Essential cohomology of finite groups

In this paper we prove that a finite group G with Cohen-Macaulay mod p cohomology will have non-trivial undetectable elements in if and only if G is a p-group such that every element of order p in G is central. Applications and examples are also provided. Received: April 18, 1996     

Measuring deviations from stationarity

Various parameters for measuring the deviation from stationarity for processes belonging to two classes of nonstationarity processes are proposed. Several new results for the two types of processes are obtained. Points of contact are established with the class of oscillatory processes and with the Hamiltonian equation of motion in quantum mechanics. The relation to processes of normal type and to innovations stable processes is also discussed.     

农艺措施对蔗糖产量影响的探讨

采用五元二次回归旋转正交组合设计方法，通过１９９０—１９９１年秋植蔗试验，建立蔗糖产量与种植密度，尿素、钙镁磷、氯化钾、桐麸的施用量等主要农艺措施之间的数学模型，得出各主要农艺措施及它们相互之间的作用对蔗糖产量的影响程度，并优选甘蔗生产的最优综合栽培农艺措施方案。     

A Geometrical Proof of Shiota's Theorem on a Conjecture of S. P. Novikov

We give a new proof of Shiota's theorem on Novikov's consecture, which states that the K.P. equation characters Jacobians among all indecomposable principally polarized abelian varieties.     

Cohomologie des groupes et corps d'invariants multiplicatifs tordus

We give a cohomological calculation of the unramified Brauer group of a field of invariants under a twisted multiplicative action of a finite group. Received: October 13, 1992; final version: July 3, 1996     

The asymptotic behavior of the set of rays

We introduce new invariants to study the asymptotic behavior of the set of rays and prove a splitting theorem for the radius of the ideal boundary of an open manifold with (Shioya's Conjecture). Received: October 26, 1995; revised: February 5, 1997     

多元样本定理及混淆误差的估计

本文证明了多元指数型整函数的一个Ｍａｒｃｉｎｋｉｅｗｉｃａ型不等式，并由此证得了多元Ｗｈｉｔｔａｋｅｒ－Ｋｏｔｅｌｎｉｋｏｖ－Ｓｈａｎｎｏｎ型的样本定理，从而得到了多元Ｓｏｂｏｌｅｖ类上的混淆误差界的阶的精确估计。     

Attainable rates of convergence of maxima

Any exponential rate of convergence can be obtained for maxima of i.i.d. random variables, while faster than exponential convergence implies that the variables have an extreme value distribution.     

Complexity of degenerations of modules

A module M over an associative algebra A over an algebraically closed field k is said to degenerate to a module N if N belongs to the closure of the isomorphism class of M in the algebraic variety of d-dimensional A-modules, . We associate a non-negative integer to a degeneration , its complexity, and study its properties. Received: January 30, 2001     

Periodic points of nonexpansive maps and nonlinear generalizations of the Perron-Frobenius theory

Let and suppose that f : K ⁿ →K ⁿ is nonexpansive with respect to the l ₁-norm, , and satisfies f (0) = 0. Let P ₃(n) denote the (finite) set of positive integers p such that there exists f as above and a periodic point of f of minimal period p. For each n≥ 1 we use the concept of 'admissible arrays on n symbols' to define a set of positive integers Q(n) which is determined solely by number theoretical and combinatorial constraints and whose computation reduces to a finite problem. In a separate paper the sets Q(n) have been explicitly determined for 1 ≤n≤ 50, and we provide this information in an appendix. In our main theorem (Theorem 3.1) we prove that P ₃(n) = Q(n) for all n≥ 1. We also prove that the set Q(n) and the concept of admissible arrays are intimately connected to the set of periodic points of other classes of nonlinear maps, in particular to periodic points of maps g : D _g→D _g, where is a lattice (or lower semilattice) and g is a lattice (or lower semilattice) homomorphism.     

Precise asymptotics for a series of T. L. Lai

Let be i.i.d. random variables with , and set . We prove that, for

under the assumption that and Necessary and sufficient conditions for the convergence of the sum above were established by Lai (1974).

     

On Embeddings of AG(tn,k) into AG(t,K) with t≥2, n≥1

Let k and K be commutative fields with dim_kK=2n, n1 and char(k)2, 3. If k satisfies one of the following conditions: (1) k is a finite field and k contains a 3-th root of unity, or (2) K is a cyclic extension of k where k is not 3-closed, and k contains a 2^a3^b-th root of unity, where 6n=2^a3^bc and c is coprime to 2, 3, then there exists an embedding of the tn-dimensional affine space AG(tn,k) into the t-dimensional affine space AG(t,K), for all t2.     

Bool阵的逆阵

We give a characterization of a regular Boolean matrix and prove that AB = I Implies that BA = I, where A and B are Boolean matrices whose elements belong to a Boolean algebra of a set with more than two elements.     

数字地震勘探中一种统计建模及求解方法

本文提出了在数字地震勘探技术使用的一种借助于首层折射滑行波特性，来提取表层厚度、速度信息的方法。本文中介绍了该提取方法得出的过程，使用的物理模型及假设，数学原理及近似解法等。本文企盼的是，这个得出过程的启迪示范作用。     

Precise rates in the law of the logarithm in the Hilbert space

Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X₁+?+Xn, n?1. Let . We prove that, for any 1<r<3/2 and a>−d/2,

     

Controlled Geometry via Smoothing

We prove that Riemannian metrics with a uniform weak norm can be smoothed to having arbitrarily high regularity. This generalizes all previous smoothing results. As a consequence we obtain a generalization of Gromov's almost flat manifold theorem. A uniform Betti number estimate is also obtained. Received: August 31, 1995.     

A Property of Sobolev Spaces and Existence in Optimal Design

Abstract. We prove that for bounded open sets Ω with continuous boundary, Sobolev spaces of type W ₀ ^l,p (Ω ) are characterized by the zero extension outside of Ω . Combining this with a compactness result for domains of class C, we obtain a general existence theorem for shape optimization problems governed by nonlinear nonhomogenous Dirichlet boundary value problems of arbitrary order, in arbitrary dimension and with general cost functionals.     

A Comtrol Model of Linear Fuzzy Silf-Regression

ＡＣｏｎｔｒｏｌＭｏｄｅｌｏｆＬｉｎｅａｒＦｕｚｚｙＳｅｌｆ－ＲｅｇｒｅｓｓｉｏｎＬｕＦｅｎｇ，ＸｕＸｉａｏｇｕａｎｇ（Ｄｅｐ．ｏｆＭａｔｈ．Ｎｏｒｔｈｅａｓｔ（ＢａｓｉｃＢｒａｎｃｈＣｈａｎｇｃｈｕｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）ＴａｘＣｏｌｌ...     

An application of rosenthal's moment inequality to the strong law of large numbers

We apply a moment inequality of H.P. Rosenthal to get various generalizations of a theorem of Brunk-Chung-Prohoroff. In particular, we show that the strong law hols provided $\text{∑}\text{n=1}\text{∞}\text{n}{}^{\mathrm{?2p}}\text{E(X}{}_{\mathrm{n}}\text{}{}^{\mathrm{2p}}\text{) < ∞}$ and $\text{∑}\text{n=1}\text{∞}\text{n}{}^{\mathrm{?2?p}}\text{(E(}\text{X}\text{n}\text{2}\text{))}{}^{\mathrm{p}}\text{< ∞}$ for one p ? 1.