R∧N上的临界非齐次多重调和方程的多解存在性

讨论了R∧N上带负扰动的临界非齐次多重调和方程的多解存在性,首先由泛函弱连续性方法获得方程的第一个解,再由山路引理获得方程的第二个解,本文的这种求解方法和这些结果不仅适用于R∧N上的二阶椭圆方程,而且也适用于尚未解决的R∧N上的双调和方程。     

To the N. N. Luzin theorem

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 1, pp. 212–215, January–February, 1992.     

Eightieth birthday of Academician N. N. Bogolyubov

Eightieth birthday of Academician N. N. Bogolyubov     

中介逻辑演算系统MPN及MFN

为满足不完全信息系统应用的需要,本文构造了基于命题联结词∧、∨、→、ヲ、～和～的中介逻辑命题演算系统ＭＰＮ和中介逻辑谓词演算系统ＭＦＮ,并证明了ＭＰＮ与ＭＰ＊、ＭＦＮ与ＭＦ＊的表达能力等价。ＭＦＮ将为进一步讨论不完全信息数据库作准备     

2N Noncollinear points determine at least 2N directions

We find sharp bounds for the number of moves required to bring a permutation to the form n(n ?1),…, 1 if a move consists of inverting some increasing substrings.If we invert every maximal increasing substring in each move we need at most n ? 1 moves.If n is even and we start with 1, 2,…, n and we do not invert the entire permutation at once, then we need at least n moves.The lower bound implies that when n ? 4 is even, n points which are not collinear determine at least n different directions, as do n + 1. These bounds are sharp.     

N=4 Multiplets in N=3 Harmonic Superspace

We show that the N=3 harmonic superfield equations of motion are invariant with respect to the fourth supersymmetry. We also use the SU(3) harmonics to analyze a more flexible form of superfield constraints for the Abelian N=4 vector multiplet and its N=3 decomposition. An unusual alternative representation of the N=4 supersymmetry is realized on infinite multiplets of analytic superfields in the N=3 harmonic superspace. An integer-valued parameter playing the role of a discrete coordinate parameterizes U(1) charges of superfields in these multiplets. Each superfield term of the N=3 Yang–Mills action has an infinite-dimensional N=4 generalization. The gauge group of this model contains an infinite number of superfield parameters.     

Classifying almost-disjoint families with applications toβN − N

A family of infinite subsets of the setN of natural numbers will be called almost disjoint iff any two of its members have finite intersection. We shall define such a family ℱ to ben-separable iff for every decompositionD = {D ₁, …D _n } ofN inton or fewer disjoint subsets there exist setsF ∈ ℱ andD ∃D such thatF ⊆D, and we shall use this and related notions to classify almost-disjoint families, using, on occasion, special axioms of set theory.     

Normal vibrations of N,N-dimethylformamide and N,N-dimethylacetamide

Infrared and Raman frequencies of N, N-dimethylformamide and N, N-dimethylacetamide as recorded by the authors, in the region 3100 cm.^?1 to 250 cm.^?1 are given. The normal co-ordinate treatment of these molecules has been carried out using general quadratic force field and the potential energy distribution of the various modes of vibrations have been calculated to study the nature of absorption frequencies arising out of the in-plane vibrations. The assignments made by the authors in the region 3100 cm.^?1 to 500 cm.^?1 are compared with those of Lumley Jones who assigned the frequencies on the basis of band contour studies. These calculations have enabled the authors also to assign the frequencies in the region 500 cm.^?1 to 250 cm.^?1 to the various bending modes of vibrations. The C-N stretching frequency in tertiary amides is considerably different from that in primary and secondary amides.     

N. N. Bogolyubov's research in mathematics and theoretical physics

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 9, pp. 1156–1164, September, 1989.     

The homomorphismM*⊗N → Hom (M,N)

In this note we prove two theorems. In theorem 1 we prove that if M andN are two non-zero reflexive modules of finite projective dimensions over a Gorenstein local ring, such that Hom (M, N) is a third module of syzygies, then the natural homomorphismM* ⊗N → Hom (M, N) is an isomorphism. This extends the result in [7]. In theorem 2, we prove that projective dimension of a moduleM over a regular local ringR is less than or equal ton if and only if Ext_R ⁿ (M, R) ⊗M → Ext_R ⁿ (M, M) is surjective; in which case it is actually bijective. This extends the usual criterion for the projectivity of a module.     

N×2N瓶颈指派问题及其阀门(threshold)算法

讨论把2N项任务(或工件)指派(安排)给N个人(或机器)的问题.已知人i处理(或加工)任务j的时间花费是cij,i=1,2,…,N,j=1,2,…,2N,要求每人恰承担2项任务,每项任务恰由1个人承担.怎样分派任务,使完成任务最慢的人所花的时间最少.