1997, 1, Algebra, logic, and applications, ISBN 9056990764, Volume 7, xii, 486

Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms...

Bilinear forms | Forms, Quadratic | Number Theory

Bilinear forms | Forms, Quadratic | Number Theory

Book

2.
Quadratics

1996, CRC Press series on discrete mathematics and its applications, ISBN 0849339839, xx, 387

Book

Journal of High Energy Physics, ISSN 1126-6708, 3/2017, Volume 2017, Issue 3, pp. 1 - 17

The light-cone Hamiltonians describing both pure (
N
$$ \mathcal{N} $$
= 0) Yang-Mills and
N
$$ \mathcal{N} $$
= 4 super Yang-Mills may be expressed as quadratic forms...

Superspaces | Gauge Symmetry | Supergravity Models | Classical Theories of Gravity | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | YANG-MILLS THEORY | TERMS | PHYSICS, PARTICLES & FIELDS | Sciences education | Analysis | Gravity | Texts | Gravitation | Quadratic forms | Supergravity | Physics - High Energy Physics - Theory | General Relativity and Quantum Cosmology | High Energy Physics | Nuclear and High Energy Physics | Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory | Fysik | Physical Sciences

Superspaces | Gauge Symmetry | Supergravity Models | Classical Theories of Gravity | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | YANG-MILLS THEORY | TERMS | PHYSICS, PARTICLES & FIELDS | Sciences education | Analysis | Gravity | Texts | Gravitation | Quadratic forms | Supergravity | Physics - High Energy Physics - Theory | General Relativity and Quantum Cosmology | High Energy Physics | Nuclear and High Energy Physics | Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory | Fysik | Physical Sciences

Journal Article

2008, Graduate studies in mathematics, ISBN 9780821844656, Volume 90, xiii, 255

Book

Acta Applicandae Mathematicae, ISSN 0167-8019, 2/2019, Volume 159, Issue 1, pp. 29 - 74

The paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space...

Computational Mathematics and Numerical Analysis | Newton-Kantorovich method | 52Axx | Stable solution | 52Bxx | Probability Theory and Stochastic Processes | 47H60 | Mathematics | Number of solutions | Rank of elliptic operator | Calculus of Variations and Optimal Control; Optimization | Quadratic operator | Elliptic operator | 47J05 | Applications of Mathematics | Partial Differential Equations | MATRIX | MATHEMATICS, APPLIED | CONVEXITY | THEOREM | CONJECTURES | OPEN QUESTIONS | INTERSECTIONS | FORMS | REGULAR ZEROS | MAPS | OPTIMIZATION | Euclidean geometry | Euclidean space | Elliptic functions | Mathematical analysis | Kantorovich method

Computational Mathematics and Numerical Analysis | Newton-Kantorovich method | 52Axx | Stable solution | 52Bxx | Probability Theory and Stochastic Processes | 47H60 | Mathematics | Number of solutions | Rank of elliptic operator | Calculus of Variations and Optimal Control; Optimization | Quadratic operator | Elliptic operator | 47J05 | Applications of Mathematics | Partial Differential Equations | MATRIX | MATHEMATICS, APPLIED | CONVEXITY | THEOREM | CONJECTURES | OPEN QUESTIONS | INTERSECTIONS | FORMS | REGULAR ZEROS | MAPS | OPTIMIZATION | Euclidean geometry | Euclidean space | Elliptic functions | Mathematical analysis | Kantorovich method

Journal Article

Mathematics of operations research, ISSN 0364-765X, 5/2018, Volume 43, Issue 2, pp. 651 - 674

In a Standard Quadratic Optimization Problem (StQP), a possibly indefinite quadratic form...

local solutions | selection stability | quadratic optimization | global optimization | replicator dynamics | evolutionary stability | Global optimization | Local solutions | Replicator dynamics | Quadratic optimization | Evolutionary stability | Selection stability | MATHEMATICS, APPLIED | NUMBER | GAMES | CP-RANK | PATTERNS | ESSS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EQUILIBRIA | DYNAMICS | STABLE STRATEGIES | Usage | Mathematical models | Research | Mathematical research | Mathematical optimization | Quadratic functions

local solutions | selection stability | quadratic optimization | global optimization | replicator dynamics | evolutionary stability | Global optimization | Local solutions | Replicator dynamics | Quadratic optimization | Evolutionary stability | Selection stability | MATHEMATICS, APPLIED | NUMBER | GAMES | CP-RANK | PATTERNS | ESSS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EQUILIBRIA | DYNAMICS | STABLE STRATEGIES | Usage | Mathematical models | Research | Mathematical research | Mathematical optimization | Quadratic functions

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 11/2017, Volume 70, Issue 11, pp. 2164 - 2190

Given a d × d quasiconvex quadratic form, d ≥ 3, we prove that if the determinant of its acoustic tensor is an irreducible extremal polynomial that is not...

Journal Article

The journal of high energy physics, ISSN 1126-6708, 09/2015, Volume 2015, Issue 9, pp. 1 - 63

... and then using a different basis coming from the free field representation in which the OPE takes a simpler quadratic form...

Field Theories in Lower Dimensions | Conformal and W Symmetry | Integrable Hierarchies | Higher Spin Symmetry | Operators (mathematics) | Commutation | Quadratic forms | Mathematical analysis | Exact solutions | Consistency | Texts | Representations

Field Theories in Lower Dimensions | Conformal and W Symmetry | Integrable Hierarchies | Higher Spin Symmetry | Operators (mathematics) | Commutation | Quadratic forms | Mathematical analysis | Exact solutions | Consistency | Texts | Representations

Journal Article

BERNOULLI, ISSN 1350-7265, 08/2019, Volume 25, Issue 3, pp. 1603 - 1639

In this paper, we provide a proof for the Hanson-Wright inequalities for sparse quadratic forms in subgaussian random variables...

STATISTICS & PROBABILITY | subgaussian concentration | TAIL PROBABILITIES | Hanson-Wright inequality | sparse quadratic forms

STATISTICS & PROBABILITY | subgaussian concentration | TAIL PROBABILITIES | Hanson-Wright inequality | sparse quadratic forms

Journal Article

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 2019, Volume 150, Issue 2, pp. 695 - 720

Let K be an imaginary quadratic field different from $\open{Q}(\sqrt {-1})$ and $\open{Q}(\sqrt {-3})$. For a positive integer N, let K-N be the ray class field of K modulo...

class groups | class field theory | complex multiplication | Binary quadratic forms | MATHEMATICS | MATHEMATICS, APPLIED | Dirichlet problem | Algorithms | Fields (mathematics) | Quadratic forms | Number theory | Subgroups

class groups | class field theory | complex multiplication | Binary quadratic forms | MATHEMATICS | MATHEMATICS, APPLIED | Dirichlet problem | Algorithms | Fields (mathematics) | Quadratic forms | Number theory | Subgroups

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2019, Volume 567, pp. 202 - 262

.... For an arbitrary such list L, we give easily verifiable necessary and sufficient conditions for L to be the list of elementary divisors and minimal indices of some T-palindromic quadratic matrix...

Quadratic realizability | Elementary divisors | Minimal indices | Quadratifications | Quasi-canonical form | T-palindromic | Matrix polynomials | Inverse problem | MATHEMATICS, APPLIED | EIGENVALUE PROBLEMS | ROBUST SOFTWARE | ARBITRARY PENCIL-A | GENERALIZED SCHUR DECOMPOSITION | LAMBDA-B | LINEARIZATIONS | MINIMAL BASES | VECTOR-SPACES | MATHEMATICS | RECOVERY | ERROR-BOUNDS | Geometric transformation | Integers | Construction | Polynomials | Realizability

Quadratic realizability | Elementary divisors | Minimal indices | Quadratifications | Quasi-canonical form | T-palindromic | Matrix polynomials | Inverse problem | MATHEMATICS, APPLIED | EIGENVALUE PROBLEMS | ROBUST SOFTWARE | ARBITRARY PENCIL-A | GENERALIZED SCHUR DECOMPOSITION | LAMBDA-B | LINEARIZATIONS | MINIMAL BASES | VECTOR-SPACES | MATHEMATICS | RECOVERY | ERROR-BOUNDS | Geometric transformation | Integers | Construction | Polynomials | Realizability

Journal Article

1997, Carus mathematical monographs, ISBN 9780883850305, Volume no. 26, xiii, 152

Book

The Ramanujan Journal, ISSN 1382-4090, 1/2018, Volume 45, Issue 1, pp. 21 - 32

A (positive definite integral) quadratic form is called diagonally 2-universal if it represents all positive definite integral binary diagonal quadratic forms...

Fourier Analysis | Primary 11E12 | 2-universal quadratic forms | Functions of a Complex Variable | Representations of binary quadratic forms | Field Theory and Polynomials | Mathematics | Diagonal quadratic forms | 11E20 | Number Theory | Combinatorics | MATHEMATICS | ODD POSITIVE INTEGERS | UNIVERSAL FORMS | RANK | Research institutes

Fourier Analysis | Primary 11E12 | 2-universal quadratic forms | Functions of a Complex Variable | Representations of binary quadratic forms | Field Theory and Polynomials | Mathematics | Diagonal quadratic forms | 11E20 | Number Theory | Combinatorics | MATHEMATICS | ODD POSITIVE INTEGERS | UNIVERSAL FORMS | RANK | Research institutes

Journal Article

PACIFIC JOURNAL OF MATHEMATICS, ISSN 0030-8730, 06/2019, Volume 300, Issue 2, pp. 375 - 404

We develop a version of the J-invariant for hermitian forms over quadratic extensions using a similar method to Alexander Vishik's approach using quadratic forms...

grassmannians | Chow groups and motives | MATHEMATICS | Hermitian and quadratic forms

grassmannians | Chow groups and motives | MATHEMATICS | Hermitian and quadratic forms

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 8/2015, Volume 2015, Issue 8, pp. 1 - 13

We show that the Hamiltonian of (
N=1
$$ \mathcal{N}=1 $$, d = 10) super Yang-Mills can be expressed as a quadratic form in a very similar manner to that of the (
N=4
$$ \mathcal{N}=4 $$, d = 4) theory...

Supersymmetric gauge theory | Extended Supersymmetry | Quantum Physics | Field Theories in Higher Dimensions | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | CUBIC INTERACTION TERMS | PHYSICS, PARTICLES & FIELDS | Yang-Mills theory | Quadratic forms | Texts | Physics - High Energy Physics - Theory | Fysik | Physical Sciences

Supersymmetric gauge theory | Extended Supersymmetry | Quantum Physics | Field Theories in Higher Dimensions | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | CUBIC INTERACTION TERMS | PHYSICS, PARTICLES & FIELDS | Yang-Mills theory | Quadratic forms | Texts | Physics - High Energy Physics - Theory | Fysik | Physical Sciences

Journal Article

Nonlinear analysis, ISSN 0362-546X, 2020, Volume 193, p. 111504

We study sequences of nonlocal quadratic forms and function spaces that are related to Markov jump processes in bounded domains with a Lipschitz boundary...

Dirichlet forms | Mosco-convergence | Sobolev spaces | Integro-differential operators | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | WEAK-CONVERGENCE | DIFFUSION | Operators (mathematics) | Sequences | Queuing theory | Function space | Quadratic forms | Convergence

Dirichlet forms | Mosco-convergence | Sobolev spaces | Integro-differential operators | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | WEAK-CONVERGENCE | DIFFUSION | Operators (mathematics) | Sequences | Queuing theory | Function space | Quadratic forms | Convergence

Journal Article

Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, 12/2017, Volume 28, Issue 6, pp. 535 - 547

...$$
F
q
with quadratic forms via a general construction and then determine the explicit complete weight enumerators of these linear codes...

11E04 | Complete weight enumerators | Minimal codeword | Theory of Computation | Linear code | Weight distribution | Quadratic form function | Computer Hardware | Computer Science | 94B05 | Artificial Intelligence (incl. Robotics) | 94A62 | Symbolic and Algebraic Manipulation | MATHEMATICS, APPLIED | CONSTANT COMPOSITION CODES | AUTHENTICATION CODES | 2-WEIGHT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSTRUCTION | 3-WEIGHT CYCLIC CODES | COMPUTER SCIENCE, THEORY & METHODS | SECRET SHARING SCHEMES | Cryptography

11E04 | Complete weight enumerators | Minimal codeword | Theory of Computation | Linear code | Weight distribution | Quadratic form function | Computer Hardware | Computer Science | 94B05 | Artificial Intelligence (incl. Robotics) | 94A62 | Symbolic and Algebraic Manipulation | MATHEMATICS, APPLIED | CONSTANT COMPOSITION CODES | AUTHENTICATION CODES | 2-WEIGHT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSTRUCTION | 3-WEIGHT CYCLIC CODES | COMPUTER SCIENCE, THEORY & METHODS | SECRET SHARING SCHEMES | Cryptography

Journal Article

Finite fields and their applications, ISSN 1071-5797, 01/2019, Volume 55, pp. 33 - 63

We propose a randomized polynomial time algorithm for computing non-trivial zeros of quadratic forms in 4 or more variables over Fq...

Quadratic forms | Function field | Polynomial time algorithm

Quadratic forms | Function field | Polynomial time algorithm

Journal Article

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