算术半格的闭包空间表示

本文主要讨论算术半格的闭包空间表示.首先通过在给定的闭包空间中增加适当的条件,提出了算术闭包空间的概念,并且给出了算术半格的闭包空间表示.接着提出了算术闭包空间之间的算术逼近映射的概念,并证明了以算术逼近映射作为态射的算术闭包空间范畴和以Scott连续函数作为态射的算术半格范畴之间的范畴等价性.     

模糊DCPO范畴的一个笛卡尔闭的满子范畴

引入了有界完备模糊dcpo的概念,研究了有界完备模糊dcpo的基本性质。证明了当赋值格L是Frame时,以模糊Scott连续映射为态射的有界完备模糊dcpo范畴BC-FDCPO是以模糊Scott连续映射为态射的模糊dcpo范畴FDCPO的笛卡尔闭子范畴。同时还给出了模糊完备交半格、强模糊完备交半格的定义,并研究了它们与有界完备模糊dcpo之间的关系。     

半格与Domain的表示

引入一种半格———Ｄ 半格，建立了Ｄ－半格的表示理论，利用它得到了Ｌ ｄｏｍａｉｎ（即局部代数格）的表示理论；证明了Ｌ ｄｏｍａｉｎ与稳定映射范畴对偶等价于稳定Ｄ 半格与Ｄ－半格同态范畴．     

关于函数空间的超连续性

超连续格(超连续完备半格)可以由函数空间刻画,并且超连续格(超连续完备半格)在Scott连续函数空间下是封闭的,进而其相应的范畴均是Cartesian闭范畴.     

关于函数空间的超连续性

超连续格(超连续完备半格)可以由函数空间刻画,并且超连续格(超连续完备半格)在Scott连续函数空间下是封闭的,进而其相应的范畴均是Cartesian闭范畴.     

Smyth幂半格及其连续domain表示

本文证明了每个Ｓｍｙｔｈ幂半格同构于一连续ｄｃｐｏ的Ｓｍｙｔｈ幂ｄｏｍａｉｎ，而每个连续ｄｃｐｏ同构于其 Ｓｍｙｔｈ幂 ｄｏｍａｉｎ的 ｗａｙ ｂｅｌｏｗ素谱．通过上幂函子建立了连续ｄｏｍａｉｎ与Ｓｍｙｔｈ幂半格之间的范畴等价性，从而揭示了上、下幂ｄｏｍａｉｎ结构之间的联系．     

T—算子，泛算术与Zadeh算子

Zadeh算子已推广到T-算子,T-算子也已推广到泛算术,本文讨论T-算子与Zadeh算子,泛算术与Zadeh算子的关系,在一定条件下,得到了它们之间相互转化的充要条件。     

幂半格与半群

给出了半格上的幂半格的概念,讨论了幂半格的相关性质,建立了半格上的幂半格与半群之间的联系。     

ω上非主算术超滤存在性的一个定理

每个非主算术超滤p∈βω-ω都可用来形成一个简单的不可数算术模型Np= {f(p):f∈ωω}N．用这个模型中的超滤(代替自然数)作成的有限分数的等价类便得到所有正实数．用分数表示实数,这正是古希腊人曾有的想法．人们已经知道,Martin 公理的较弱形式MAcountable蕴涵着下面的命题Q: (Q)若B■P(ω)具有sfip(强有限交性质)且|B|<2ω,则存在Q点qB．本文证明命题Q蕴涵着结论:ω上非主算术超滤存在．     

超连续Domain与拟超连续Domian

讨论了超连续domain与拟超连续domain的相关性质,证明了超连续半格范畴为有性质M*的拟超连续domain范畴的反射子范畴。     

On the arithmetic product of combinatorial species

We introduce two new binary operations on combinatorial species; the arithmetic product and the modified arithmetic product. The arithmetic product gives combinatorial meaning to the product of Dirichlet series and to the Lambert series in the context of species. It allows us to introduce the notion of multiplicative species, a lifting to the combinatorial level of the classical notion of multiplicative arithmetic function. Interesting combinatorial constructions are introduced; cloned assemblies of structures, hyper-cloned trees, enriched rectangles, etc. Recent research of Cameron, Gewurz and Merola, about the product action in the context of oligomorphic groups, motivated the introduction of the modified arithmetic product. By using the modified arithmetic product we obtain new enumerative results. We also generalize and simplify some results of Canfield, and Pittel, related to the enumerations of tuples of partitions with the restrictions met.     

Quantum protocols for untrusted computations

In this paper, we propose new quantum arithmetic protocols among multiple parties. Let some parties have values. A problem is to find a protocol such that under the condition that any eavesdropper intercepting any quantum system being exchanged among the parties must not be able to acquire information, the parties compute an arithmetic operation such as addition and multiplication, and transfer its computing result to another party. One of main ideas to solve this problem is based on operating state phases. A quantum addition algorithm based on operating phases has been proposed by Draper, but his algorithm was not considered being eavesdropped. We propose secure quantum arithmetic protocols.     

Minimal arithmetic thickness connecting discrete planes

While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the three-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector , we provide algorithms either to determine whether a given arithmetic discrete plane with as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector is connected.     

论数值修约

数值修约的已有定义是从其现象来定义的。现在提出的定义是从数值修约的本质(用加减法使尾数化零)来定义的。因而按定义可直接推导得到种种结论。并可以此来定义各种数值修约规则。对一个数值连续修约的可行性作了解释。对修约间隔亦有论述。本文提出了五轮换规则的想法。关于两个数值修约规则的中文名称,主要是指出它们用常量(四、五、六)表示变量,因而产生逻辑上的错误。本文也讨论产生错误的原因,并同时指出其他错误。新名称的提出已不犯原有错误。     

Smooth numbers and the norms of arithmetic Dirichlet convolutions

In this paper we consider the problem of exactly evaluating the p-norm of a linear operator linked with arithmetic Dirichlet convolutions. We prove that a simply derived upper bound for this norm is actually attained for several different classes of arithmetic functions including completely multiplicative functions, but not for certain multiplicative functions. Our proof depends fundamentally on the asymptotic distribution properties of smooth numbers.     

Arithmetic progressions on Pell equations

In this paper we consider arithmetic progressions on Pell equations, i.e. integral solutions (X,Y) whose X-coordinates or Y-coordinates are in arithmetic progression.     

Sub-Ramsey Numbers for Arithmetic Progressions

Let the integers 1, . . . ,n be assigned colors. Szemerédi's theorem implies that if there is a dense color class then there is an arithmetic progression of length three in that color. We study the conditions on the color classes forcing totally multicolored arithmetic progressions of length 3. Let f(n) be the smallest integer k such that there is a coloring of {1, . . . ,n} without totally multicolored arithmetic progressions of length three and such that each color appears on at most k integers. We provide an exact value for f(n) when n is sufficiently large, and all extremal colorings. In particular, we show that f(n)=8n/17+O(1). This completely answers a question of Alon, Caro and Tuza.     

Equational fragments of systems for arithmetic

We investigate the equational fragments of formal systems for arithmetic by means of the equational theory of f-rings and of their positive cones, starting from the observation that a model of arithmetic is the positive cone of a discretely ordered ring. A consequence of the discreteness of the order is the presence of a discriminator, which allows us to derive many properties of the models of our equational theories. For example, the spectral topology of discrete f-rings is a Stone topology. We also characterize the equational fragment of Iopen, and we obtain an equational version of G?del's First Incompleteness Theorem. Finally, we prove that the lattice of subvarieties of the variety of discrete f-rings is uncountable, and that the lattice of filters of the countably generated distributive free lattice can be embedded into it. Received April 17, 1998; accepted in final form January 23, 2001.     

An Additive Problem with Primes in Arithmetic Progressions

In this paper, we extend a classical result of Hua to arithmetic progressions with large moduli. The result implies the Linnik Theorem on the least prime in an arithmetic progression.     

求等差数列k次幂和的微分法

本文用微分法给出求等差数列ｋ次幂和的较简洁的计算公式．