International Journal of Number Theory, ISSN 1793-0421, 02/2016, Volume 12, Issue 1, pp. 15 - 25

In this paper, we extend the Euler decomposition theorem to a much more general form of the decomposition of the product of n multiple zeta values of height one...

Multiple zeta value | Euler decomposition theorem | MATHEMATICS | SUM FORMULA

Multiple zeta value | Euler decomposition theorem | MATHEMATICS | SUM FORMULA

Journal Article

Journal of Number Theory, ISSN 0022-314X, 05/2015, Volume 150, pp. 1 - 20

The classical Euler decomposition theorem expresses a product of two Riemann zeta values in terms of double Euler sums...

Multiple zeta value | Euler decomposition theorem | MATHEMATICS

Multiple zeta value | Euler decomposition theorem | MATHEMATICS

Journal Article

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1364-5021, 11/2011, Volume 467, Issue 2135, pp. 3206 - 3221

A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler...

Conservation laws | Mathematical theorems | Euler Lagrange equation | Algebra | Difference equations | Lagrange multipliers | Differentials | Mathematical independent variables | Mathematical functions | Lagrangian function | MATHEMATICS | applied mathematics | mathematical physics | differential equations | Research articles | DECOMPOSITION ALGORITHMS | SYMMETRY | conservation laws | gauge symmetries | MULTIDISCIPLINARY SCIENCES | CONSERVATION-LAWS | DIFFERENTIAL-DIFFERENCE EQUATIONS | difference equations

Conservation laws | Mathematical theorems | Euler Lagrange equation | Algebra | Difference equations | Lagrange multipliers | Differentials | Mathematical independent variables | Mathematical functions | Lagrangian function | MATHEMATICS | applied mathematics | mathematical physics | differential equations | Research articles | DECOMPOSITION ALGORITHMS | SYMMETRY | conservation laws | gauge symmetries | MULTIDISCIPLINARY SCIENCES | CONSERVATION-LAWS | DIFFERENTIAL-DIFFERENCE EQUATIONS | difference equations

Journal Article

Journal of Symplectic Geometry, ISSN 1527-5256, 2016, Volume 14, Issue 3, pp. 737 - 766

A polytope cone decomposition expresses the characteristic function of a polytope as a sum of characteristic functions of convex cones associated to its faces...

MATHEMATICS | INTEGRAL POLYTOPES | LOCALIZATION | EQUIVARIANT COHOMOLOGY | THEOREM | EULER-MACLAURIN | FORMULAS

MATHEMATICS | INTEGRAL POLYTOPES | LOCALIZATION | EQUIVARIANT COHOMOLOGY | THEOREM | EULER-MACLAURIN | FORMULAS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 06/2017, Volume 175, pp. 200 - 222

..., α ≥2 and positive numbers x ,x ,…,x . Especially, we extend Euler decomposition theorem which expressed a product of two Riemann zeta values in terms of Euler double sums, to a more general decomposition theorem which expressed products...

Multiple zeta value | Hurwitz zeta functions | Euler decomposition theorem | MATHEMATICS | Business schools

Multiple zeta value | Hurwitz zeta functions | Euler decomposition theorem | MATHEMATICS | Business schools

Journal Article

Annales de l'Institut Henri Poincaré. Analyse non linéaire, ISSN 0294-1449, 2018, Volume 35, Issue 1, pp. 161 - 186

...–Poisson system in a cylinder supplemented with non-small boundary data. A special Helmholtz decomposition of the velocity field is introduced for 3-D axisymmetric flow with a nonzero swirl...

Transport equation | Axisymmetric | Subsonic | Swirl | Helmholtz decomposition | Elliptic system | Steady Euler–Poisson system | Singular elliptic equation | EXISTENCE THEOREM | MATHEMATICS, APPLIED | HYDRODYNAMIC MODEL | SEMICONDUCTORS | STABILITY | NOZZLE | EQUATIONS | VARIABLE END PRESSURE | Steady Euler-Poisson system | POTENTIAL FLOW | TRANSONIC SHOCK SOLUTIONS

Transport equation | Axisymmetric | Subsonic | Swirl | Helmholtz decomposition | Elliptic system | Steady Euler–Poisson system | Singular elliptic equation | EXISTENCE THEOREM | MATHEMATICS, APPLIED | HYDRODYNAMIC MODEL | SEMICONDUCTORS | STABILITY | NOZZLE | EQUATIONS | VARIABLE END PRESSURE | Steady Euler-Poisson system | POTENTIAL FLOW | TRANSONIC SHOCK SOLUTIONS

Journal Article

Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, 2017, Volume 97, Issue 7, pp. 843 - 871

In any geometrically nonlinear, isotropic and quadratic Cosserat micropolar extended continuum model formulated in the deformation gradient field F≔∇φ:Ω→ GL...

quaternions | micropolar | polar media | 74N15 | non‐symmetric stretch | polar decomposition | equality constraints | Cosserat | 74G05 | Lagrange multiplier | 15A24 | Grioli’s theorem | 74G65 | 74A35 | 22E30 | Cosserat couple modulus | 74B20 | rotations | 74A30 | non-symmetric stretch | EXISTENCE | MATHEMATICS, APPLIED | Grioli's theorem | PROPERTY | MODEL | FORMULATION | DEFORMATION | TENSION-COMPRESSION ASYMMETRY | STRESSES | ELASTICITY | MECHANICS | MINIMIZATION | CONTINUUM | Analysis | Algebra | Monte Carlo method | Shear | Deformation | Energy levels | Computer simulation | Exact solutions | Derivation | Optimization | Quaternions | Mathematical analysis | Formulas (mathematics) | Computer algebra

quaternions | micropolar | polar media | 74N15 | non‐symmetric stretch | polar decomposition | equality constraints | Cosserat | 74G05 | Lagrange multiplier | 15A24 | Grioli’s theorem | 74G65 | 74A35 | 22E30 | Cosserat couple modulus | 74B20 | rotations | 74A30 | non-symmetric stretch | EXISTENCE | MATHEMATICS, APPLIED | Grioli's theorem | PROPERTY | MODEL | FORMULATION | DEFORMATION | TENSION-COMPRESSION ASYMMETRY | STRESSES | ELASTICITY | MECHANICS | MINIMIZATION | CONTINUUM | Analysis | Algebra | Monte Carlo method | Shear | Deformation | Energy levels | Computer simulation | Exact solutions | Derivation | Optimization | Quaternions | Mathematical analysis | Formulas (mathematics) | Computer algebra

Journal Article

Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 11/2012, Volume 109, Issue 45, pp. 18324 - 18326

... observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on ℍn whenever n ≥ 3...

Harmonic functions | Riemann manifold | Navier Stokes equation | Applied mathematics | Geometric planes | Vector fields | Differentials | Dirichlet problem | Hydrodynamics | Euler equations | Dodziuk's theorem | Steady flows | Ill-posedness | Harmonic forms | INFINITY | MULTIDISCIPLINARY SCIENCES | harmonic forms | ill-posedness | MANIFOLDS | steady flows | Hamiltonian systems | Hydrofoil boats | Research | Navier-Stokes equations | Decomposition (Mathematics) | Physical Sciences

Harmonic functions | Riemann manifold | Navier Stokes equation | Applied mathematics | Geometric planes | Vector fields | Differentials | Dirichlet problem | Hydrodynamics | Euler equations | Dodziuk's theorem | Steady flows | Ill-posedness | Harmonic forms | INFINITY | MULTIDISCIPLINARY SCIENCES | harmonic forms | ill-posedness | MANIFOLDS | steady flows | Hamiltonian systems | Hydrofoil boats | Research | Navier-Stokes equations | Decomposition (Mathematics) | Physical Sciences

Journal Article

Journal of Number Theory, ISSN 0022-314X, 08/2013, Volume 133, Issue 8, pp. 2475 - 2495

The classical Euler decomposition theorem expressed a product of two Riemann zeta values in terms of double Euler sums...

Euler sums | Multiple zeta values | Euler decomposition theorem | Shuffle product formula | Drinfeld integrals | MATHEMATICS | VALUES | SUM FORMULA

Euler sums | Multiple zeta values | Euler decomposition theorem | Shuffle product formula | Drinfeld integrals | MATHEMATICS | VALUES | SUM FORMULA

Journal Article

Journal of combinatorics and number theory, ISSN 1942-5600, 05/2015, Volume 7, Issue 2, p. 111

... ... multiple zeta values of weight m+n. The well-known Euler decomposition theorem can be obtained from the shuffle product of two Riemann zeta values...

Eulers equations | Mathematics | Combinatorics | Number theory

Eulers equations | Mathematics | Combinatorics | Number theory

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2012, Volume 25, Issue 3, pp. 486 - 489

In an attempt to present a refinement of Faulhaber’s theorem concerning sums of powers of natural numbers, the authors investigate and derive all the possible decompositions of the polynomial S a , b k ( x...

Bernoulli polynomials and Bernoulli numbers | Decomposition | Laguerre polynomials | Ring of polynomials | Sums of powers of natural numbers | Faulhaber’s polynomials | Faulhaber's polynomials | MATHEMATICS, APPLIED | EULER POLYNOMIALS | BERNOULLI

Bernoulli polynomials and Bernoulli numbers | Decomposition | Laguerre polynomials | Ring of polynomials | Sums of powers of natural numbers | Faulhaber’s polynomials | Faulhaber's polynomials | MATHEMATICS, APPLIED | EULER POLYNOMIALS | BERNOULLI

Journal Article

Mathematical methods in the applied sciences, ISSN 1099-1476, 2008, Volume 31, Issue 9, pp. 1113 - 1130

...}$, and set up its blow‐up criterion. The tool we mainly use is Littlewood–Paley decomposition, by which we obtain a Beale–Kato–Majda‐type blow...

the magneto‐micropolar equations | blow‐up | Littlewood–Paley decomposition | Besov space | Littlewood-Paley decomposition | Blow-up | The magneto-micropolar equations | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | REGULARITY | the magneto-micropolar equations | blow-up | 3D MHD EQUATIONS | WEAK SOLUTIONS | EULER | UNIQUENESS | Mathematics - Analysis of PDEs

the magneto‐micropolar equations | blow‐up | Littlewood–Paley decomposition | Besov space | Littlewood-Paley decomposition | Blow-up | The magneto-micropolar equations | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | REGULARITY | the magneto-micropolar equations | blow-up | 3D MHD EQUATIONS | WEAK SOLUTIONS | EULER | UNIQUENESS | Mathematics - Analysis of PDEs

Journal Article

Milan Journal of Mathematics, ISSN 1424-9286, 6/2015, Volume 83, Issue 1, pp. 21 - 45

... qu - j v v T j v , : w j : F , , ( ) := k H ( ( ) ) - u ﬁ A ﬁ v u u qu w w : W w y b : ? O , , ( )= ( 1) ( ) Eu ( ), W w y b : ? Vol.83 (2015) Support Theorems...

Primary 14D05 | Stratification theory | Analysis | Mathematics, general | Mathematics | local Euler Obstruction | Intersection Cohomology | Secondary 14F45 | HODGE | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | Intersection cohomology | DECOMPOSITION THEOREM

Primary 14D05 | Stratification theory | Analysis | Mathematics, general | Mathematics | local Euler Obstruction | Intersection Cohomology | Secondary 14F45 | HODGE | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | Intersection cohomology | DECOMPOSITION THEOREM

Journal Article

14.
Full Text
An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

Communications in Mathematical Physics, ISSN 0010-3616, 4/2018, Volume 359, Issue 2, pp. 733 - 763

... An Onsager Singularity Theorem for T urbulent Solutions of Compressible Euler Equations Theodore D. Drivas 1,3 , Gregory L. Eyink 1,2 1 Department of Applied Mathematics...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | DISSIPATION | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | ENERGY-CONSERVATION | CONJECTURE | Thermodynamics | Astronomy | Force and energy

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | DISSIPATION | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | ENERGY-CONSERVATION | CONJECTURE | Thermodynamics | Astronomy | Force and energy

Journal Article

Economic theory, ISSN 0938-2259, 11/2013, Volume 54, Issue 3, pp. 623 - 674

Using order-theoretic methods, we derive sufficient conditions for the existence, characterization, and computation of minimal state space recursive...

Economic models | Mathematical monotonicity | Economic theory | Mathematical lattices | Uniqueness | Partially ordered sets | Mathematical functions | Stochastic models | Euler equations | Capital income | Order-theoretic fixed point theory | D62 | E20 | Economics general | Recursive equilibrium | Monotone Comparative statics | Economic Theory | Game Theory, Economics, Social and Behav. Sciences | Economics / Management Science | Stationary Markov equilibrium | Equilibrium computation | EXISTENCE | OVERLAPPING-GENERATIONS ECONOMIES | NONEXISTENCE | DYNAMIC ECONOMIES | UNIQUENESS | DISTRIBUTIONS | FIXED-POINT THEOREMS | GROWTH-MODELS | STATIONARY MARKOV EQUILIBRIA | UNCERTAINTY | ECONOMICS | Learning models (Stochastic processes) | Usage | Equilibrium (Economics) | Mathematical models | Labor market | Analysis | Models | Game theory | Decomposition (Mathematics) | Equilibrium | Markov analysis

Economic models | Mathematical monotonicity | Economic theory | Mathematical lattices | Uniqueness | Partially ordered sets | Mathematical functions | Stochastic models | Euler equations | Capital income | Order-theoretic fixed point theory | D62 | E20 | Economics general | Recursive equilibrium | Monotone Comparative statics | Economic Theory | Game Theory, Economics, Social and Behav. Sciences | Economics / Management Science | Stationary Markov equilibrium | Equilibrium computation | EXISTENCE | OVERLAPPING-GENERATIONS ECONOMIES | NONEXISTENCE | DYNAMIC ECONOMIES | UNIQUENESS | DISTRIBUTIONS | FIXED-POINT THEOREMS | GROWTH-MODELS | STATIONARY MARKOV EQUILIBRIA | UNCERTAINTY | ECONOMICS | Learning models (Stochastic processes) | Usage | Equilibrium (Economics) | Mathematical models | Labor market | Analysis | Models | Game theory | Decomposition (Mathematics) | Equilibrium | Markov analysis

Journal Article

Taiwanese journal of mathematics, ISSN 1027-5487, 2/2016, Volume 20, Issue 1, pp. 13 - 24

The classical Euler decomposition theorem expressed a product of two Riemann zeta values...

Integers | Mathematical theorems | Value theorems | Multiple zeta values | Shuffle product | Euler decomposition theorem | MATHEMATICS | SUM FORMULAS

Integers | Mathematical theorems | Value theorems | Multiple zeta values | Shuffle product | Euler decomposition theorem | MATHEMATICS | SUM FORMULAS

Journal Article

Annals of Applied Probability, ISSN 1050-5164, 04/2018, Volume 28, Issue 2, pp. 912 - 940

..., we establish a limit theorem for the discretization errors in simulation of supremum and its time, which extends the result in [Ann. Appl. Probab. 5 (1995) 875-896] for a linear Brownian motion. Additionally, complete characterization of the domains of attraction when zooming in on a Levy process is provided.

Small-time behaviour | Discretization error | High frequency statistics | Functional limit theorem | Invariance principle | Domains of attraction | Conditioned to stay positive | Euler scheme | Scaling limits | Mixing convergence | Self-similarity | mixing convergence | WIENER-HOPF FACTORIZATION | TIMES | APPROXIMATIONS | invariance principle | SMALL JUMPS | STATISTICS & PROBABILITY | small-time behaviour | self-similarity | SIMULATION | high frequency statistics | discretization error | PATH DECOMPOSITIONS | scaling limits | RANDOM-WALKS | INVARIANCE-PRINCIPLES | DISCRETE | PASSAGE | domains of attraction | functional limit theorem

Small-time behaviour | Discretization error | High frequency statistics | Functional limit theorem | Invariance principle | Domains of attraction | Conditioned to stay positive | Euler scheme | Scaling limits | Mixing convergence | Self-similarity | mixing convergence | WIENER-HOPF FACTORIZATION | TIMES | APPROXIMATIONS | invariance principle | SMALL JUMPS | STATISTICS & PROBABILITY | small-time behaviour | self-similarity | SIMULATION | high frequency statistics | discretization error | PATH DECOMPOSITIONS | scaling limits | RANDOM-WALKS | INVARIANCE-PRINCIPLES | DISCRETE | PASSAGE | domains of attraction | functional limit theorem

Journal Article

Annals of Probability, ISSN 0091-1798, 11/2018, Volume 46, Issue 6, pp. 3188 - 3228

We establish here a quantitative central limit theorem (in Wasserstein distance) for the Euler-Poincare characteristic of excursion sets of random spherical eigenfunctions in dimension 2...

Gaussian kinematic formula | Berry's cancellation phenomenon | Wiener-chaos expansion | Spherical harmonics | Quantitative central limit theorem | Euler-Poincaré characteristic | NUMBER | quantitative central limit theorem | Euler-Poincare characteristic | STATISTICS & PROBABILITY | HARMONICS | ARITHMETIC RANDOM WAVES | spherical harmonics | GAUSSIAN RANDOM-FIELDS | EXCURSION PROBABILITY | FLUCTUATIONS

Gaussian kinematic formula | Berry's cancellation phenomenon | Wiener-chaos expansion | Spherical harmonics | Quantitative central limit theorem | Euler-Poincaré characteristic | NUMBER | quantitative central limit theorem | Euler-Poincare characteristic | STATISTICS & PROBABILITY | HARMONICS | ARITHMETIC RANDOM WAVES | spherical harmonics | GAUSSIAN RANDOM-FIELDS | EXCURSION PROBABILITY | FLUCTUATIONS

Journal Article

19.
Full Text
Explicit double shuffle relations and a generalization of Eulerʼs decomposition formula

Journal of Algebra, ISSN 0021-8693, 04/2013, Volume 380, pp. 46 - 77

.... As an application, we generalize the well-known decomposition formula of Euler that expresses the product of two Riemann zeta values as a sum of double zeta values to a formula that expresses...

Multiple zeta values | Double shuffle relation | Eulerʼs decomposition formula | Multiple polylogarithm values | Euler's decomposition formula | MATHEMATICS | MULTIPLE ZETA-VALUES | ALGEBRAS | FEYNMAN DIAGRAMS | MOTIVES | RENORMALIZATION

Multiple zeta values | Double shuffle relation | Eulerʼs decomposition formula | Multiple polylogarithm values | Euler's decomposition formula | MATHEMATICS | MULTIPLE ZETA-VALUES | ALGEBRAS | FEYNMAN DIAGRAMS | MOTIVES | RENORMALIZATION

Journal Article

Mathematical Sciences, ISSN 2008-1359, 12/2015, Volume 9, Issue 4, pp. 215 - 223

.... The first application is a hypergeometric-type decomposition formula for elementary special functions and the second one is a generalization of the well-known Euler identity $$e^{i\,x} = \cos x + i\,\sin x$$ e i x = cos x...

Hypergeometric functions | Classical hypergeometric orthogonal polynomials | Classical summation theorems | 33C15 | Euler identity | 33C20 | Mathematics | Applications of Mathematics | Hyperbolic functions | 33C05 | Functions (mathematics) | Theorems | Mathematical analysis | Texts | Polynomials | Decomposition

Hypergeometric functions | Classical hypergeometric orthogonal polynomials | Classical summation theorems | 33C15 | Euler identity | 33C20 | Mathematics | Applications of Mathematics | Hyperbolic functions | 33C05 | Functions (mathematics) | Theorems | Mathematical analysis | Texts | Polynomials | Decomposition

Journal Article

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