2016, Second edition., Graduate studies in mathematics, ISBN 1470409860, Volume 175., xviii, 453 pages

Book

2017, Graduate studies in mathematics, ISBN 9781470436605, Volume 185, xi, 289 pages

Book

2015, Mathematical surveys and monographs, ISBN 9781470417376, Volume no. 208., x, 410

Differential geometry -- Symplectic geometry, contact geometry -- Contact manifolds, general | Homology theory | Knot theory | Manifolds and cell complexes -- Low-dimensional topology -- Invariants of knots and 3-manifolds | Link theory | Manifolds and cell complexes -- Differential topology -- Floer homology

Book

Communications in Mathematical Physics, ISSN 0010-3616, 10/2017, Volume 355, Issue 2, pp. 561 - 602

...Digital Object Identiﬁer (DOI) 10.1007/s00220-017-2965-z Commun. Math. Phys. 355, 561–602 (2017) Communications in Mathematical Physics Differential T opology...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHASES | BUNDLES | EULER STRUCTURES | INVARIANTS | TORSION | SYSTEMS | VECTOR-FIELDS | PHYSICS, MATHEMATICAL | DISCOVERY | EDGE STATES

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHASES | BUNDLES | EULER STRUCTURES | INVARIANTS | TORSION | SYSTEMS | VECTOR-FIELDS | PHYSICS, MATHEMATICAL | DISCOVERY | EDGE STATES

Journal Article

Nonlinear analysis. Hybrid systems, ISSN 1751-570X, 02/2018, Volume 27, pp. 13 - 28

In this paper, asymptotic behavior analysis is addressed for a class of nonlinear complex-valued impulsive differential systems with time-varying delays...

Exponentially attractive set | Complex-valued | Impulsive | Weak-invariant set | Delay | MATHEMATICS, APPLIED | EXPONENTIAL STABILITY | GLOBAL STABILITY | STABILIZATION | INEQUALITY | EQUATIONS | RECURRENT NEURAL-NETWORKS | ROBUST STABILITY ANALYSIS | SAMPLED-DATA SYSTEMS | QUANTUM-SYSTEMS | AUTOMATION & CONTROL SYSTEMS

Exponentially attractive set | Complex-valued | Impulsive | Weak-invariant set | Delay | MATHEMATICS, APPLIED | EXPONENTIAL STABILITY | GLOBAL STABILITY | STABILIZATION | INEQUALITY | EQUATIONS | RECURRENT NEURAL-NETWORKS | ROBUST STABILITY ANALYSIS | SAMPLED-DATA SYSTEMS | QUANTUM-SYSTEMS | AUTOMATION & CONTROL SYSTEMS

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 02/2018, Volume 14

.... In this paper we construct complexes of invariant differential operators which live on homogeneous spaces of $|2...

Weighted jets | Penrose transform | Relative BGG complexes | Complexes of invariant differential operators | Formal exactness | Mathematics - Differential Geometry

Weighted jets | Penrose transform | Relative BGG complexes | Complexes of invariant differential operators | Formal exactness | Mathematics - Differential Geometry

Journal Article

Geometric and Functional Analysis, ISSN 1016-443X, 4/2014, Volume 24, Issue 2, pp. 403 - 492

.... We then apply this method to give a thorough account of the integral geometry of the complex space forms, i.e...

Analysis | Mathematics | MATHEMATICS | CURVATURE MEASURES | SETS | TUBES | MULTIPLICATIVE STRUCTURE | MANIFOLDS | INVARIANT VALUATIONS | Valuation | Mathematics - Differential Geometry

Analysis | Mathematics | MATHEMATICS | CURVATURE MEASURES | SETS | TUBES | MULTIPLICATIVE STRUCTURE | MANIFOLDS | INVARIANT VALUATIONS | Valuation | Mathematics - Differential Geometry

Journal Article

Journal of mathematical imaging and vision, ISSN 1573-7683, 2019, Volume 62, Issue 1, pp. 120 - 148

.... We first present a general sufficiency argument for obtaining scale covariance, which holds for a wide class of networks defined from linear and nonlinear differential expressions expressed in terms...

Hierarchical | MATHEMATICS, APPLIED | Handcrafted | Texture classification | COMPLEX CELLS | Deep learning | SPACE | Feature detection | Network | OBJECT RECOGNITION | Complex cell | Differential expression | ROTATION-INVARIANT | Scale invariance | Computer vision | Texture analysis | Scale space | Scale covariance | Structured | Deep | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | TEXTURE | MODELS | CONVOLUTIONAL NEURAL-NETWORKS | Quasi quadrature | SELECTION | RECEPTIVE-FIELDS | Computer Science - Computer Vision and Pattern Recognition

Hierarchical | MATHEMATICS, APPLIED | Handcrafted | Texture classification | COMPLEX CELLS | Deep learning | SPACE | Feature detection | Network | OBJECT RECOGNITION | Complex cell | Differential expression | ROTATION-INVARIANT | Scale invariance | Computer vision | Texture analysis | Scale space | Scale covariance | Structured | Deep | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | TEXTURE | MODELS | CONVOLUTIONAL NEURAL-NETWORKS | Quasi quadrature | SELECTION | RECEPTIVE-FIELDS | Computer Science - Computer Vision and Pattern Recognition

Journal Article

Neural Processing Letters, ISSN 1370-4621, 2/2019, Volume 49, Issue 1, pp. 121 - 139

In this paper, a class of fractional-order complex-valued Cohen–Grossberg neural networks is investigated...

Complex-valued Cohen–Grossberg neural network | Computational Intelligence | Mittag-Leffler boundedness | Artificial Intelligence | Complex Systems | Computer Science | Fractional-order | Global Mittag-Leffler attractive set | Fractional-order differential inequality | EXPONENTIAL STABILITY | LAGRANGE STABILITY | LYAPUNOV FUNCTIONS | INVARIANT | DELAYS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | NONLINEAR DIFFERENTIAL-EQUATIONS | UNIFORM STABILITY | SYNCHRONIZATION | CHAOS | DYNAMICS | Complex-valued Cohen-Grossberg neural network | Neural networks

Complex-valued Cohen–Grossberg neural network | Computational Intelligence | Mittag-Leffler boundedness | Artificial Intelligence | Complex Systems | Computer Science | Fractional-order | Global Mittag-Leffler attractive set | Fractional-order differential inequality | EXPONENTIAL STABILITY | LAGRANGE STABILITY | LYAPUNOV FUNCTIONS | INVARIANT | DELAYS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | NONLINEAR DIFFERENTIAL-EQUATIONS | UNIFORM STABILITY | SYNCHRONIZATION | CHAOS | DYNAMICS | Complex-valued Cohen-Grossberg neural network | Neural networks

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 11/2017, Volume 58, Issue 11, p. 111512

We give a geometric construction of the Bernstein-Gel’fand-Gel’fand (BGG) resolutions in singular infinitesimal character in the case of 1-graded complex Lie...

MODULES | SEQUENCES | PHYSICS, MATHEMATICAL | INVARIANT OPERATORS | Lie groups | Mathematics - Differential Geometry

MODULES | SEQUENCES | PHYSICS, MATHEMATICAL | INVARIANT OPERATORS | Lie groups | Mathematics - Differential Geometry

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 2/2019, Volume 231, Issue 2, pp. 971 - 1044

The goal of this paper is to develop a KAM theory for tori with hyperbolic directions, which applies to Hamiltonian partial differential equations, even to some ill-posed ones...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | MATHEMATICS, APPLIED | MECHANICS | PERTURBATIONS | INVARIANT TORI | QUASI-PERIODIC SOLUTIONS | CENTER MANIFOLD | ELLIPTIC-EQUATIONS | COMPUTATION | LOWER-DIMENSIONAL TORI | EXPONENTIAL DICHOTOMY | IMPLICIT FUNCTION THEOREMS | Theorems | Boussinesq equations | Approximation | Partial differential equations | Parameterization | Invariants | Dichotomies | Water waves | Toruses | Format | Initial conditions | Functional equations | Dependence | Evolution | Mathematical models | Ill-posed problems (mathematics) | Iterative methods

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | MATHEMATICS, APPLIED | MECHANICS | PERTURBATIONS | INVARIANT TORI | QUASI-PERIODIC SOLUTIONS | CENTER MANIFOLD | ELLIPTIC-EQUATIONS | COMPUTATION | LOWER-DIMENSIONAL TORI | EXPONENTIAL DICHOTOMY | IMPLICIT FUNCTION THEOREMS | Theorems | Boussinesq equations | Approximation | Partial differential equations | Parameterization | Invariants | Dichotomies | Water waves | Toruses | Format | Initial conditions | Functional equations | Dependence | Evolution | Mathematical models | Ill-posed problems (mathematics) | Iterative methods

Journal Article

European Journal of Cancer, ISSN 0959-8049, 2009, Volume 45, Issue 9, pp. 1654 - 1663

Abstract CD74 (major histocompatibility complex (MHC) Class II invariant chain) has recently been identified as the cell-surface receptor for the pro-tumorigenic cytokine macrophage migration inhibitory factor (MIF...

Hematology, Oncology and Palliative Medicine | Macrophage migration inhibitory factor | CD74 | Class II trans-activator | Adenoma | Invariant chain | Colorectal cancer | ENCODES | CIITA | MIGRATION INHIBITORY FACTOR | TRANSACTIVATOR GENE | RECEPTOR | MIF | CANCER | HLA-DR | MODELS | ONCOLOGY | LINK | Antigens, Differentiation, B-Lymphocyte - genetics | Antigens, Neoplasm - genetics | Humans | Mice, Inbred C57BL | RNA, Messenger - genetics | Adenoma - immunology | Gene Expression Regulation, Neoplastic - immunology | Macrophage Migration-Inhibitory Factors - metabolism | Animals | Colorectal Neoplasms - immunology | Down-Regulation - immunology | Reverse Transcriptase Polymerase Chain Reaction - methods | Antigens, Neoplasm - metabolism | RNA, Neoplasm - genetics | Histocompatibility Antigens Class II - metabolism | Trans-Activators - metabolism | Mice | Antigens, Differentiation, B-Lymphocyte - metabolism | Histocompatibility Antigens Class II - genetics | Intramolecular Oxidoreductases - metabolism | Messenger RNA | Major histocompatibility complex | Macrophages | Gene expression | Analysis | Index Medicus

Hematology, Oncology and Palliative Medicine | Macrophage migration inhibitory factor | CD74 | Class II trans-activator | Adenoma | Invariant chain | Colorectal cancer | ENCODES | CIITA | MIGRATION INHIBITORY FACTOR | TRANSACTIVATOR GENE | RECEPTOR | MIF | CANCER | HLA-DR | MODELS | ONCOLOGY | LINK | Antigens, Differentiation, B-Lymphocyte - genetics | Antigens, Neoplasm - genetics | Humans | Mice, Inbred C57BL | RNA, Messenger - genetics | Adenoma - immunology | Gene Expression Regulation, Neoplastic - immunology | Macrophage Migration-Inhibitory Factors - metabolism | Animals | Colorectal Neoplasms - immunology | Down-Regulation - immunology | Reverse Transcriptase Polymerase Chain Reaction - methods | Antigens, Neoplasm - metabolism | RNA, Neoplasm - genetics | Histocompatibility Antigens Class II - metabolism | Trans-Activators - metabolism | Mice | Antigens, Differentiation, B-Lymphocyte - metabolism | Histocompatibility Antigens Class II - genetics | Intramolecular Oxidoreductases - metabolism | Messenger RNA | Major histocompatibility complex | Macrophages | Gene expression | Analysis | Index Medicus

Journal Article

Annals of global analysis and geometry, ISSN 1572-9060, 2019, Volume 56, Issue 4, pp. 631 - 665

We are interested in global properties of systems of left-invariant differential operators on compact Lie groups...

58J10 | Mathematical Physics | Differential complexes | Locally integrable structures | 35A01 | Mathematics | Left-invariant operators | Geometry | Analysis | Global Analysis and Analysis on Manifolds | 35R03 | Differential Geometry | Solvability | Regularity | Operators (mathematics) | Properties (attributes) | Function space | Differential equations | Lie groups | Homology | Invariants

58J10 | Mathematical Physics | Differential complexes | Locally integrable structures | 35A01 | Mathematics | Left-invariant operators | Geometry | Analysis | Global Analysis and Analysis on Manifolds | 35R03 | Differential Geometry | Solvability | Regularity | Operators (mathematics) | Properties (attributes) | Function space | Differential equations | Lie groups | Homology | Invariants

Journal Article

Journal of Topology, ISSN 1753-8416, 12/2017, Volume 10, Issue 4, pp. 995 - 1028

...) case, the Donaldson–Uhlenbeck compactification is not a complex space, and the set U ss can be a complicated subset of the base space U that is neither open or closed in the classical topology, nor locally closed in the Zariski topology...

32G13 | 53C07 | 53C55 (primary) | EXT | MATHEMATICS | CLASS-VII SURFACES | SPACES | STABLE VECTOR-BUNDLES | CONNECTIONS | DONALDSON POLYNOMIAL INVARIANTS | Complex Variables | Differential Geometry | Mathematics

32G13 | 53C07 | 53C55 (primary) | EXT | MATHEMATICS | CLASS-VII SURFACES | SPACES | STABLE VECTOR-BUNDLES | CONNECTIONS | DONALDSON POLYNOMIAL INVARIANTS | Complex Variables | Differential Geometry | Mathematics

Journal Article

Advances in Mathematics, ISSN 0001-8708, 09/2016, Volume 300, pp. 473 - 504

We define and study representation categories based on Deligne categories Rep(GLt), Rep(Ot), Rep(Sp2t), where t is any (non-integer) complex number. Namely...

Symmetric tensor category | Deligne category | Complex rank | LIE-ALGEBRAS | MATHEMATICS | INVARIANT DIFFERENTIAL OPERATORS | Analysis | Algebra

Symmetric tensor category | Deligne category | Complex rank | LIE-ALGEBRAS | MATHEMATICS | INVARIANT DIFFERENTIAL OPERATORS | Analysis | Algebra

Journal Article

Complexity (New York, N.Y.), ISSN 1099-0526, 2019, Volume 2019, pp. 1 - 15

.... First we characterize ordinary differential equation models in only measurable variables using differential-algebra elimination...

INDISTINGUISHABILITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | COMPLEX ISOTHERMAL REACTORS | STABILITY | MULTIDISCIPLINARY SCIENCES | REACTION NETWORK STRUCTURE | IDENTIFIABILITY | Economic models | Parameter estimation | Model testing | Parameters | Time series | Computational mathematics | Biology | Statistical tests | Invariants | System theory | Geometry | Algebra | Algorithms | Coding | Linear algebra | Differential equations | Ordinary differential equations | Mathematical models | Methods

INDISTINGUISHABILITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | COMPLEX ISOTHERMAL REACTORS | STABILITY | MULTIDISCIPLINARY SCIENCES | REACTION NETWORK STRUCTURE | IDENTIFIABILITY | Economic models | Parameter estimation | Model testing | Parameters | Time series | Computational mathematics | Biology | Statistical tests | Invariants | System theory | Geometry | Algebra | Algorithms | Coding | Linear algebra | Differential equations | Ordinary differential equations | Mathematical models | Methods

Journal Article

International Journal of Dynamics and Control, ISSN 2195-268X, 6/2019, Volume 7, Issue 2, pp. 496 - 509

.... We have found Lie point symmetries of this equation and then we reduced combined MCBS–nMCBS equation to ordinary differential equation through two successive reductions...

Conservation laws | Engineering | Vibration, Dynamical Systems, Control | Lie point symmetries | Invariant solution | Control and Systems Theory | Optimal system | ( $$2+1$$ 2 + 1 )-Dimensional combined MCBS–nMCBS equation | Complexity | (2 + 1)-Dimensional combined MCBS–nMCBS equation

Conservation laws | Engineering | Vibration, Dynamical Systems, Control | Lie point symmetries | Invariant solution | Control and Systems Theory | Optimal system | ( $$2+1$$ 2 + 1 )-Dimensional combined MCBS–nMCBS equation | Complexity | (2 + 1)-Dimensional combined MCBS–nMCBS equation

Journal Article

European physical journal plus, ISSN 2190-5444, 2018, Volume 133, Issue 1, pp. 1 - 15

In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation...

Condensed Matter Physics | Atomic, Molecular, Optical and Plasma Physics | Applied and Technical Physics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MULTIDISCIPLINARY | FINITE-ELEMENT-METHOD | SOLITON

Condensed Matter Physics | Atomic, Molecular, Optical and Plasma Physics | Applied and Technical Physics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MULTIDISCIPLINARY | FINITE-ELEMENT-METHOD | SOLITON

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2011, Volume 227, Issue 2, pp. 830 - 846

The space of Minkowski valuations on an m-dimensional complex vector space which are continuous, translation invariant and contravariant under the complex special linear group is explicitly described...

Convex bodies | Minkowski valuation | Brunn–Minkowski inequality | Projection body | Brunn-Minkowski inequality | MATHEMATICS | CONVEX-BODIES | INTEGRAL GEOMETRY | SETS | MANIFOLDS | INVARIANT VALUATIONS | AFFINE ISOPERIMETRIC-INEQUALITIES | MINKOWSKI VALUATIONS | Valuation | Real property

Convex bodies | Minkowski valuation | Brunn–Minkowski inequality | Projection body | Brunn-Minkowski inequality | MATHEMATICS | CONVEX-BODIES | INTEGRAL GEOMETRY | SETS | MANIFOLDS | INVARIANT VALUATIONS | AFFINE ISOPERIMETRIC-INEQUALITIES | MINKOWSKI VALUATIONS | Valuation | Real property

Journal Article