JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 08/2019, Volume 52, Issue 34, p. 345401

In this work, we generalize a recursive enumerative formula for connected Feynman diagrams with two external legs. The Feynman diagrams are defined from a...

counting Feynman diagrams | PHYSICS, MULTIDISCIPLINARY | Wick theorem | asymptotics methods | enumerative combinatorics | non-relativistic interaction gas | zero-dimensional field theory | PHYSICS, MATHEMATICAL | connected Feynman diagrams

counting Feynman diagrams | PHYSICS, MULTIDISCIPLINARY | Wick theorem | asymptotics methods | enumerative combinatorics | non-relativistic interaction gas | zero-dimensional field theory | PHYSICS, MATHEMATICAL | connected Feynman diagrams

Journal Article

International Journal of Quantum Chemistry, ISSN 0020-7608, 12/2009, Volume 109, Issue 15, pp. 3858 - 3884

The history of many‐body perturbation theory (MBPT) and its impact on Quantum Chemistry is reviewed, starting with Brueckner's conjecture of a linked‐cluster...

MBPT (many‐body perturbation theory) | Fock space Hamiltonian | coupled‐cluster (CC) theory | connected diagram theorem | MBPT (many-body perturbation theory) | Fock space hamiltonian | Coupled-cluster (CC) theory | Connected diagram theorem | N-ELECTRON SYSTEMS | IRREDUCIBLE BRILLOUIN CONDITIONS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | MOLLER-PLESSET THEORY | COUPLED-CLUSTER APPROACH | coupled-cluster (CC) theory | MECHANICAL DENSITY-MATRIX | CONNECTED-DIAGRAM EXPANSIONS | FOCK SPACE | INCOMPLETE MODEL SPACES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PAIR CORRELATION ENERGIES | CONTRACTED SCHRODINGER-EQUATIONS

MBPT (many‐body perturbation theory) | Fock space Hamiltonian | coupled‐cluster (CC) theory | connected diagram theorem | MBPT (many-body perturbation theory) | Fock space hamiltonian | Coupled-cluster (CC) theory | Connected diagram theorem | N-ELECTRON SYSTEMS | IRREDUCIBLE BRILLOUIN CONDITIONS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | MOLLER-PLESSET THEORY | COUPLED-CLUSTER APPROACH | coupled-cluster (CC) theory | MECHANICAL DENSITY-MATRIX | CONNECTED-DIAGRAM EXPANSIONS | FOCK SPACE | INCOMPLETE MODEL SPACES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PAIR CORRELATION ENERGIES | CONTRACTED SCHRODINGER-EQUATIONS

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 01/2001, Volume 114, Issue 3, pp. 1133 - 1141

A quasi-degenerate perturbation theory (QDPT) is presented that is based on quasi-complete active space self-consistent field (QCAS-SCF) reference functions....

CONNECTED-DIAGRAM EXPANSIONS | FOCK SPACE | INCOMPLETE MODEL SPACES | QUANTUM-CHEMISTRY | WAVE-FUNCTIONS | GENERALIZED MOLLER-PLESSET | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | STATE BARRIER HEIGHT | EFFECTIVE-HAMILTONIANS | LINKED-CLUSTER THEOREM | COUPLED-CLUSTER

CONNECTED-DIAGRAM EXPANSIONS | FOCK SPACE | INCOMPLETE MODEL SPACES | QUANTUM-CHEMISTRY | WAVE-FUNCTIONS | GENERALIZED MOLLER-PLESSET | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | STATE BARRIER HEIGHT | EFFECTIVE-HAMILTONIANS | LINKED-CLUSTER THEOREM | COUPLED-CLUSTER

Journal Article

4.
Full Text
Analysis of spatial chaos appearance in cascade connected nonlinear electrical circuits

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 02/2017, Volume 95, pp. 14 - 20

•Theorems with defined necessary and sufficient conditions for chaos appearance in cascade nonlinear systems are given.•Proofs of the above theorems are given...

Chaos | Escape-time diagram | Bifurcation diagram | Cascade-connected nonlinear electrical system | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | MULTIAGENT SYSTEMS | CONSENSUS | PHYSICS, MATHEMATICAL | Occupational health and safety | Analysis | Electric properties

Chaos | Escape-time diagram | Bifurcation diagram | Cascade-connected nonlinear electrical system | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | MULTIAGENT SYSTEMS | CONSENSUS | PHYSICS, MATHEMATICAL | Occupational health and safety | Analysis | Electric properties

Journal Article

2018, ISBN 9780128048368

We now take up the important problem of proceeding beyond the Gaussian approximation to generate the partition functions and correlation functions for the...

Correlation functions involving a single and multiple variables | Vacuum fluctuations | Construction of Feynman diagrams | Contractions | Expectation values | Generating functions | Wick's theorem | Functional differentiation | Infinity loops | External points | Vertices | Exact propagator to first order | Rules for construction of Feynman diagrams in direct space | Gaussian distributions in one and in several dimensions | First and second order expansions | Pictorial representations of correlation functions | Partition functionals | Two point, four point, and higher order correlation functions | Hubbard–Strantonovich transformation | Feynman diagrams | Internal points | Connected and disconnected diagrams | Exercises in use of Feynman diagrams

Correlation functions involving a single and multiple variables | Vacuum fluctuations | Construction of Feynman diagrams | Contractions | Expectation values | Generating functions | Wick's theorem | Functional differentiation | Infinity loops | External points | Vertices | Exact propagator to first order | Rules for construction of Feynman diagrams in direct space | Gaussian distributions in one and in several dimensions | First and second order expansions | Pictorial representations of correlation functions | Partition functionals | Two point, four point, and higher order correlation functions | Hubbard–Strantonovich transformation | Feynman diagrams | Internal points | Connected and disconnected diagrams | Exercises in use of Feynman diagrams

Book Chapter

The Journal of Symbolic Logic, ISSN 0022-4812, 12/2001, Volume 66, Issue 4, pp. 1524 - 1542

This paper presents a new correctness criterion for marked Danos-Reginer graphs (D-R graphs, for short) of Multiplicative Cyclic Linear Logic MCLL and...

Linear logic | Tensors | Lambek calculus | Mathematical theorems | Logical theorems | Logical proofs | Connectivity | Mathematical logic | Grammar | Connected regions | MATHEMATICS | Symbolic and mathematical logic | Proof theory | Analysis | Logic diagrams

Linear logic | Tensors | Lambek calculus | Mathematical theorems | Logical theorems | Logical proofs | Connectivity | Mathematical logic | Grammar | Connected regions | MATHEMATICS | Symbolic and mathematical logic | Proof theory | Analysis | Logic diagrams

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2000, Volume 352, Issue 12, pp. 5525 - 5561

Let \mathbf{T} be a finite set of tiles, and \mathcal{B} a set of regions \Gamma tileable by \mathbf{T}. We introduce a {\em tile counting group}...

Maps | Mathematical theorems | Tiles | Rectangles | Tessellations | Tiling | Combinatorics | Tableaux | Simply connected regions | Vertices | Tile invariants | Polyomino tilings | Young tableaux | Symmetric group | Conway group | Rim hook bijection | Young diagrams | Rim (ribbon) hooks | MATHEMATICS | polyomino tilings | rim hook bijection | tile invariants | symmetric group | rim (ribbon) hooks

Maps | Mathematical theorems | Tiles | Rectangles | Tessellations | Tiling | Combinatorics | Tableaux | Simply connected regions | Vertices | Tile invariants | Polyomino tilings | Young tableaux | Symmetric group | Conway group | Rim hook bijection | Young diagrams | Rim (ribbon) hooks | MATHEMATICS | polyomino tilings | rim hook bijection | tile invariants | symmetric group | rim (ribbon) hooks

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 7/2018, Volume 34, Issue 4, pp. 523 - 534

Given two cycles A and B in a graph, such that $$A\cap B$$ A∩B is a non-trivial path, the connected sum $$A\hat{+} B$$ A+^B is the cycle whose edges are the...

Connected sum | Groupoid | Robust cycle basis | 20L05 | Mathematics | Engineering Design | Ear basis | Cycle basis | Commutative diagram | Geodesic cycle | 18A10 | Combinatorics | 05C38 | MATHEMATICS | CONSTRUCTION | DIGRAPHS | ROBUST CYCLE BASES

Connected sum | Groupoid | Robust cycle basis | 20L05 | Mathematics | Engineering Design | Ear basis | Cycle basis | Commutative diagram | Geodesic cycle | 18A10 | Combinatorics | 05C38 | MATHEMATICS | CONSTRUCTION | DIGRAPHS | ROBUST CYCLE BASES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 03/2014, Volume 142, Issue 3, pp. 737 - 752

can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.]]>

Circles | Equivalence relation | Mathematical theorems | Braiding | Polynomials | Mathematical surfaces | Graph theory | Data smoothing | Connected regions | Vertices | MATHEMATICS | MATHEMATICS, APPLIED

Circles | Equivalence relation | Mathematical theorems | Braiding | Polynomials | Mathematical surfaces | Graph theory | Data smoothing | Connected regions | Vertices | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2017, Volume 369, Issue 4, pp. 2879 - 2896

We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be...

Rational cohomology of algebraic group | De Rham cohomology of solvmanifold | Group cohomology of torsion-free virtually polycyclic group | Continuous cohomology of simply connected solvable Lie group | ALGEBRAIC-GROUPS | MATHEMATICS | continuous cohomology of simply connected solvable Lie group | RIGIDITY | SOLVMANIFOLDS | SUBGROUPS | rational cohomology of algebraic group | de Rham cohomology of solvmanifold

Rational cohomology of algebraic group | De Rham cohomology of solvmanifold | Group cohomology of torsion-free virtually polycyclic group | Continuous cohomology of simply connected solvable Lie group | ALGEBRAIC-GROUPS | MATHEMATICS | continuous cohomology of simply connected solvable Lie group | RIGIDITY | SOLVMANIFOLDS | SUBGROUPS | rational cohomology of algebraic group | de Rham cohomology of solvmanifold

Journal Article

Mathematische Annalen, ISSN 0025-5831, 2/2018, Volume 370, Issue 1, pp. 669 - 726

The paper is devoted to the problem when a map from some closed connected manifold to an aspherical closed manifold approximately fibers, i.e., is homotopic to...

Mathematics, general | Mathematics | 19J10 | 55R65 | MATHEMATICS | TOPOLOGICAL MANIFOLDS | FIBRATIONS | HILBERT-CUBE MANIFOLDS | WHITEHEAD TORSION | SPACES | FARRELL-JONES CONJECTURE | OBSTRUCTION | ALGEBRAIC K-THEORY | CONNECTED LIE-GROUPS | CIRCLE

Mathematics, general | Mathematics | 19J10 | 55R65 | MATHEMATICS | TOPOLOGICAL MANIFOLDS | FIBRATIONS | HILBERT-CUBE MANIFOLDS | WHITEHEAD TORSION | SPACES | FARRELL-JONES CONJECTURE | OBSTRUCTION | ALGEBRAIC K-THEORY | CONNECTED LIE-GROUPS | CIRCLE

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 06/2013, Volume 138, Issue 22, p. 224108

A mean-field (or one-particle) theory to represent electron correlation at the level of the second-order Moller-Plesset perturbation (MP2) theory is presented....

CONNECTED-DIAGRAM EXPANSIONS | INCOMPLETE MODEL SPACES | QUANTUM RENORMALIZATION-GROUPS | BRUECKNER DOUBLES METHOD | COUPLED-CLUSTER SINGLES | QUASI-PARTICLE ENERGIES | CANONICAL TRANSFORMATION THEORY | SYMMETRY-BREAKING PROBLEMS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | DENSITY-FUNCTIONAL THEORY | GAUSSIAN-BASIS SETS

CONNECTED-DIAGRAM EXPANSIONS | INCOMPLETE MODEL SPACES | QUANTUM RENORMALIZATION-GROUPS | BRUECKNER DOUBLES METHOD | COUPLED-CLUSTER SINGLES | QUASI-PARTICLE ENERGIES | CANONICAL TRANSFORMATION THEORY | SYMMETRY-BREAKING PROBLEMS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | DENSITY-FUNCTIONAL THEORY | GAUSSIAN-BASIS SETS

Journal Article

Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 07/2011, Volume 20, Issue 7, pp. 1059 - 1071

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear...

κ-Almost alternating diagram | dealternator reduced diagram | circle number | dealternator connected diagram | Jones polynomial | span | surgery | MATHEMATICS | k-Almost alternating diagram | LINKS | Links | Polynomials | Knot theory | Upper bounds | Mathematics - Geometric Topology

κ-Almost alternating diagram | dealternator reduced diagram | circle number | dealternator connected diagram | Jones polynomial | span | surgery | MATHEMATICS | k-Almost alternating diagram | LINKS | Links | Polynomials | Knot theory | Upper bounds | Mathematics - Geometric Topology

Journal Article

The College Mathematics Journal, ISSN 0746-8342, 6/1984, Volume 15, Issue 3, pp. 238 - 247

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 7/2009, Volume 42, Issue 1, pp. 94 - 130

We give a complete description of the Voronoi diagram, in ℝ3, of three lines in general position, that is, that are pairwise skew and not all parallel to a...

Computational geometry | Computational Mathematics and Numerical Analysis | Voronoi diagram | Mathematics | Medial axis | Combinatorics | Quadric surface intersection | Computer algebra | ARRANGEMENT | DECOMPOSITION | REAL ALGEBRAIC SET | LEAST ONE-POINT | QUADRICS | MATHEMATICS | INTERSECTION | CONNECTED COMPONENT | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | NEAR-OPTIMAL PARAMETERIZATION | EFFICIENT | Computer science | Geometry | Algebra | Algorithms | Computer Science | Computational Geometry

Computational geometry | Computational Mathematics and Numerical Analysis | Voronoi diagram | Mathematics | Medial axis | Combinatorics | Quadric surface intersection | Computer algebra | ARRANGEMENT | DECOMPOSITION | REAL ALGEBRAIC SET | LEAST ONE-POINT | QUADRICS | MATHEMATICS | INTERSECTION | CONNECTED COMPONENT | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | NEAR-OPTIMAL PARAMETERIZATION | EFFICIENT | Computer science | Geometry | Algebra | Algorithms | Computer Science | Computational Geometry

Journal Article

お茶の水女子大學自然科學報告, ISSN 0029-8190, 09/2006, Volume 57, pp. 31 - 35

In this short paper, the author would like to correct some errors and supplement the classification theorem of palette diagrams without area and moment in the...

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 08/2017, Volume 85, Issue 4, pp. 814 - 838

A graph G has maximal local edge‐connectivity k if the maximum number of edge‐disjoint paths between every pair of distinct vertices x and y is at most k. We...

local connectivity | coloring | vertex degree | minimally k‐connected | Brooks’ theorem | local edge‐connectivity | local edge-connectivity | minimally k-connected | MATHEMATICS | Brooks' theorem | Computer Science | Discrete Mathematics

local connectivity | coloring | vertex degree | minimally k‐connected | Brooks’ theorem | local edge‐connectivity | local edge-connectivity | minimally k-connected | MATHEMATICS | Brooks' theorem | Computer Science | Discrete Mathematics

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 9/2017, Volume 209, Issue 3, pp. 749 - 835

We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there...

58J20 | 57R90 | 58D17 | 58D05 | 19K56 | 53C27 | Mathematics | 57R65 | 19D06 | 55R35 | 55S35 | 57R22 | 55P47 | Mathematics, general | HOMOTOPY TYPE | MATHEMATICS | THEOREM | SIMPLY CONNECTED MANIFOLDS | METRICS | CLASSIFICATION | INDEX | Theorems | Homotopy theory | Manifolds (mathematics) | Curvature

58J20 | 57R90 | 58D17 | 58D05 | 19K56 | 53C27 | Mathematics | 57R65 | 19D06 | 55R35 | 55S35 | 57R22 | 55P47 | Mathematics, general | HOMOTOPY TYPE | MATHEMATICS | THEOREM | SIMPLY CONNECTED MANIFOLDS | METRICS | CLASSIFICATION | INDEX | Theorems | Homotopy theory | Manifolds (mathematics) | Curvature

Journal Article

The Journal of Symbolic Logic, ISSN 0022-4812, 6/1965, Volume 30, Issue 2, pp. 113 - 118

The attempt to find usable diagrams for n terms of the sort devised by John Venn seems to have originated with Venn himself, who published diagrams for up to...

Mathematical theorems | Rectangles | Diagrams | Geometric planes | Mathematical logic | Connected regions | Classical literature | Simply connected regions

Mathematical theorems | Rectangles | Diagrams | Geometric planes | Mathematical logic | Connected regions | Classical literature | Simply connected regions

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 1/1933, Volume 35, Issue 1, pp. 88 - 111

Journal Article

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