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Lavrent'ev, P. Convergence of the distributions of functionals of random sequences and processes that are given on the entire axis A. Binary additive problems and multiplicative functions B. Bredikhin, L. Two-sided difference methods for solving linear boundary-value problems for ordinary differential equations E. Large deviations of additive arithmetic functions J. Linear integral part functions, their application and properties K.

The method of trigonometric sums in the metric theory of Diophantine approximations of dependent variables V. A certain application of number theory to multidimensional crystallography D. The expansion of functions of a mixed class in a series of algebraic polynomials V. Constructive variants of the laws of large numbers N. The complexity of the expansion of algebraic irrationalities in continued fractions V.

Identification of the symmetry predicate by means of multihead Turing machines with input A. A hierarchy of ways of understanding judgments in constructive mathematics N. Unconditionally convergent spectral decompositions and interpolation problems V. Bases of invariant subspaces and operator interpolation N. The problem of simultaneous approximation and of removal of the singularities of Cauchy type integrals S.

Ideals and factorization in algebras of analytic functions that are smooth up to the boundary N. Multiplicative estimates for integral norms of differentiable functions of several variables O. Estimates for the moduli of continuity of abstract functions defined in a domain O. A constructive characterization of classes of functions with a dominating mixed derivative Ya. Sobolev's integral representation and Taylor's formula V.

The density of infinitely differentiable functions in Sobolev spaces for an arbitrary open set V. On the search for the maximum of a function and on the approximate global solution of a system of nonlinear equations E. The comparison of differential operators and differential operators of constant strength G.

A method of fictitious domains for the second and third boundary value problems V. Some weighted imbedding theorems in a domain with a nonsmooth boundary A. Certain inequalities for fractional seminorms Yu. Imbedding of classes of functions with a dominating mixed modulus of smoothness M. The structural and constructive characterization of certain classes of functions M. Properties of the solution of a certain class of quasilinear second order elliptic equations in divergence form G. Report at the opening ceremony of the Conference M.

Exponential sums in the development of number theory K. Recent works of I. Vinogradov Yu. Some exponential sums L. Artin's conjectures and the law of reciprocity A. Pyatetskii-Shapiro, I. The Hubert modular group and some algebraic surfaces F. Recent advances in transcendence theory A. The principal of nonstandard functional equations theory for Dirichlet's functions, consequences and applications of it A.

On the uniform boundedness of the torsion of elliptic curves over algebraic number fields V. On the partition function of positive definite matrices T. On the distribution of arithmetic functions J. On sums of squares J. Siegel's forms and zeta-functions A. Applications of trigonometric sums method to metric theory of Diophantine approximation of dependent variables V. Reducibility of quadrinomials A. Lattice points in moredimensional ellipsoid B. The geometry of linear algebraic groups V. The arithmetic theory of linear algebraic groups and number theory V.

On arithmetic properties of values of analytic functions A. Dirichlet characters and polynomials D. On the extended Hecke theta-formula T. Modular correspondences, heights and isogenes of abelian varieties A. Constructive method in the theory of equations over finite fields S. On sums of real characters M. On large sieve inequalities and their applications E.

On some problems of prime numbers theory, connected with I. Vinogradov's method A. Petr Sergeevich Novikov photo. Gilenko, E. The works of P. Novikov in the area of descriptive set theory A. Novikov and his students on algorithmic questions of algebra S. Generalized computations N. The operators of logical approximation D. Bochvar, V. Graphs with prescribed environments of the vertices V.

Mathematical methods for studying natural languages A. The method of transfinite indices in the theory of operations over sets A. Regular, linear and probabilistic events A. Muchnik, A. On the conjugacy problem in semigroups V. The reconstruction of words Ya. Certain works connected with descriptive set theory and topology A.

The extension of linear operators A. Frequency computations B. Universal functions for certain classes of recursive functions and sets V. Uniformization of sets of certain classes E. The construction of irredundant multiple experiments for automata S. Sergei Mikhailovich Nikol'skii: On the occasion of his 70th birthday. Optimal impulse and continuous control: method of nonlinear quasi-variational inequalities A. Bensoussan, J. Besov, S. Certain classes of the solutions of the Maxwell—Einstein equation A.

Bitsadze, V. Nikol'skii V. Certain relations between the approximative characteristics of classes of periodic functions N. Some inequalities for trigonometric and algebraic polynomials and their derivatives G. An approximate method for finding the critical points of even functionals J. An estimate for the approximation of continuous functions by sequences of Fourier sum K.

Approximation of the semicircle by algebraic polynomials B. Telyakovskii, G. Certain properties of the solutions of quasilinear elliptic equations G.

Alebastrov, G. Relative Hamiltonian for states of von Neumann algebras H.

### Homology, Homotopy and Applications

On automodel asymptotic in quantum field theory N. Vladimirov, A. Causality and local analyticity: general results and some applications to quantum field theory J. Bros, D. Analytic functions of several complex variables, and quantum field theory V. Local gauge models predicting their own superselection rules J. Bonnard, R. Exponential interaction of scalar massless fields third order M. The renormalized Hamiltonian, the local fields, and the scattering theory for some translationally-invariant models of quantum field theory I.

Aref'eva, A. Pogrebkov, V. Sushko, I. Particals and fields J. Locality and particle statistics S. Feynman's path integral C. Renormalization and indefinite metric O. Equivalence properties of coherent superselection sectors and description of physical symmetries in algebraic axiomatic theory Yu. Zinoviev, V. Sushko, S. On the dynamical contents of two-particle structure, positivity, crossing symmetry, and analyticity G. On the analytic renormalization of Green's functions E. Lassner, A. Chiral-invariant field theory and pionpion scattering H.

Medvedev, V. Pavlov, M. Polivanov, A. Medvedev, A. Higher order perturbation theory of exponential Lagrangians: fourth order K. Differential-geometric structures, and quantum field theory L. Remarks on axiomatic quantization of the gravitational field M. Flato, J.

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Simon, D. Mathematical problems in the theory of quantum channels A. Covariant expansions for field commutators at an equal-time point Yu. Scattering of infraparticles O. Review on recent progress in renormalization theory B. Fields and Particles. Application of the Newton—Kantorovich method in elementary particles physics A. Amatuni, V. Causality of the invariant form factors in the decomposition of the current commutators P.

Low-energy dispersion theories A. Vall, V. Scale invariance, elementary particles and high-energy scattering in quantum field theory I. Ginzburg, A. Statistical method in DRM M. Gorenshtein, V. Miransky, V. Shelest, B. Struminskii, G.

Donkov, V. Kadyshevskii, M. Mateev, R. Asymptotic behaviour of the planar one-loop correction to the Regge trajectory in the dual model H. Dorn, H. Quasipotential type equations for the relativistic three-particle system A. Kvinikhidze, D. Kuleshov, V. Matveev, A. Sisakyan, M. Analyticity in several variables and physical parametric sum rules N.

Khuri, G. On casuality tests for inelastic electron scattering H. Analyticity, unitarity and restrictions on inclusive cross-sections at high energies A. Logunov, M. Dynamic form of the Low type equations V. Higher order corrections to weak processes G. Pron'ko, L. Duality in properly infinite von Neumann algebras M.

Conformal invariant Euclidean quantum field theory I. The Dyson equations for the two-particle Green function and the bound state problem R. Singular potentials and their applications to composite models of hadrons with indefinitely rising Regge trajectories A. On phase transitions in open systems far from thermal equilibrium K. Ultraviolet asymptotics of propagators and higher Green functions D. Bogolyubov Jr. Moskalenko, A. Ursu, N. The Cauchy problem for Bogoljubov's kinetic equations D. Petrina, A. Some applications of Feynman integrals to the theory of Bose systems V.

Problems of the ground state of the infinite Heisenberg antiferromagnet H. An inequality of N. Bogoljubov in models of statistical mechanics B. Sadovnikov, V. Regularity in the critical phenomena Y. The spectrum and correlation functions of Heisenberg's anisotropic ferromagnet Yu. Tserkovnikov, Yu. The method of displacements and collective variables I.

Ryshkov, E. Some extremal problems for differentiable functions of one variable V. Approximation of linear operators, and related extremal problems V. Convergence of an interpolation process for parabolic and cubic splines N. Extremal problems of functional interpolation, and mean interpolation splines Yu. Moduli of families of curves and quadratic differentials G. Multiplicative estimates for functions of several variables in weight spaces with mixed norm S. Multiplicative estimates of integral moduli of smoothness O.

The method of composite regular nets for the Laplace equation on polygons E. Estimates of differential operators, and hypoelliptic operators G. The local solvability of certain singular partial differential equations I. Kipriyanov, A. Imbedding theorems for nonisotropic weight spaces of differentiable functions Yu. Sobolev projection operators for seminorms with infinite-dimensional kernels V.

Some tests of F. Riesz type in the theory of set functions K. The extension of functions from an infinite cylinder B. Geometric problems of the theory of infinite-dimensional probability distributions V. Periodic products of groups S. Estimates for Weyl's double trigonometric sums G. On the theory of systems of partial differential equations A.

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On the theory of sufficient conditions for optimality V. The compression method in nonlinear additive problems B. Voronetskii, A. The zeros of zeta-functions of quadratic forms S. Distribution of values of nonprincipal characters A. An equation in permutations M. Mineev, A. On the theory of Jacobsthal sums A. Postnikov, S. On the problem of determining perfect quadratic forms of several variables S.

Takhtadzhyan, L. Arkhipov, A. Karatsuba, V. Some properties of lacunary series and the integrability of trigonometric series L. Balashov, S. Intercellular averagings and an error estimate for cubature formulas in S. Sobolev's spaces and their generalizations O. The controllability problem for linear systems V. Some properties of orthogonal convergence system B.

Mishchenko, M. Nikol'skii, N. Sequences of norms of Fourier sums of bounded functions K. An analytic method for estimates of the concentration function L. Postnikova, A. The arithmetic structure of integer polynomials and class numbers V. Lower bounds for incomplete sums of the characters of polynomials S. Binary functions on ordered sets inversion theorems B. Tauberian theory and its applications A.

Approximation of operators of convolution type by linear bounded operators V. Differentiation of functions defined with an error V. Some extremal properties of polynomials and inverse inequalities of approximation theory V.

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Estimation of the remainder for the Fourier series for differentiable functions S. Extremal problems of the theory of approximation of functions with incomplete information Yu. Approximation of classes of differentiable functions by splines in weighted spaces N. The method of averaging in the theory of orthogonal series and some questions in the theory of bases S.

Spectral theory and scattering for the d'Alembert operator with vector potential V. Deich, D. Solvability of the first boundary value problem for some classes of second-order degenerate quasilinear elliptic equations A. Ivanov, P. Plancherel's formula for hyperboloids V. Functional model of perturbation theory and its applications to scattering theory S. Small perturbations of an integrable dynamical system with an integral invariant N.

Solonnikov, A. Andrianov, G. Complementary and dual torsions V. Andrunakievich, Yu. Bashmakov, A. Algebraically closed and simple Lie algebras L. Borevich, N. Borevich, E. On the classification of integral even unimodular dimensional quadratic forms B. The reciprocity law in an algebraic number field S. Related kinds of simple forms of crystals R. Gutsul, V. Combinatorial and metric theory of planigons B.

Dolbilin, M. Dzhumadil'daev, A. Quasi-Frobenius rings and Gorenstein orders V. Polyquivers of infinite type L. Polyquivers of finite type L. Nazarova, S. Ovsienko, A. Roots of integral quadratic forms A. Multidimensional sails S. Monomial minimal irreducible groups D. Galois theory for sheaves of sets A. Besov, V. Estimates of the error of cubature formulas with respect to smoothness of function O. Partitions of unity V. Burenkov, M. Extension of functions from anisotropic spaces with preservation of class V.

Burenkov, B. On the smoothness of solutions of the Dirichlet problem, and the composite mesh method on polyhedra E. Description of traces for certain function spaces M. Hypoellipticity criteria in terms of power and strength of operators G. Kazaryan, V. Comparison of the power of polynomials and their hypoellipticity G. Description of traces for anisotropic spaces of Triebel—Lizorkin type G.

Behavior at infinity of functions from Liouville classes. Riesz potentials of arbitrary order P. Inequalities between different seminorms of differentiable functions of several variables Yu. Multiple trigonometric sums G. Editor's preface S. The reduction domain, in the sense of Selling, of positive quadratic forms of five variables E. Compact three-dimensional manifolds of constant negative curvature I. Noncompact three-dimensional manifolds of constant negative curvature that have finite measure V.

Makarov, I. On the theory of construction of the Minkowski reduction domain S. Ryshkov, M. Cohn, Z. Ryshkov, Z. On the Rankin—Sobolev problem of the multidimensional zeta function estimate of the origin of the ray of extremality of the principal perfect form S. Spectral theory of automorphic functions A. From the editor P. Parametric canonical homology and cohomology groups over pairs of copresheaves and presheaves, respectively D. The current state of Alexander—Pontryagin duality F. Axiomatics of the Steenrod—Sitnikov homology theory on the category of compact Hausdorff spaces N.

Brown Jr. Lipschitz topology J. The ring of symplectic cobordisms V. Linearization of actions of locally compact groups J.

## A geometrical method for low-dimensional representations of simulations

Some unsolvable questions relating to Radon measures R. Gardner, W. Duality, trace and transfer A. Dold, D. Limits of local systems of sheaves and zero-dimensional mappings A. Local analysis of nonlinear Fredholm equations V. Zachepa, Yu. Cardinals as orbits of groups of automorphisms of ordered sets S. An existence theorem for an infinite set of closed geodesics W.

Klingenberg, Y. Resolutions of generalized manifolds R. Spherical space forms in the dimension equal to the period I. Maximally decomposable spaces E. Some results in the topology of manifolds, the theory of multivalued mappings and Morse theory Yu. Trokhimchuk, Yu. Zelinskii, V.

Normally situated subspaces V. Topological semifields and Boolean algebras corresponding to them J. Some generalizations of homogeneity of spaces J. Mappings and dimension properties of spaces M. Minimal resolvents and Morse functions V. Constructive characterization of S. Sobolev and O. Besov classes E.

Fourier coefficients of boundary values of functions that are analytic in the disc and bidisc S. Positive projectors in symmetric KB-spaces V. Analogue of J. We show that a homotopy algebra structure on a vector space can be lifted to its Hochschild complex, and also suggest an induction method to generate some of the explicit weakly homotopy Gerstenhaber algebra maps on a topological vertex operator algebra TVOA , their existence having been indicated by Kimura, Voronov, and Zuckerman in later amended by Voronov.

The contention that this is the fundamental structure on a TVOA is substantiated by providing an annotated dictionary of weakly homotopy BV algebra maps and identities found by Lian and Zuckerman in Source Homology Homotopy Appl. Zentralblatt MATH identifier Chicken or egg? It may helps up to Archetypes before you received it. The sample will Die designed to your Kindle error. It may is up to books before you played it.

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