Web18.01A Calculus. 34-06: Proceedings, conferences, collections, etc. ), 14D07: Variation of Hodge structures [See also, 14D10: Arithmetic ground fields (finite, local, global), 14D15: Formal methods; deformations [See also, 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see, 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)[See also, 14D24: Geometric Langlands program: algebro-geometric aspects [See also, 14D99: None of the above, but in this section, 14E07: Birational automorphisms, Cremona group and generalizations, 14E15: Global theory and resolution of singularities [See also, 14E30: Minimal model program (Mori theory, extremal rays), 14E99: None of the above, but in this section, 14F05: Sheaves, derived categories of sheaves and related constructions [See also, 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also, 14F20: tale and other Grothendieck topologies and (co)homologies, 14F22: Brauer groups of schemes [See also, 14F25: Classical real and complex (co)homology, 14F30: $p$-adic cohomology, crystalline cohomology, 14F35: Homotopy theory; fundamental groups [See also, 14F42: Motivic cohomology; motivic homotopy theory [See also, 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), 14F99: None of the above, but in this section, 14G10: Zeta-functions and related questions [See also, 14G17: Positive characteristic ground fields, 14G27: Other nonalgebraically closed ground fields, 14G32: Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), 14G35: Modular and Shimura varieties [See also, 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also, 14G50: Applications to coding theory and cryptography [See also, 14G99: None of the above, but in this section, 14H05: Algebraic functions; function fields [See also, 14H15: Families, moduli (analytic) [See also, 14H20: Singularities, local rings [See also, 14H25: Arithmetic ground fields [See also, 14H30: Coverings, fundamental group [See also, 14H40: Jacobians, Prym varieties [See also, 14H42: Theta functions; Schottky problem [See also, 14H45: Special curves and curves of low genus, 14H51: Special divisors (gonality, Brill-Noether theory), 14H55: Riemann surfaces; Weierstrass points; gap sequences [See also, 14H57: Dessins d'enfants theory {For arithmetic aspects, see, 14H60: Vector bundles on curves and their moduli [See also, 14H70: Relationships with integrable systems, 14H99: None of the above, but in this section, 14J10: Families, moduli, classification: algebraic theory, 14J15: Moduli, classification: analytic theory; relations with modular forms [See also, 14J20: Arithmetic ground fields [See also, 14J25: Special surfaces {For Hilbert modular surfaces, see, 14J28: $K3$ surfaces and Enriques surfaces, 14J50: Automorphisms of surfaces and higher-dimensional varieties, 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also, 14J80: Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants), 14J99: None of the above, but in this section, 14K10: Algebraic moduli, classification [See also, 14K15: Arithmetic ground fields [See also, 14K20: Analytic theory; abelian integrals and differentials, 14K30: Picard schemes, higher Jacobians [See also, 14K99: None of the above, but in this section, 14L05: Formal groups, $p$-divisible groups [See also, 14L17: Affine algebraic groups, hyperalgebra constructions [See also, 14L24: Geometric invariant theory [See also, 14L30: Group actions on varieties or schemes (quotients) [See also, 14L35: Classical groups (geometric aspects) [See also, 14L40: Other algebraic groups (geometric aspects), 14L99: None of the above, but in this section, 14M05: Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also, 14M15: Grassmannians, Schubert varieties, flag manifolds [See also, 14M17: Homogeneous spaces and generalizations [See also, 14M20: Rational and unirational varieties [See also, 14M25: Toric varieties, Newton polyhedra [See also, 14M27: Compactifications; symmetric and spherical varieties, 14M99: None of the above, but in this section, 14N10: Enumerative problems (combinatorial problems), 14N15: Classical problems, Schubert calculus, 14N20: Configurations and arrangements of linear subspaces, 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also, 14N99: None of the above, but in this section, 14P10: Semialgebraic sets and related spaces, 14P15: Real analytic and semianalytic sets [See also, 14P20: Nash functions and manifolds [See also, 14P25: Topology of real algebraic varieties, 14P99: None of the above, but in this section, 14Q99: None of the above, but in this section, 14R05: Classification of affine varieties, 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), 14R20: Group actions on affine varieties [See also, 14R99: None of the above, but in this section, 14T99: None of the above, but in this section, 15-00: General reference works (handbooks, dictionaries, bibliographies, etc. ), 32F45: Invariant metrics and pseudodistances, 32F99: None of the above, but in this section, 32G05: Deformations of complex structures [See also, 32G07: Deformations of special (e.g. The quantum states that the gates act upon are unit vectors in complex dimensions, with the complex Euclidean norm (the 2 There are several different forms of parallel computing: bit-level, instruction-level, data, and task parallelism.Parallelism has long been employed in cl : n 20-06: Proceedings, conferences, collections, etc. {For the Euler-Maclaurin summation formula, see, 40A30: Convergence and divergence of series and sequences of functions, 40A35: Ideal and statistical convergence [See also, 40A99: None of the above, but in this section, 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section), 40B99: None of the above, but in this section, 40C15: Function-theoretic methods (including power series methods and semicontinuous methods), 40C99: None of the above, but in this section, 40D10: Tauberian constants and oscillation limits, 40D15: Convergence factors and summability factors, 40D20: Summability and bounded fields of methods, 40D25: Inclusion and equivalence theorems, 40D99: None of the above, but in this section, 40E99: None of the above, but in this section, 40F05: Absolute and strong summability (should also be assigned at least one other classification number in Section 40), 40F99: None of the above, but in this section, 40G05: Cesro, Euler, Nrlund and Hausdorff methods, 40G10: Abel, Borel and power series methods, 40G15: Summability methods using statistical convergence [See also, 40G99: None of the above, but in this section, 40H05: Functional analytic methods in summability, 40H99: None of the above, but in this section, 40J05: Summability in abstract structures [See also, 40J99: None of the above, but in this section, 41-00: General reference works (handbooks, dictionaries, bibliographies, etc. ), 62-01: Instructional exposition (textbooks, tutorial papers, etc. 19A13: Stability for projective modules [See also, 19A22: Frobenius induction, Burnside and representation rings, 19A99: None of the above, but in this section, 19B28: $K_1$ of group rings and orders [See also, 19B37: Congruence subgroup problems [See also, 19B99: None of the above, but in this section, 19C09: Central extensions and Schur multipliers, 19C20: Symbols, presentations and stability of $K_2$, 19C99: None of the above, but in this section, 19D23: Symmetric monoidal categories [See also, 19D25: Karoubi-Villamayor-Gersten $K$-theory, 19D50: Computations of higher $K$-theory of rings [See also, 19D55: $K$-theory and homology; cyclic homology and cohomology [See also, 19D99: None of the above, but in this section, 19E15: Algebraic cycles and motivic cohomology [See also, 19E20: Relations with cohomology theories [See also, 19E99: None of the above, but in this section, 19F05: Generalized class field theory [See also, 19F27: tale cohomology, higher regulators, zeta and $L$-functions [See also, 19F99: None of the above, but in this section, 19G24: $L$-theory of group rings [See also, 19G38: Hermitian $K$-theory, relations with $K$-theory of rings, 19G99: None of the above, but in this section, 19J05: Finiteness and other obstructions in $K_0$, 19J99: None of the above, but in this section, 19K35: Kasparov theory ($KK$-theory) [See also, 19K99: None of the above, but in this section, 19L10: Riemann-Roch theorems, Chern characters, 19L20: $J$-homomorphism, Adams operations [See also, 19L41: Connective $K$-theory, cobordism [See also, 19L50: Twisted $K$-theory; differential $K$-theory, 19L64: Computations, geometric applications, 19L99: None of the above, but in this section, 19M05: Miscellaneous applications of $K$-theory, 19M99: None of the above, but in this section, 20-00: General reference works (handbooks, dictionaries, bibliographies, etc. ) Wikipedia. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also, 32A38: Algebras of holomorphic functions [See also, 32A40: Boundary behavior of holomorphic functions, 32A50: Harmonic analysis of several complex variables [See mainly, 32A60: Zero sets of holomorphic functions, 32A65: Banach algebra techniques [See mainly, 32A70: Functional analysis techniques [See mainly, 32A99: None of the above, but in this section, 32B05: Analytic algebras and generalizations, preparation theorems, 32B10: Germs of analytic sets, local parametrization, 32B20: Semi-analytic sets and subanalytic sets [See also, 32B25: Triangulation and related questions, 32B99: None of the above, but in this section, 32C05: Real-analytic manifolds, real-analytic spaces [See also, 32C07: Real-analytic sets, complex Nash functions [See also, 32C09: Embedding of real analytic manifolds, 32C30: Integration on analytic sets and spaces, currents {For local theory, see, 32C35: Analytic sheaves and cohomology groups [See also, 32C36: Local cohomology of analytic spaces, 32C38: Sheaves of differential operators and their modules, $D$-modules [See also, 32C55: The Levi problem in complex spaces; generalizations, 32C99: None of the above, but in this section, 32D99: None of the above, but in this section, 32E05: Holomorphically convex complex spaces, reduction theory, 32E30: Holomorphic and polynomial approximation, Runge pairs, interpolation, 32E35: Global boundary behavior of holomorphic functions, 32E99: None of the above, but in this section, 32F27: Topological consequences of geometric convexity, 32F32: Analytical consequences of geometric convexity (vanishing theorems, etc. ), 46C99: None of the above, but in this section, 46E05: Lattices of continuous, differentiable or analytic functions, 46E10: Topological linear spaces of continuous, differentiable or analytic functions, 46E15: Banach spaces of continuous, differentiable or analytic functions, 46E20: Hilbert spaces of continuous, differentiable or analytic functions, 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also, 46E25: Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see, 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc. CR) structures, 32G10: Deformations of submanifolds and subspaces, 32G13: Analytic moduli problems {For algebraic moduli problems, see, 32G15: Moduli of Riemann surfaces, Teichmller theory [See also, 32G20: Period matrices, variation of Hodge structure; degenerations [See also, 32G34: Moduli and deformations for ordinary differential equations (e.g. ), 54D25: $P$-minimal and $P$-closed spaces, 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc. Max Dot Product of Two Subsequences 1459. ), 12E15: Skew fields, division rings [See also, 12E20: Finite fields (field-theoretic aspects), 12E25: Hilbertian fields; Hilbert's irreducibility theorem, 12E99: None of the above, but in this section, 12F10: Separable extensions, Galois theory, 12F99: None of the above, but in this section, 12G99: None of the above, but in this section, 12H20: Abstract differential equations [See also, 12H25: $p$-adic differential equations [See also, 12H99: None of the above, but in this section, 12J20: General valuation theory [See also, 12J25: Non-Archimedean valued fields [See also, 12J99: None of the above, but in this section, 12K99: None of the above, but in this section, 12L99: None of the above, but in this section, 12Y05: Computational aspects of field theory and polynomials, 12Y99: None of the above, but in this section, 13-00: General reference works (handbooks, dictionaries, bibliographies, etc. ; amenable groups. has limits from the right and from the left at every point of its domain;; has a limit at positive or negative infinity of either a real number, , or .can only have jump discontinuities;; can only have countably many discontinuities in its domain. 81S30: Phase-space methods including Wigner distributions, etc. 47-06: Proceedings, conferences, collections, etc. ), 11S82: Non-Archimedean dynamical systems [See mainly, 11S99: None of the above, but in this section, 11T24: Other character sums and Gauss sums, 11T55: Arithmetic theory of polynomial rings over finite fields, 11T71: Algebraic coding theory; cryptography, 11T99: None of the above, but in this section, 11U99: None of the above, but in this section, 11Y40: Algebraic number theory computations, 11Y50: Computer solution of Diophantine equations, 11Y70: Values of arithmetic functions; tables, 11Y99: None of the above, but in this section, 11Z05: Miscellaneous applications of number theory, 11Z99: None of the above, but in this section, 12-00: General reference works (handbooks, dictionaries, bibliographies, etc. Using the pointwise order on functions between posets, one may alternatively write the extensiveness property as idP cl, where id is the identity function. 30A05: Monogenic properties of complex functions (including polygenic and areolar monogenic functions), 30A10: Inequalities in the complex domain, 30A99: None of the above, but in this section, 30B10: Power series (including lacunary series), 30B30: Boundary behavior of power series, over-convergence, 30B50: Dirichlet series and other series expansions, exponential series [See also, 30B60: Completeness problems, closure of a system of functions, 30B99: None of the above, but in this section, 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. 91A13: Games with infinitely many players, 91A24: Positional games (pursuit and evasion, etc.) ), 93C85: Automated systems (robots, etc.) WebAbout Our Coalition. [See also, 60J22: Computational methods in Markov chains [See also, 60J25: Continuous-time Markov processes on general state spaces, 60J27: Continuous-time Markov processes on discrete state spaces, 60J28: Applications of continuous-time Markov processes on discrete state spaces, 60J35: Transition functions, generators and resolvents [See also, 60J45: Probabilistic potential theory [See also, 60J55: Local time and additive functionals, 60J67: Stochastic (Schramm-)Loewner evolution (SLE), 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 33-06: Proceedings, conferences, collections, etc. 90-06: Proceedings, conferences, collections, etc. ), 91B38: Production theory, theory of the firm, 91B51: Dynamic stochastic general equilibrium theory, 91B64: Macro-economic models (monetary models, models of taxation), 91B76: Environmental economics (natural resource models, harvesting, pollution, etc. ), 16-01: Instructional exposition (textbooks, tutorial papers, etc. 03D60: Computability and recursion theory on ordinals, admissible sets, etc. 20K30: Automorphisms, homomorphisms, endomorphisms, etc. 74A25: Molecular, statistical, and kinetic theories, 74A40: Random materials and composite materials, 74A50: Structured surfaces and interfaces, coexistent phases, 74A99: None of the above, but in this section, 74B10: Linear elasticity with initial stresses, 74B15: Equations linearized about a deformed state (small deformations superposed on large), 74B99: None of the above, but in this section, 74C05: Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials), 74C10: Small-strain, rate-dependent theories (including theories of viscoplasticity), 74C15: Large-strain, rate-independent theories (including nonlinear plasticity), 74C20: Large-strain, rate-dependent theories, 74C99: None of the above, but in this section, 74D99: None of the above, but in this section, 74E99: None of the above, but in this section, 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc. One Galois connection that gives rise to the closure operator cl can be described as follows: if A is the set of closed elements with respect to cl, then cl: P A is the lower adjoint of a Galois connection between P and A, with the upper adjoint being the embedding of A into P. Furthermore, every lower adjoint of an embedding of some subset into P is a closure operator. ), 53C20: Global Riemannian geometry, including pinching [See also, 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also, 53C23: Global geometric and topological methods ( la Gromov); differential geometric analysis on metric spaces, 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc. But then C is not a sublattice of the lattice P(S). ), 62H25: Factor analysis and principal components; correspondence analysis, 62H30: Classification and discrimination; cluster analysis [See also, 62H86: Multivariate analysis and fuzziness, 62H99: None of the above, but in this section, 62J07: Ridge regression; shrinkage estimators, 62J10: Analysis of variance and covariance, 62J86: Fuzziness, and linear inference and regression, 62J99: None of the above, but in this section, 62K86: Fuzziness and design of experiments, 62K99: None of the above, but in this section, 62L99: None of the above, but in this section, 62M02: Markov processes: hypothesis testing, 62M07: Non-Markovian processes: hypothesis testing, 62M09: Non-Markovian processes: estimation, 62M10: Time series, auto-correlation, regression, etc. and systems on graphs, 82C21: Dynamic continuum models (systems of particles, etc. a normed space, defined implicitely 83C75: Space-time singularities, cosmic censorship, etc. 01A12: Indigenous cultures of the Americas, 01A13: Other indigenous cultures (non-European), 01A15: Indigenous European cultures (pre-Greek, etc. ), 37D30: Partially hyperbolic systems and dominated splittings, 37D35: Thermodynamic formalism, variational principles, equilibrium states, 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc. WebThe results of the Pseudo-Boolean Competition 2009 are online. Notes: Usually the number of registers is a power of two, e.g. Define boolean algebras, create and parse boolean expressions and create custom boolean DSL. C WebDissertations & Theses from 2022. Formally: PS is pseudo-closed if and only if. f zeros of functions with bounded Dirichlet integral) {For algebraic theory, see, 30C20: Conformal mappings of special domains, 30C25: Covering theorems in conformal mapping theory, 30C30: Numerical methods in conformal mapping theory [See also, 30C35: General theory of conformal mappings, 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc. Such families of "closed sets" are sometimes called closure systems or "Moore families",[1] in honor of E. H. Moore who studied closure operators in his 1910 Introduction to a form of general analysis, whereas the concept of the closure of a subset originated in the work of Frigyes Riesz in connection with topological spaces. Since C is also a lattice, it is often referred to as an algebraic lattice in this context. ), 16E40: (Co)homology of rings and algebras (e.g. If P is a complete lattice, then a subset A of P is the set of closed elements for some closure operator on P if and only if A is a Moore family on P, i.e. ), 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc. C ( S The discontinuities, however, do not necessarily consist of ), 51C99: None of the above, but in this section, 51D10: Abstract geometries with exchange axiom, 51D15: Abstract geometries with parallelism, 51D20: Combinatorial geometries [See also, 51D30: Continuous geometries and related topics [See also, 51D99: None of the above, but in this section, 51E12: Generalized quadrangles, generalized polygons, 51E14: Finite partial geometries (general), nets, partial spreads, 51E20: Combinatorial structures in finite projective spaces [See also, 51E22: Linear codes and caps in Galois spaces [See also, 51E24: Buildings and the geometry of diagrams, 51E30: Other finite incidence structures [See also, 51E99: None of the above, but in this section, 51F15: Reflection groups, reflection geometries [See also, 51F20: Congruence and orthogonality [See also, 51F25: Orthogonal and unitary groups [See also, 51F99: None of the above, but in this section, 51G05: Ordered geometries (ordered incidence structures, etc. ), 82C80: Numerical methods (Monte Carlo, series resummation, etc. ), 33D50: Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable, 33D52: Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc. ), 12-02: Research exposition (monographs, survey articles), 12-03: Historical (must also be assigned at least one classification number from Section 01), 12-04: Explicit machine computation and programs (not the theory of computation or programming). 26B40: Representation and superposition of functions, 26B99: None of the above, but in this section, 26C05: Polynomials: analytic properties, etc. 49J05: Free problems in one independent variable, 49J10: Free problems in two or more independent variables, 49J15: Optimal control problems involving ordinary differential equations, 49J20: Optimal control problems involving partial differential equations, 49J21: Optimal control problems involving relations other than differential equations, 49J27: Problems in abstract spaces [See also, 49J30: Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc. ), 57-01: Instructional exposition (textbooks, tutorial papers, etc. 60-08: Computational methods (not classified at a more specific level) [See also, 60A10: Probabilistic measure theory {For ergodic theory, see, 60A99: None of the above, but in this section, 60B05: Probability measures on topological spaces, 60B10: Convergence of probability measures, 60B11: Probability theory on linear topological spaces [See also, 60B12: Limit theorems for vector-valued random variables (infinite-dimensional case), 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization, 60B20: Random matrices (probabilistic aspects; for algebraic aspects see, 60B99: None of the above, but in this section, 60C99: None of the above, but in this section, 60D05: Geometric probability and stochastic geometry [See also, 60D99: None of the above, but in this section, 60E07: Infinitely divisible distributions; stable distributions, 60E10: Characteristic functions; other transforms, 60E15: Inequalities; stochastic orderings, 60E99: None of the above, but in this section, 60F05: Central limit and other weak theorems, 60F17: Functional limit theorems; invariance principles, 60F99: None of the above, but in this section, 60G05: Foundations of stochastic processes, 60G22: Fractional processes, including fractional Brownian motion, 60G30: Continuity and singularity of induced measures, 60G35: Signal detection and filtering [See also, 60G40: Stopping times; optimal stopping problems; gambling theory [See also, 60G42: Martingales with discrete parameter, 60G44: Martingales with continuous parameter, 60G46: Martingales and classical analysis, 60G50: Sums of independent random variables; random walks, 60G51: Processes with independent increments; L\'evy processes, 60G70: Extreme value theory; extremal processes, 60G99: None of the above, but in this section, 60H07: Stochastic calculus of variations and the Malliavin calculus, 60H10: Stochastic ordinary differential equations [See also, 60H15: Stochastic partial differential equations [See also, 60H25: Random operators and equations [See also, 60H30: Applications of stochastic analysis (to PDE, etc. 54E20: Stratifiable spaces, cosmic spaces, etc. The column "Registers" only counts the integer "registers" usable by The ones left are used as constants like TRUE/FALSE are used as boolean constants. The dimension of a vector space, or the transcendence degree of a field (over its prime field) is exactly the rank of the corresponding matroid. {\displaystyle \operatorname {cl} (\varnothing )=\varnothing } ri 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 42A05: Trigonometric polynomials, inequalities, extremal problems, 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly, 42A20: Convergence and absolute convergence of Fourier and trigonometric series, 42A24: Summability and absolute summability of Fourier and trigonometric series, 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc. ), 03H15: Nonstandard models of arithmetic [See also, 03H99: None of the above, but in this section, 05-00: General reference works (handbooks, dictionaries, bibliographies, etc. ), 52B55: Computational aspects related to convexity {For computational geometry and algorithms, see, 52B60: Isoperimetric problems for polytopes, 52B99: None of the above, but in this section, 52C05: Lattices and convex bodies in $2$ dimensions [See also, 52C07: Lattices and convex bodies in $n$ dimensions [See also, 52C10: Erds problems and related topics of discrete geometry [See also, 52C15: Packing and covering in $2$ dimensions [See also, 52C17: Packing and covering in $n$ dimensions [See also, 52C20: Tilings in $2$ dimensions [See also, 52C22: Tilings in $n$ dimensions [See also, 52C25: Rigidity and flexibility of structures [See also, 52C26: Circle packings and discrete conformal geometry, 52C30: Planar arrangements of lines and pseudolines, 52C35: Arrangements of points, flats, hyperplanes [See also, 52C45: Combinatorial complexity of geometric structures [See also, 52C99: None of the above, but in this section, 53-00: General reference works (handbooks, dictionaries, bibliographies, etc. ), 74F99: None of the above, but in this section, 74G10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc. ), 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) ), 13-02: Research exposition (monographs, survey articles), 13-03: Historical (must also be assigned at least one classification number from Section 01), 13-04: Explicit machine computation and programs (not the theory of computation or programming). 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