Journal of High Energy Physics, ISSN 1126-6708, 11/2017, Volume 2017, Issue 11, pp. 1 - 124

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian,...

Scattering Amplitudes | Supersymmetric Gauge Theory | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | CLUSTER | THEOREM | PHYSICS, PARTICLES & FIELDS | Polytopes | Triangulation | Singularities | Mathematical analysis | Integrals | Differential geometry | Canonical forms | Mathematics - Algebraic Geometry | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory | Mathematics - Combinatorics | MATHEMATICS AND COMPUTING

Scattering Amplitudes | Supersymmetric Gauge Theory | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | CLUSTER | THEOREM | PHYSICS, PARTICLES & FIELDS | Polytopes | Triangulation | Singularities | Mathematical analysis | Integrals | Differential geometry | Canonical forms | Mathematics - Algebraic Geometry | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory | Mathematics - Combinatorics | MATHEMATICS AND COMPUTING

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 8/2018, Volume 2018, Issue 8, pp. 1 - 32

We present a general construction of two types of differential forms, based on any (n−3)-dimensional subspace in the kinematic space of n massless particles....

Scattering Amplitudes | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, PARTICLES & FIELDS | Amplitudes | Singularities | Mathematical analysis | Scattering | Kinematics | Canonical forms | Subspaces | Formulas (mathematics) | Nuclear and particle physics. Atomic energy. Radioactivity | Mathematical Physics | High Energy Physics - Theory

Scattering Amplitudes | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, PARTICLES & FIELDS | Amplitudes | Singularities | Mathematical analysis | Scattering | Kinematics | Canonical forms | Subspaces | Formulas (mathematics) | Nuclear and particle physics. Atomic energy. Radioactivity | Mathematical Physics | High Energy Physics - Theory

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 10/2018, Volume 2018, Issue 10, pp. 1 - 25

Inspired by the idea of viewing amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM as differential forms on momentum twistor space, we introduce differential forms on...

Scattering Amplitudes | Supersymmetric Gauge Theory | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, PARTICLES & FIELDS | String theory | Momentum | Amplitudes | Gauge theory | Helicity | Canonical forms | Physics - High Energy Physics - Theory

Scattering Amplitudes | Supersymmetric Gauge Theory | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, PARTICLES & FIELDS | String theory | Momentum | Amplitudes | Gauge theory | Helicity | Canonical forms | Physics - High Energy Physics - Theory

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 05/2015, Volume 32, Issue 9, pp. 95005 - 95054

We consider the De Donder-Weyl (DW) Hamiltonian formulation of the Palatini action of vielbein gravity formulated in terms of the solder form and spin...

Geometry | De Donder-Weyl | Palatini gravity | Multisymplectic | Vielbein gravity | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | SPIN STRUCTURES | CLASSICAL FIELD-THEORY | ASHTEKAR VARIABLES | CANONICAL STRUCTURE | GAUGE-NATURAL BUNDLES | L-INFINITY-ALGEBRAS | QUANTIZED-FIELDS | SYMPLECTIC APPROACH | POISSON BRACKET | vielbein gravity | ASTRONOMY & ASTROPHYSICS | multisymplectic geometry | PHYSICS, PARTICLES & FIELDS | Formulations | Gravitation | Construction | Solders | Brackets | Mathematical analysis | Independent variables | Quantum gravity | General Relativity and Quantum Cosmology | Mathematics | Mathematical Physics | Physics

Geometry | De Donder-Weyl | Palatini gravity | Multisymplectic | Vielbein gravity | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | SPIN STRUCTURES | CLASSICAL FIELD-THEORY | ASHTEKAR VARIABLES | CANONICAL STRUCTURE | GAUGE-NATURAL BUNDLES | L-INFINITY-ALGEBRAS | QUANTIZED-FIELDS | SYMPLECTIC APPROACH | POISSON BRACKET | vielbein gravity | ASTRONOMY & ASTROPHYSICS | multisymplectic geometry | PHYSICS, PARTICLES & FIELDS | Formulations | Gravitation | Construction | Solders | Brackets | Mathematical analysis | Independent variables | Quantum gravity | General Relativity and Quantum Cosmology | Mathematics | Mathematical Physics | Physics

Journal Article

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 07/2018, Volume 376, Issue 2124, p. 20170384

A global framework for treating nonlinear differential dynamical systems is presented. It rests on the fact that most systems can be transformed into the...

Nonlinear dynamics | Taylor series | Lie algebra | Lotka-Volterra | Urn process | Canonical form | urn process | STABILITY ANALYSIS | INVARIANTS | MULTIDISCIPLINARY SCIENCES | QUASI-POLYNOMIAL SYSTEMS | canonical form | DIFFERENTIAL-EQUATIONS | LOTKA-VOLTERRA EQUATIONS | nonlinear dynamics

Nonlinear dynamics | Taylor series | Lie algebra | Lotka-Volterra | Urn process | Canonical form | urn process | STABILITY ANALYSIS | INVARIANTS | MULTIDISCIPLINARY SCIENCES | QUASI-POLYNOMIAL SYSTEMS | canonical form | DIFFERENTIAL-EQUATIONS | LOTKA-VOLTERRA EQUATIONS | nonlinear dynamics

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 02/2014, Volume 443, pp. 245 - 259

We present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms. Beginning from basic results developed...

Bilinear forms | Congruence | Canonical forms | CONJUNCTIVITY | MATHEMATICS | SESQUILINEAR FORMS | MATHEMATICS, APPLIED | MATRICES | FIELD | CLASSIFICATION | SYSTEMS

Bilinear forms | Congruence | Canonical forms | CONJUNCTIVITY | MATHEMATICS | SESQUILINEAR FORMS | MATHEMATICS, APPLIED | MATRICES | FIELD | CLASSIFICATION | SYSTEMS

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 06/2017, Volume 348, pp. 12 - 32

•An extension of Ref. [15] to the case of noncanonical coordinates.•Detailed description of normal form expansions in variational approaches to quantum...

Poincaré–Birkhoff normal form | Quantum dynamics | Canonical coordinate | Poincare-Birkhoff normal form | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | DECAY-RATES | PHYSICS, MATHEMATICAL | TRANSITION-STATE THEORY | Quantum theory

Poincaré–Birkhoff normal form | Quantum dynamics | Canonical coordinate | Poincare-Birkhoff normal form | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | DECAY-RATES | PHYSICS, MATHEMATICAL | TRANSITION-STATE THEORY | Quantum theory

Journal Article

Physics Letters B, ISSN 0370-2693, 06/2018, Volume 781, pp. 270 - 278

Feynman integrals are easily solved if their system of differential equations is in ε-form. In this letter we show by the explicit example of the kite integral...

RECURRENCE RELATIONS | QUASIMODULAR FORMS | PHYSICS, NUCLEAR | SUNRISE GRAPH | MASTER INTEGRALS | DIAGRAMS | SPACE | ASTRONOMY & ASTROPHYSICS | CANONICAL BASIS | ARBITRARY MASSES | AMPLITUDES | SELF-ENERGY | PHYSICS, PARTICLES & FIELDS | High Energy Physics - Theory | High Energy Physics - Phenomenology | Physics

RECURRENCE RELATIONS | QUASIMODULAR FORMS | PHYSICS, NUCLEAR | SUNRISE GRAPH | MASTER INTEGRALS | DIAGRAMS | SPACE | ASTRONOMY & ASTROPHYSICS | CANONICAL BASIS | ARBITRARY MASSES | AMPLITUDES | SELF-ENERGY | PHYSICS, PARTICLES & FIELDS | High Energy Physics - Theory | High Energy Physics - Phenomenology | Physics

Journal Article

International Journal of Modern Physics D, ISSN 0218-2718, 06/2018, Volume 27, Issue 8, p. 1850085

Classical equivalence between Jordan’s and Einstein’s frame counterparts of F ( R ) theory of gravity has recently been questioned, since the two produce...

Einstein's frame | F (R) theory | equivalence | Lagrangian multiplier technique | Jordan's frame | TRANSFORMATION | EINSTEIN-HILBERT ACTION | VIABILITY | DARK ENERGY | F(R) theory | COSMOLOGY | MODELS | SPHERICALLY SYMMETRIC-SOLUTIONS | ASTRONOMY & ASTROPHYSICS | SINGULARITY | NOETHER SYMMETRY | HISTORY | Gravity

Einstein's frame | F (R) theory | equivalence | Lagrangian multiplier technique | Jordan's frame | TRANSFORMATION | EINSTEIN-HILBERT ACTION | VIABILITY | DARK ENERGY | F(R) theory | COSMOLOGY | MODELS | SPHERICALLY SYMMETRIC-SOLUTIONS | ASTRONOMY & ASTROPHYSICS | SINGULARITY | NOETHER SYMMETRY | HISTORY | Gravity

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2018, Volume 51, Issue 39

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2017, Volume 531, pp. 533 - 536

In the note, all indecomposable canonical forms of linear systems with dimension less than or equals to 4 are determined based on Belitskii's algorithm.

Linear dynamical system | Indecomposability | Belitskii's canonical form | MATHEMATICS | MATHEMATICS, APPLIED | Linear systems

Linear dynamical system | Indecomposability | Belitskii's canonical form | MATHEMATICS | MATHEMATICS, APPLIED | Linear systems

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 04/2020, Volume 590, pp. 32 - 61

Motivated by a problem in local differential geometry of Cauchy–Riemann (CR) structures of hypersurface type, we find a canonical form for pairs consisting of...

Antilinear operators | Uniformly Levi degenerate CR structures | Pencils | Canonical forms | Indefinite Hermitian forms | MATHEMATICS | MATHEMATICS, APPLIED | MATRICES | Operators (mathematics) | Hyperspaces | Differential geometry

Antilinear operators | Uniformly Levi degenerate CR structures | Pencils | Canonical forms | Indefinite Hermitian forms | MATHEMATICS | MATHEMATICS, APPLIED | MATRICES | Operators (mathematics) | Hyperspaces | Differential geometry

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 03/2019, Volume 565, pp. 177 - 207

This paper collects results about Riordan arrays in the framework of matrix functions; actually, the following methodology applies to any square matrix m×m...

Hermite interpolating polynomials | Matrices functions | Riordan arrays | Jordan canonical forms | MATHEMATICS | MATHEMATICS, APPLIED | Functions (mathematics) | Eigenvalues | Hermite polynomials | Mathematical analysis | Canonical forms

Hermite interpolating polynomials | Matrices functions | Riordan arrays | Jordan canonical forms | MATHEMATICS | MATHEMATICS, APPLIED | Functions (mathematics) | Eigenvalues | Hermite polynomials | Mathematical analysis | Canonical forms

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 2, pp. 1308 - 1326

In this paper we present some linear algebra behind quadratic parts of quadratically flat complex points of codimension two real submanifold in a complex...

Complex points | Simultaneous reduction | CR manifolds | Normal forms | MATHEMATICS, APPLIED | C-N | LOCAL HULL | REAL SURFACES | HOLOMORPHY | CONSIMILARITY | CANONICAL FORM | MATHEMATICS | LEVI-FLAT HYPERSURFACES | NONSINGULAR PENCIL | HERMITIAN MATRICES | TRANSFORMATIONS | Mathematics - Complex Variables

Complex points | Simultaneous reduction | CR manifolds | Normal forms | MATHEMATICS, APPLIED | C-N | LOCAL HULL | REAL SURFACES | HOLOMORPHY | CONSIMILARITY | CANONICAL FORM | MATHEMATICS | LEVI-FLAT HYPERSURFACES | NONSINGULAR PENCIL | HERMITIAN MATRICES | TRANSFORMATIONS | Mathematics - Complex Variables

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 02/2020, Volume 81, p. 105012

•Global connections in the Z2-symmetric Takens-Bogdanov normal form are studied.•A very efficient iterative procedure with the nonlinear time transformation...

Global connection | Perturbation method | Nonlinear time transformation | Takens-Bogdanov bifurcation

Global connection | Perturbation method | Nonlinear time transformation | Takens-Bogdanov bifurcation

Journal Article

SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2017, Volume 38, Issue 2, pp. 656 - 681

In applications where the tensor rank decomposition arises, one often relies on its identifiability properties for interpreting the individual rank-1 terms...

Waring decomposition | Hilbert function | Reshaped Kruskal criterion | Tensor rank decomposition | Effective identifiability | MATHEMATICS, APPLIED | SYMMETRIC TENSORS | re-shaped Kruskal criterion | SEGRE VARIETIES | UNIQUENESS | CANONICAL POLYADIC DECOMPOSITION | 3-WAY ARRAYS | MATRICES | tensor rank decomposition | SECANT VARIETIES | effective identifiability | POINTS | LOW-RANK | Mathematics - Algebraic Geometry

Waring decomposition | Hilbert function | Reshaped Kruskal criterion | Tensor rank decomposition | Effective identifiability | MATHEMATICS, APPLIED | SYMMETRIC TENSORS | re-shaped Kruskal criterion | SEGRE VARIETIES | UNIQUENESS | CANONICAL POLYADIC DECOMPOSITION | 3-WAY ARRAYS | MATRICES | tensor rank decomposition | SECANT VARIETIES | effective identifiability | POINTS | LOW-RANK | Mathematics - Algebraic Geometry

Journal Article

Automatica, ISSN 0005-1098, 07/2013, Volume 49, Issue 7, pp. 2192 - 2198

This paper concerns the design of a nonlinear observer through a transformation of a nonlinear system into an observer form that supports a high gain observer....

Epidemic model | Extended normal form | Nonlinear system | Observer | TRANSFORMATION | DESIGN | ENGINEERING, ELECTRICAL & ELECTRONIC | CANONICAL FORM | NONLINEAR OBSERVERS | DYNAMICS | SYSTEMS | OBSERVER ERROR LINEARIZATION | AUTOMATION & CONTROL SYSTEMS | Nonlinear dynamics | Design engineering | Observers | Nonlinearity | Mathematical models | Transformations | High gain | Dynamical systems | Computer Science | Automatic Control Engineering

Epidemic model | Extended normal form | Nonlinear system | Observer | TRANSFORMATION | DESIGN | ENGINEERING, ELECTRICAL & ELECTRONIC | CANONICAL FORM | NONLINEAR OBSERVERS | DYNAMICS | SYSTEMS | OBSERVER ERROR LINEARIZATION | AUTOMATION & CONTROL SYSTEMS | Nonlinear dynamics | Design engineering | Observers | Nonlinearity | Mathematical models | Transformations | High gain | Dynamical systems | Computer Science | Automatic Control Engineering

Journal Article

International Journal of Computer Vision, ISSN 0920-5691, 3/2013, Volume 102, Issue 1, pp. 221 - 238

Measuring the dissimilarity between non-rigid objects is a challenging problem in 3D shape retrieval. One potential solution is to construct the models’ 3D...

Non-rigid | Pattern Recognition | Computer Science | Computer Imaging, Vision, Pattern Recognition and Graphics | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | 3D shape retrieval | Multidimensional scaling | Canonical form | RECOGNITION | RETRIEVAL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Analysis | Algorithms | Retrieval | Canonical forms | Nonlinearity | Mathematical models | Boundaries | Optimization | Three dimensional

Non-rigid | Pattern Recognition | Computer Science | Computer Imaging, Vision, Pattern Recognition and Graphics | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | 3D shape retrieval | Multidimensional scaling | Canonical form | RECOGNITION | RETRIEVAL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Analysis | Algorithms | Retrieval | Canonical forms | Nonlinearity | Mathematical models | Boundaries | Optimization | Three dimensional

Journal Article