Showing papers in "Journal of Mathematical Sciences in 1980"
TL;DR: A survey of the birational theory of three-dimensional algebraic Fano varieties can be found in this paper, where the authors focus on three dimensional algebraic algebraic varieties.
Abstract: The survey is devoted to the birational theory of three-dimensional algebraic Fano varieties.
177 citations
TL;DR: In this paper, it was proved that the initial bounding-box value problem for the system of equations describing the motion of a compressible fluid with a constant viscosity is locally solvable with respect to time.
Abstract: It is proved that the initial-boundary-value problem for the system of equations describing the motion of a compressible fluid with a constant viscosity is locally solvable with respect to time. The heat conductivity is not taken into account. The solution is found in the class Wq2.1, q>3.
171 citations
TL;DR: The present state of the biregular theory of three-dimensional algebraic varieties with negative canonical sheaf is surveyed in this article. But this survey is restricted to the case of algebraic algebraic types.
Abstract: The survey reflects the present state of the biregular theory of three-dimensional algebraic varieties with negative canonical sheaf.
167 citations
TL;DR: In this paper, an analytically systematic exposition of modern problems in the investigation of differentiable manifolds and the geometry of fields of geometric objects on such manifolds is presented.
Abstract: The work is an analytically systematic exposition of modern problems in the investigation of differentiable manifolds and the geometry of fields of geometric objects on such manifolds.
114 citations
TL;DR: In this paper, a new method is considered for constructing the dynamics of motion of a shock front moving with speed close to that of sound in a nonviscous, isentropic gas.
Abstract: A new method is considered for constructing the dynamics of motion of a shock front moving with speed close to that of sound in a nonviscous, isentropic gas. The algorithm for constructing the solution reduces to the problem of successively solving systems of ordinary differential equations which provides considerable economy as compared with the known method of difference schemes for computer calculations.
49 citations
TL;DR: It is shown that the standard algorithm for multiplying matrices or polynomials may be realized by a circuit of boolean functions in a way that is optimal with respect to a selected complexity measure.
Abstract: This note consists of two independent parts. In the first part the concept of an (m,c)-system for a set of linear forms is introduced, and a lower bound is obtained for the algebraic complexity of the computation of (m,c)-systems on algebraic circuits of a special form. In the second part, the notion of an l-independent set of boolean functions is introduced and a lower bound is obtained for a certain complexity measure for circuits of boolean functions computing l-independent sets. As a corollary it is shown that the standard algorithm for multiplying matrices or polynomials may be realized by a circuit of boolean functions in a way that is optimal with respect to a selected complexity measure.
48 citations
TL;DR: In this paper, the class of quantifier-free formulas constructed from atomic formulas of the form (x+y= z),(x=1), and (x¦y) is considered, where the predicate symbol "¦" is interpreted as the divisibility relation on nonnegative integers.
Abstract: The class of all quantifier-free formulas constructed from atomic formulas of the form (x+y= z),(x=1), and (x¦y) is considered, where the predicate symbol “¦” is interpreted as the divisibility relation on nonnegative integers. The decidability isproved of the set of all formulas of this form which are true for at least one choice of values for the variables. This result is equivalent to the decidability of the universal theory of natural numbers with addition and divisibility.
30 citations
TL;DR: A survey of the most recent transcendental methods in the theory of three-dimensional algebraic manifolds can be found in this article, where the authors also give a survey of some of the related works.
Abstract: The paper gives a survey of the most recent transcendental methods in the theory of three-dimensional algebraic manifolds.
29 citations
TL;DR: A survey of papers on the theory of compositions and their application to the investigation of manifolds in spaces with fundamental groups is presented in this article, where the authors present a survey of compositional theory and its application to manifolds.
Abstract: A survey of papers on the theory of compositions and their application to the investigation of manifolds in spaces with fundamental groups is presented.
23 citations
TL;DR: The second part of the survey as mentioned in this paper is devoted to the description of the set of all restrictions of analytic functions from the class X onto a fixed subset E of their domain of definition.
Abstract: The second part of the survey (the first part has been published in Vol. 47 of the same publication) is basically devoted to the description of the set of all restrictions of analytic functions from the class X onto a fixed subset E of their domain of definition. Contents: the proof of Earl's theorem on interpolation by Blaschke products and some of their applications to interpolation on subclasses of the space H∞; interpolation in the spaces of all functions analytic in the unit circle with a sequence of coefficients from lp(1⩽p⩽∞); interpolation in some Banach spaces consisting of functions which are analytic in the open unit circle and continuous in its closure (in this case the results are similar to the well-known Rudin-Carleson theorem). In conclusion, one considers problems of interpolation in spaces of analytic functions which are smooth up to the boundary.
21 citations
TL;DR: A new proof is given for the well-known theorem of Putnam, Davis, and Robinson on exponential diophantine representation of recursively enumerable sets that leads directly to a purely existential exponential formula.
Abstract: A new proof is given for the well-known theorem of Putnam, Davis, and Robinson on exponential diophantine representation of recursively enumerable sets. Starting from the usual definition of r.e. sets via Turing machines, a new method of arithmetization is given. This new method leads directly to a purely existential exponential formula. The new proof may be more suitable for a course on the theory of algorithms because it requires less knowledge of number theory.
TL;DR: In this paper, the theory of isometric immersions of Riemannian spaces in Euclidean spaces was studied and applications of the theory in the general theory of relativity were considered.
Abstract: Questions of the theory of isometric immersions of Riemannian spaces in Euclidean spaces beginning with the very first results onthis topic and also results on immersions of pseudo-Riemannian spaces in pseudo-Euclidean spaces and applications of the theory of immersions in the general theory of relativity are considered.
TL;DR: In this paper, the authors present a study of differential geometric structures arising on manifolds imbedded in almost complex spaces and the differential geometry of such manifolds, and show that such structures can be obtained by approximating the geometry of the manifold with a complex manifold.
Abstract: In this paper we present a study of differential geometric structures arising on manifolds imbedded in almost complex spaces and the differential geometry of such manifolds.
TL;DR: In this article, a new class of manifolds is introduced which is a natural generalization of real Lagrangian manifolds to the complex case, and the theory of the canonical Maslov operator is constructed in this class of manifold.
Abstract: Differential equations with a small parameter in the derivative are considered. A method is developed for constructing formal asymptotic solutions for the case of complex characteristics. For this a new class of manifolds is introduced which is a natural generalization of real Lagrangian manifolds to the complex case. The theory of the canonical Maslov operator is constructed in this class of manifolds. Asymptotic solutions are expressed in terms of the canonical Maslov operator.
TL;DR: A predicate is constructed which is recognizable in real time by a Kolmogoroff algorithm but which is not recognizable inRealTime by a machine with polynomial accessibility.
Abstract: A predicate is constructed which is recognizable in real time by a Kolmogoroff algorithm but which is not recognizable in real time by a machine with polynomial accessibility.
TL;DR: In this paper, it was shown that even if the spectra of the operators A, B are contained in the segment [0, 1] the operator norm ∣A-B ∣ is arbitrarily small.
Abstract: One proves that
, where
is a segment containing the spectra of the self-adjoint operators A and B,
is the Lipschitz constant of the function
, and ∣·∣ is the operator norm. It is shown on examples that an estimate of the type
cannot be true for all
with
even if the spectra of the operators A, B are contained in the segment [0, 1] the norm ∣A–B∣ is arbitrarily small.
TL;DR: In this article, a number of geometric questions related to the complex theory of the canonical Maslov operator are considered, including quantization conditions and the problem of finding the asymptotics of eigenvalues.
Abstract: A number of geometric questions related to the complex theory of the canonical Maslov operator are considered. The investigations center around the following themes: 1) quantization conditions and the problem of finding the asymptotics of eigenvalues; 2) universal characteristics of the theory of the complex canonical operator; 3) complex Hamiltonian fields and their trajectories.
TL;DR: A survey of results on the theory of automorphisms in classical spaces with connections, Finsler spaces, and spaces of support elements is presented in this article, where the authors present a survey of the main results.
Abstract: A survey of results on the theory of automorphisms in classical spaces with connections, Finsler spaces, and spaces of support elements are presented.
TL;DR: In this article, the authors consider a system S+ in which the induction rule is permitted to apply only to quantifier-free formulas and to formulas not containing functional variables, while the convolution axiom is permitted only to formulas without functional variables.
Abstract: Let S+ denote system JRΠ
°
2
+ AC
°
1
in a classical second-order arithmetic, in which the induction rule is permitted to apply only to quantifier-free formulas and to Π
°
2
-formulas not containing functional variables, while the convolution axiom is permitted to apply only to Π
°
1
-formulas without functional variables. Also postulated is the closedness of the function class being examined, relative to primitive recursive operations. System, S+ turns out to be sufficiently rich: in it a theory of recursions and an elementary recursive analysis can be developed, a theorem on the continuity of effective operators and a theorem on cuteliminability from ω -deductions can be proved, and the usual analytic proofs of many number-theoretic theorems, including the prime distribution law, can be derived (with insignificant changes). (A formalization in S+ of the proof of Konig's lemma on paths in binary trees and of Godel's completeness theorem is described in the note.) On the other hand, the system admits of an interpretation in primitive recursive arithmetic (PRA). In particular, quantifier-free theorems in S+ are deducible in PRA, while theorems of form ∀x∃yR(x,y) with a quantifier-free formula R have calculi R (x,ϕ(x)) with primitive recursive function ϕ, deducible in PRA. Thus, the suppressing part of operating constructive analysis can be developed already at the finite stages of the Shanin majorant hierarchy. In addition, a purely mechanical method exists for obtaining elementary number-theoretic proofs from many analytic proofs.
TL;DR: In this article, the problems of developing the apparatus of differential-geometric investigations based on the calculus of differential operators on bundles of semiholonomic jets of Ehresmann are considered.
Abstract: The problems of developing the apparatus of differential-geometric investigations based on the calculus of differential operators on bundles of semiholonomic jets of Ehresmann are considered.
TL;DR: A survey of mathematical methods in the theory of the Feynman path integral can be found in this paper, where principal attention is devoted to new results making it possible to represent the solution of the Cauchy problem for the Schrodinger equation and a quasilinear equation of Hartree type in the form of the mathematical expectation of functionals on jump-type Markov processes and use Monte Carlo methods for solving these equations.
Abstract: A survey is presented of mathematical methods in the theory of the Feynman path integral. Principal attention is devoted to new results making it possible to represent the solution of the Cauchy problem for the Schrodinger equation and a quasilinear equation of Hartree type in the form of the mathematical expectation of functionals on jump-type Markov processes and to use Monte Carlo methods for solving these equations. A brief survey of results on complex Markov chains is presented.
TL;DR: For the domains of the space Rn,n⩾2, with a finite number of conical points, the authors proves embedding theorems for the spaces of harmonic functions which generalize the Littlewood-Paley and Carleson theorem.
Abstract: For the domains of the space Rn,n⩾2, with a finite number of conical points, one proves embedding theorems for the spaces of harmonic functions which generalize the Littlewood-Paley and Carleson theorems. Let ∥·∥p, Ω be a norm which is transferred in some natural manner to the space of harmonic functions in the domain Ω and which in the unit circle of the space ℝ2 turns into the norm of the Hardy space Hp and let ℋp(Ω) be the space of harmonic functions in Ω with this norm. One establishes, in particular, sufficient conditions on the measureV, for which one has the inequality
.
TL;DR: In this article, a survey is devoted to arithmetic questions in the theory of modular forms and arithmetic applications of modular functions; mainly only elementary and analytic aspects of this topic, as a rule, for the case of a single variable are presented.
Abstract: The survey is devoted to arithmetic questions in the theory of modular forms and, in particular, to arithmetic applications of modular functions; mainly only elementary and analytic aspects of this topic, as a rule, for the case of a single variable are presented.
TL;DR: A signature-preserving method for the elimination of positive occurrences of equality is described as well and conditions are formulated sufficient for the carrying out of quantifier ∀ from a disjunction and the permutations of quantifiers ∀ and ∃ to preserve decidability in the constructive calculus.
Abstract: For constructive (intuitionistic) predicate calculus without functional symbols and equality a complete description is derived, in terms of prefixes and signatures, of reduction classes and of classes of pseudoprenex formulas, i.e., formulas representable in form
, where
is a quantifier-free formula and is a finite sequence of quantifier complexes and expressions ⌈⌈. The operation
plays a fundamental role in the construction of solvable classes. From any pseudoprenex formulaA this operation constructs, preserving signature, a formula list Г such thatA is decidable in the constructive calculus if and only if some formula from Г is decidable in classical calculus. In the paper conditions are formulated sufficient for the carrying out of quantifier ∀ from a disjunction and the permutations of quantifiers ∀ and ∃ to preserve decidability in the constructive calculus. A signature-preserving method for the elimination of positive occurrences of equality is described as well. This method and the conditions mentioned play an important role in the construction of reduction classes. Also examined is the problem of recognition of refutability of pseudoprenex formulas on completely finite Kripke models, i.e., on those Kripke models in which both the set of “time instants” and also the union of objective domains are finite. A complete description in terms of prefixes and signatures is given for classes of pseudoprenex formulas for which the problem of recognition of refutability on completely finite Kripke models is solvable. This description differs essentially from the description of solvable pseudoprenex formulas for constructive predicate calculus.
TL;DR: A survey of results on bending of nonregular convex surfaces is presented in this article, where the authors consider bending of convex and non-convex surfaces, respectively.
Abstract: A survey of results on bending of nonregular convex surfaces is presented.
TL;DR: This paper presents an investigation of convex surfaces with definite metrics in E3in(2;1) and of the question of imbedding definite metric in the form of conveX surfaces.
Abstract: This paper presents an investigation of convex surfaces with definite metrics in E3in(2;1) and of the question of imbedding definite metrics in the form of convex surfaces.
TL;DR: In this paper, a survey is devoted to various aspects of the theory of complex spaces related to the concept of pseudoconvexity, positive and negative vector bundles, and their generalizations.
Abstract: The survey is devoted to various aspects of the theory of complex spaces related to the concept of pseudoconvexity, positive and negative vector bundles, and their generalizations.
TL;DR: In this article, a survey of the literature on almost-contact manifolds is given, where the authors present an investigation of differential geometric structures arising on immersed manifolds in almost contact manifolds and also in the subbundles associated with them.
Abstract: In this paper we present an investigation of differential geometric structures arising on immersed manifolds in almost-contact manifolds and also in the subbundles associated with them. A survey of the literature on this theme is given.