一个因式相通定理及其应用

证明了一个因式相通定理,它是奇点理论中等价性定理的一个推广.这个定理表明单纯高阶项的开折对普适开折因式相通中的参数映射没有贡献.据此本文提出了一种因式相通中参数映射的简洁有效的近似计算方法     

A theorem on parastatistics and its application

Proceeding from the assumption that nature chooses a riskless strategy, we consequently obtain a distribution over parastatistics. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 3, pp. 511–512, March, 2007.     

A strengthening of Borel's theorem and its application

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 43, pp. 132–136, 1985.     

A non-central banach valued limit theorem and its application

This note is devoted to the generalization of a limit theorem on sums of strongly dependent random variables (non-central limit theorem) to the case when the initial Gaussian sequence, functions of which are considered, assumes values in the Banach space of continuous functions on a compactum; special attention is given to the transition case, when the limit distribution changes by a jump.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 114–119, 1989.     

A general impossibility theorem and its application to individual rights

In this paper, we generalize Green and Laffont’s (1979) impossibility theorem to the following form: in quasi-linear environments, when the set of each agent’s types is sufficiently rich, we cannot find mechanisms that allow bounded deviations from the decisive efficiency, incentive compatibility and budget-balance at the same time. Hence, it is impossible to find an incentive compatible mechanism with minimum social welfare losses. Furthermore, we discuss the compatibility problems between incentive and individual rights in a quasi-linear environment (see Sen, 1970a,b; Deb et al., 1997). Specifically, some new impossibility results are established.     

A density theorem with an application in relaxation of nonconvex-valued differential equations

We present first a result on density of extremal selections for measurable multifunctions. Next, we use this result to establish a relaxation theorem for nonconvex-valued differential equations in Banach spaces.     

A structural theorem on embedded graphs and its application to colorings

In this paper, a Lebesgue type theorem on the structure of graphs embedded in the surface of characteristic σ≤ 0 is given, that generalizes a result of Borodin on plane graphs. As a consequence, it is proved that every such graph without i-circuits for 4 ≤ i ≤ 11 - 3σ is 3-choosable, that offers a new upper bound to a question of Y. Zhao.     

A generalization of the Leggett-Williams fixed point theorem and its application

A generalization of the Leggett-Williams fixed point theorem is established. As an application, the existence of multiple nondecreasing positive solutions for a class of third-order m-point boundary value problems is obtained.     

A stability theorem of backward stochastic differential equations and its application

In this Note, we establish a stability theorem for backward stochastic differential equations, and we apply this theorem to study the homogenization of systems of semilinear parabolic partial differential equations.     

A theorem on non-associative algebras and its application to differential equations

For a given field F, the set of F-algebras (resp. commutative F-algebras) of arity n≥2 and F-dimension m can be identified with the mⁿ⁺¹ (resp. m(^m+n?1 _n)) dimensional F-affine space S of structure coefficients. We show: If F is algebraically closed, then there exists an affine subvariety A of S with A≠S, which is defined over the prime field of F, such that all F-algebras corresponding to the points of S-A posses precisely n^m?1 idempotent elements ≠0 and fail to have nil potent elements ≠0. This implies for a system of ordinary differential equations $$\left( * \right)\dot X_i = D_i \left( {X_l ,..,X_m } \right),i = l,..,m,$$ with D_i(X_i,...,X_m)∈?[X₁,...,X_m] homogeneous polynomials of degree n: If the coefficients of the polynomials D_i, i=1,...,m, are algebraically independent over the field of rationals, then (*) possesses precisely n^m?1 ray solutions and fails to have a critical point other than the origin.     

A supplement to Chebotarev's density theorem

Let L/K be a Galois extension of number fields with Galois group G.We show that if the density of prime ideals in K that split totally in L tends to 1/|G| with a power saving error term,then the density of prime ideals in K whose Frobenius is a given conjugacy class C■G tends to |C|/|G| with the same power saving error term.We deduce this by relating the poles of the corresponding Dirichlet series to the zeros of ζ_L(s)/ζ_K(s).     

Uniqueness theorem for integral equations and its application

This paper is devoted to answering a question asked recently by Y. Li regarding geometrically interesting integral equations. The main result is to give a necessary and sufficient condition on the parameters so that the integral equation with parameters to be discussed in this paper have regular solutions. In the case such condition is satisfied, we will write down the exact solution. As its application of our method, we should show that the non-existence theory of the solutions of prescribed scalar curvature equation on Sn can be generalized to that of prescribed Branson-Paneitz Q-curvature equations on Sn.     

A mean value theorem on the binary Goldbach problem and its application

We study the binary Goldbach problem with one prime number in a given residue class, and obtain a mean value theorem. As an application, we prove that for almost all sufficiently large even integers n satisfying n ≢ 2(mod 6), the equation p ₁ + p ₂ = n is solvable in prime variables p ₁, p ₂ such that p ₁ + 2 = P ₃, and for every sufficiently large odd integer satisfying ≢ 1(mod 6), the equation p ₁ + p ₂ + p ₃ = is solvable in prime variables p ₁, p ₂, p ₃ such that p ₁ + 2 = P ₂, p ₂ + 2 = P ₃. Here P _k denotes any integer with no more than k prime factors, counted according to multiplicity.