广义Dedekind和与Hardy和

本文给出了广义Dedekind和与Hardy和的定义,研究了广义Dedekind和的算术性质,并把Hardy和表示成广义Dedekind和的形式．提出了广义Subrahmanyam等式和Knopp定理,并给出了证明．     

Sums of moran sets

We find conditions on the dissection of Moran set so that the group it generates under addition has positive Lebesgue measure.     

SUMS OF MORAN SETS

We find conditions on the dissection of moran set so that the group it generates under addition has positive Lebesgue masure.     

广义二次Gauss和与广义Kloosterman和的混合均值

利用分析的方法及经典二次Gauss和的性质,研究了一类广义二次Gauss和与广义Kloosterman和的混合均值的计算问题,并得到了一个精确的计算公式.     

Sums of Three or More Primes

It has long been known that, under the assumption of the Riemann Hypothesis, one can give upper and lower bounds for the error in the Prime Number Theorem, such bounds being within a factor of of each other and this fact being equivalent to the Riemann Hypothesis. In this paper we show that, provided ``Riemann Hypothesis' is replaced by ``Generalized Riemann Hypothesis', results of similar (often greater) precision hold in the case of the corresponding formula for the representation of an integer as the sum of primes for , and, in a mean square sense, for . We also sharpen, in most cases to best possible form, the original estimates of Hardy and Littlewood which were based on the assumption of a ``Quasi-Riemann Hypothesis'. We incidentally give a slight sharpening to a well-known exponential sum estimate of Vinogradov-Vaughan.

     

广义Fibonacci序列的有限和

通过定义广义的Fibonacci序列{Hn,m}:Hn,m=p1Hn-1,m+p2Hn-2,m+…+pmHn-m,m,其中H1,m=a1,H2,m=a2,…,Hm,m=am,n≥m+1,m 2.给出了序列{Hn,m}一些有限和Un,m=∑ni=1Hi,m、U′n,m=∑ni=1(-1)iHi,m、Vn,m=∑ni=1iHi,m、Vn′,m=∑ni=1(-1)iiHi,m的计算公式.     

Generalized Sidon sets

We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers, answering an old question of Simon Sidon.     

Generalized analytic sets

We study completely valued algebraically closed fields in languages with integral analytic functions. it is shown that a nontrivial model theory of integral functions can be developed on a condition that a language is chosen properly. Supported by ISF grant No. RKE300. Translated from Algebra i Logika, Vol. 36, No. 4, pp. 387–406, July–August, 1997.     

Generalized Sierpinski sets

The notion of a Sierpinski topological space is introduced and some properties of such spaces connected with Borel measures are considered.     

More DD difference sets

Dillon and Dobbertin proved that if L := GF(2 ^m ), gcd(k, m) = 1, d := 4 ^k ? 2 ^k + 1 and Δ _k (x) := (x + 1) ^d + x ^d + 1, then B _k := L\Δ _k (L) is a difference set in the cyclic multiplicative group L  ^×  of L. Used in the proof were the auxiliary functions $c_k^{\gamma}(x) := b_k(\gamma x^{2^k+1})$ , where γ is in L  ^×  and b _k is the characteristic function of B _k on L. When m is odd $c_k^{\gamma}$ is itself the characteristic function of a cyclic difference set which is equivalent to B _k . In this paper we point out that when m is even and γ is not a cube in L then $c_k^{\gamma}$ is the characteristic function of a difference set in the elementary abelian additive group of L; i.e. $c_k^{\gamma}$ is a bent function.     

Barrelledness of Generalized Sums of Normed Spaces

Let (E _i ) _iI be a family of normed spaces and a space of scalar generalized sequences. The -sum of the family (E _i ) _iI of spaces is

Supersaturated Design with More Than Two Levels

gO. IntroductionA fractional factorial design is called supersaturated if the number of factors includedexceeds the limitation for keeping all the factors estimable, ignoring interactions. Sincesupersaturated designS can accommodate large nUInbers of factors, they are thought usefulin screening experhoellts.The research work on tWO-level supersaturated design was st8lted in the late fifties andearly staies (see [1,101). The subject has been gaining more and more renewed interest inthe last …     

Sums and Differences of Two Cubic Polynomials

 When f(x) is a cubic polynomial with integral coefficients, we show that almost all integers represented as the sum or difference of two values of f(x), with , are thus represented essentially uniquely. (Received 18 January 1999; in revised form 17 May 1999)     

Sums and Differences of Two Cubic Polynomials

 When f(x) is a cubic polynomial with integral coefficients, we show that almost all integers represented as the sum or difference of two values of f(x), with , are thus represented essentially uniquely.     

广义对角多项式指数和的估计

利用高斯和与次数矩阵Smith标准形的不变因子,给出了有限域上广义对角多项式指数和的估计,从而改进了Deligne-Weil型估计这类多项式指数和的结果.     

Generalized projections onto convex sets

This paper introduces the notion of projection onto a closed convex set associated with a convex function. Several properties of the usual projection are extended to this setting. In particular, a generalization of Moreau’s decomposition theorem about projecting onto closed convex cones is given. Several examples of distances and the corresponding generalized projections associated to particular convex functions are presented.     

广义高阶Bernoulli数,Gauss和及广义Kloosterman和(英文)

利用广义高阶Bernoulli数的性质及Dirichlet L-函数的均值定理,研究了Gauss和及广义Kloosterman和与广义高阶Bernoulli数的均值性质,并给出两个有趣的渐近公式.