Journal of the ACM (JACM), ISSN 0004-5411, 12/2019, Volume 66, Issue 6, pp. 1 - 49

The geometric intersection number of a curve on a surface is the minimal number of self-intersections of any homotopic curve, i.e...

combinatorial geodesic | curves on surfaces | Computational topology | intersection number | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | LOOPS | ALGORITHMS | Homotopy theory | Algorithms | Computation | Polynomials | Intersections | Combinatorial analysis | Curves | Complexity | Geometric Topology | Mathematics | Computational Geometry | Computer Science | Discrete Mathematics

combinatorial geodesic | curves on surfaces | Computational topology | intersection number | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | LOOPS | ALGORITHMS | Homotopy theory | Algorithms | Computation | Polynomials | Intersections | Combinatorial analysis | Curves | Complexity | Geometric Topology | Mathematics | Computational Geometry | Computer Science | Discrete Mathematics

Journal Article

MANUSCRIPTA MATHEMATICA, ISSN 0025-2611, 05/2020, Volume 162, Issue 1-2, pp. 241 - 269

We present a formula to compute the Brasselet number of f : (Y, 0) -> (C, 0) where Y. X is a non-degenerate complete intersection in a toric variety X...

MATHEMATICS | FIBERS | FORMULA | DEFORMATIONS | EULER OBSTRUCTION | QUOTIENT SINGULARITIES

MATHEMATICS | FIBERS | FORMULA | DEFORMATIONS | EULER OBSTRUCTION | QUOTIENT SINGULARITIES

Journal Article

Computer Aided Geometric Design, ISSN 0167-8396, 11/2019, Volume 75, p. 101791

•Describes a 2-Norm Condition Number for Bézier Curve Intersection.•Condition number is straightforward to compute...

Condition number | Numerical analysis | Bézier curve | Curve intersection | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Bezier curve

Condition number | Numerical analysis | Bézier curve | Curve intersection | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Bezier curve

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 07/2016, Volume 327, pp. 30 - 57

.... In particular applications, our formulation gives closed formulæ of a new type for the generating series of intersection numbers of ψ...

Correlation function | Intersection numbers | Tau-function | KdV hierarchy | Wave function | Formulations | Correlation | Hierarchies | Nonlinear phenomena | Mathematical analysis | Images | Intersections

Correlation function | Intersection numbers | Tau-function | KdV hierarchy | Wave function | Formulations | Correlation | Hierarchies | Nonlinear phenomena | Mathematical analysis | Images | Intersections

Journal Article

Discrete Mathematics, ISSN 0012-365X, 02/2017, Volume 340, Issue 2, pp. 107 - 118

...}. It is known that the r-color Ramsey number for P is R(P;r)=r+6 for r⩽7. The proof of this result relies on a careful analysis of the Turán numbers for P...

3-uniform hypergraphs | MATHEMATICS | SYSTEMS | INTERSECTION-THEOREMS

3-uniform hypergraphs | MATHEMATICS | SYSTEMS | INTERSECTION-THEOREMS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2017, Volume 37, Issue 2, pp. 443 - 464

...}. It is known that the r-color Ramsey number for P is R(P; r) = r + 6 for r ≤ 9. The proof of this result relies on a careful analysis of the Turán numbers for P...

Ramsey numbers | Turán numbers | MATHEMATICS | SYSTEMS | Turan numbers | INTERSECTION-THEOREMS

Ramsey numbers | Turán numbers | MATHEMATICS | SYSTEMS | Turan numbers | INTERSECTION-THEOREMS

Journal Article

Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 10/2011, Volume 20, Issue 10, pp. 1325 - 1343

In this paper we provide a mathematical reconstruction of what might have been Gauss' own derivation of the linking number of 1833, providing also an alternative, explicit proof of its modern...

Linking number | degree | signed crossings | oriented area | potential | intersection number | TOPOLOGY | MATHEMATICS | ENERGY | KNOTS | Reconstruction | Mathematical analysis | Proving | Derivation | Joining | Magnetism | Intersections | Linking

Linking number | degree | signed crossings | oriented area | potential | intersection number | TOPOLOGY | MATHEMATICS | ENERGY | KNOTS | Reconstruction | Mathematical analysis | Proving | Derivation | Joining | Magnetism | Intersections | Linking

Journal Article

Discrete Mathematics, ISSN 0012-365X, 02/2016, Volume 339, Issue 2, pp. 533 - 538

A graph G has p-intersection number at most d if it is possible to assign to every vertex u of G, a subset S(u...

Forbidden induced subgraph | [formula omitted]-intersection number | Intersection number | Intersection graph | p-intersection number | MATHEMATICS | DOT PRODUCT REPRESENTATIONS | GRAPHS

Forbidden induced subgraph | [formula omitted]-intersection number | Intersection number | Intersection graph | p-intersection number | MATHEMATICS | DOT PRODUCT REPRESENTATIONS | GRAPHS

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 1/2016, Volume 2016, Issue 1, pp. 1 - 51

Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of r-spin intersection numbers...

Integrable Hierarchies | Integrable Equations in Physics | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | HURWITZ NUMBERS | QUANTUM-GRAVITY | CURVES | MODULI SPACES | WITTEN TAU-FUNCTION | 2D GRAVITY | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Information science | Statistics | Analysis | Operators | Partitions | Fermions | Integrals | Texts | Mathematical models | Polynomials | Intersections | Mathematics - Algebraic Geometry | Mathematical Physics | Nuclear and High Energy Physics | High Energy Physics - Theory

Integrable Hierarchies | Integrable Equations in Physics | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | HURWITZ NUMBERS | QUANTUM-GRAVITY | CURVES | MODULI SPACES | WITTEN TAU-FUNCTION | 2D GRAVITY | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Information science | Statistics | Analysis | Operators | Partitions | Fermions | Integrals | Texts | Mathematical models | Polynomials | Intersections | Mathematics - Algebraic Geometry | Mathematical Physics | Nuclear and High Energy Physics | High Energy Physics - Theory

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2013, Volume 27, Issue 1, pp. 550 - 561

.... It has been conjectured for a long time that for every fixed k, the maximum number of edges of a k-quasi-planar graph with n vertices is O(n...

Quasi-planar graphs | Topological graphs | Turan-type problems | MATHEMATICS, APPLIED | DAVENPORT-SCHINZEL SEQUENCES | topological graphs | INTERSECTION PATTERNS | quasi-planar graphs | Graphs | Inverse | Planes | Upper bounds | Mathematical analysis

Quasi-planar graphs | Topological graphs | Turan-type problems | MATHEMATICS, APPLIED | DAVENPORT-SCHINZEL SEQUENCES | topological graphs | INTERSECTION PATTERNS | quasi-planar graphs | Graphs | Inverse | Planes | Upper bounds | Mathematical analysis

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 1/2017, Volume 2017, Issue 1, pp. 1 - 35

We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces...

Superstring Vacua | Space-Time Symmetries | Superstrings and Heterotic Strings | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | CALABI-YAU MANIFOLDS | PHYSICS, PARTICLES & FIELDS | Statistics | Astronomy | Manifolds | Intersections | Computation | Quotients | Classification | Physics - High Energy Physics - Theory | Fysik | Physical Sciences | Nuclear and High Energy Physics | High Energy Physics - Theory

Superstring Vacua | Space-Time Symmetries | Superstrings and Heterotic Strings | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | CALABI-YAU MANIFOLDS | PHYSICS, PARTICLES & FIELDS | Statistics | Astronomy | Manifolds | Intersections | Computation | Quotients | Classification | Physics - High Energy Physics - Theory | Fysik | Physical Sciences | Nuclear and High Energy Physics | High Energy Physics - Theory

Journal Article

Chemistry – A European Journal, ISSN 0947-6539, 05/2017, Volume 23, Issue 25, pp. 6150 - 6164

The fractional occupation number weighted density (FOD) analysis is explored as a general theoretical diagnostic for complicated electronic structures...

protein structures | quantum chemistry | computational chemistry | electronic structure | O-BENZYNE | MECHANISM | STATE PERTURBATION-THEORY | IMPLEMENTATION | OPEN-SHELL | CHEMISTRY, MULTIDISCIPLINARY | CYTOCHROME-P450 COMPOUND I | MULTIREFERENCE | PHOTOCHEMISTRY | CONICAL-INTERSECTION | VALENCE | Protonation

protein structures | quantum chemistry | computational chemistry | electronic structure | O-BENZYNE | MECHANISM | STATE PERTURBATION-THEORY | IMPLEMENTATION | OPEN-SHELL | CHEMISTRY, MULTIDISCIPLINARY | CYTOCHROME-P450 COMPOUND I | MULTIREFERENCE | PHOTOCHEMISTRY | CONICAL-INTERSECTION | VALENCE | Protonation

Journal Article

13.
Full Text
Zone of influence for particle number concentrations at signalised traffic intersections

Atmospheric Environment, ISSN 1352-2310, 12/2015, Volume 123, pp. 25 - 38

Estimation of zone of influences (ZoI) at signalised traffic intersections (TI) is important to accurately model particle number concentrations (PNCs...

Number size distribution | Driving condition | Traffic intersection | PNC profile | Positive matrix factorisation

Number size distribution | Driving condition | Traffic intersection | PNC profile | Positive matrix factorisation

Journal Article

ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 07/2017, Volume 24, Issue 3

...}. It is known that the r-colored Ramsey number for P is R(P;r) - r + 6 for r - 2,3, and that R...

MATHEMATICS | MATHEMATICS, APPLIED | SYSTEMS | INTERSECTION-THEOREMS

MATHEMATICS | MATHEMATICS, APPLIED | SYSTEMS | INTERSECTION-THEOREMS

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 9/2013, Volume 29, Issue 5, pp. 1221 - 1234

We define the Helly number of a polyomino P as the smallest number h such that the h-Helly property holds for the family of symmetric and translated copies of P on the integer grid...

Combinatorics | Mathematics | Engineering Design | MATHEMATICS | EDGE INTERSECTION GRAPHS | PATHS | THEOREM | Computer science | Statistics | Geometry | Graph theory | Integers | Graphs | Reproduction | Rectangles | Combinatorial analysis | Computer Science - Computational Geometry

Combinatorics | Mathematics | Engineering Design | MATHEMATICS | EDGE INTERSECTION GRAPHS | PATHS | THEOREM | Computer science | Statistics | Geometry | Graph theory | Integers | Graphs | Reproduction | Rectangles | Combinatorial analysis | Computer Science - Computational Geometry

Journal Article

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Full Text
Brauer–Manin obstruction and families of generalised Châtelet surfaces over number fields

International Journal of Number Theory, ISSN 1793-0421, 03/2019, Volume 15, Issue 2, pp. 289 - 308

Over infinitely many number fields k (including all finite Galois extensions k / Q of odd degree unramified at 2...

Châtelet surfaces | Brauer-Manin obstruction | rational points | Hasse principle | MATHEMATICS | Chatelet surfaces | 2 QUADRICS | INTERSECTIONS

Châtelet surfaces | Brauer-Manin obstruction | rational points | Hasse principle | MATHEMATICS | Chatelet surfaces | 2 QUADRICS | INTERSECTIONS

Journal Article

Journal of Combinatorial Designs, ISSN 1063-8539, 11/2015, Volume 23, Issue 11, pp. 463 - 480

Intersection numbers for subspace designs are introduced and q‐analogs of the Mendelsohn...

block design | subspace design | q‐analog | Fano plane | intersection number | q-analog | MATHEMATICS | Q-ANALOGS | 2-DESIGNS | T-DESIGNS | Mathematics - Combinatorics

block design | subspace design | q‐analog | Fano plane | intersection number | q-analog | MATHEMATICS | Q-ANALOGS | 2-DESIGNS | T-DESIGNS | Mathematics - Combinatorics

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 04/2014, Volume 167, pp. 144 - 162

We investigate edge-intersection graphs of paths in the plane grid, regarding a parameter called the bend-number, i.e...

Grid paths | Intersection graphs | MATHEMATICS, APPLIED | INTERVAL NUMBER | CATERPILLAR ARBORICITY | STAR ARBORICITY | Lower bounds | Graphs | Bends | Planes | Mathematical analysis | Recognition | Computer Science

Grid paths | Intersection graphs | MATHEMATICS, APPLIED | INTERVAL NUMBER | CATERPILLAR ARBORICITY | STAR ARBORICITY | Lower bounds | Graphs | Bends | Planes | Mathematical analysis | Recognition | Computer Science

Journal Article

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