Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 360, Issue 2, pp. 609 - 623

It is well known that a (linear) operator T ∈ L ( X , Y ) between Banach spaces is completely continuous if and only if its adjoint T ∗ ∈ L ( Y ∗ , X ∗ ) takes...

Derivative | Banach space not containing [formula omitted] | Differentiable mapping | Weakly sequentially continuous mapping | Completely continuous mapping | Hereditary Dunford–Pettis property | Banach space not containing ℓ | Hereditary Dunford-Pettis property | Banach space not containing l | C(K,E) | MATHEMATICS, APPLIED | SMOOTH FUNCTIONS | FACTORIZATION | L1(E) | DUNFORD-PETTIS PROPERTY | MULTILINEAR OPERATORS | MATHEMATICS | BANACH-SPACES | SETS | C(K)

Derivative | Banach space not containing [formula omitted] | Differentiable mapping | Weakly sequentially continuous mapping | Completely continuous mapping | Hereditary Dunford–Pettis property | Banach space not containing ℓ | Hereditary Dunford-Pettis property | Banach space not containing l | C(K,E) | MATHEMATICS, APPLIED | SMOOTH FUNCTIONS | FACTORIZATION | L1(E) | DUNFORD-PETTIS PROPERTY | MULTILINEAR OPERATORS | MATHEMATICS | BANACH-SPACES | SETS | C(K)

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2009, Volume 137, Issue 5, pp. 1743 - 1752

Results on factorization (through linear operators) of polynomials and holomorphic mappings between Banach spaces have been obtained in recent years by several...

Mean value theorems | Mathematical theorems | Polynomials | Banach space | Factorization | Cilia | Perceptron convergence procedure | Compact operator | Weakly continuous function | Fréchet differentiable mapping | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | BANACH-SPACES | weakly continuous function | Frechet differentiable mapping | HOLOMORPHIC MAPPINGS | factorization | compact operator

Mean value theorems | Mathematical theorems | Polynomials | Banach space | Factorization | Cilia | Perceptron convergence procedure | Compact operator | Weakly continuous function | Fréchet differentiable mapping | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | BANACH-SPACES | weakly continuous function | Frechet differentiable mapping | HOLOMORPHIC MAPPINGS | factorization | compact operator

Journal Article

Bulletin of the Brazilian Mathematical Society, ISSN 1678-7544, 09/2009, Volume 40, Issue 3, pp. 371 - 380

Given real Banach spaces X and Y, let C (wbu) (1) (X, Y) be the space, introduced by R.M. Aron and J.B. Prolla, of C (1) mappings from X into Y such that the...

Factorization of differentiable mappings | Gâteaux differentiable mapping | Fréchet differentiable mapping | Weakly uniformly continuous mapping on bounded sets | MATHEMATICS | factorization of differentiable mappings | Frechet differentiable mapping | weakly uniformly continuous mapping on bounded sets | Gateaux differentiable mapping

Factorization of differentiable mappings | Gâteaux differentiable mapping | Fréchet differentiable mapping | Weakly uniformly continuous mapping on bounded sets | MATHEMATICS | factorization of differentiable mappings | Frechet differentiable mapping | weakly uniformly continuous mapping on bounded sets | Gateaux differentiable mapping

Journal Article

RIMS Kokyuroku Bessatsu, ISSN 1881-6193, 04/2016, Volume 55, pp. 185 - 203

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 1999, Volume 264, Issue 1, pp. 264 - 293

We propose a conjecture for the exact expression of the unweighted dynamical zeta function for a family of birational transformations of two variables,...

Cremona transformations | Topological entropy | Discrete dynamical systems | Birational mappings | Arnold complexity | Rational dynamical zeta functions | 47.52.+j | 05.45.+b | topological entropy | FACTORIZATION | discrete dynamical systems | PHYSICS, MULTIDISCIPLINARY | STRANGE ATTRACTORS | DIMENSIONS | MODELS | cremona transformations | ORBITS | MAPPINGS | birational mappings | rational dynamical zeta functions | Mathematics | Physics

Cremona transformations | Topological entropy | Discrete dynamical systems | Birational mappings | Arnold complexity | Rational dynamical zeta functions | 47.52.+j | 05.45.+b | topological entropy | FACTORIZATION | discrete dynamical systems | PHYSICS, MULTIDISCIPLINARY | STRANGE ATTRACTORS | DIMENSIONS | MODELS | cremona transformations | ORBITS | MAPPINGS | birational mappings | rational dynamical zeta functions | Mathematics | Physics

Journal Article

Multimedia Tools and Applications, ISSN 1380-7501, 04/2018, Volume 77, Issue 8, pp. 9417 - 9439

The main purpose of this study is to analyze the intrinsic tumor physiologic characteristics in patients with sarcoma through model-free analysis of dynamic...

Dynamic MR imaging | Tumor hypoxia | Matrix factorization | Pattern recognition | Biomedical image processing | Soft tissue sarcomas | CONTRAST-ENHANCED MRI | SOFT-TISSUE SARCOMAS | FEASIBILITY | COMPUTER SCIENCE, INFORMATION SYSTEMS | MODEL | PARAMETERS | ALGORITHMS | BREAST | ENGINEERING, ELECTRICAL & ELECTRONIC | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, THEORY & METHODS | NONNEGATIVE MATRIX FACTORIZATION | Computer science | Equipment and supplies | Algorithms | Image processing | Sarcoma | Methods | Image segmentation | Magnetic resonance imaging | Hypoxia | Pharmacology | Patients

Dynamic MR imaging | Tumor hypoxia | Matrix factorization | Pattern recognition | Biomedical image processing | Soft tissue sarcomas | CONTRAST-ENHANCED MRI | SOFT-TISSUE SARCOMAS | FEASIBILITY | COMPUTER SCIENCE, INFORMATION SYSTEMS | MODEL | PARAMETERS | ALGORITHMS | BREAST | ENGINEERING, ELECTRICAL & ELECTRONIC | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, THEORY & METHODS | NONNEGATIVE MATRIX FACTORIZATION | Computer science | Equipment and supplies | Algorithms | Image processing | Sarcoma | Methods | Image segmentation | Magnetic resonance imaging | Hypoxia | Pharmacology | Patients

Journal Article

Journal of Chemometrics, ISSN 0886-9383, 11/2015, Volume 29, Issue 11, pp. 615 - 626

The nonlinear, nonnegative single‐mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into...

sparseness | mass spectrometry | explicit feature maps | empirical kernel maps | single‐mixture nonlinear blind source separation | nonnegative matrix factorization | Single-mixture nonlinear blind source separation | Empirical kernel maps | Explicit feature maps | Nonnegative matrix factorization | Mass spectrometry | Sparseness | MATRIX | CHEMISTRY, ANALYTICAL | BIOMARKER | INFORMATION | STATISTICS & PROBABILITY | single-mixture nonlinear blind source separation | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | EMPIRICAL-MODE DECOMPOSITION | METABOLOMICS | INSTRUMENTS & INSTRUMENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DISEASE | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Kernels | Separation | Profiling | Nonlinearity | Mass spectroscopy | Hilbert space | Blinds | Mass spectra

sparseness | mass spectrometry | explicit feature maps | empirical kernel maps | single‐mixture nonlinear blind source separation | nonnegative matrix factorization | Single-mixture nonlinear blind source separation | Empirical kernel maps | Explicit feature maps | Nonnegative matrix factorization | Mass spectrometry | Sparseness | MATRIX | CHEMISTRY, ANALYTICAL | BIOMARKER | INFORMATION | STATISTICS & PROBABILITY | single-mixture nonlinear blind source separation | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | EMPIRICAL-MODE DECOMPOSITION | METABOLOMICS | INSTRUMENTS & INSTRUMENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DISEASE | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Kernels | Separation | Profiling | Nonlinearity | Mass spectroscopy | Hilbert space | Blinds | Mass spectra

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 03/2005, Volume 133, Issue 3, pp. 931 - 936

The Pontrjagin-Thom construction expresses a relation between the oriented bordism groups of framed immersions M^m\looparrowright \mathbb{R}^n, m Mathematical manifolds | Homomorphisms | Tangents | Mathematical theorems | Differential topology | Group structure | Factorization | Topological spaces | Special generic mappings | Pontrjagin-Thom construction | Bordisms | MATHEMATICS | MATHEMATICS, APPLIED | bordisms | special generic mappings

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 4/2010, Volume 81, Issue 2, pp. 236 - 250

Let N* be a Hilbert inductive limit and X a Banach space. In this paper, we obtain a necessary and sufficient condition for an analytic mapping Psi : N* bar...

white noise | Fock factorization | B-valued analytic mapping | inductive limit | MATHEMATICS

white noise | Fock factorization | B-valued analytic mapping | inductive limit | MATHEMATICS

Journal Article

NeuroImage, ISSN 1053-8119, 02/2020, Volume 206, p. 116314

We propose a novel optimization framework to predict clinical severity from resting state fMRI (rs-fMRI) data. Our model consists of two coupled terms. The...

Functional magnetic resonance imaging | Clinical severity | Matrix factorization | Dictionary learning | AUTISM | NEUROSCIENCES | NEUROIMAGING | DYSPRAXIA | CHILDREN | CONNECTIVITY | MOTOR | SPECTRUM | TRAITS | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Network management systems | Autism | Statistical analysis | Optimization | Brain mapping

Functional magnetic resonance imaging | Clinical severity | Matrix factorization | Dictionary learning | AUTISM | NEUROSCIENCES | NEUROIMAGING | DYSPRAXIA | CHILDREN | CONNECTIVITY | MOTOR | SPECTRUM | TRAITS | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Network management systems | Autism | Statistical analysis | Optimization | Brain mapping

Journal Article

NeuroImage, ISSN 1053-8119, 06/2018, Volume 173, pp. 580 - 591

The focus of this paper is on evaluating brain responses to different stimuli and identifying brain regions with different responses using multi-subject,...

fMRI | Matrix factorization | Regularization | Hemodynamic response function | Optimization | Spline | ANTERIOR CINGULATE CORTEX | FUNCTIONAL MRI | NEUROSCIENCES | NEUROIMAGING | INDEPENDENT COMPONENT ANALYSIS | STATISTICAL-ANALYSIS | HEMODYNAMIC-RESPONSE | IMPACT | HIERARCHICAL MODEL | TENSOR REGRESSION | CORPUS-CALLOSUM | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Models | Algorithms | Magnetic resonance imaging | Mathematical optimization | Design | Neuroimaging | Brain | Time series | Brain mapping | Functional magnetic resonance imaging | Experiments | Estimates | Methods

fMRI | Matrix factorization | Regularization | Hemodynamic response function | Optimization | Spline | ANTERIOR CINGULATE CORTEX | FUNCTIONAL MRI | NEUROSCIENCES | NEUROIMAGING | INDEPENDENT COMPONENT ANALYSIS | STATISTICAL-ANALYSIS | HEMODYNAMIC-RESPONSE | IMPACT | HIERARCHICAL MODEL | TENSOR REGRESSION | CORPUS-CALLOSUM | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Models | Algorithms | Magnetic resonance imaging | Mathematical optimization | Design | Neuroimaging | Brain | Time series | Brain mapping | Functional magnetic resonance imaging | Experiments | Estimates | Methods

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 8/2017, Volume 72, Issue 2, pp. 700 - 734

Nonconvex optimization arises in many areas of computational science and engineering. However, most nonconvex optimization algorithms are only known to have...

Computational Mathematics and Numerical Analysis | Algorithms | Nonconvex optimization | Prox-linear | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Block coordinate descent | Whole sequence convergence | Mathematics | Nonsmooth optimization | Kurdyka–Łojasiewicz inequality | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | FACTORIZATION | PROXIMAL GRADIENT-METHOD | REWEIGHTED ALGORITHMS | NONNEGATIVE MATRIX | NONSMOOTH FUNCTIONS | MODEL | VARIABLE SELECTION | DESCENT METHOD | MINIMIZATION | Mathematical optimization | Analysis

Computational Mathematics and Numerical Analysis | Algorithms | Nonconvex optimization | Prox-linear | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Block coordinate descent | Whole sequence convergence | Mathematics | Nonsmooth optimization | Kurdyka–Łojasiewicz inequality | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | FACTORIZATION | PROXIMAL GRADIENT-METHOD | REWEIGHTED ALGORITHMS | NONNEGATIVE MATRIX | NONSMOOTH FUNCTIONS | MODEL | VARIABLE SELECTION | DESCENT METHOD | MINIMIZATION | Mathematical optimization | Analysis

Journal Article

Remote Sensing, ISSN 2072-4292, 07/2018, Volume 10, Issue 7, p. 1106

Dictionary pruning step is often employed prior to the sparse unmixing process to improve the performance of library aided unmixing. This paper presents a...

Hyperspectral unmixing | Dictionary pruning | Low-rank representation | Linear unmixing | Hyperspectral image processing | Recursive PCA | Mutual coherence reduction | Semi-supervised unmixing | NUMBER | dictionary pruning | ALGORITHM | SUBSPACE IDENTIFICATION | INDEPENDENT COMPONENT ANALYSIS | ENDMEMBER EXTRACTION | mutual coherence reduction | PURSUIT | REMOTE SENSING | low-rank representation | linear unmixing | hyperspectral unmixing | recursive PCA | SIGNAL SOURCES | NONNEGATIVE MATRIX FACTORIZATION | semi-supervised unmixing | hyperspectral image processing

Hyperspectral unmixing | Dictionary pruning | Low-rank representation | Linear unmixing | Hyperspectral image processing | Recursive PCA | Mutual coherence reduction | Semi-supervised unmixing | NUMBER | dictionary pruning | ALGORITHM | SUBSPACE IDENTIFICATION | INDEPENDENT COMPONENT ANALYSIS | ENDMEMBER EXTRACTION | mutual coherence reduction | PURSUIT | REMOTE SENSING | low-rank representation | linear unmixing | hyperspectral unmixing | recursive PCA | SIGNAL SOURCES | NONNEGATIVE MATRIX FACTORIZATION | semi-supervised unmixing | hyperspectral image processing

Journal Article

Biological Cybernetics, ISSN 0340-1200, 2015, Volume 109, Issue 2, pp. 203 - 214

Studying the flow of information between different areas of the brain can be performed using the so-called partial directed coherence (PDC). This measure is...

Connectivity | Partial directed coherence | Spectral factorization | Granger causality | LINEAR-DEPENDENCE | INFORMATION-FLOW | TIME-SERIES | SIGNALS | NEUROSCIENCES | FEEDBACK | COMPUTER SCIENCE, CYBERNETICS | Algorithms | Animals | Fourier Analysis | Sleep, REM - physiology | Statistics, Nonparametric | Brain Mapping | Mice | Models, Neurological | Analysis | Models | Neurosciences | Mathematical models | Cybernetics | Fourier transforms | Coherence | Time series | Inverse | Spectra | Density | Factorization | Autoregressive processes | Engineering Sciences | Signal and Image processing

Connectivity | Partial directed coherence | Spectral factorization | Granger causality | LINEAR-DEPENDENCE | INFORMATION-FLOW | TIME-SERIES | SIGNALS | NEUROSCIENCES | FEEDBACK | COMPUTER SCIENCE, CYBERNETICS | Algorithms | Animals | Fourier Analysis | Sleep, REM - physiology | Statistics, Nonparametric | Brain Mapping | Mice | Models, Neurological | Analysis | Models | Neurosciences | Mathematical models | Cybernetics | Fourier transforms | Coherence | Time series | Inverse | Spectra | Density | Factorization | Autoregressive processes | Engineering Sciences | Signal and Image processing

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 7/2006, Volume 26, Issue 3, pp. 297 - 311

McCann showed that, if the potential of a gradient-mapping, on a compact riemannian manifold, is c-convex, the length of its gradient cannot exceed the...

POLAR FACTORIZATION | REARRANGEMENT | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | MAPS | REGULARITY | MANIFOLDS

POLAR FACTORIZATION | REARRANGEMENT | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | MAPS | REGULARITY | MANIFOLDS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 01/2014, Volume 266, Issue 2, pp. 616 - 659

The well-known factorization theorem of Lozanovskiĭ may be written in the form L1≡E⊙E′, where ⊙ means the pointwise product of Banach ideal spaces. A natural...

Banach ideal spaces | Symmetric spaces | Sequence spaces | Calderón–Lozanovskiĭ spaces | Pointwise multiplication | Banach function spaces | Pointwise multipliers | Calderón spaces | Factorization | Orlicz spaces | Calderón-Lozanovskiǐ spaces | CALDERON-LOZANOVSKII CONSTRUCTION | HARDYS INEQUALITY | LORENTZ SPACES | INTERPOLATION | MATHEMATICS | Calderon spaces | ORDER CONVEXITY | REARRANGEMENT-INVARIANT SPACES | THEOREMS | LATTICES | Calderon-Lozanovskii spaces | OPERATORS | Mathematics | Naturvetenskap | Natural Sciences | Matematisk analys | Matematik | Mathematical Analysis

Banach ideal spaces | Symmetric spaces | Sequence spaces | Calderón–Lozanovskiĭ spaces | Pointwise multiplication | Banach function spaces | Pointwise multipliers | Calderón spaces | Factorization | Orlicz spaces | Calderón-Lozanovskiǐ spaces | CALDERON-LOZANOVSKII CONSTRUCTION | HARDYS INEQUALITY | LORENTZ SPACES | INTERPOLATION | MATHEMATICS | Calderon spaces | ORDER CONVEXITY | REARRANGEMENT-INVARIANT SPACES | THEOREMS | LATTICES | Calderon-Lozanovskii spaces | OPERATORS | Mathematics | Naturvetenskap | Natural Sciences | Matematisk analys | Matematik | Mathematical Analysis

Journal Article

Kyushu Journal of Mathematics, ISSN 1340-6116, 2005, Volume 59, Issue 2, pp. 351 - 363

Ikegami and Saeki have proved that the cobordism group of Morse functions on oriented surfaces is an infinite cyclic group. Their method is applicable, with a...

Morse function | fold singularity | cobordism | Reeb graph | Stein factorization | MATHEMATICS | MAPS

Morse function | fold singularity | cobordism | Reeb graph | Stein factorization | MATHEMATICS | MAPS

Journal Article

International Journal of Computer Vision, ISSN 0920-5691, 9/2015, Volume 114, Issue 2, pp. 195 - 216

This paper introduces a new dictionary learning strategy based on atoms obtained by translating the composition of $$K$$ K convolutions with $$S$$ S -sparse...

Pattern Recognition | Global optimization | Computer Science | Computer Imaging, Vision, Pattern Recognition and Graphics | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | Sparse representation | Matrix factorization | Fast transform | Dictionary learning | Gauss–Seidel | SIGNAL | ALGORITHM | DECOMPOSITION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | IMAGE | MINIMIZATION | CONVERGENCE | Gauss-Seidel | DICTIONARIES | Algorithms | Machine learning | Studies | Artificial intelligence | Analysis | Optimization | Data dictionaries | Learning | Dictionaries | Searching | Images | Translating | Texts | Strategy | Mathematics | Optimization and Control | Engineering Sciences | Signal and Image processing

Pattern Recognition | Global optimization | Computer Science | Computer Imaging, Vision, Pattern Recognition and Graphics | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | Sparse representation | Matrix factorization | Fast transform | Dictionary learning | Gauss–Seidel | SIGNAL | ALGORITHM | DECOMPOSITION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | IMAGE | MINIMIZATION | CONVERGENCE | Gauss-Seidel | DICTIONARIES | Algorithms | Machine learning | Studies | Artificial intelligence | Analysis | Optimization | Data dictionaries | Learning | Dictionaries | Searching | Images | Translating | Texts | Strategy | Mathematics | Optimization and Control | Engineering Sciences | Signal and Image processing

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 12/1995, Volume 32, Issue 6, pp. 1808 - 1838

We prove the convergence of an overlapping domain decomposition method for the polar factorization of vector-valued mappings. We introduce a consistent...

Lebesgue measures | Decomposition methods | Vector fields | Mathematical functions | Convexity | Factorization | Vector valued functions | Perceptron convergence procedure | Continuous functions | Linearization | Measure-preserving mappings | Convex functions | Assignment problem | Polar factorization | Domain decomposition | POLAR FACTORIZATION | ATMOSPHERIC FRONTOGENESIS MODELS | MATHEMATICS, APPLIED | ASSIGNMENT PROBLEM | DOMAIN DECOMPOSITION | CONVEX FUNCTIONS | MEASURE-PRESERVING MAPPINGS

Lebesgue measures | Decomposition methods | Vector fields | Mathematical functions | Convexity | Factorization | Vector valued functions | Perceptron convergence procedure | Continuous functions | Linearization | Measure-preserving mappings | Convex functions | Assignment problem | Polar factorization | Domain decomposition | POLAR FACTORIZATION | ATMOSPHERIC FRONTOGENESIS MODELS | MATHEMATICS, APPLIED | ASSIGNMENT PROBLEM | DOMAIN DECOMPOSITION | CONVEX FUNCTIONS | MEASURE-PRESERVING MAPPINGS

Journal Article