITY | Differential equations

Fuzzy-valued vector function | Fuzzy Green's theorem | Fuzzy Green's identity | Fuzzy Poisson equation | Fuzzy partial differential equation | Fuzzy divergence theorem | INTERVAL | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | PARTIAL-DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | VALUED FUNCTIONS | GENERALIZED HUKUHARA DIFFERENTIABILITY | Differential equations

Journal Article

Communications in mathematical physics, ISSN 1432-0916, 2016, Volume 346, Issue 3, pp. 877 - 906

In this paper, we deal with the electrostatic Born–Infeld equation
$$\left\{\begin{array}{ll}-\operatorname{div}
\left(\displaystyle\frac{\nabla\phi}{\sqrt{1...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | NONLINEAR KLEIN-GORDON | SOLITARY WAVES | FIELD-THEORY | HYPERSURFACES | MEAN-CURVATURE | MAXIMAL SURFACE EQUATION | MINKOWSKI SPACE | FOUNDATIONS | PHYSICS, MATHEMATICAL | Electric fields | Analysis | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | NONLINEAR KLEIN-GORDON | SOLITARY WAVES | FIELD-THEORY | HYPERSURFACES | MEAN-CURVATURE | MAXIMAL SURFACE EQUATION | MINKOWSKI SPACE | FOUNDATIONS | PHYSICS, MATHEMATICAL | Electric fields | Analysis | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 05/2018, Volume 333, pp. 74 - 93

We consider boundary value problems for the Poisson equation on polygonal domains with general nonhomogeneous mixed boundary conditions and derive, on the one hand, explicit extraction formulas...

Poisson equation | Singularities | A priori error estimates | Finite element methods | CORNER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SINGULAR FUNCTIONS | BOUNDARY-VALUE-PROBLEMS | MESH-REFINEMENT | Finite element method | Algorithms | Analysis | Methods

Poisson equation | Singularities | A priori error estimates | Finite element methods | CORNER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SINGULAR FUNCTIONS | BOUNDARY-VALUE-PROBLEMS | MESH-REFINEMENT | Finite element method | Algorithms | Analysis | Methods

Journal Article

IEEE Transactions on Electron Devices, ISSN 0018-9383, 11/2007, Volume 54, Issue 11, pp. 2901 - 2909

We propose an efficient and fast algorithm to solve the coupled Poisson-Schrodinger and Boltzmann transport equations (BTE) in two dimensions...

modeling | Computational modeling | Scattering | Boltzmann transport equation | SchrÖdinger equation | Ballistic transport | nanoscale MOSFET device | Mathematical model | Approximation methods | Equations | MOSFETs | Distribution functions | Nanoscale MOSFET device | Modeling | Schrödinger equation | PHYSICS, APPLIED | Schrodinger equation | ELECTRONS | DEVICES | MODEL | SIMULATION | ballistic transport | ENGINEERING, ELECTRICAL & ELECTRONIC | Metal oxide semiconductor field effect transistors | Analysis | Design and construction | Transport theory | Electrons

modeling | Computational modeling | Scattering | Boltzmann transport equation | SchrÖdinger equation | Ballistic transport | nanoscale MOSFET device | Mathematical model | Approximation methods | Equations | MOSFETs | Distribution functions | Nanoscale MOSFET device | Modeling | Schrödinger equation | PHYSICS, APPLIED | Schrodinger equation | ELECTRONS | DEVICES | MODEL | SIMULATION | ballistic transport | ENGINEERING, ELECTRICAL & ELECTRONIC | Metal oxide semiconductor field effect transistors | Analysis | Design and construction | Transport theory | Electrons

Journal Article

Engineering fracture mechanics, ISSN 0013-7944, 2016, Volume 158, pp. 116 - 143

.... It consists of a localization limiter in the form of the screened Poisson equation with local mesh refinement...

Local mesh refinement | Element erosion | Screened Poisson equation | Crack nucleation and propagation | CRACK-PROPAGATION | DISCONTINUITIES | VOID NUCLEATION | SIMULATION | FAILURE | MECHANICS | FINITE | PHASE-FIELD MODELS | GROWTH | Algorithms | Subdivisions | Fracture mechanics | Mathematical analysis | Poisson equation | Damage | Position (location) | Crack propagation

Local mesh refinement | Element erosion | Screened Poisson equation | Crack nucleation and propagation | CRACK-PROPAGATION | DISCONTINUITIES | VOID NUCLEATION | SIMULATION | FAILURE | MECHANICS | FINITE | PHASE-FIELD MODELS | GROWTH | Algorithms | Subdivisions | Fracture mechanics | Mathematical analysis | Poisson equation | Damage | Position (location) | Crack propagation

Journal Article

Journal of algebra and its applications, ISSN 0219-4988, 01/2018, Volume 17, Issue 1

In this work, we compute solutions of the Yang-Baxter associative equation in dimensions one and two...

Yang-Baxter equation | Frobenius algebra | Connes cocycle | dendriform algebra | D -equation | Associative algebra | D-equation | MATHEMATICS, APPLIED | HOPF-ALGEBRAS | MATHEMATICS | TREES | POISSON ALGEBRAS | HOMOLOGY | BIALGEBRAS

Yang-Baxter equation | Frobenius algebra | Connes cocycle | dendriform algebra | D -equation | Associative algebra | D-equation | MATHEMATICS, APPLIED | HOPF-ALGEBRAS | MATHEMATICS | TREES | POISSON ALGEBRAS | HOMOLOGY | BIALGEBRAS

Journal Article

Journal of physics. Condensed matter, ISSN 1361-648X, 2019, Volume 31, Issue 37, p. 375101

The classical Poisson-Boltzmann equation (CPBE), which is a mean field theory by averaging the ion fluctuation, has been widely used to study ion distributions in charged fluids...

INTERACTION FREE-ENERGY | PHYSICS, CONDENSED MATTER | path integral | stochastic process | IONS | FORCES | DOUBLE-LAYER | Poisson-Boltzmann equation | monte carlo | charged fluids | field theory | SURFACES

INTERACTION FREE-ENERGY | PHYSICS, CONDENSED MATTER | path integral | stochastic process | IONS | FORCES | DOUBLE-LAYER | Poisson-Boltzmann equation | monte carlo | charged fluids | field theory | SURFACES

Journal Article

European journal of physics, ISSN 0143-0807, 07/2018, Volume 39, Issue 5, p. 53002

The description of a conducting medium in thermal equilibrium, such as an electrolyte solution or a plasma, involves nonlinear electrostatics, a subject rarely...

electric double layer | Poisson-Boltzmann theory | Gibbs variational principle | double-layer free energies | inter-plate forces in electrolytes | PHYSICS, MULTIDISCIPLINARY | ADSORPTION | MOLECULES | VARIATIONAL APPROACH | PLASMA | LIOUVILLE EQUATION | ELECTRODE | FORCES | DOUBLE-LAYER | IONIC LIQUIDS | FREE-ENERGY | EDUCATION, SCIENTIFIC DISCIPLINES

electric double layer | Poisson-Boltzmann theory | Gibbs variational principle | double-layer free energies | inter-plate forces in electrolytes | PHYSICS, MULTIDISCIPLINARY | ADSORPTION | MOLECULES | VARIATIONAL APPROACH | PLASMA | LIOUVILLE EQUATION | ELECTRODE | FORCES | DOUBLE-LAYER | IONIC LIQUIDS | FREE-ENERGY | EDUCATION, SCIENTIFIC DISCIPLINES

Journal Article

Journal of membrane science, ISSN 0376-7388, 2013, Volume 442, pp. 131 - 139

To describe Donnan equilibrium at the membrane–solution interface, the simplest approach uses the classical Boltzmann equation, based on a mean-field...

Reverse osmosis | Donnan exclusion | Poisson-Boltzmann theory | Donnan equilibrium | Electrodialysis | sulfonated polymers | spherical colloids | transport-properties | partition equilibrium | cylindrical pores | ion-exchange membrane | capacitive deionization | nanofiltration membranes | dielectric exclusion model | fixed charge groups | POLYMER SCIENCE | TRANSPORT-PROPERTIES | SPHERICAL COLLOIDS | MASS-TRANSPORT | ENGINEERING, CHEMICAL | ION-EXCHANGE MEMBRANE | DIVALENT-CATIONS | NANOFILTRATION | PARTITION EQUILIBRIUM | SULFONATED POLYMERS | CHARGED MEMBRANE | DOUBLE-LAYER | Green technology | Membranes | Boltzmann equation | Balancing | Mathematical analysis | Charge | Boltzmann transport equation | Double layer | Deviation

Reverse osmosis | Donnan exclusion | Poisson-Boltzmann theory | Donnan equilibrium | Electrodialysis | sulfonated polymers | spherical colloids | transport-properties | partition equilibrium | cylindrical pores | ion-exchange membrane | capacitive deionization | nanofiltration membranes | dielectric exclusion model | fixed charge groups | POLYMER SCIENCE | TRANSPORT-PROPERTIES | SPHERICAL COLLOIDS | MASS-TRANSPORT | ENGINEERING, CHEMICAL | ION-EXCHANGE MEMBRANE | DIVALENT-CATIONS | NANOFILTRATION | PARTITION EQUILIBRIUM | SULFONATED POLYMERS | CHARGED MEMBRANE | DOUBLE-LAYER | Green technology | Membranes | Boltzmann equation | Balancing | Mathematical analysis | Charge | Boltzmann transport equation | Double layer | Deviation

Journal Article

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1471-2946, 2018, Volume 474, Issue 2213, p. 20180052

We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler-Poincare equations defined on the Virasoro-Bott group, by using the inverse map...

Hunter-saxton equation | Multisymplectic partial differential equations | Camassa-holm equation | Korteweg-de vries equation | Variational principles | Virasoro-bott group | multisymplectic partial differential equations | Virasoro-Bott group | MULTIDISCIPLINARY SCIENCES | POISSON BRACKETS | SHALLOW-WATER EQUATION | PRINCIPLES | Korteweg-de Vries equation | WAVES | MECHANICS | Hunter-Saxton equation | variational principles | DYNAMICS | KDV EQUATION | Camassa-Holm equation | MULTI-SYMPLECTIC INTEGRATION | SCHEMES | 1008 | Camassa–Holm equation | Hunter–Saxton equation | 120 | Virasoro–Bott group

Hunter-saxton equation | Multisymplectic partial differential equations | Camassa-holm equation | Korteweg-de vries equation | Variational principles | Virasoro-bott group | multisymplectic partial differential equations | Virasoro-Bott group | MULTIDISCIPLINARY SCIENCES | POISSON BRACKETS | SHALLOW-WATER EQUATION | PRINCIPLES | Korteweg-de Vries equation | WAVES | MECHANICS | Hunter-Saxton equation | variational principles | DYNAMICS | KDV EQUATION | Camassa-Holm equation | MULTI-SYMPLECTIC INTEGRATION | SCHEMES | 1008 | Camassa–Holm equation | Hunter–Saxton equation | 120 | Virasoro–Bott group

Journal Article

Engineering with computers, ISSN 1435-5663, 2018, Volume 35, Issue 1, pp. 75 - 86

...–subdiffusion equation. First by a finite difference approach, time fractional derivative which is defined in Riemann...

Two-dimensional Haar wavelets | Systems Theory, Control | Classical Mechanics | Fractional two-dimensional problem | Two-dimensional reaction–subdiffusion | Calculus of Variations and Optimal Control; Optimization | Numerical solution | 65M70 | Computer-Aided Engineering (CAD, CAE) and Design | Computer Science | Mathematical and Computational Engineering | 35R11 | 65T60 | Math. Applications in Chemistry | INTEGRAL-EQUATIONS | SIMULATION | ENGINEERING, MECHANICAL | STATE ANALYSIS | OPERATIONAL MATRIX | SCHEME | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | Two-dimensional reaction-subdiffusion | DIFFUSION | POISSON EQUATIONS | COLLOCATION | Finite element method | Wavelet transforms | Alternating direction implicit methods | Error analysis | Discretization | Mathematical analysis | Meshless methods | Wavelet analysis | Implicit methods | Methods | Finite difference method

Two-dimensional Haar wavelets | Systems Theory, Control | Classical Mechanics | Fractional two-dimensional problem | Two-dimensional reaction–subdiffusion | Calculus of Variations and Optimal Control; Optimization | Numerical solution | 65M70 | Computer-Aided Engineering (CAD, CAE) and Design | Computer Science | Mathematical and Computational Engineering | 35R11 | 65T60 | Math. Applications in Chemistry | INTEGRAL-EQUATIONS | SIMULATION | ENGINEERING, MECHANICAL | STATE ANALYSIS | OPERATIONAL MATRIX | SCHEME | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | Two-dimensional reaction-subdiffusion | DIFFUSION | POISSON EQUATIONS | COLLOCATION | Finite element method | Wavelet transforms | Alternating direction implicit methods | Error analysis | Discretization | Mathematical analysis | Meshless methods | Wavelet analysis | Implicit methods | Methods | Finite difference method

Journal Article

Physical chemistry chemical physics : PCCP, ISSN 1463-9084, 2017, Volume 19, Issue 36, pp. 24583 - 24593

...) simulations and assess the ability of the Poisson–Boltzmann (PB) equation to describe the ion distribution predicted by the MD simulations...

SALT | AQUEOUS-SOLUTIONS | COUNTERION CONDENSATION | DNA COMPLEXES | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | FORCE-FIELD | ELECTROLYTE-SOLUTIONS | MONTE-CARLO SIMULATIONS | MULTILAYER | FREE-ENERGY | WATER

SALT | AQUEOUS-SOLUTIONS | COUNTERION CONDENSATION | DNA COMPLEXES | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | FORCE-FIELD | ELECTROLYTE-SOLUTIONS | MONTE-CARLO SIMULATIONS | MULTILAYER | FREE-ENERGY | WATER

Journal Article

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On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane

The Ramanujan journal, ISSN 1572-9303, 2008, Volume 16, Issue 1, pp. 105 - 129

...) which is a discrete version of the classical logarithmic derivative estimates of f(z). We apply these results to give new growth estimates of meromorphic solutions to higher order linear difference equations...

30D30 | Poisson–Jensen formula | Functions of a Complex Variable | Field Theory and Polynomials | 39A05 | Mathematics | Meromorphic functions | 30D35 | Fourier Analysis | Order of growth | Difference equations | Number Theory | Combinatorics | Poisson-Jensen formula | MATHEMATICS | ORDER | DISCRETE PAINLEVE EQUATIONS | order of growth | ANALOG | PROPERTY | meromorphic functions | MEROMORPHIC SOLUTIONS | difference equations

30D30 | Poisson–Jensen formula | Functions of a Complex Variable | Field Theory and Polynomials | 39A05 | Mathematics | Meromorphic functions | 30D35 | Fourier Analysis | Order of growth | Difference equations | Number Theory | Combinatorics | Poisson-Jensen formula | MATHEMATICS | ORDER | DISCRETE PAINLEVE EQUATIONS | order of growth | ANALOG | PROPERTY | meromorphic functions | MEROMORPHIC SOLUTIONS | difference equations

Journal Article

16.
Transport equations with unbounded force fields and application to the vlasov - Poisson equation

Mathematical models & methods in applied sciences, ISSN 0218-2025, 02/2009, Volume 19, Issue 2, pp. 199 - 228

The aim of this paper is to give new dispersive tools for certain kinetic equations...

Vlasov-Poisson equation | Dispersion estimate | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | dispersion estimate | GLOBAL CLASSICAL-SOLUTIONS | PROPAGATION | MOMENTS

Vlasov-Poisson equation | Dispersion estimate | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | dispersion estimate | GLOBAL CLASSICAL-SOLUTIONS | PROPAGATION | MOMENTS

Journal Article