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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
Journal Article
Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2019, Volume 52, Issue 50, p. 50LT01
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
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
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
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
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
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
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
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
Journal Article
Aequationes mathematicae, ISSN 0001-9054, 2/2017, Volume 91, Issue 1, pp. 83 - 98
Journal Article
Knowledge-Based Systems, ISSN 0950-7051, 05/2016, Volume 100, pp. 59 - 73
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2012, Volume 364, Issue 2, pp. 767 - 784
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
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
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 05/2020, Volume 409, p. 109355
Journal Article
Miskolc Mathematical Notes, ISSN 1787-2405, 2013, Volume 14, Issue 3, pp. 1041 - 1057
Journal Article
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