Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, 2016, Volume 2016, Issue 7

The detection of the magnetic type B-mode polarization is the main goal of future cosmic microwave background (CMB) experiments. In the standard model, the...

CMBR polarization | cosmological parameters from CMBR | PLANCK | WMAP OBSERVATIONS | CMBR polarisation | MICROWAVE BACKGROUND POLARIZATION | ANISOTROPY POWER SPECTRUM | PRIMORDIAL NON-GAUSSIANITY | TEMPERATURE | GRAVITATIONAL-WAVES | ASTRONOMY & ASTROPHYSICS | SCALE | E/B DECOMPOSITION | C-L ESTIMATORS | PHYSICS, PARTICLES & FIELDS | Physics - Cosmology and Nongalactic Astrophysics | CORRELATION FUNCTIONS | STANDARD MODEL | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | RELICT RADIATION | MINKOWSKI SPACE | CORRELATIONS | DETECTION | FUNCTIONAL ANALYSIS | POLARIZATION

CMBR polarization | cosmological parameters from CMBR | PLANCK | WMAP OBSERVATIONS | CMBR polarisation | MICROWAVE BACKGROUND POLARIZATION | ANISOTROPY POWER SPECTRUM | PRIMORDIAL NON-GAUSSIANITY | TEMPERATURE | GRAVITATIONAL-WAVES | ASTRONOMY & ASTROPHYSICS | SCALE | E/B DECOMPOSITION | C-L ESTIMATORS | PHYSICS, PARTICLES & FIELDS | Physics - Cosmology and Nongalactic Astrophysics | CORRELATION FUNCTIONS | STANDARD MODEL | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | RELICT RADIATION | MINKOWSKI SPACE | CORRELATIONS | DETECTION | FUNCTIONAL ANALYSIS | POLARIZATION

Journal Article

Results in Mathematics, ISSN 1422-6383, 3/2019, Volume 74, Issue 1, pp. 1 - 12

We consider several functionals associated with inequalities which involve derivatives of functions. As a consequence of those results we get new refinements...

39B62 | functional | Hölder type inequality | superadditivity | Minkowski type inequality | 26D10 | Derivative | Mathematics, general | Mathematics | the Gauss–Pólya inequalities | monotonicity | 26D15 | the Gauss-Polya inequalities | MATHEMATICS, APPLIED | MATHEMATICS | Holder type inequality | MOMENTS

39B62 | functional | Hölder type inequality | superadditivity | Minkowski type inequality | 26D10 | Derivative | Mathematics, general | Mathematics | the Gauss–Pólya inequalities | monotonicity | 26D15 | the Gauss-Polya inequalities | MATHEMATICS, APPLIED | MATHEMATICS | Holder type inequality | MOMENTS

Journal Article

Astrophysical Journal, ISSN 0004-637X, 05/2014, Volume 786, Issue 1, pp. 43 - 14

The measurement of cosmic shear using weak gravitational lensing is a challenging task that involves a number of complicated procedures. We study in detail the...

gravitational lensing: weak | FIELDS | COSMOLOGY | PHOTOMETRIC REDSHIFTS | ASTRONOMY & ASTROPHYSICS | PROBE WMAP OBSERVATIONS | CONVERGENCE | SIMULATIONS | MODEL | NON-GAUSSIANITY | COSMIC SHEAR | CFHTLENS | Errors | Red shift | Shear | Functionals | Systematic errors | Mathematical models | Statistics | Catalogs | Physics - Cosmology and Nongalactic Astrophysics | CORRECTIONS | CALIBRATION | CORRELATION FUNCTIONS | RED SHIFT | ERRORS | GRAVITATIONAL LENSES | STATISTICS | CATALOGS | EQUATIONS | MINKOWSKI SPACE | COMPARATIVE EVALUATIONS | COMPUTER-AIDED MANUFACTURING | DENSITY | NONLUMINOUS MATTER | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | COSMOLOGICAL MODELS | GALAXIES

gravitational lensing: weak | FIELDS | COSMOLOGY | PHOTOMETRIC REDSHIFTS | ASTRONOMY & ASTROPHYSICS | PROBE WMAP OBSERVATIONS | CONVERGENCE | SIMULATIONS | MODEL | NON-GAUSSIANITY | COSMIC SHEAR | CFHTLENS | Errors | Red shift | Shear | Functionals | Systematic errors | Mathematical models | Statistics | Catalogs | Physics - Cosmology and Nongalactic Astrophysics | CORRECTIONS | CALIBRATION | CORRELATION FUNCTIONS | RED SHIFT | ERRORS | GRAVITATIONAL LENSES | STATISTICS | CATALOGS | EQUATIONS | MINKOWSKI SPACE | COMPARATIVE EVALUATIONS | COMPUTER-AIDED MANUFACTURING | DENSITY | NONLUMINOUS MATTER | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | COSMOLOGICAL MODELS | GALAXIES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2014, Volume 409, Issue 2, pp. 643 - 648

We show that the equality m1(f(x))=m2(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps,...

quasi-circular domains | Proper holomorphic maps | Minkowski functionals | Balanced domains | Open maps | Quasi-circular domains | MATHEMATICS | MATHEMATICS, APPLIED | COMPLETE CIRCULAR DOMAINS

quasi-circular domains | Proper holomorphic maps | Minkowski functionals | Balanced domains | Open maps | Quasi-circular domains | MATHEMATICS | MATHEMATICS, APPLIED | COMPLETE CIRCULAR DOMAINS

Journal Article

Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, 06/2017, Volume 2017, Issue 6, pp. 23 - 23

Tensor Minkowski Functionals (TMFs) are tensor generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use...

CMBR experiments | CMBR polarisation | MORPHOLOGICAL MEASURES | STATISTICS | ELLIPTICITY | COLD SPOT | HOT | ANISOTROPY | RADIATION | PRIMORDIAL NON-GAUSSIANITY | ASTRONOMY & ASTROPHYSICS | CONSTRAINTS | POLARIZATION | PHYSICS, PARTICLES & FIELDS | Physics - Cosmology and Nongalactic Astrophysics | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | DISTRIBUTION | ISOTROPY | MINKOWSKI SPACE | TWO-DIMENSIONAL SYSTEMS | COMPARATIVE EVALUATIONS | SIMULATION | TWO-DIMENSIONAL CALCULATIONS | DENSITY | EIGENVALUES | STANDARD MODEL | SIGNAL-TO-NOISE RATIO | COSMOLOGY | FORECASTING | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | FLUCTUATIONS | RELICT RADIATION | EUCLIDEAN SPACE

CMBR experiments | CMBR polarisation | MORPHOLOGICAL MEASURES | STATISTICS | ELLIPTICITY | COLD SPOT | HOT | ANISOTROPY | RADIATION | PRIMORDIAL NON-GAUSSIANITY | ASTRONOMY & ASTROPHYSICS | CONSTRAINTS | POLARIZATION | PHYSICS, PARTICLES & FIELDS | Physics - Cosmology and Nongalactic Astrophysics | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | DISTRIBUTION | ISOTROPY | MINKOWSKI SPACE | TWO-DIMENSIONAL SYSTEMS | COMPARATIVE EVALUATIONS | SIMULATION | TWO-DIMENSIONAL CALCULATIONS | DENSITY | EIGENVALUES | STANDARD MODEL | SIGNAL-TO-NOISE RATIO | COSMOLOGY | FORECASTING | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | FLUCTUATIONS | RELICT RADIATION | EUCLIDEAN SPACE

Journal Article

Journal of High Energy Physics, ISSN 1029-8479, 12/2019, Volume 2019, Issue 12, pp. 1 - 70

We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum...

Amplitudes | Decay rate | Saddle points | Minkowski space | Variations | Real time | Forward scattering | Mathematical analysis | Integrals | Quantum mechanics | Construction methods | Saddles | Eigenvalues | Field theory | Euclidean space | Eigenvectors | Nonperturbative Effects | Solitons Monopoles and Instantons

Amplitudes | Decay rate | Saddle points | Minkowski space | Variations | Real time | Forward scattering | Mathematical analysis | Integrals | Quantum mechanics | Construction methods | Saddles | Eigenvalues | Field theory | Euclidean space | Eigenvectors | Nonperturbative Effects | Solitons Monopoles and Instantons

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 04/2017, Volume 34, Issue 9, p. 94002

Despite the wealth of Planck results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the...

cosmic microwave background | non-Gaussianities | approximations and expansions | Minkowski-functionals | statistical and morphological analysis | TOPOLOGY | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | LARGE-SCALE STRUCTURE | STATISTICS | PROBE WMAP OBSERVATIONS | FLUCTUATIONS | ASTRONOMY & ASTROPHYSICS | CONSTRAINTS | VARIANCE | MORPHOLOGY | PHYSICS, PARTICLES & FIELDS

cosmic microwave background | non-Gaussianities | approximations and expansions | Minkowski-functionals | statistical and morphological analysis | TOPOLOGY | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | LARGE-SCALE STRUCTURE | STATISTICS | PROBE WMAP OBSERVATIONS | FLUCTUATIONS | ASTRONOMY & ASTROPHYSICS | CONSTRAINTS | VARIANCE | MORPHOLOGY | PHYSICS, PARTICLES & FIELDS

Journal Article

Transport in Porous Media, ISSN 0169-3913, 10/2019, Volume 130, Issue 1, pp. 305 - 335

An elementary question in porous media research is in regard to the relationship between structure and function. In most fields, the porosity and permeability...

X-ray microcomputed tomography | Earth Sciences | Hydrology/Water Resources | Hydrogeology | Pore morphology | Classical and Continuum Physics | Civil Engineering | Euler characteristic | Geotechnical Engineering & Applied Earth Sciences | Minkowski functionals | Industrial Chemistry/Chemical Engineering | Persistence homology | 2-PHASE FLOW | PERMEABILITY | TOPOLOGICAL PERSISTENCE | BONE INGROWTH | RECONSTRUCTION | COMPUTED-TOMOGRAPHY | ENGINEERING, CHEMICAL | FLUID | IMAGES | MORSE-SMALE COMPLEXES | SCALE | Usage | Permeability | Porosity

X-ray microcomputed tomography | Earth Sciences | Hydrology/Water Resources | Hydrogeology | Pore morphology | Classical and Continuum Physics | Civil Engineering | Euler characteristic | Geotechnical Engineering & Applied Earth Sciences | Minkowski functionals | Industrial Chemistry/Chemical Engineering | Persistence homology | 2-PHASE FLOW | PERMEABILITY | TOPOLOGICAL PERSISTENCE | BONE INGROWTH | RECONSTRUCTION | COMPUTED-TOMOGRAPHY | ENGINEERING, CHEMICAL | FLUID | IMAGES | MORSE-SMALE COMPLEXES | SCALE | Usage | Permeability | Porosity

Journal Article

Astrophysical Journal, ISSN 0004-637X, 11/2012, Volume 760, Issue 1, pp. 45 - 6

We study the cosmological information contained in the Minkowski functionals (MFs) of weak gravitational lensing convergence maps. We show that the MFs provide...

large-scale structure of universe | cosmological parameters | FIELDS | COSMOLOGY | CLUSTERS | MODELS | STATISTICS | ASTRONOMY & ASTROPHYSICS | SIMULATIONS | WMAP OBSERVATIONS | ANISOTROPIES | Gravitational lenses | Constraints | Maps | Functionals | Simulation | Nonlinearity | Dynamical systems | Convergence | Physics - Cosmology and Nongalactic Astrophysics | TELESCOPES | RED SHIFT | GRAVITATIONAL LENSES | MINKOWSKI SPACE | COMPUTERIZED SIMULATION | NONLUMINOUS MATTER | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | ASTRONOMY | NONLINEAR PROBLEMS | ASTROPHYSICS | FLUCTUATIONS | MATRICES | CONVERGENCE | EQUATIONS OF STATE | AMPLITUDES | GALAXIES | UNIVERSE

large-scale structure of universe | cosmological parameters | FIELDS | COSMOLOGY | CLUSTERS | MODELS | STATISTICS | ASTRONOMY & ASTROPHYSICS | SIMULATIONS | WMAP OBSERVATIONS | ANISOTROPIES | Gravitational lenses | Constraints | Maps | Functionals | Simulation | Nonlinearity | Dynamical systems | Convergence | Physics - Cosmology and Nongalactic Astrophysics | TELESCOPES | RED SHIFT | GRAVITATIONAL LENSES | MINKOWSKI SPACE | COMPUTERIZED SIMULATION | NONLUMINOUS MATTER | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | ASTRONOMY | NONLINEAR PROBLEMS | ASTROPHYSICS | FLUCTUATIONS | MATRICES | CONVERGENCE | EQUATIONS OF STATE | AMPLITUDES | GALAXIES | UNIVERSE

Journal Article

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, ISSN 1078-0947, 12/2019, Volume 39, Issue 12, pp. 6785 - 6799

We define a family of functionals, called p-oscillation functionals, that can be interpreted as discrete versions of the classical total variation functional...

MATHEMATICS | MATHEMATICS, APPLIED | minimizers | discrete total variation functional | p-oscillation functional | Minkowski content | one-dimensional solutions

MATHEMATICS | MATHEMATICS, APPLIED | minimizers | discrete total variation functional | p-oscillation functional | Minkowski content | one-dimensional solutions

Journal Article

Journal of Microscopy, ISSN 0022-2720, 12/2010, Volume 240, Issue 3, pp. 181 - 196

Summary The Minkowski functionals, a family of statistical measures based on the Euler–Poincaré characteristic of n‐dimensional space, are the complete set of...

complex materials | Minkowski functional | porous media | Morphology | Porous media | Complex materials | MORPHOLOGICAL FILTERS | TRANSPORT-PROPERTIES | CURVATURE MEASURES | SETS | PATTERNS | MODEL | MICROSCOPY | Functionals | Blurring | Samples | Distortion | Mathematical models | Drift | Statistical methods | Three dimensional

complex materials | Minkowski functional | porous media | Morphology | Porous media | Complex materials | MORPHOLOGICAL FILTERS | TRANSPORT-PROPERTIES | CURVATURE MEASURES | SETS | PATTERNS | MODEL | MICROSCOPY | Functionals | Blurring | Samples | Distortion | Mathematical models | Drift | Statistical methods | Three dimensional

Journal Article

Journal of Microscopy, ISSN 0022-2720, 04/2010, Volume 238, Issue 1, pp. 57 - 74

Summary Quantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology of microstructured heterogeneous...

strain and deformation | integral geometry | morphology | Anisotropy | materials | microstructured and cellular | Turing patterns | Minkowski functionals | Integral geometry | Microstructured and cellular | Morphology | Materials | Strain and deformation | CORE | GRAIN-BOUNDARIES | MICROSCOPY | DEFORMATION | TRABECULAR BONE | FOAM | STRUCTURAL ANISOTROPY | VALUATIONS | SYSTEMS | REARRANGING DISORDERED PATTERNS | POLAR ICE | Permeability

strain and deformation | integral geometry | morphology | Anisotropy | materials | microstructured and cellular | Turing patterns | Minkowski functionals | Integral geometry | Microstructured and cellular | Morphology | Materials | Strain and deformation | CORE | GRAIN-BOUNDARIES | MICROSCOPY | DEFORMATION | TRABECULAR BONE | FOAM | STRUCTURAL ANISOTROPY | VALUATIONS | SYSTEMS | REARRANGING DISORDERED PATTERNS | POLAR ICE | Permeability

Journal Article

Advances in Applied Mathematics, ISSN 0196-8858, 10/2016, Volume 81, pp. 78 - 114

In this paper, we develop a basic theory of Orlicz affine and geominimal surface areas for convex and s-concave functions. We prove some basic properties for...

Orlicz–Brunn–Minkowski theory | Geometrization of probability | The Blaschke–Santaló inequality | [formula omitted] geominimal surface area | Geominimal surface area | Affine surface area | Functional inequality | Orlicz–Minkowski inequality | Affine isoperimetric inequalities | [formula omitted] affine surface area | [formula omitted]-Brunn–Minkowski theory | Brunn–Minkowski theory | MATHEMATICS, APPLIED | L-p-Brunn-Minkowski theory | The Blaschke-Santalo inequality | SOBOLEV | Orlicz-Brunn-Minkowski theory | CONCAVE | L-p geominimal surface area | Orlicz-Minkowski inequality | DIVERGENCE | L-p affine surface area

Orlicz–Brunn–Minkowski theory | Geometrization of probability | The Blaschke–Santaló inequality | [formula omitted] geominimal surface area | Geominimal surface area | Affine surface area | Functional inequality | Orlicz–Minkowski inequality | Affine isoperimetric inequalities | [formula omitted] affine surface area | [formula omitted]-Brunn–Minkowski theory | Brunn–Minkowski theory | MATHEMATICS, APPLIED | L-p-Brunn-Minkowski theory | The Blaschke-Santalo inequality | SOBOLEV | Orlicz-Brunn-Minkowski theory | CONCAVE | L-p geominimal surface area | Orlicz-Minkowski inequality | DIVERGENCE | L-p affine surface area

Journal Article

Journal of Magnetic Resonance Imaging, ISSN 1053-1807, 04/2016, Volume 43, Issue 4, pp. 903 - 910

Background This work aims to see whether Minkowski Functionals can be used to distinguish between cancer types before chemotherapy treatment has begun, and...

image processing | breast cancer | Minkowski functionals | contrast enhanced MRI | texture analysis | AUTOMATED CLASSIFICATION | RISK | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | CHEMOTHERAPY | PREDICTION | Cyclophosphamide - administration & dosage | Antineoplastic Combined Chemotherapy Protocols - administration & dosage | Prognosis | Area Under Curve | Humans | Middle Aged | Epirubicin - administration & dosage | Triple Negative Breast Neoplasms - drug therapy | Statistics, Nonparametric | Triple Negative Breast Neoplasms - pathology | Adult | Female | Retrospective Studies | Breast Neoplasms - diagnostic imaging | Reproducibility of Results | Triple Negative Breast Neoplasms - diagnostic imaging | Treatment Outcome | Lymphatic Metastasis | Image Processing, Computer-Assisted - methods | Breast Neoplasms - drug therapy | Magnetic Resonance Imaging | Taxoids - administration & dosage | Algorithms | Biopsy | Breast Neoplasms - pathology | Drug Therapy - methods | Aged | Software | Chemotherapy | Breast cancer | Magnetic resonance imaging | Image processing | Cancer | Confidence intervals

image processing | breast cancer | Minkowski functionals | contrast enhanced MRI | texture analysis | AUTOMATED CLASSIFICATION | RISK | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | CHEMOTHERAPY | PREDICTION | Cyclophosphamide - administration & dosage | Antineoplastic Combined Chemotherapy Protocols - administration & dosage | Prognosis | Area Under Curve | Humans | Middle Aged | Epirubicin - administration & dosage | Triple Negative Breast Neoplasms - drug therapy | Statistics, Nonparametric | Triple Negative Breast Neoplasms - pathology | Adult | Female | Retrospective Studies | Breast Neoplasms - diagnostic imaging | Reproducibility of Results | Triple Negative Breast Neoplasms - diagnostic imaging | Treatment Outcome | Lymphatic Metastasis | Image Processing, Computer-Assisted - methods | Breast Neoplasms - drug therapy | Magnetic Resonance Imaging | Taxoids - administration & dosage | Algorithms | Biopsy | Breast Neoplasms - pathology | Drug Therapy - methods | Aged | Software | Chemotherapy | Breast cancer | Magnetic resonance imaging | Image processing | Cancer | Confidence intervals

Journal Article

Magnetic Resonance in Medicine, ISSN 0740-3194, 01/2014, Volume 71, Issue 1, pp. 402 - 410

Purpose The acquisition of ever increasing volumes of high resolution magnetic resonance imaging (MRI) data has created an urgent need to develop automated and...

Minkowski functionals | image analysis | tumor | heterogeneity | TOPOLOGICAL TEXTURE FEATURES | APOPTOSIS | MEANS CLUSTERING-ALGORITHM | TISSUE | CLASSIFICATION | CANCER | LESIONS | IN-VITRO | SPECTROSCOPY | BENIGN | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Reproducibility of Results | Prognosis | Stilbenes - therapeutic use | Image Interpretation, Computer-Assisted - methods | Mice, Inbred C57BL | Magnetic Resonance Imaging - methods | Etoposide - therapeutic use | Treatment Outcome | Antineoplastic Agents - therapeutic use | Lymphoma - drug therapy | Animals | Sensitivity and Specificity | Cell Line, Tumor | Female | Lymphoma - pathology | Mice | Neoplasm Staging | Usage | Algorithms | Drug therapy | Contrast media | Tumors

Minkowski functionals | image analysis | tumor | heterogeneity | TOPOLOGICAL TEXTURE FEATURES | APOPTOSIS | MEANS CLUSTERING-ALGORITHM | TISSUE | CLASSIFICATION | CANCER | LESIONS | IN-VITRO | SPECTROSCOPY | BENIGN | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Reproducibility of Results | Prognosis | Stilbenes - therapeutic use | Image Interpretation, Computer-Assisted - methods | Mice, Inbred C57BL | Magnetic Resonance Imaging - methods | Etoposide - therapeutic use | Treatment Outcome | Antineoplastic Agents - therapeutic use | Lymphoma - drug therapy | Animals | Sensitivity and Specificity | Cell Line, Tumor | Female | Lymphoma - pathology | Mice | Neoplasm Staging | Usage | Algorithms | Drug therapy | Contrast media | Tumors

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2016, Volume 65, Issue 1, pp. 69 - 91

Integral representations are obtained of positive additive functionals on finite products of the space of continuous functions (or of bounded Borel functions)...

Hausdorff spaces | Geometry | Mathematical set theory | Mathematical theorems | Mathematical integrals | Tomography | Mathematical functions | Polynomials | Vector spaces | Borel sets | Dual mixed volume | Additive functional | Positive functional | Star set | Brunn-Minkowski theory | Convex body | Star body | Dual Brunn-Minkowski theory | Mixed volume | TOMOGRAPHY | additive functional | star body | positive functional | MATHEMATICS | dual Brunn-Minkowski theory | CONVEX | mixed volume | dual mixed volume | convex body | BUSEMANN-PETTY PROBLEM

Hausdorff spaces | Geometry | Mathematical set theory | Mathematical theorems | Mathematical integrals | Tomography | Mathematical functions | Polynomials | Vector spaces | Borel sets | Dual mixed volume | Additive functional | Positive functional | Star set | Brunn-Minkowski theory | Convex body | Star body | Dual Brunn-Minkowski theory | Mixed volume | TOMOGRAPHY | additive functional | star body | positive functional | MATHEMATICS | dual Brunn-Minkowski theory | CONVEX | mixed volume | dual mixed volume | convex body | BUSEMANN-PETTY PROBLEM

Journal Article

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 08/2013, Volume 404, Issue 1, pp. 172 - 184

For a measure space (Omega, Sigma, mu) denote by S = S(Omega, Sigma, mu) the set of all mu-integrable simple functions x : Omega -> R. For a bijection phi :...

MATHEMATICS | CONVERSE THEOREM | MATHEMATICS, APPLIED | Geometrical convex function | Subadditivity | Subhomogeneity | Convex function | MINKOWSKI INEQUALITY | Wright-convex function

MATHEMATICS | CONVERSE THEOREM | MATHEMATICS, APPLIED | Geometrical convex function | Subadditivity | Subhomogeneity | Convex function | MINKOWSKI INEQUALITY | Wright-convex function

Journal Article

Mechanics of Materials, ISSN 0167-6636, 11/2015, Volume 90, pp. 185 - 201

•Extended optimization problem is proposed for the construction of SSRVEs.•New measures for microstructure description are proposed.•New measures are defined...

Minkowski functionals | Statistical measures | Spectral density | Multiscale modeling | DP steel | Lineal-path function | MATERIALS SCIENCE, MULTIDISCIPLINARY | SIZE | COMPOSITES | MICROSTRUCTURES | MECHANICS | MODELS | COMPUTATIONAL HOMOGENIZATION | MACRO | SIMULATIONS | MECHANICAL-BEHAVIOR | PLASTICITY | Parametrization | Weighting | Functionals | Mathematical analysis | Morphology | Mathematical models | Microstructure | Optimization

Minkowski functionals | Statistical measures | Spectral density | Multiscale modeling | DP steel | Lineal-path function | MATERIALS SCIENCE, MULTIDISCIPLINARY | SIZE | COMPOSITES | MICROSTRUCTURES | MECHANICS | MODELS | COMPUTATIONAL HOMOGENIZATION | MACRO | SIMULATIONS | MECHANICAL-BEHAVIOR | PLASTICITY | Parametrization | Weighting | Functionals | Mathematical analysis | Morphology | Mathematical models | Microstructure | Optimization

Journal Article