Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 03/2019, Volume 377, Issue 2140, p. 20180035

By looking at concrete examples from elementary geometry, we analyse the manner in which the simplicity of proofs could be defined. We first find that, when...

Elementary geometry | Hilbert’s 24th problem | Simple proofs | Ordered geometry | Direct proof | Multiple uses of axioms | ordered geometry | multiple uses of axioms | elementary geometry | direct proof | AXIOMS | MULTIDISCIPLINARY SCIENCES | Hilbert's 24th problem | simple proofs

Elementary geometry | Hilbert’s 24th problem | Simple proofs | Ordered geometry | Direct proof | Multiple uses of axioms | ordered geometry | multiple uses of axioms | elementary geometry | direct proof | AXIOMS | MULTIDISCIPLINARY SCIENCES | Hilbert's 24th problem | simple proofs

Journal Article

The Annals of Probability, ISSN 0091-1798, 1/2011, Volume 39, Issue 1, pp. 104 - 138

We consider the family of two-sided Bernoulli initial conditions for TASEP which, as the left and right densities (ρ₋, ρ₊) are varied, give rise to shock waves...

Fluctuation theorem | Mathematical theorems | Critical points | Eigenvalues | Boundary conditions | Hydrodynamics | Mathematical functions | Rarefaction | Random variables | Asymmetric simple exclusion process | Interacting particle systems | Last passage percolation | ASEP | PARTICLE | interacting particle systems | last passage percolation | STATISTICS & PROBABILITY | EXTERNAL SOURCES | SHOCK FLUCTUATIONS | PROFILE | ASYMMETRIC SIMPLE EXCLUSION | POLYNUCLEAR GROWTH-MODEL | SAMPLE COVARIANCE MATRICES | FORMULAS | LIMITING DISTRIBUTIONS | 60K35 | 82C22

Fluctuation theorem | Mathematical theorems | Critical points | Eigenvalues | Boundary conditions | Hydrodynamics | Mathematical functions | Rarefaction | Random variables | Asymmetric simple exclusion process | Interacting particle systems | Last passage percolation | ASEP | PARTICLE | interacting particle systems | last passage percolation | STATISTICS & PROBABILITY | EXTERNAL SOURCES | SHOCK FLUCTUATIONS | PROFILE | ASYMMETRIC SIMPLE EXCLUSION | POLYNUCLEAR GROWTH-MODEL | SAMPLE COVARIANCE MATRICES | FORMULAS | LIMITING DISTRIBUTIONS | 60K35 | 82C22

Journal Article

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 02/2018, Volume 54, Issue 1, pp. 514 - 528

We review product form blocking measures in the general framework of nearest neighbor asymmetric one dimensional misanthrope processes. This class includes...

Reversible stationary distribution | Blocking measure | Jacobi triple product | Interacting particle systems | EXISTENCE | DEPOSITION MODELS | FLUCTUATIONS | HYDRODYNAMICS | STATISTICS & PROBABILITY | ZERO-RANGE PROCESS | SIMPLE EXCLUSION PROCESS

Reversible stationary distribution | Blocking measure | Jacobi triple product | Interacting particle systems | EXISTENCE | DEPOSITION MODELS | FLUCTUATIONS | HYDRODYNAMICS | STATISTICS & PROBABILITY | ZERO-RANGE PROCESS | SIMPLE EXCLUSION PROCESS

Journal Article

ACM Transactions on Computational Logic (TOCL), ISSN 1529-3785, 04/2014, Volume 15, Issue 2, pp. 1 - 30

A propositional proof system is weakly automatizable if there is a polynomial time algorithm that separates satisfiable formulas from formulas that have a...

mean payoff games | weak automatizability | parity games | simple stochastic sames | Bounded arithmetic | resolution | Parity games | Simple stochastic sames | Weak automatizability | Mean payoff games | Resolution | Theory | LOGIC | NP SEARCH PROBLEMS | FRAGMENTS | LOWER BOUNDS | AUTOMATIZABILITY | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS

mean payoff games | weak automatizability | parity games | simple stochastic sames | Bounded arithmetic | resolution | Parity games | Simple stochastic sames | Weak automatizability | Mean payoff games | Resolution | Theory | LOGIC | NP SEARCH PROBLEMS | FRAGMENTS | LOWER BOUNDS | AUTOMATIZABILITY | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2014, Volume 398, pp. 350 - 363

A new proof of Glaubermanʼs Solvable Signalizer Functor Theorem is presented. The Solvable Signalizer Functor Theorem is one of the background results needed...

Finite group | Classification of finite simple groups | Signalizer functor | 20D45 | MATHEMATICS

Finite group | Classification of finite simple groups | Signalizer functor | 20D45 | MATHEMATICS

Journal Article

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 03/2019, Volume 377, Issue 2140, p. 20180045

Proof plays a central role in developing, establishing and communicating mathematical knowledge. Nevertheless, it is not such a central element in school...

Proof | Simple proof | Functions of proof | simple proof | proof | ENGAGING STUDENTS | MULTIDISCIPLINARY SCIENCES | functions of proof | KNOWLEDGE | 1008 | 2

Proof | Simple proof | Functions of proof | simple proof | proof | ENGAGING STUDENTS | MULTIDISCIPLINARY SCIENCES | functions of proof | KNOWLEDGE | 1008 | 2

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 1/2015, Volume 16, Issue 1, pp. 99 - 112

We give a partially alternate proof of reality of the spectrum of the imaginary cubic oscillator in quantum mechanics.

Maximum Modulus Principle | Mathematical Methods in Physics | Riemann Surface | Theoretical, Mathematical and Computational Physics | Simple Eigenvalue | Quantum Physics | Polygonal Chain | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Real Spectrum | Physics | Elementary Particles, Quantum Field Theory | PERTURBATION-THEORY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Maximum Modulus Principle | Mathematical Methods in Physics | Riemann Surface | Theoretical, Mathematical and Computational Physics | Simple Eigenvalue | Quantum Physics | Polygonal Chain | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Real Spectrum | Physics | Elementary Particles, Quantum Field Theory | PERTURBATION-THEORY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2013, Volume 394, pp. 221 - 222

A simple alternative ring without nilpotent elements of characteristic not 2 has no divisors of zero. This was the main part of my doctoral dissertation. Here...

Alternative ring | Simple | No nilpotent elements | MATHEMATICS

Alternative ring | Simple | No nilpotent elements | MATHEMATICS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 02/2014, Volume 76, pp. 10 - 24

In a recent paper Dubrovin etal. (1998), it is proved that the genus two free energy of an arbitrary semisimple Frobenius manifold can be represented as a sum...

Simple singularities | Frobenius manifold | G-function | Dual graph | Free energy

Simple singularities | Frobenius manifold | G-function | Dual graph | Free energy

Journal Article

10.
Full Text
A Combinatorial Proof for the Alternating Convolution of the Central Binomial Coefficients

The American Mathematical Monthly, ISSN 0002-9890, 06/2014, Volume 121, Issue 6, pp. 537 - 540

We give a combinatorial proof of the identity for the alternating convolution of the central binomial coefficients. Our proof entails applying an involution to...

Binomial coefficients | NOTES | MATHEMATICS | Permutations | Mathematics/Data Analysis and Probability/Probability/Simple Events/Permutations and Combinations | Analysis | Geometric probabilities | Probabilities | Combinatorial probabilities

Binomial coefficients | NOTES | MATHEMATICS | Permutations | Mathematics/Data Analysis and Probability/Probability/Simple Events/Permutations and Combinations | Analysis | Geometric probabilities | Probabilities | Combinatorial probabilities

Journal Article

Notre Dame Journal of Formal Logic, ISSN 0029-4527, 2012, Volume 53, Issue 4, pp. 439 - 456

We give a simple and direct proof that super-consistency implies the cut-elimination property in deduction modulo. This proof can be seen as a simplification...

Cut elimination | Deduction modulo | Super-consistency | Simple type theory | MATHEMATICS | cut elimination | deduction modulo | THEOREM | super-consistency | PHILOSOPHY | INTUITIONISTIC THEORY | simple type theory | COMPLETENESS | LOGIC | Logic in Computer Science | Formal Languages and Automata Theory | Computer Science | 03B99 | 03F05 | 03C90 | 03B15

Cut elimination | Deduction modulo | Super-consistency | Simple type theory | MATHEMATICS | cut elimination | deduction modulo | THEOREM | super-consistency | PHILOSOPHY | INTUITIONISTIC THEORY | simple type theory | COMPLETENESS | LOGIC | Logic in Computer Science | Formal Languages and Automata Theory | Computer Science | 03B99 | 03F05 | 03C90 | 03B15

Journal Article

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 10/2005, Volume 363, Issue 1835, pp. 2401 - 2406

Conventional wisdom says the ideal proof should be short, simple, and elegant. However there are now examples of very long, complicated proofs, and as...

Mathematical theorems | Communities | Insect swarms | Group theory | Mathematical objects | Mathematics | Biology | Information classification | Mathematical models | Physics | Proof | Simple group | Classification | Complex | simple group | proof | classification | MULTIDISCIPLINARY SCIENCES | complex | Models, Theoretical | Software | Algorithms | Numerical Analysis, Computer-Assisted | Mathematical Computing | Software Validation

Mathematical theorems | Communities | Insect swarms | Group theory | Mathematical objects | Mathematics | Biology | Information classification | Mathematical models | Physics | Proof | Simple group | Classification | Complex | simple group | proof | classification | MULTIDISCIPLINARY SCIENCES | complex | Models, Theoretical | Software | Algorithms | Numerical Analysis, Computer-Assisted | Mathematical Computing | Software Validation

Journal Article

13.
Full Text
A cohomological proof that real representations of semisimple lie algebras have Q-Forms

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2015, Volume 11

A Lie algebra gQ over Q is said to be I universal if every homomorphism from gQ to gl(n, R) is conjugate to a homomorphism into gi(n,Q) (for every n). By using...

Semisimple Lie algebra | Tits algebra | Global field | Galois cohomology | Linear algebraic group | Finite-dimensional representation | global field | linear algebraic group | semisimple Lie algebra | finite-dimensional representation | PHYSICS, MATHEMATICAL

Semisimple Lie algebra | Tits algebra | Global field | Galois cohomology | Linear algebraic group | Finite-dimensional representation | global field | linear algebraic group | semisimple Lie algebra | finite-dimensional representation | PHYSICS, MATHEMATICAL

Journal Article

Kodai Mathematical Journal, ISSN 0386-5991, 2014, Volume 37, Issue 2, pp. 427 - 433

We give a shorter proof of the following theorem of Kathryn Mann [M]: the identity component of the group of the compactly supported Cr diffeomorphisms of Rn...

action on the circle | group of diffeomorphisms | action on the real line | simple groups | Group of diffeomorphisms | Action on the circle | Action on the real line | Simple groups | MATHEMATICS

action on the circle | group of diffeomorphisms | action on the real line | simple groups | Group of diffeomorphisms | Action on the circle | Action on the real line | Simple groups | MATHEMATICS

Journal Article

Games and Economic Behavior, ISSN 0899-8256, 11/2019, Volume 118, pp. 486 - 490

•We axiomatically characterize the symmetrically balanced VCG mechanism in the queueing problem.•Our main axiom is either upward or downward invariance, weaker...

Simple proof | Queueing problem | Symmetrically balanced VCG rule | Axiomatic characterization | ECONOMICS | STRATEGY-PROOF

Simple proof | Queueing problem | Symmetrically balanced VCG rule | Axiomatic characterization | ECONOMICS | STRATEGY-PROOF

Journal Article

Molecular and Cellular Biology, ISSN 0270-7306, 05/1997, Volume 17, Issue 5, pp. 2859 - 2865

Article Usage Stats Services MCB Citing Articles Google Scholar PubMed Related Content Social Bookmarking CiteULike Delicious Digg Facebook Google+ Mendeley...

SIMPLE REPETITIVE DNA | CARCINOMA CELL-LINES | SEQUENCES | MICROSATELLITE INSTABILITY | BIOCHEMISTRY & MOLECULAR BIOLOGY | SACCHAROMYCES-CEREVISIAE | CELL BIOLOGY | BETA RECEPTOR | COLON-CANCER | GENE | K CQ BIOCHEMISTRY & MOLECULAR BIOLOGY | K DR CELL BIOLOGY | REPLICATION ERRORS | SPONTANEOUS MUTATIONS | Frameshift Mutation | Nucleic Acid Heteroduplexes - genetics | Humans | Molecular Sequence Data | Fungal Proteins | DNA Repair - genetics | Deoxyadenosines - metabolism | MutS Homolog 2 Protein | DNA Polymerase II - metabolism | DNA-Binding Proteins - genetics | DNA-Binding Proteins - metabolism | Mutagenesis | Base Sequence | DNA, Fungal - metabolism | Saccharomyces cerevisiae Proteins | DNA-Directed DNA Polymerase - metabolism | Saccharomyces cerevisiae

SIMPLE REPETITIVE DNA | CARCINOMA CELL-LINES | SEQUENCES | MICROSATELLITE INSTABILITY | BIOCHEMISTRY & MOLECULAR BIOLOGY | SACCHAROMYCES-CEREVISIAE | CELL BIOLOGY | BETA RECEPTOR | COLON-CANCER | GENE | K CQ BIOCHEMISTRY & MOLECULAR BIOLOGY | K DR CELL BIOLOGY | REPLICATION ERRORS | SPONTANEOUS MUTATIONS | Frameshift Mutation | Nucleic Acid Heteroduplexes - genetics | Humans | Molecular Sequence Data | Fungal Proteins | DNA Repair - genetics | Deoxyadenosines - metabolism | MutS Homolog 2 Protein | DNA Polymerase II - metabolism | DNA-Binding Proteins - genetics | DNA-Binding Proteins - metabolism | Mutagenesis | Base Sequence | DNA, Fungal - metabolism | Saccharomyces cerevisiae Proteins | DNA-Directed DNA Polymerase - metabolism | Saccharomyces cerevisiae

Journal Article

BIOTECHNIQUES, ISSN 0736-6205, 01/2020, Volume 68, Issue 2, pp. 85 - 90

Carbohydrate-deficient transferrin (CDT) is a reliable biomarker for chronic alcohol abuse. We developed a method for CDT analysis by capillary isoelectric...

imaged capillary isoelectric focusing | carbohydrate-deficient transferrin | immunodetection | Simple Western | CDT | BIOCHEMISTRY & MOLECULAR BIOLOGY | BIOCHEMICAL RESEARCH METHODS | SERUM | IDENTIFICATION

imaged capillary isoelectric focusing | carbohydrate-deficient transferrin | immunodetection | Simple Western | CDT | BIOCHEMISTRY & MOLECULAR BIOLOGY | BIOCHEMICAL RESEARCH METHODS | SERUM | IDENTIFICATION

Journal Article

Proceedings of the Japan Academy Series A: Mathematical Sciences, ISSN 0386-2194, 03/2010, Volume 86, Issue 3, pp. 60 - 63

We introduce an operator which enable us to give a simple construction of the isomorphism from the so-called Fock space to the L-2-space with respect to a...

Random point field | Poisson measure | Fock space | MATHEMATICS | random point field | RANDOM POINT FIELDS | FERMION | 60G60 | 82B05 | 60G55

Random point field | Poisson measure | Fock space | MATHEMATICS | random point field | RANDOM POINT FIELDS | FERMION | 60G60 | 82B05 | 60G55

Journal Article

ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 07/2019, Volume 26, Issue 3

Much work has been done to count the number of domino tilings for Aztec diamonds and augmented Aztec diamonds. Augmented Aztec rectangles and their chains are...

MATHEMATICS | MATHEMATICS, APPLIED | ENUMERATION | DETERMINANTS | SENSITIVE GRAPHICAL SUBSETS | SIMPLE PROOF

MATHEMATICS | MATHEMATICS, APPLIED | ENUMERATION | DETERMINANTS | SENSITIVE GRAPHICAL SUBSETS | SIMPLE PROOF

Journal Article

Conformal Geometry and Dynamics, ISSN 1088-4173, 10/2008, Volume 12, Issue 11, pp. 174 - 186

Journal Article

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