华林-哥德巴赫问题:两个平方,两个立方和两个四次方

令P_r表示素因子不超过r的殆素数,按重数计.作者证明了对于充分大的偶数N,方程N=x~2+p_1~2+p_2~3+p_3~3+p_4~4+p_5~4有解,其中x是殆素数P_6,p_j(j=1,…,5)是素数.     

涉及两个n维单形的两类不等式

本文给出了涉及两个 n维单形的两类不等式 ,并得到了两个推论 .     

Two orientations

All trivializations of an Euclidean line bundle π: ? → B over a connected base B split in two classes which can be naturally named orientations of π. In the case of an orienting sheaf of a manifold or a vector bundle, they admit a natural interpretation as orientations of these objects. This approach establishes an extension of standard classical constructions to all manifolds and vector bundles independently of orientability restrictions in the usual sense.     

Two stars

The authors investigate an operation * on the subsets of ${\mathcal{P}(\mathbb{R})}$ . It is connected with Borel’s strong measure zero sets as well as strongly meager. The results concern the behaviour of the family of countable sets when * is applied.     

Cayley-Hamilton定理的两种简单证法和两个表现定理

本文对Cayley-Hamilton定理提出两种简单证法并应用该定理和罗必塔法则给出两个有关二阶张量函数的表现定理.     

关于两个n维单形的棱长与体积的两类不等式

给出了联系两个n维单形的棱长与体积的两类不等式,从而推广和改进了相关文献的结果.     

双辅助信息随机化回答模型的两种估计量

随机化回答技术是进行敏感性问题调查和推算总体特征比例的一种有效方法.通过在随机化回答技术中使用辅助信息,可以提高估计量的精度,从而得到更为合理的调查结果.在随机化回答技术中引入两个辅助信息,提出比方法和比方法与回归方法组合的两种估计量,计算了这两种估计量的均方误差,并通过数值计算验证了两种估计量的合理性.     

Two divergence-rate counterexamples

An example is constructed of a pair of ergodic processes for which the upper and lower divergence rates are not equal. An example is also constructed of a pair of ergodic processes for which the limiting rate is 0, yet the processes are not equal. In both cases it is shown how the techniques will yieldB-process counterexamples.Partially supported by NSF Grant DMS-9024240.From 9/1 to 12/1 each year: Mathematics Institute, POB 127, 1364 Budapest, Hungary. 011-361-1-177-175. At other time: Department of Mathematics, University of Toledo, Toledo, Ohio 43606. (419) 537-2069.     

一类三角级数的收敛性

利用Euler公式求三角级∞∑m=1 sinmx/n与∞∑m=1 cosmx/m的和函数并讨论其一致收敛性.     

Two cardinal compactness

We prove that ifλ≧μ ^ℵo=μ≧|T | and if every finite subtheory ofT has a (λ, μ)-model (i.e. a model with a domain of powerλ, in which a distinguished predicate is interpreted as a set ofμ elements) thenT has such a model. There are generalizations forμ-like models (or, equivalently, to languages with generalized quantifiers).     

Two integral inequalities

Let (X, S, μ) and (Y, T, ν) be two measure spaces,K(g)=∫ _Y k(x,y)g(y)dv(y) ξ ⁺=max (ξ,0), and . Two integral inequalities (the first of which has a simple geometrical interpretation) involvingδ(K) are proved. Generalizations of theorems about infinite stochastic matrices and convergence of superpositions of sequences of integral operators are obtained. Dedicated to the memory of E. Jabotinsky An erratum to this article is available at .     

Two poset polytopes

Two convex polytopes, called theorder polytope (P) andchain polytope (P), are associated with a finite posetP. There is a close interplay between the combinatorial structure ofP and the geometric structure of (P). For instance, the order polynomial (P, m) ofP and Ehrhart polynomiali((P),m) of (P) are related by (P, m+1)=i((P),m). A transfer map then allows us to transfer properties of (P) to (P). In particular, we transfer known inequalities involving linear extensions ofP to some new inequalities.Partially supported by NSF Grant No. 8104855-MCS and by a Guggenheim Fellowship.     

Two distance-regular graphs

We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B ₃(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D ₄(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.     

Opening Two Envelopes

In the two-envelope problem, one is offered a choice between two envelopes, one containing twice as much money as the other. After seeing the contents of the chosen envelope, the chooser is offered the opportunity to make an exchange for the other envelope. However, it appears to be advantageous to switch, regardless of what is observed in the chosen envelope. This problem has an extensive literature with connections to probability and decision theory. The literature is roughly divided between those that attempt to explain what is flawed in arguments for the advantage of switching and those that attempt to explain when such arguments can be correct if counterintuitive. We observe that arguments in the literature of the two-envelope problem that the problem is paradoxical are not supported by the probability distributions meant to illustrate the paradoxical nature. To correct this, we present a distribution that does support the usual arguments. Aside from questions about the interpretation of variables, algebraic ambiguity, modal confusions and the like, most of the interesting aspects of the two-envelope problem are assumed to require probability distributions on an infinite space. Our next main contribution is to show that the same counterintuitive arguments can be reflected in finite versions of the problem; thus they do not inherently require reasoning about infinite values. A topological representation of the problem is presented that captures both finite and infinite cases, explicating intuitions underlying the arguments both that there is an advantage to switching and that there is not.