Annals of Mathematics, ISSN 0003-486X, 3/2011, Volume 173, Issue 2, pp. 907 - 945

We give in explicit form the principal kinematic formula for the action of the affine unitary group on ℂ n , together with a straightforward algebraic method...

Geometry | Algebra | Mathematical theorems | Mathematical integrals | Kinematics | Fourier transformations | Vector spaces | Curvature | Symmetry | MATHEMATICS | MULTIPLICATIVE STRUCTURE | MANIFOLDS | SPACES | HARD LEFSCHETZ THEOREM | VALUATIONS

Geometry | Algebra | Mathematical theorems | Mathematical integrals | Kinematics | Fourier transformations | Vector spaces | Curvature | Symmetry | MATHEMATICS | MULTIPLICATIVE STRUCTURE | MANIFOLDS | SPACES | HARD LEFSCHETZ THEOREM | VALUATIONS

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2019, Volume 52, Issue 50, p. 50LT01

Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields...

multiplicative Langevin equations | PHYSICS, MULTIDISCIPLINARY | QUANTUM | EQUATIONS | FORMULATION | PHYSICS, MATHEMATICAL | path integrals | functional calculus | diffusion processes | FLUCTUATIONS | DYNAMICS | SYSTEMS | ONSAGER-MACHLUP FUNCTION | TRANSFORMATIONS | RENORMALIZATION | Condensed Matter | Statistical Mechanics | Mathematical Physics | Physics

multiplicative Langevin equations | PHYSICS, MULTIDISCIPLINARY | QUANTUM | EQUATIONS | FORMULATION | PHYSICS, MATHEMATICAL | path integrals | functional calculus | diffusion processes | FLUCTUATIONS | DYNAMICS | SYSTEMS | ONSAGER-MACHLUP FUNCTION | TRANSFORMATIONS | RENORMALIZATION | Condensed Matter | Statistical Mechanics | Mathematical Physics | Physics

Journal Article

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

We show how Alesker’s theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space...

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

GEOMETRY & TOPOLOGY, ISSN 1465-3060, 2019, Volume 23, Issue 6, pp. 3041 - 3110

Generalizing Weyl's tube formula and building on Chem's work, Alesker reinterpreted the Lipschitz-Killing curvature integrals as a family of valuations...

SPACE | MATHEMATICS | CROFTON FORMULAS | PRODUCT | VOLUME | CLASSIFICATION | MULTIPLICATIVE STRUCTURE | MANIFOLDS | INVARIANT VALUATIONS

SPACE | MATHEMATICS | CROFTON FORMULAS | PRODUCT | VOLUME | CLASSIFICATION | MULTIPLICATIVE STRUCTURE | MANIFOLDS | INVARIANT VALUATIONS

Journal Article

Journal of quantitative spectroscopy & radiative transfer, ISSN 0022-4073, 2019, Volume 224, pp. 383 - 395

....•Strong discrete operators require fewer matvecs than their weak counterparts. We consider the simulation of electromagnetic scattering by single and multiple isotropic homogeneous dielectric particles using boundary integral equations...

Ice crystals | Electromagnetic scattering | Boundary element method | Calderón preconditioning | TIME-DOMAIN METHOD | DISCRETE-DIPOLE APPROXIMATION | T-MATRIX | ELEMENT METHOD | LIGHT-SCATTERING | IMPLEMENTATION | MULTIPLICATIVE PRECONDITIONER | SPECTROSCOPY | Calderon preconditioning | OPTICS | MODELING DIFFRACTION

Ice crystals | Electromagnetic scattering | Boundary element method | Calderón preconditioning | TIME-DOMAIN METHOD | DISCRETE-DIPOLE APPROXIMATION | T-MATRIX | ELEMENT METHOD | LIGHT-SCATTERING | IMPLEMENTATION | MULTIPLICATIVE PRECONDITIONER | SPECTROSCOPY | Calderon preconditioning | OPTICS | MODELING DIFFRACTION

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2014, Volume 263, pp. 1 - 44

The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit...

Valuation | Area measure | Kinematic formula | THEOREM | PATTERNS | POLYTOPES | CONVEX-SETS | FORMS | MATHEMATICS | MULTIPLICATIVE STRUCTURE | MANIFOLDS | TRANSLATION-INVARIANT VALUATIONS | MINKOWSKI VALUATIONS | Algebra | Algorithms

Valuation | Area measure | Kinematic formula | THEOREM | PATTERNS | POLYTOPES | CONVEX-SETS | FORMS | MATHEMATICS | MULTIPLICATIVE STRUCTURE | MANIFOLDS | TRANSLATION-INVARIANT VALUATIONS | MINKOWSKI VALUATIONS | Algebra | Algorithms

Journal Article

Progress in Electromagnetics Research, ISSN 1070-4698, 2014, Volume 149, pp. 15 - 44

.... Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems...

PHYSICS, APPLIED | COMPUTATIONAL ELECTROMAGNETICS | AUGMENTED ELECTRIC-FIELD | FAST-MULTIPOLE ALGORITHM | NUMERICAL EVALUATION | TELECOMMUNICATIONS | GENERALIZED-METHOD | ENGINEERING, ELECTRICAL & ELECTRONIC | CALDERON MULTIPLICATIVE PRECONDITIONER | MIXED DISCRETIZATION | BOUNDARY-ELEMENT METHODS | SENSITIVITY-ANALYSIS | ELECTROMAGNETIC SCATTERING

PHYSICS, APPLIED | COMPUTATIONAL ELECTROMAGNETICS | AUGMENTED ELECTRIC-FIELD | FAST-MULTIPOLE ALGORITHM | NUMERICAL EVALUATION | TELECOMMUNICATIONS | GENERALIZED-METHOD | ENGINEERING, ELECTRICAL & ELECTRONIC | CALDERON MULTIPLICATIVE PRECONDITIONER | MIXED DISCRETIZATION | BOUNDARY-ELEMENT METHODS | SENSITIVITY-ANALYSIS | ELECTROMAGNETIC SCATTERING

Journal Article

Physical review. E, Statistical, nonlinear, and soft matter physics, ISSN 1550-2376, 2007, Volume 76, Issue 1, p. 011123

The friction coefficient of a particle can depend on its position, as it does when the particle is near a wall. We formulate the dynamics of particles with...

BROWNIAN-MOTION | MULTIPLICATIVE NOISE | PARTICLES | FLUID | PHYSICS, FLUIDS & PLASMAS | STATISTICAL DYNAMICS | COLLOIDAL SPHERES | EQUATIONS | SYSTEMS | WALKER | PHYSICS, MATHEMATICAL

BROWNIAN-MOTION | MULTIPLICATIVE NOISE | PARTICLES | FLUID | PHYSICS, FLUIDS & PLASMAS | STATISTICAL DYNAMICS | COLLOIDAL SPHERES | EQUATIONS | SYSTEMS | WALKER | PHYSICS, MATHEMATICAL

Journal Article

IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, 04/2014, Volume 62, Issue 4, pp. 2022 - 2030

...) objects embedded in a layered medium. The electric field integral equation (EFIE) is formulated with the kernel of layered medium Green's function to account for the effects from the multilayered background...

Calderón preconditioner | layered medium Green's function | electric field integral equation | surface integral equations | Scattering | Nonhomogeneous media | Vectors | Electromagnetics | Integral equations | numerical analysis | Calderón projector | method of moments | Green's function methods | Kernel | LINEAR-SYSTEMS | ARBITRARY SHAPE | FAST-MULTIPOLE ALGORITHM | OBJECTS | TELECOMMUNICATIONS | FORMULATION | RADIATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Calderon preconditioner | MULTIPLICATIVE PRECONDITIONER | Calderon projector | FREQUENCY PROBLEMS | ELECTROMAGNETIC SCATTERING | EFIE | Finite element method | Usage | Numerical analysis | Kernel functions | Innovations | Electric fields | Antennas (Electronics) | Kernels | Projectors | Green's functions | Discretization | Density | Antennas

Calderón preconditioner | layered medium Green's function | electric field integral equation | surface integral equations | Scattering | Nonhomogeneous media | Vectors | Electromagnetics | Integral equations | numerical analysis | Calderón projector | method of moments | Green's function methods | Kernel | LINEAR-SYSTEMS | ARBITRARY SHAPE | FAST-MULTIPOLE ALGORITHM | OBJECTS | TELECOMMUNICATIONS | FORMULATION | RADIATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Calderon preconditioner | MULTIPLICATIVE PRECONDITIONER | Calderon projector | FREQUENCY PROBLEMS | ELECTROMAGNETIC SCATTERING | EFIE | Finite element method | Usage | Numerical analysis | Kernel functions | Innovations | Electric fields | Antennas (Electronics) | Kernels | Projectors | Green's functions | Discretization | Density | Antennas

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2013, Volume 232, Issue 1, pp. 36 - 56

We construct a finite subgroup of Brauer–Manin obstruction for detecting the existence of integral points on integral models of homogeneous spaces of linear algebraic groups of multiplicative type...

Strong approximation | Linear algebraic group of multiplicative type | Integral point | Galois cohomology | Brauer–Manin obstruction | Sum of two squares | Brauer-Manin obstruction | MATHEMATICS | QUADRATIC FIELDS | SQUARES

Strong approximation | Linear algebraic group of multiplicative type | Integral point | Galois cohomology | Brauer–Manin obstruction | Sum of two squares | Brauer-Manin obstruction | MATHEMATICS | QUADRATIC FIELDS | SQUARES

Journal Article

Nonlinearity, ISSN 0951-7715, 01/2016, Volume 29, Issue 2, pp. 426 - 464

.... For application, integral moments, covariance structure, multiscaling spectrum, and asymptotics associated with the exponential functional are computed in closed form using the known meromorphic...

Riemann zeroes | Selberg integral | gaussian free field | infinite divisibility | multiplicative chaos | multifractal stochastic measure | double gamma function | MATRIX | MATHEMATICS, APPLIED | STATISTICS | EQUATIONS | FORMULA | PHYSICS, MATHEMATICAL | MULTIFRACTAL RANDOM-WALKS | ZETA-FUNCTION | PRODUCTS | FLUCTUATIONS | CONVERGENCE | Covariance | Integrals | Asymptotic properties | Mathematical analysis | Transforms | Exact solutions | Nonlinearity | Statistics

Riemann zeroes | Selberg integral | gaussian free field | infinite divisibility | multiplicative chaos | multifractal stochastic measure | double gamma function | MATRIX | MATHEMATICS, APPLIED | STATISTICS | EQUATIONS | FORMULA | PHYSICS, MATHEMATICAL | MULTIFRACTAL RANDOM-WALKS | ZETA-FUNCTION | PRODUCTS | FLUCTUATIONS | CONVERGENCE | Covariance | Integrals | Asymptotic properties | Mathematical analysis | Transforms | Exact solutions | Nonlinearity | Statistics

Journal Article

Transactions of the American Mathematical Society, ISSN 1088-6850, 2016, Volume 369, Issue 3, pp. 1935 - 2002

For Holder continuous random field W(t, x) and stochastic process phi(t), we define nonlinear integral integral(b)(a) W(dt, phi...

Nonlinear Young integral | Transport equation | Multiplicative noise | Feynman-Kac formula | Sample path property | Diffusion process | Stochastic parabolic equation | Exponential integrability of the Hölder norm of diffusion process | Gaussian random field | Malliavin calculus | Nonlinear Itô-Skorohod integral | Majorizing measure | sample path property | nonlinear Young integral | INEQUALITY | PDES | multiplicative noise | HEAT-EQUATION DRIVEN | nonlinear Ito-Skorohod integral | MATHEMATICS | exponential integrability of the Holder norm of diffusion process | CONTINUITY | majorizing measure | stochastic parabolic equation | diffusion process | transport equation

Nonlinear Young integral | Transport equation | Multiplicative noise | Feynman-Kac formula | Sample path property | Diffusion process | Stochastic parabolic equation | Exponential integrability of the Hölder norm of diffusion process | Gaussian random field | Malliavin calculus | Nonlinear Itô-Skorohod integral | Majorizing measure | sample path property | nonlinear Young integral | INEQUALITY | PDES | multiplicative noise | HEAT-EQUATION DRIVEN | nonlinear Ito-Skorohod integral | MATHEMATICS | exponential integrability of the Holder norm of diffusion process | CONTINUITY | majorizing measure | stochastic parabolic equation | diffusion process | transport equation

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 2/2017, Volume 91, Issue 1, pp. 83 - 98

In this paper we study the solutions of the integral Van Vleck’s functional equation for the sine $$\begin{aligned} \int _{S}f(x\tau (y)t)d\mu (t)-\int _{S}f...

39B52 | Van Vleck’s equation | Involution | 39B32 | Analysis | d’Alembert’s equation | Mathematics | Semigroup | Kannappan’s equation | Multiplicative function | Complex measure | Combinatorics | MATHEMATICS | Kannappan's equation | MATHEMATICS, APPLIED | Van Vleck's equation | d'Alembert's equation | Functional equations | Integrals | Functions (mathematics) | Texts | Mathematical analysis | Formulas (mathematics) | Group theory

39B52 | Van Vleck’s equation | Involution | 39B32 | Analysis | d’Alembert’s equation | Mathematics | Semigroup | Kannappan’s equation | Multiplicative function | Complex measure | Combinatorics | MATHEMATICS | Kannappan's equation | MATHEMATICS, APPLIED | Van Vleck's equation | d'Alembert's equation | Functional equations | Integrals | Functions (mathematics) | Texts | Mathematical analysis | Formulas (mathematics) | Group theory

Journal Article

14.
Full Text
Definite integrals of multiplicative intuitionistic fuzzy information in decision making

Knowledge-Based Systems, ISSN 0950-7051, 05/2016, Volume 100, pp. 59 - 73

In this paper, we investigate the definite integrals of multiplicative intuitionistic fuzzy information in decision making...

Fundamental theorem of calculus | Subtraction definite integral | Decision making | Multiplicative intuitionistic fuzzy function | Division definite integral | PREFERENCE RELATIONS | AGGREGATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Decision-making | Business schools | Integrals | Mathematical analysis | Calculus | Knowledge base | Fuzzy | Constraining | Fuzzy systems

Fundamental theorem of calculus | Subtraction definite integral | Decision making | Multiplicative intuitionistic fuzzy function | Division definite integral | PREFERENCE RELATIONS | AGGREGATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Decision-making | Business schools | Integrals | Mathematical analysis | Calculus | Knowledge base | Fuzzy | Constraining | Fuzzy systems

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2012, Volume 364, Issue 2, pp. 767 - 784

Using an inequality by Corvaja and Zannier about gcd's of polynomials in S \mathbb{G}_m^2

Geometry | Integrality | Mathematical theorems | Mathematical integrals | Triangles | Mathematical inequalities | Mathematics | Polynomials | Diophantine sets | Arithmetic | Farey sequences | Multiplicative groups | Rational surfaces | Vojta's conjecture | Integral points | Blowups | Greatest common divisors | MATHEMATICS | ABELIAN-VARIETIES | blowups | multiplicative groups | integral points | greatest common divisors | rational surfaces

Geometry | Integrality | Mathematical theorems | Mathematical integrals | Triangles | Mathematical inequalities | Mathematics | Polynomials | Diophantine sets | Arithmetic | Farey sequences | Multiplicative groups | Rational surfaces | Vojta's conjecture | Integral points | Blowups | Greatest common divisors | MATHEMATICS | ABELIAN-VARIETIES | blowups | multiplicative groups | integral points | greatest common divisors | rational surfaces

Journal Article

IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, 08/2010, Volume 58, Issue 8, pp. 2680 - 2690

A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE...

Calderón preconditioning | Dielectrics | Electromagnetic analysis | Information technology | surface electric field integral equation | volume electric field integral equations | Message-oriented middleware | Surface waves | Integral equations | Coupling circuits | Antenna feeds | Microwave theory and techniques | Microwave circuits | multiplicative preconditioning | COMPLEX | OPERATOR | ALGORITHM | Calderon preconditioning | ELECTROMAGNETIC SCATTERING | TELECOMMUNICATIONS | RADIATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric fields | Analysis | Electromagnetism | Operators | Iterative solution | Vanadium | Wave interaction | Composite structures | Well posed problems | Antennas

Calderón preconditioning | Dielectrics | Electromagnetic analysis | Information technology | surface electric field integral equation | volume electric field integral equations | Message-oriented middleware | Surface waves | Integral equations | Coupling circuits | Antenna feeds | Microwave theory and techniques | Microwave circuits | multiplicative preconditioning | COMPLEX | OPERATOR | ALGORITHM | Calderon preconditioning | ELECTROMAGNETIC SCATTERING | TELECOMMUNICATIONS | RADIATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric fields | Analysis | Electromagnetism | Operators | Iterative solution | Vanadium | Wave interaction | Composite structures | Well posed problems | Antennas

Journal Article

Geometric and Functional Analysis, ISSN 1016-443X, 11/2010, Volume 20, Issue 5, pp. 1073 - 1143

.... Relations of these operations to yet another classical type of integral geometry, Crofton and kinematic formulas, are indicated.

Radon transform | manifolds | Mathematics | Analysis | Valuations | 52B45 (52A39, 53C65, 44A12) | MATHEMATICS | MULTIPLICATIVE STRUCTURE | FORMULA | Valuation | Universities and colleges

Radon transform | manifolds | Mathematics | Analysis | Valuations | 52B45 (52A39, 53C65, 44A12) | MATHEMATICS | MULTIPLICATIVE STRUCTURE | FORMULA | Valuation | Universities and colleges

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2012, Volume 437, Issue 6, pp. 1408 - 1421

.... Integral circulant graphs can be characterised by their order n and a set D of positive divisors of n in such a way that they have vertex set Z/nZ and edge set {(a,b):a,b∈Z/nZ,gcd(a-b,n)∈D...

Circulant graph | Graph spectrum | Integral graph | Graph energy | Multiplicative function | Cayley graph | MATHEMATICS | MATHEMATICS, APPLIED

Circulant graph | Graph spectrum | Integral graph | Graph energy | Multiplicative function | Cayley graph | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 05/2020, Volume 409, p. 109355

...•Our new fast preconditioners significantly reduce assembly and computation times for 3D Helmholtz boundary integral operators...

Helmholtz equations | Hierarchical matrices | Fast solvers | Operator preconditioning | Boundary elements method | Calderón preconditioning | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MULTIPLICATIVE PRECONDITIONER | OPERATOR | Calderon preconditioning | PHYSICS, MATHEMATICAL

Helmholtz equations | Hierarchical matrices | Fast solvers | Operator preconditioning | Boundary elements method | Calderón preconditioning | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MULTIPLICATIVE PRECONDITIONER | OPERATOR | Calderon preconditioning | PHYSICS, MATHEMATICAL

Journal Article

Miskolc Mathematical Notes, ISSN 1787-2405, 2013, Volume 14, Issue 3, pp. 1041 - 1057

Journal Article

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