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A trinity of duality: Non-separable planar maps, β(1,0)-trees and synchronized intervals

Advances in Applied Mathematics, ISSN 0196-8858, 04/2018, Volume 95, pp. 1 - 30

The dual of a map is a fundamental construction on combinatorial maps, but many other combinatorial objects also possess their notion of duality. For instance,...

Recursive decomposition | Bijection | Non-separable planar maps | Map duality | β-(1,0) trees | Synchronized intervals | CENSUS | MATHEMATICS, APPLIED | ENUMERATION | beta-(1,0) trees | GENERALIZED TAMARI INTERVALS | Mathematics - Combinatorics | Combinatorics | Mathematics

Recursive decomposition | Bijection | Non-separable planar maps | Map duality | β-(1,0) trees | Synchronized intervals | CENSUS | MATHEMATICS, APPLIED | ENUMERATION | beta-(1,0) trees | GENERALIZED TAMARI INTERVALS | Mathematics - Combinatorics | Combinatorics | Mathematics

Journal Article

Topology and its Applications, ISSN 0166-8641, 04/2018, Volume 239, pp. 126 - 141

The primary purpose of this paper concerns the relation of (compact) generalized manifolds to finite Poincaré duality complexes (PD complexes). The problem is...

Gromov–Hausdorff metric | 2-patch space | Controlled surgery | Controlled structure set | Generalized manifold | ENR | Resolution obstruction | [formula omitted]-surgery | Poincaré duality complex | Cell-like map | Wall obstruction | surgery | MATHEMATICS, APPLIED | Poincare duality complex | TORSION | Gromov-Hausdorff metric | CONJECTURE | MATHEMATICS | MAPS | MAPPINGS | L-q-surgery | BORSUK | HOMOLOGY MANIFOLDS | APPROXIMATE FIBRATIONS

Gromov–Hausdorff metric | 2-patch space | Controlled surgery | Controlled structure set | Generalized manifold | ENR | Resolution obstruction | [formula omitted]-surgery | Poincaré duality complex | Cell-like map | Wall obstruction | surgery | MATHEMATICS, APPLIED | Poincare duality complex | TORSION | Gromov-Hausdorff metric | CONJECTURE | MATHEMATICS | MAPS | MAPPINGS | L-q-surgery | BORSUK | HOMOLOGY MANIFOLDS | APPROXIMATE FIBRATIONS

Journal Article

Positivity, ISSN 1385-1292, 6/2016, Volume 20, Issue 2, pp. 295 - 298

The note points out that the sufficiency of proposition 2.1 in Anh (Positivity 18:449–473, 2014) is erroneous and we provide an example to illustrate it. Also...

Generalized subconvexlike | 90C29 | Mathematics | 32F17 | Convex cone | Set-valued map | Operator Theory | Fourier Analysis | Potential Theory | 90C46 | Calculus of Variations and Optimal Control; Optimization | Econometrics | 46G05 | MATHEMATICS | VECTOR OPTIMIZATION | MAPS | SUBCONVEXLIKENESS | Studies | Convex analysis

Generalized subconvexlike | 90C29 | Mathematics | 32F17 | Convex cone | Set-valued map | Operator Theory | Fourier Analysis | Potential Theory | 90C46 | Calculus of Variations and Optimal Control; Optimization | Econometrics | 46G05 | MATHEMATICS | VECTOR OPTIMIZATION | MAPS | SUBCONVEXLIKENESS | Studies | Convex analysis

Journal Article

Publicationes Mathematicae, ISSN 0033-3883, 2012, Volume 80, Issue 3-4, pp. 255 - 293

In this paper we obtain some extensions of the Stone Duality Theorem to the categories BoolSp and PerfBoolSp of zero-dimensional locally compact Hausdorff...

Perfect map | (quasi-)open map | Duality | Local Boolean algebra | ZLB-algebra | Skeletal map | (Dense) embedding | Generalized Boolean algebra | Locally compact (compact) zero-dimensional space | Contravariant adjunction | Injective (surjective) map | locally compact (compact) zero-dimensional space | local Boolean algebra | injective (surjective) map | contravariant adjunction | BOOLEAN-ALGEBRAS | duality | MATHEMATICS | perfect map | (dense) embedding | skeletal map | generalized Boolean algebra

Perfect map | (quasi-)open map | Duality | Local Boolean algebra | ZLB-algebra | Skeletal map | (Dense) embedding | Generalized Boolean algebra | Locally compact (compact) zero-dimensional space | Contravariant adjunction | Injective (surjective) map | locally compact (compact) zero-dimensional space | local Boolean algebra | injective (surjective) map | contravariant adjunction | BOOLEAN-ALGEBRAS | duality | MATHEMATICS | perfect map | (dense) embedding | skeletal map | generalized Boolean algebra

Journal Article

Positivity, ISSN 1385-1292, 9/2014, Volume 18, Issue 3, pp. 449 - 473

In this paper, we introduce upper and lower Studniarski derivatives of set-valued maps. By virtue of these derivatives, higher-order necessary and sufficient...

Generalized subconvexlike | 90C29 | Mathematics | Duality | 32F17 | Optimality conditions | Operator Theory | Fourier Analysis | Potential Theory | 90C46 | Calculus of Variations and Optimal Control; Optimization | Efficiency | Econometrics | 46G05 | Studniarski derivatives | Set-valued optimization problem | RADIAL DERIVATIVES | NONSMOOTH VECTOR OPTIMIZATION | VARIATIONAL SETS | PROPER EFFICIENCY | CONTINGENT EPIDERIVATIVES | SPACE | MATHEMATICS | MAPS | STRICT EFFICIENCY | Computer science | Studies | Mathematical analysis | Analysis | Optimization

Generalized subconvexlike | 90C29 | Mathematics | Duality | 32F17 | Optimality conditions | Operator Theory | Fourier Analysis | Potential Theory | 90C46 | Calculus of Variations and Optimal Control; Optimization | Efficiency | Econometrics | 46G05 | Studniarski derivatives | Set-valued optimization problem | RADIAL DERIVATIVES | NONSMOOTH VECTOR OPTIMIZATION | VARIATIONAL SETS | PROPER EFFICIENCY | CONTINGENT EPIDERIVATIVES | SPACE | MATHEMATICS | MAPS | STRICT EFFICIENCY | Computer science | Studies | Mathematical analysis | Analysis | Optimization

Journal Article

Journal fur die Reine und Angewandte Mathematik, ISSN 0075-4102, 06/2009, Volume 631, Issue 631, pp. 181 - 220

We formulate a strange duality map for parabolic symplectic bundles. We shall prove that as a smooth curve degenerates to a nodal curve, the strange duality...

MATHEMATICS | FACTORIZATION | GENERALIZED THETA-FUNCTIONS | CURVES | MODULI SPACES

MATHEMATICS | FACTORIZATION | GENERALIZED THETA-FUNCTIONS | CURVES | MODULI SPACES

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2006, Volume 358, Issue 2, pp. 687 - 702

We develop a new approach to the pulling back fixed points theorem of W. Browder and use it in order to prove various generalizations of this result.

Mathematical manifolds | Integers | Mathematical theorems | Topological theorems | Mathematics | Mathematical duality | Mathematical vectors | Topology | Power series | General topology | Topological manifold | Generalized homology | Group action | MATHEMATICS | generalized homology | topological manifold | BUNDLES | group action

Mathematical manifolds | Integers | Mathematical theorems | Topological theorems | Mathematics | Mathematical duality | Mathematical vectors | Topology | Power series | General topology | Topological manifold | Generalized homology | Group action | MATHEMATICS | generalized homology | topological manifold | BUNDLES | group action

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2008, Volume 136, Issue 8, pp. 2749 - 2754

We prove a duality theorem for graded algebras over a field that implies several known duality results: graded local duality, versions of Serre duality for...

Morphisms | Mathematical duality | Mathematical rings | Algebra | Maps | Mathematical theorems | Duality | Generalized local cohomology

Morphisms | Mathematical duality | Mathematical rings | Algebra | Maps | Mathematical theorems | Duality | Generalized local cohomology

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 07/2018, Volume 129, pp. 269 - 278

We begin by presenting a symmetric version of the circle equivariant T-duality result in a joint work of the second author with Siye Wu, thereby generalizing...

Equivariant T-duality | Equivariant Generalized Geometry | Twisted equivariant de Rham complex | Singular compactifications | Equivariant exact Courant algebroids | MATHEMATICS | COMPLEX | SYMMETRY | PHYSICS, MATHEMATICAL | HOMOLOGY | GEOMETRY

Equivariant T-duality | Equivariant Generalized Geometry | Twisted equivariant de Rham complex | Singular compactifications | Equivariant exact Courant algebroids | MATHEMATICS | COMPLEX | SYMMETRY | PHYSICS, MATHEMATICAL | HOMOLOGY | GEOMETRY

Journal Article

Glasgow Mathematical Journal, ISSN 0017-0895, 09/2016, Volume 58, Issue 3, pp. 649 - 676

We show that the Z/2-equivariant nth integral Morava K-theory with reality is self-dual with respect to equivariant Anderson duality. In particular, there is a...

MATHEMATICS | GENERALIZED HOMOLOGY | Algebra | Sequences | Integrals | Mathematical analysis | Group theory | Symmetry | Mathematics - Algebraic Topology

MATHEMATICS | GENERALIZED HOMOLOGY | Algebra | Sequences | Integrals | Mathematical analysis | Group theory | Symmetry | Mathematics - Algebraic Topology

Journal Article

Physics Reports, ISSN 0370-1573, 03/2019, Volume 798, pp. 1 - 122

This review provides an introduction to non-geometric backgrounds in string theory. Starting from a discussion of T-duality, geometric and non-geometric...

String theory | T-duality | Non-geometric | FLUX-SCALING SCENARIO | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | NON-ABELIAN DUALITY | DIMENSIONAL REDUCTION | MIRROR SYMMETRY | GENERALIZED COMPLEX-GEOMETRY | LIE T-DUALITY | MODULI STABILIZATION | TARGET-SPACE DUALITY | D-BRANES | Physics - High Energy Physics - Theory

String theory | T-duality | Non-geometric | FLUX-SCALING SCENARIO | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | NON-ABELIAN DUALITY | DIMENSIONAL REDUCTION | MIRROR SYMMETRY | GENERALIZED COMPLEX-GEOMETRY | LIE T-DUALITY | MODULI STABILIZATION | TARGET-SPACE DUALITY | D-BRANES | Physics - High Energy Physics - Theory

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 09/2014, Volume 83, pp. 82 - 98

We study dg-manifolds which are R[2]-bundles over R[1]-bundles over manifolds, we calculate its symmetries, its derived symmetries and we introduce the concept...

Exact Courant algebroids | dg-manifolds | Generalized geometry | [formula omitted]-duality | Exceptional generalized geometry | T-duality | Dg-manifolds | Exact courant algebroids | MATHEMATICS | ALGEBROIDS | PHYSICS, MATHEMATICAL | Algebra

Exact Courant algebroids | dg-manifolds | Generalized geometry | [formula omitted]-duality | Exceptional generalized geometry | T-duality | Dg-manifolds | Exact courant algebroids | MATHEMATICS | ALGEBROIDS | PHYSICS, MATHEMATICAL | Algebra

Journal Article

IEEE Transactions on Circuits and Systems II: Express Briefs, ISSN 1549-7747, 01/2015, Volume 62, Issue 1, pp. 21 - 25

In this brief, a direct and universal method of finding the adjoint of a multiport element is proposed. This is achieved by expressing the characteristic...

Pathology | Sensitivity | Circuits and systems | Adjoint element | generalized duality | inter-reciprocity | Educational institutions | hybrid-transmission matrix | Mathematical model | Admittance | Equations | sensitivity calculation | ACTIVE DEVICES | NULLOR | CURRENT CONVEYORS | NETWORK | VOLTAGE MIRRORS | EQUIVALENTS | ENGINEERING, ELECTRICAL & ELECTRONIC | CIRCUITS | REALIZATIONS | interreciprocity | CDBA | Integrated circuits | Measurement | Usage | Innovations | Voltage | Mathematical models | Mathematical optimization | Semiconductor chips | Theorems | Circuits | Mathematical analysis | Adjoints | Proving | Impedance | Electrical impedance

Pathology | Sensitivity | Circuits and systems | Adjoint element | generalized duality | inter-reciprocity | Educational institutions | hybrid-transmission matrix | Mathematical model | Admittance | Equations | sensitivity calculation | ACTIVE DEVICES | NULLOR | CURRENT CONVEYORS | NETWORK | VOLTAGE MIRRORS | EQUIVALENTS | ENGINEERING, ELECTRICAL & ELECTRONIC | CIRCUITS | REALIZATIONS | interreciprocity | CDBA | Integrated circuits | Measurement | Usage | Innovations | Voltage | Mathematical models | Mathematical optimization | Semiconductor chips | Theorems | Circuits | Mathematical analysis | Adjoints | Proving | Impedance | Electrical impedance

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2015, Volume 423, Issue 1, pp. 770 - 796

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so-called set relations. Contrary...

Dini derivative | Residuation | Generalized convexity | Variational inequalities | Set optimization | MATHEMATICS, APPLIED | INEQUALITIES | LAGRANGIAN-DUALITY | CONVEXITY | MAXIMIZATIONS | MATHEMATICS | CONTINUITY | MAPS | VALUED FUNCTIONS | OPTIMALITY CONDITIONS | Mathematics - Optimization and Control

Dini derivative | Residuation | Generalized convexity | Variational inequalities | Set optimization | MATHEMATICS, APPLIED | INEQUALITIES | LAGRANGIAN-DUALITY | CONVEXITY | MAXIMIZATIONS | MATHEMATICS | CONTINUITY | MAPS | VALUED FUNCTIONS | OPTIMALITY CONDITIONS | Mathematics - Optimization and Control

Journal Article

Mathematics of Operations Research, ISSN 0364-765X, 5/2011, Volume 36, Issue 2, pp. 321 - 339

We introduce a notion of complete monotone quasiconcave duality, motivated by some economic applications. We show that this duality holds for important classes...

quasiconcave functions | generalized conjugation | monotonicity | duality | quasiconvex functions | Mathematical theorems | Mathematical monotonicity | Economic theory | Voile | Handbooks | Mathematical functions | Mathematical duality | Convexity | Vector spaces | Quasiconvex functions | Quasiconcave functions | Duality | Generalized conjugation | Monotonicity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX | INDIRECT UTILITY-FUNCTIONS | Employee motivation | Usage | Duality theory (Mathematics) | Economic conditions | Analysis | Methods

quasiconcave functions | generalized conjugation | monotonicity | duality | quasiconvex functions | Mathematical theorems | Mathematical monotonicity | Economic theory | Voile | Handbooks | Mathematical functions | Mathematical duality | Convexity | Vector spaces | Quasiconvex functions | Quasiconcave functions | Duality | Generalized conjugation | Monotonicity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX | INDIRECT UTILITY-FUNCTIONS | Employee motivation | Usage | Duality theory (Mathematics) | Economic conditions | Analysis | Methods

Journal Article

Topology and its Applications, ISSN 0166-8641, 2011, Volume 158, Issue 17, pp. 2371 - 2381

We develop a duality theory for Lawvereʼs generalized metric spaces that extends the Lawson duality for continuous dcpos and open filter reflecting maps: we...

Lawson duality | Generalized metric space | Way-below | Continuous dcpo | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | COMPLETION

Lawson duality | Generalized metric space | Way-below | Continuous dcpo | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | COMPLETION

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 10/2017, Volume 107, Issue 10, pp. 1823 - 1835

We use a generalized Ricci tensor, defined for generalized metrics in Courant algebroids, to show that Poisson–Lie T-duality is compatible with the 1-loop...

Geometry | T-duality | Courant algebroids | Theoretical, Mathematical and Computational Physics | Complex Systems | Generalized Ricci tensor | Ricci flow | Group Theory and Generalizations | Renormalization group flow | 81T17 | Physics | 53D18 | NONLINEAR SIGMA-MODELS | PHYSICS, MATHEMATICAL

Geometry | T-duality | Courant algebroids | Theoretical, Mathematical and Computational Physics | Complex Systems | Generalized Ricci tensor | Ricci flow | Group Theory and Generalizations | Renormalization group flow | 81T17 | Physics | 53D18 | NONLINEAR SIGMA-MODELS | PHYSICS, MATHEMATICAL

Journal Article

Mathematical Physics, Analysis and Geometry, ISSN 1385-0172, 12/2019, Volume 22, Issue 4, pp. 1 - 40

We describe a construction of generalized Maxwell theories – higher analogues of abelian gauge theories – in the factorization algebra formalism of Costello...

Theoretical, Mathematical and Computational Physics | Generalized Maxwell theories | Physics | Abelian duality | Factorization algebras | Geometry | 81T13 | Analysis | 81T70 | Group Theory and Generalizations | Applications of Mathematics | Higher Abelian gauge theories | BV quantization | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Algebra

Theoretical, Mathematical and Computational Physics | Generalized Maxwell theories | Physics | Abelian duality | Factorization algebras | Geometry | 81T13 | Analysis | 81T70 | Group Theory and Generalizations | Applications of Mathematics | Higher Abelian gauge theories | BV quantization | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Algebra universalis, ISSN 0002-5240, 6/2012, Volume 67, Issue 4, pp. 397 - 416

We establish two theorems that refine the classical Stone duality between generalized Boolean algebras and locally compact Boolean spaces. In the first...

Stone duality | locally compact Boolean spaces | skew Boolean algebras | étale spaces | Mathematics | Secondary: 06E15 | 18F20 | Algebra | generalized Boolean algebras | 18B30 | cohomomorphisms of étale spaces | 03G05 | Primary: 06E75 | 54B40 | MATHEMATICS | RINGS | LATTICES | cohomomorphisms of etale spaces | etale spaces

Stone duality | locally compact Boolean spaces | skew Boolean algebras | étale spaces | Mathematics | Secondary: 06E15 | 18F20 | Algebra | generalized Boolean algebras | 18B30 | cohomomorphisms of étale spaces | 03G05 | Primary: 06E75 | 54B40 | MATHEMATICS | RINGS | LATTICES | cohomomorphisms of etale spaces | etale spaces

Journal Article