Nonlinear Analysis, Theory, Methods and Applications, ISSN 0362-546X, 2014, Volume 106, pp. 138 - 150

This paper provides a quantitative version of the classical image recovery problem to find an ε-approximate solution of the problem. The rate of asymptotic...

Metric projection | Uniformly convex space | Common fixed point | Proof mining | Asymptotic regularity | Image recovery | Nonexpansive mapping | FEASIBILITY PROBLEMS | ITERATION | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | CONVEX COMBINATIONS | MATHEMATICS | BANACH-SPACES | FUNCTIONAL-ANALYSIS | LOGICAL METATHEOREMS | HYPERBOLIC SPACES | PROJECTIONS | Image processing | Analysis | Algorithms | Approximation | Asymptotic properties | Images | Recovery | Regularity | Optimization | Convergence

Metric projection | Uniformly convex space | Common fixed point | Proof mining | Asymptotic regularity | Image recovery | Nonexpansive mapping | FEASIBILITY PROBLEMS | ITERATION | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | CONVEX COMBINATIONS | MATHEMATICS | BANACH-SPACES | FUNCTIONAL-ANALYSIS | LOGICAL METATHEOREMS | HYPERBOLIC SPACES | PROJECTIONS | Image processing | Analysis | Algorithms | Approximation | Asymptotic properties | Images | Recovery | Regularity | Optimization | Convergence

Journal Article

Science, ISSN 0036-8075, 6/2013, Volume 340, Issue 6137, pp. 1177 - 1178

The term "controversial theorem" sounds like an oxymoron, but Bayes' theorem has played this part for two-and-a-half centuries. Twice it has soared to...

Scientific method | Mathematical theorems | Logical theorems | Statistical theories | PERSPECTIVES | Twins | Statistics | Bayes theorem | Empirical evidence | MULTIDISCIPLINARY SCIENCES | Science | Theorems | Boom | Reasoning | Inference | Landmarks | Acoustics | Bayesian analysis

Scientific method | Mathematical theorems | Logical theorems | Statistical theories | PERSPECTIVES | Twins | Statistics | Bayes theorem | Empirical evidence | MULTIDISCIPLINARY SCIENCES | Science | Theorems | Boom | Reasoning | Inference | Landmarks | Acoustics | Bayesian analysis

Journal Article

Economic Theory, ISSN 0938-2259, 1/2013, Volume 52, Issue 1, pp. 41 - 73

This paper provides a set-theoretic model of knowledge and unawareness. A new property called Awareness Leads to Knowledge shows that unawareness of theorems...

Trade | Economic models | Wisdom | Economic theory | Logical theorems | Information asymmetry | Reasoning | Syntactic models | Introspection | Game theory | Uncertainty | Economics general | Unawareness | Interactive epistemology | Bounded perception | Game Theory, Economics, Social and Behav. Sciences | Knowledge | Economics / Management Science | Economic Theory | C70 | D80 | C72 | D82 | FLEXIBILITY | MODEL | AWARENESS | DISAGREE | PROBABILITY | INTERACTIVE UNAWARENESS | ECONOMICS | PARTITIONAL INFORMATION STRUCTURES | STATE-SPACE | PREFERENCE | Fuzzy sets | Set theory | Usage | Models | Awareness | Studies | Epistemology

Trade | Economic models | Wisdom | Economic theory | Logical theorems | Information asymmetry | Reasoning | Syntactic models | Introspection | Game theory | Uncertainty | Economics general | Unawareness | Interactive epistemology | Bounded perception | Game Theory, Economics, Social and Behav. Sciences | Knowledge | Economics / Management Science | Economic Theory | C70 | D80 | C72 | D82 | FLEXIBILITY | MODEL | AWARENESS | DISAGREE | PROBABILITY | INTERACTIVE UNAWARENESS | ECONOMICS | PARTITIONAL INFORMATION STRUCTURES | STATE-SPACE | PREFERENCE | Fuzzy sets | Set theory | Usage | Models | Awareness | Studies | Epistemology

Journal Article

Social Choice and Welfare, ISSN 0176-1714, 7/2007, Volume 29, Issue 1, pp. 19 - 33

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether...

Aggregation | Binary relations | Logical theorems | Model theory | Dictators | Dictatorship | Paradoxes | Predicate logic | Judgment | Logical impossibility | SOCIAL SCIENCES, MATHEMATICAL METHODS | DECISIONS | PROPOSITIONS | ECONOMICS | SETS | Studies | Theorems | Group dynamics | Decision making

Aggregation | Binary relations | Logical theorems | Model theory | Dictators | Dictatorship | Paradoxes | Predicate logic | Judgment | Logical impossibility | SOCIAL SCIENCES, MATHEMATICAL METHODS | DECISIONS | PROPOSITIONS | ECONOMICS | SETS | Studies | Theorems | Group dynamics | Decision making

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 4/2014, Volume 18, Issue 2, pp. 451 - 462

We study the minimax theorems for set-valued mappings with several hierarchical process, and propose three versions for minimax theorems in topological vector...

Minimax | Mathematical theorems | Topological theorems | Logical theorems | Saddle points | Topological vector spaces | Scalars | Mathematical inequalities | Mathematical vectors | Topological spaces | Minimax theorems | Cone-saddle points | Cone-convexities | MATHEMATICS | OPTIMIZATION

Minimax | Mathematical theorems | Topological theorems | Logical theorems | Saddle points | Topological vector spaces | Scalars | Mathematical inequalities | Mathematical vectors | Topological spaces | Minimax theorems | Cone-saddle points | Cone-convexities | MATHEMATICS | OPTIMIZATION

Journal Article

Economic Theory, ISSN 0938-2259, 10/2013, Volume 54, Issue 2, pp. 249 - 271

This paper identifies and illuminates a common impossibility principle underlying a number of impossibility theorems in social choice. We consider social...

Social choice | Economic theory | Logical theorems | Voting | Dictators | Social welfare | Dictatorship | Nash equilibrium | Mathematical functions | Logical impossibility | Economics general | Impossibility theorem | Economic Theory | Game Theory, Economics, Social and Behav. Sciences | Independence of losing alternatives | Independence of infeasible alternatives | Economics / Management Science | D71 | ARROWS THEOREM | MANIPULATION | VOTING PROCEDURES | CORRESPONDENCES | STRATEGIC CANDIDACY | DIRECT PROOF | INDEPENDENCE | SOCIAL CHOICE RULES | PIVOTAL VOTERS | ECONOMICS | GIBBARD-SATTERTHWAITE THEOREM | Analysis | Studies | Economic models | Theorems | Economic statistics

Social choice | Economic theory | Logical theorems | Voting | Dictators | Social welfare | Dictatorship | Nash equilibrium | Mathematical functions | Logical impossibility | Economics general | Impossibility theorem | Economic Theory | Game Theory, Economics, Social and Behav. Sciences | Independence of losing alternatives | Independence of infeasible alternatives | Economics / Management Science | D71 | ARROWS THEOREM | MANIPULATION | VOTING PROCEDURES | CORRESPONDENCES | STRATEGIC CANDIDACY | DIRECT PROOF | INDEPENDENCE | SOCIAL CHOICE RULES | PIVOTAL VOTERS | ECONOMICS | GIBBARD-SATTERTHWAITE THEOREM | Analysis | Studies | Economic models | Theorems | Economic statistics

Journal Article

Annals of Mathematics, ISSN 0003-486X, 11/2004, Volume 160, Issue 3, pp. 1099 - 1127

Let X be a smooth quasiprojective subscheme of P of dimension m ≥ 0 over F . Then there exist homogeneous polynomials f over F for which the intersection of X...

Integers | Mathematical theorems | Logical proofs | Hypersurfaces | Hyperplanes | Coordinate systems | Polynomials | Curves | Arithmetic | SPACE-FILLING CURVES | MATHEMATICS | VARIETIES

Integers | Mathematical theorems | Logical proofs | Hypersurfaces | Hyperplanes | Coordinate systems | Polynomials | Curves | Arithmetic | SPACE-FILLING CURVES | MATHEMATICS | VARIETIES

Journal Article

Studia Logica, ISSN 0039-3215, 06/2017, Volume 105, Issue 3, pp. 611 - 624

Starting in 2005, general logical metatheorems have been developed that guarantee the extractability of uniform effective bounds from large classes of proofs...

CAT(κ) -spaces | Effective bounds | Proof mining | MATHEMATICS | GEODESIC SPACES | PHILOSOPHY | FUNCTIONAL-ANALYSIS | CAT(kappa)-spaces | LOGICAL METATHEOREMS | LOGIC | Mineral industry | Numerical analysis | Mining industry | Analysis

CAT(κ) -spaces | Effective bounds | Proof mining | MATHEMATICS | GEODESIC SPACES | PHILOSOPHY | FUNCTIONAL-ANALYSIS | CAT(kappa)-spaces | LOGICAL METATHEOREMS | LOGIC | Mineral industry | Numerical analysis | Mining industry | Analysis

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2004, Volume 356, Issue 4, pp. 1637 - 1689

We consider a large class of partially hyperbolic systems containing, among others, affine maps, frame flows on negatively curved manifolds, and mostly...

Ergodic theory | Mathematical manifolds | Mathematical theorems | Central limit theorem | Logical theorems | Lebesgue measures | Mathematics | Topology | Dynamical systems | Martingales | Gibbs measure | Absolute continuity | Partial hyperbolicity | UNIQUE ERGODICITY | MARKOV-CHAINS | HOMOGENEOUS SPACES | BERNOULLI | partial hyperbolicity | GROUP EXTENSIONS | ANOSOV-FLOWS | MATHEMATICS | central limit theorem | STABLY ERGODIC DIFFEOMORPHISMS | DYNAMICAL-SYSTEMS | LARGE DEVIATIONS | absolute continuity | POISSON LAW

Ergodic theory | Mathematical manifolds | Mathematical theorems | Central limit theorem | Logical theorems | Lebesgue measures | Mathematics | Topology | Dynamical systems | Martingales | Gibbs measure | Absolute continuity | Partial hyperbolicity | UNIQUE ERGODICITY | MARKOV-CHAINS | HOMOGENEOUS SPACES | BERNOULLI | partial hyperbolicity | GROUP EXTENSIONS | ANOSOV-FLOWS | MATHEMATICS | central limit theorem | STABLY ERGODIC DIFFEOMORPHISMS | DYNAMICAL-SYSTEMS | LARGE DEVIATIONS | absolute continuity | POISSON LAW

Journal Article

The Monist, ISSN 0026-9662, 10/2014, Volume 97, Issue 4, pp. 503 - 570

The author will use quantifier variance to label the conjunction of conciliationism about some ontological question with the view that the relevant languages...

Emperors | Logical theorems | Quantification | Semantics | Metaphysics | International community | Predicates | Entailment | Variance | Eggs | PHILOSOPHY | Science | Theorems (Mathematics) | Research | Mathematical research | Beliefs, opinions and attitudes | Information content | Language | Theory | Pragmatism | Quantifiers | Philosophy

Emperors | Logical theorems | Quantification | Semantics | Metaphysics | International community | Predicates | Entailment | Variance | Eggs | PHILOSOPHY | Science | Theorems (Mathematics) | Research | Mathematical research | Beliefs, opinions and attitudes | Information content | Language | Theory | Pragmatism | Quantifiers | Philosophy

Journal Article

Operations Research, ISSN 0030-364X, 12/2014, Volume 62, Issue 6, pp. 1453 - 1466

Bandwidth-sharing networks provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers in computer and...

networks | limit theorems | Markovian | Approximation | Mathematical theorems | Lagrange multipliers | Directional derivatives | Network traffic | Utility functions | Logical givens | Equilibrium flow | Mathematical vectors | Random variables | METHODS | Networks | Limit theorems | PERFORMANCE ANALYSIS | FLUID LIMITS | OVERLOAD | POLICY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANAGEMENT | SERVICES | STABILITY | PROPORTIONAL FAIRNESS | MODEL | OPTIMALITY

networks | limit theorems | Markovian | Approximation | Mathematical theorems | Lagrange multipliers | Directional derivatives | Network traffic | Utility functions | Logical givens | Equilibrium flow | Mathematical vectors | Random variables | METHODS | Networks | Limit theorems | PERFORMANCE ANALYSIS | FLUID LIMITS | OVERLOAD | POLICY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANAGEMENT | SERVICES | STABILITY | PROPORTIONAL FAIRNESS | MODEL | OPTIMALITY

Journal Article

The Bulletin of Symbolic Logic, ISSN 1079-8986, 6/2019, Volume 25, Issue 2, pp. 208 - 212

We show that if (𝑀, ∈₁, ∈₂) satisfies the first-order Zermelo–Fraenkel axioms of set theory when the membership relation is ∈₁ and also when the membership...

Mathematical set theory | Categoricity | Mathematical theorems | Logical theorems | Communications | Mathematical logic | Zermelo Frankel set theory | Mathematical relations | First order theories | Conference proceedings | MATHEMATICS | Zermelo | set theory | categoricity | LOGIC | second-order logic

Mathematical set theory | Categoricity | Mathematical theorems | Logical theorems | Communications | Mathematical logic | Zermelo Frankel set theory | Mathematical relations | First order theories | Conference proceedings | MATHEMATICS | Zermelo | set theory | categoricity | LOGIC | second-order logic

Journal Article

Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, 10/2011, Volume 99, Issue 1/3, pp. 279 - 319

Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT—a syntactic notion introduced here for arbitrary...

Universal algebra | Linear logic | Algebra | Mathematical theorems | Logical theorems | Axioms | Deduction theorem | Finite model property | Mathematical congruence | Abstract algebraic logic | deduction-detachment theorem | modular | Computational Linguistics | algebraizable | quasivariety | substructural logics | EDPC | Deductive system | protoalgebraic | Logic | distributive | Philosophy | Mathematical Logic and Foundations | LINEAR LOGIC | EXTENSIONS | FINITE-MODEL PROPERTY | LOGIC | MATHEMATICS | PHILOSOPHY | QUASIVARIETIES | Analysis | Universities and colleges

Universal algebra | Linear logic | Algebra | Mathematical theorems | Logical theorems | Axioms | Deduction theorem | Finite model property | Mathematical congruence | Abstract algebraic logic | deduction-detachment theorem | modular | Computational Linguistics | algebraizable | quasivariety | substructural logics | EDPC | Deductive system | protoalgebraic | Logic | distributive | Philosophy | Mathematical Logic and Foundations | LINEAR LOGIC | EXTENSIONS | FINITE-MODEL PROPERTY | LOGIC | MATHEMATICS | PHILOSOPHY | QUASIVARIETIES | Analysis | Universities and colleges

Journal Article

Journal of Logic, Language and Information, ISSN 0925-8531, 6/2019, Volume 28, Issue 2, pp. 183 - 216

$${ CatLog3}$$ C a t L o g 3 is a 7000 line Prolog parser/theorem-prover for logical categorial grammar. In such logical categorial grammar syntax is universal...

Information Systems Applications (incl.Internet) | Semantics | Focusing | Logical categorial grammar | Parsing-as-deduction | Grammar-as-logic | Logic | Count-invariance | Philosophy | Computer science | Grammar, Comparative and general | Language processing | Computational linguistics | Analysis | Natural language interfaces | Intel·ligència artificial | Categorial grammar | Informàtica | Gramàtica categorial | Llenguatge natural | Àrees temàtiques de la UPC

Information Systems Applications (incl.Internet) | Semantics | Focusing | Logical categorial grammar | Parsing-as-deduction | Grammar-as-logic | Logic | Count-invariance | Philosophy | Computer science | Grammar, Comparative and general | Language processing | Computational linguistics | Analysis | Natural language interfaces | Intel·ligència artificial | Categorial grammar | Informàtica | Gramàtica categorial | Llenguatge natural | Àrees temàtiques de la UPC

Journal Article

Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, 10/2014, Volume 102, Issue 5, pp. 1003 - 1020

In the late 1960s and early 1970s, Dana Scott introduced a kind of generalization (or perhaps simplification would be a better description) of the notion of...

Logical disjunction | Algebra | Mathematical monotonicity | Logical theorems | Sequents | Inference | Mathematical logic | Cut elimination theorem | Entailment | Abstract entailment relations | Structural rules | Computational Linguistics | Dana Scott | Lindenbaum | Logic | Philosophy | Mathematical Logic and Foundations | MATHEMATICS | PHILOSOPHY | LOGIC | Computer science

Logical disjunction | Algebra | Mathematical monotonicity | Logical theorems | Sequents | Inference | Mathematical logic | Cut elimination theorem | Entailment | Abstract entailment relations | Structural rules | Computational Linguistics | Dana Scott | Lindenbaum | Logic | Philosophy | Mathematical Logic and Foundations | MATHEMATICS | PHILOSOPHY | LOGIC | Computer science

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2014, Volume 142, Issue 1, pp. 335 - 349

We exhibit a close correspondence between L1-computable functions and Schnorr tests. Using this correspondence, we prove that a point x ∈ [0, 1]d is Schnorr...

Ergodic theory | Mathematical differentiation | Lebesgue theorem | Mathematical theorems | Logical theorems | Cubes | Randomness | Polynomials | Step functions | Computability | MARTIN-LOF RANDOMNESS | MATHEMATICS | MATHEMATICS, APPLIED | POINTS | BIRKHOFFS ERGODIC THEOREM

Ergodic theory | Mathematical differentiation | Lebesgue theorem | Mathematical theorems | Logical theorems | Cubes | Randomness | Polynomials | Step functions | Computability | MARTIN-LOF RANDOMNESS | MATHEMATICS | MATHEMATICS, APPLIED | POINTS | BIRKHOFFS ERGODIC THEOREM

Journal Article

Annals of Mathematics, ISSN 0003-486X, 11/2012, Volume 176, Issue 3, pp. 1427 - 1482

We prove that certain compact cube complexes have special finite covers. This means they have finite covers whose fundamental groups are quasiconvex subgroups...

Integers | Mathematical theorems | Logical theorems | Hyperplanes | Cubes | Convexity | Topographical elevation | Vertices | Arithmetic | MATHEMATICS | SUBGROUPS

Integers | Mathematical theorems | Logical theorems | Hyperplanes | Cubes | Convexity | Topographical elevation | Vertices | Arithmetic | MATHEMATICS | SUBGROUPS

Journal Article

The Bulletin of Symbolic Logic, ISSN 1079-8986, 9/2016, Volume 22, Issue 3, pp. 305 - 331

We study algorithmic randomness notions via effective versions of almostevery where theorems from analysis and ergodic theory. The effectivization is in terms...

Ergodic theory | Lebesgue theorem | Logical theorems | Randomness | Dyadics | Integral test | Porosity | Density | Martingales | Perceptron convergence procedure | ergodic theory | randomness | almost-everywhere theorem | Lebesgue density | MATHEMATICS | BIRKHOFFS ERGODIC THEOREM | LOGIC | COMPUTABILITY | Theorems | Equivalence | Mathematical functions | Convergence | Ergodic processes

Ergodic theory | Lebesgue theorem | Logical theorems | Randomness | Dyadics | Integral test | Porosity | Density | Martingales | Perceptron convergence procedure | ergodic theory | randomness | almost-everywhere theorem | Lebesgue density | MATHEMATICS | BIRKHOFFS ERGODIC THEOREM | LOGIC | COMPUTABILITY | Theorems | Equivalence | Mathematical functions | Convergence | Ergodic processes

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2011, Volume 139, Issue 10, pp. 3553 - 3560

This paper deals with a strengthening of the Bishop-Phelps property for operators that in the literature is called the Bishop-Phelps-Bollobás property. Let X...

Hausdorff spaces | Frechet topologies | Mathematical theorems | Topological theorems | Logical theorems | Adjoints | Mathematics | Banach space | Continuous functions | Bollobás | Asplund operator | Weakly compact operator | Bishop-phelps | Norm-attaining | Fragmentability | Bollobas | fragmentability | MATHEMATICS | CONJUGATE BANACH-SPACES | MATHEMATICS, APPLIED | weakly compact operator | norm-attaining | RADON-NIKODYM PROPERTY | Bishop-Phelps | NORM ATTAINING OPERATORS

Hausdorff spaces | Frechet topologies | Mathematical theorems | Topological theorems | Logical theorems | Adjoints | Mathematics | Banach space | Continuous functions | Bollobás | Asplund operator | Weakly compact operator | Bishop-phelps | Norm-attaining | Fragmentability | Bollobas | fragmentability | MATHEMATICS | CONJUGATE BANACH-SPACES | MATHEMATICS, APPLIED | weakly compact operator | norm-attaining | RADON-NIKODYM PROPERTY | Bishop-Phelps | NORM ATTAINING OPERATORS

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 07/2014, Volume 27, Issue 3, pp. 863 - 892

Metamathematics | Mathematical theorems | Mathematical monotonicity | Logical theorems | Infinite sets | Natural numbers | Mathematical logic | Recursion theory | Mathematical preconditioning | Arithmetic | MATHEMATICS | RCA | Reverse mathematics | Sigma-bounding | Ramsey's Theorem for Pairs | Stable Ramsey's Theorem for Pairs

Journal Article

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