Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 09/2013, Volume 264, pp. 95 - 107

We present a method to blend local maximum entropy (LME) meshfree approximants and isogeometric analysis. The coupling strategy exploits the optimization...

Isogeometric analysis | Max-ent approximants | Volume discretization | Local refinement | High-fidelity geometry | 2ND-ORDER | CAD | NURBS | REFINEMENT | ORDER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | CONSTRUCTION | FINITE-ELEMENT-ANALYSIS | SURFACES | SCHEMES | Subdivisions | Discretization | Basis functions | Meshless methods | Approximants | Preserves | Maximum entropy | Optimization | 51 Geometry | 51K Distance geometry | Classificació AMS | Geometria computacional | Geometry | Geometria | Matemàtiques i estadística | 51P05 Geometry and physics | Àrees temàtiques de la UPC | Geometria algebraica | Geometry, Algebraic

Isogeometric analysis | Max-ent approximants | Volume discretization | Local refinement | High-fidelity geometry | 2ND-ORDER | CAD | NURBS | REFINEMENT | ORDER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | CONSTRUCTION | FINITE-ELEMENT-ANALYSIS | SURFACES | SCHEMES | Subdivisions | Discretization | Basis functions | Meshless methods | Approximants | Preserves | Maximum entropy | Optimization | 51 Geometry | 51K Distance geometry | Classificació AMS | Geometria computacional | Geometry | Geometria | Matemàtiques i estadística | 51P05 Geometry and physics | Àrees temàtiques de la UPC | Geometria algebraica | Geometry, Algebraic

Journal Article

Science China Mathematics, ISSN 1674-7283, 11/2019, Volume 62, Issue 11, pp. 2195 - 2210

We make some observations concerning the one-dimensional collapsing geometry of four-dimensional hyperkähler metrics.

K3 manifold | hyperkähler metrics | collapsing | Mathematics | Applications of Mathematics | 53C25 | 51P05

K3 manifold | hyperkähler metrics | collapsing | Mathematics | Applications of Mathematics | 53C25 | 51P05

Journal Article

3.
Full Text
Isometric deformations of unstretchable material surfaces, a spatial variational treatment

Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 07/2018, Volume 116, pp. 290 - 322

The stored energy of an unstretchable material surface is assumed to depend only upon the curvature tensor. By control of its edge(s), the surface is deformed...

14J26 | Isometry | MSC 49Q10 | 49S05 | Relative minimum | Developable | 37D35 | 35Q74 | 35J58 | Ruled | Unstretchable | 51P05 | Inextensional | PHYSICS, CONDENSED MATTER | MATERIALS SCIENCE, MULTIDISCIPLINARY | REPRESENTATION | MOBIUS BAND | SHAPE | MECHANICS | Force and energy

14J26 | Isometry | MSC 49Q10 | 49S05 | Relative minimum | Developable | 37D35 | 35Q74 | 35J58 | Ruled | Unstretchable | 51P05 | Inextensional | PHYSICS, CONDENSED MATTER | MATERIALS SCIENCE, MULTIDISCIPLINARY | REPRESENTATION | MOBIUS BAND | SHAPE | MECHANICS | Force and energy

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 2/2019, Volume 109, Issue 2, pp. 243 - 293

Vector bundles and double vector bundles, or twofold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie...

Geometry | Double vector bundle | 32C11 | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Graded manifold | Group Theory and Generalizations | 51P05 | Physics | 53D17

Geometry | Double vector bundle | 32C11 | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Graded manifold | Group Theory and Generalizations | 51P05 | Physics | 53D17

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 1/2017, Volume 107, Issue 1, pp. 1 - 30

We explore a new connection between Seiberg–Witten theory and quantum statistical systems by relating the dual partition function of SU(2) Super Yang–Mills...

70S15 | Fermi gas | 82D05 | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Quantum and spectral theory | 55P50 | Geometry | 15B52 | 81T13 | Supersymmetric gauge theories | Topological string | 57R56 | Matrix models | 81T60 | Group Theory and Generalizations | 81Q10 | 51P05 | 81Q80 | 81Q60 | Fermi gas, Matrix models | PAINLEVE-III | TOPOLOGICAL STRINGS | RANDOM LATTICE | DUALITY | MATRIX MODELS | PHYSICS, MATHEMATICAL | O(N) MODEL

70S15 | Fermi gas | 82D05 | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Quantum and spectral theory | 55P50 | Geometry | 15B52 | 81T13 | Supersymmetric gauge theories | Topological string | 57R56 | Matrix models | 81T60 | Group Theory and Generalizations | 81Q10 | 51P05 | 81Q80 | 81Q60 | Fermi gas, Matrix models | PAINLEVE-III | TOPOLOGICAL STRINGS | RANDOM LATTICE | DUALITY | MATRIX MODELS | PHYSICS, MATHEMATICAL | O(N) MODEL

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 9/2019, Volume 109, Issue 9, pp. 1961 - 2001

We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of...

Topological string theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Supersymmetric gauge theory | Painlevé equations | 34M55 | Physics | Geometry | 15B52 | 81T13 | Spectral theory | 14H70 | 81T60 | Group Theory and Generalizations | 51P05 | 81Q10 | STRINGS | Painleve equations | INTEGRABLE MAPPINGS | SYMMETRY | DUALITY | SYSTEMS | PHYSICS, MATHEMATICAL | OPERATORS | String theory | Resveratrol

Topological string theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Supersymmetric gauge theory | Painlevé equations | 34M55 | Physics | Geometry | 15B52 | 81T13 | Spectral theory | 14H70 | 81T60 | Group Theory and Generalizations | 51P05 | 81Q10 | STRINGS | Painleve equations | INTEGRABLE MAPPINGS | SYMMETRY | DUALITY | SYSTEMS | PHYSICS, MATHEMATICAL | OPERATORS | String theory | Resveratrol

Journal Article

Journal of Geometry, ISSN 0047-2468, 4/2016, Volume 107, Issue 1, pp. 169 - 185

A non-zero element of the Lie algebra $${\mathfrak{se}(3)}$$ se ( 3 ) of the special Euclidean spatial isometry group SE(3) is known as a twist and the...

Geometry | 70B15 | Secondary 51P05 | Primary 13A50 | Mathematics | Euclidean isometry group | polynomial invariant | dual number | Robots | Algebra

Geometry | 70B15 | Secondary 51P05 | Primary 13A50 | Mathematics | Euclidean isometry group | polynomial invariant | dual number | Robots | Algebra

Journal Article

Journal of Geometry, ISSN 0047-2468, 12/2015, Volume 106, Issue 3, pp. 455 - 463

We derive several results in classical Euclidean elementary geometry using the steering ellipsoid formalism from quantum mechanics. This gives a physically...

Geometry | Mathematics | 51P05 | 51M16 | 51M04 | 81P40 | Quantum theory

Geometry | Mathematics | 51P05 | 51M16 | 51M04 | 81P40 | Quantum theory

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 6/2019, Volume 109, Issue 6, pp. 1271 - 1302

Recently, an exact duality between topological string and the spectral theory of operators constructed from mirror curves to toric Calabi–Yau threefold has...

70S15 | Theoretical, Mathematical and Computational Physics | Complex Systems | 14N35 | Supersymmetric gauge theory | 14D21 | Physics | Quantum and spectral theory | 55P50 | Geometry | 81T13 | Topological string | 57R56 | Blowup equations | 81T60 | Group Theory and Generalizations | 51P05 | 81Q10 | 81Q80 | 81Q60 | TOPOLOGICAL STRINGS | DONALDSON INVARIANTS | DUALITY | FORMULA | PHYSICS, MATHEMATICAL | CURVES

70S15 | Theoretical, Mathematical and Computational Physics | Complex Systems | 14N35 | Supersymmetric gauge theory | 14D21 | Physics | Quantum and spectral theory | 55P50 | Geometry | 81T13 | Topological string | 57R56 | Blowup equations | 81T60 | Group Theory and Generalizations | 51P05 | 81Q10 | 81Q80 | 81Q60 | TOPOLOGICAL STRINGS | DONALDSON INVARIANTS | DUALITY | FORMULA | PHYSICS, MATHEMATICAL | CURVES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2015, Volume 422, Issue 2, pp. 1402 - 1413

In this paper first we describe all (not necessarily linear or bijective) transformations on Rd with 2≤d<∞ which preserve the area of parallelograms spanned by...

Commutativity of self-adjoint operators | Area of parallelogram | Preserver problems | Unitarily invariant norm | MATHEMATICS | COMMUTATIVITY | MATHEMATICS, APPLIED | WIGNERS THEOREM | PROOF | TRANSFORMATIONS | Analysis | Quantum theory | Mathematics - Functional Analysis

Commutativity of self-adjoint operators | Area of parallelogram | Preserver problems | Unitarily invariant norm | MATHEMATICS | COMMUTATIVITY | MATHEMATICS, APPLIED | WIGNERS THEOREM | PROOF | TRANSFORMATIONS | Analysis | Quantum theory | Mathematics - Functional Analysis

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 12/2017, Volume 27, Issue 6, pp. 1743 - 1787

We present an algorithm to simulate random sequential adsorption (random “parking”) of discs on constant curvature surfaces: the plane, sphere, hyperboloid,...

Hyperbolic geometry | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | 82D80 | Random parking | Simulation | Analysis | Sphere packing | Mathematical and Computational Engineering | 82-08 | 51P05 | MATHEMATICS, APPLIED | MECHANICS | PACKING | PHYSICS, MATHEMATICAL | Adsorption | Algorithms | Mechanics | Physics

Hyperbolic geometry | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | 82D80 | Random parking | Simulation | Analysis | Sphere packing | Mathematical and Computational Engineering | 82-08 | 51P05 | MATHEMATICS, APPLIED | MECHANICS | PACKING | PHYSICS, MATHEMATICAL | Adsorption | Algorithms | Mechanics | Physics

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 2/2017, Volume 68, Issue 1, pp. 1 - 38

A theory of deformation of continuous media based on concepts from Finsler differential geometry is presented. The general theory accounts for finite...

Phase transformations | Differential geometry | Elasticity | Fracture | Theoretical and Applied Mechanics | Engineering | Mathematical Methods in Physics | 74A05 | Continuum mechanics | 74A45 | 51P05 | Microstructure | 74B20 | MATHEMATICS, APPLIED | DEFECTS | ENERGY | FINITE ELASTOPLASTICITY | SLIP | BRITTLE-FRACTURE | MODEL | DEFORMATION | NONLINEAR ELASTICITY | BORON-CARBIDE | CRYSTALS | Fractures (Geology)

Phase transformations | Differential geometry | Elasticity | Fracture | Theoretical and Applied Mechanics | Engineering | Mathematical Methods in Physics | 74A05 | Continuum mechanics | 74A45 | 51P05 | Microstructure | 74B20 | MATHEMATICS, APPLIED | DEFECTS | ENERGY | FINITE ELASTOPLASTICITY | SLIP | BRITTLE-FRACTURE | MODEL | DEFORMATION | NONLINEAR ELASTICITY | BORON-CARBIDE | CRYSTALS | Fractures (Geology)

Journal Article

Vietnam Journal of Mathematics, ISSN 2305-221X, 3/2019, Volume 47, Issue 1, pp. 183 - 193

The “Monstrous Moonshine” conjecture (now a theorem) of Conway and Nortan has given rise to a large body of new mathematics. This theorem has been extended to...

String theory | 11F46 | 83C45 | Mock moonshine | Black holes | 83C57 | Mathematics | Moonshine | 81T30 | Mathematics, general | Mock modular forms | 51P05 | Quantum gravity

String theory | 11F46 | 83C45 | Mock moonshine | Black holes | 83C57 | Mathematics | Moonshine | 81T30 | Mathematics, general | Mock modular forms | 51P05 | Quantum gravity

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 11/2018, Volume 28, Issue 5, pp. 1 - 17

In this paper we give a complete characterization of the nth roots of a coquaternion $$\mathsf {q}$$ q . In particular, we show that the number and type of...

Coquaternions | Similarity class and quasi-similarity class of a coquaternion | Secondary 51P05 | Theoretical, Mathematical and Computational Physics | Roots | Physics | Polar form | Mathematical Methods in Physics | Primary 15A66 | 15A24 | Matrix equations | Applications of Mathematics | Physics, general | MATHEMATICS, APPLIED | ROTATIONS | MATRICES | SQUARE ROOTS | PHYSICS, MATHEMATICAL | QUATERNIONS | Economic policy

Coquaternions | Similarity class and quasi-similarity class of a coquaternion | Secondary 51P05 | Theoretical, Mathematical and Computational Physics | Roots | Physics | Polar form | Mathematical Methods in Physics | Primary 15A66 | 15A24 | Matrix equations | Applications of Mathematics | Physics, general | MATHEMATICS, APPLIED | ROTATIONS | MATRICES | SQUARE ROOTS | PHYSICS, MATHEMATICAL | QUATERNIONS | Economic policy

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 9/2017, Volume 18, Issue 9, pp. 3049 - 3096

Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime. To prepare...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | LOCALIZATION | PHYSICS, MULTIDISCIPLINARY | QUANTUM | RECONSTRUCTION | INFORMATION | SPACETIME | TIME | PHYSICS, MATHEMATICAL | UNIVERSE | PHYSICS, PARTICLES & FIELDS | Computer science | Information science

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | LOCALIZATION | PHYSICS, MULTIDISCIPLINARY | QUANTUM | RECONSTRUCTION | INFORMATION | SPACETIME | TIME | PHYSICS, MATHEMATICAL | UNIVERSE | PHYSICS, PARTICLES & FIELDS | Computer science | Information science

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 04/2018, Volume 15, Issue 4

We associate the lepton-quark families with the vertices of the 4D polytopes 5-cell (0001) (A4) and the rectified 5-cell (0100) (A4) derived from the SU(5)...

Coxeter groups | Delone cells | Voronoi cell | polytope | SU GUT | LEPTONS | GROUP-THEORETICAL-ANALYSIS | COXETER GROUP W(H-4) | MODEL | PHYSICS, MATHEMATICAL | QUATERNIONS

Coxeter groups | Delone cells | Voronoi cell | polytope | SU GUT | LEPTONS | GROUP-THEORETICAL-ANALYSIS | COXETER GROUP W(H-4) | MODEL | PHYSICS, MATHEMATICAL | QUATERNIONS

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 11/2015, Volume 53, Issue 10, pp. 2184 - 2190

It is shown that the extent of deviation of a molecular shape from spherical can be characterized by comparing the distribution of the circular variances, a...

Theoretical and Computational Chemistry | Chemistry | Sphericity | Circular variance | Physical Chemistry | Accessible surface | 92C05 | Moments | 51P05 | Math. Applications in Chemistry | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PROTEIN | CHEMISTRY, MULTIDISCIPLINARY | Sphere | Molecular dynamics | Research | Mathematical research | accessible surface | circular variance | moments

Theoretical and Computational Chemistry | Chemistry | Sphericity | Circular variance | Physical Chemistry | Accessible surface | 92C05 | Moments | 51P05 | Math. Applications in Chemistry | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PROTEIN | CHEMISTRY, MULTIDISCIPLINARY | Sphere | Molecular dynamics | Research | Mathematical research | accessible surface | circular variance | moments

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 3/2017, Volume 27, Issue 1, pp. 805 - 828

A new general method of computational electromagnetism based on extremizing the electromagnetic action using the geometric algebra of space-time is described....

Mathematical Methods in Physics | Computational electromagnetism | Lagrangian | Least action | Theoretical, Mathematical and Computational Physics | 83A05 | Geometric algebra | 78M10 | Applications of Mathematics | Physics, general | 51P05 | Physics | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Methods | Algebra | Electromagnetism

Mathematical Methods in Physics | Computational electromagnetism | Lagrangian | Least action | Theoretical, Mathematical and Computational Physics | 83A05 | Geometric algebra | 78M10 | Applications of Mathematics | Physics, general | 51P05 | Physics | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Methods | Algebra | Electromagnetism

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 7/2018, Volume 28, Issue 3, pp. 1 - 15

In the present paper a general setup for the determination of imperfect geometry of radiotherapeutic devices has been proposed that is based on a geometric...

Mathematical Methods in Physics | Secondary 51P05 | 70Q05 | Linac | Theoretical, Mathematical and Computational Physics | Geometric algebra | Applications of Mathematics | Physics, general | Radiotherapy | Physics | Primary 51A05 | Computer science | Algebra | Mechanical engineering | Analysis | Radiation | Physics - Medical Physics

Mathematical Methods in Physics | Secondary 51P05 | 70Q05 | Linac | Theoretical, Mathematical and Computational Physics | Geometric algebra | Applications of Mathematics | Physics, general | Radiotherapy | Physics | Primary 51A05 | Computer science | Algebra | Mechanical engineering | Analysis | Radiation | Physics - Medical Physics

Journal Article

The College Mathematics Journal, ISSN 0746-8342, 03/2018, Volume 49, Issue 2, pp. 93 - 102

Journal Article