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This paper proves that the (2,2) path chromatic number problem of graphs with maximum degree 4 is NPcomplete.


In general, this problem is NPcomplete and it is proved that forn=2 and 3 this problem is polynomialtime solvable.


MKP (B,S,m,n) is strongly NPComplete and no polynomialtime approximation algorithm can have an approximation ratio better than 0.5.


It is known that the problem for general graphs is NPhard while it is polynomially solvable for trees.


Many difficult (often NPcomplete) optimization problems can be solved efficiently on graphs of small treewidth with a given treedecomposition.

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 A more general mathematical analysis of the kinetics of polycondensationdepolycondensation reactions is given in the article. Three different types of reactions are considered, namely, (1) reactions between molecules AB and AB, (2) reactions between molecules AA and BB, (3) reactions between molecules AA and BC. One of the condensation products is assumed (without loss of generality) to be water.For reactions of the first type, [p_n], the number of molecules of the nmer (AB)_n, obeys the following Flory distribution:... A more general mathematical analysis of the kinetics of polycondensationdepolycondensation reactions is given in the article. Three different types of reactions are considered, namely, (1) reactions between molecules AB and AB, (2) reactions between molecules AA and BB, (3) reactions between molecules AA and BC. One of the condensation products is assumed (without loss of generality) to be water.For reactions of the first type, [p_n], the number of molecules of the nmer (AB)_n, obeys the following Flory distribution: [p_n]=N_0p~(n1)(1p)~2 where N_0 denotes the total number of AB segments (including the unreacted monomers). and p, as defined by is a measure of the degree of condensation. It is shown that p is the solution of the following differential equation: dp/dt=k/2N_0(1p)~2k_(1)p[H_2O] where K and k_(1) are velocity constants of condensation and hydrolysis respectively, and [H_2O] denotes the number of water molecules. Three special cases are discussed.For reactions of the second type, three different types of condensation products are possible besides water; they obey the following distributions: [p_(2n)]=2N′_0r~(n1)p~(2n1)(1p)(1rp) [p′_(2n1)]=N′_0r~(n1)p~(2n2)(1p)~2 [p″_(2n1)]=N′_0r~(n2)p~(2n2)(1rp)~2 where N′_0 and N″_0 denote the total number of segments AA and BB respectively, r denotes the ratio N′_0/N″_0, and p, as defined by is the solution of the following differential equation: dp/dt=kn′_0/r(1p)(1rp)k_(1)P[H_2O]For reactions of the third type, six different types of condensation products are possible besides water; they obey the following distributions: [P′_(2n)]=NP~(n1)q~n(1p/2q/2)(1p) [p″_(2n)]=Np~nq~(n1)(1p/2q/2_(?))(1q) [p_(2n1)=Np~(n1)q~(n1)(1p/2q/2)~2 [p′_(2n1)]=N/4p~(n2)q~n(1p)~2 [p″_(2n1)]=N/4p~nq~(n2)(1p)~2 [p′″_(2nn)]=∈(n)N/4p~(n1)q~(n1)(1p)(1q),where N denotes either the total number of segments AA or that of BC, while p and q, as defined by satisfy the following set of differential equations: dp/dt=k′N/2(1p)(2pq)k′_(1)p[H_O] dq/dt=k″N/2(1q)(2pq)k″_(1)q[H_2O]  本文討論AB型,AA和BB型以及AA和BC型分子间的缩聚裂解反應,由動力学方程出發,得到这三种类型反應过程中高聚分子的分佈情况,并求得几种不同反應條件下的缩聚度p和q是何种時间的函数,利用它们和实验数值比較,可以求得縮聚反應速度常数K和水解反應速度常数k_(1),并在AA和BC型分子间的反應中,可以求得K＇和K″的此值,藉以比较官能團B和C的活潑度。还討論了三种平均分子量的表示式、数值以及它们相互的比值,後者僅在没有水解作用的情况下,才和Flory的结果相同。  A synchronised accumulation technique is used to achieve a resolution of up to 1013 cm for the oscillating amplitude of a laser interferometer. Such a technique is applied to observe the 60.4 Hz gravitational radiation which is possibly emitted from the pulsar NP 0532 of the Crab Nebula. Present experiments show that no such signal is received.  本文采用同步积累技术,使激光干涉仪对于微小振动振幅的检测能力达到10~(13)厘米的水平;运用这一技术对蟹状星云中的NP0532脉冲星可能存在的60.4赫芝引力辐射进行了观测。实验表明:未收到这一信息。  In this paper", the further development of a new type of generalpurpose Supercomputer "Cellular Vector Computer of Vertical and Horizontal Processing" (CVCVHP) from "with Common Memory "to "with Virtual Common Memory", is diseussed. The subsystem of "CVCVHP with Virtual Common Memory" is equivalent to a multidimentional array processor.Starting from the "Vector Computer of Vertical and Horizontal Processing" (m×np type) based on small and medium scale integrated circuits, we briefly describe "CVCVHP... In this paper", the further development of a new type of generalpurpose Supercomputer "Cellular Vector Computer of Vertical and Horizontal Processing" (CVCVHP) from "with Common Memory "to "with Virtual Common Memory", is diseussed. The subsystem of "CVCVHP with Virtual Common Memory" is equivalent to a multidimentional array processor.Starting from the "Vector Computer of Vertical and Horizontal Processing" (m×np type) based on small and medium scale integrated circuits, we briefly describe "CVCVHP with Common Memory" (m X n type, m × np type), which is introduced because of the development of very large scale integrated circuits. This, is a new type of vector computer which employs a multiple data stream and multiple instruction stream architecture.On this basis, for the sake of raising the speed of a system by largely increasing the number of cells, in this paper we emphasize a new type of supercomputer, i.e. CVCVHP with "Virtual Common Memory in Addition to Common Memory". This system may consists of thousands of cells. And we conclude that its subsystem is equivalent to a multidimentional array processor. Seen from another angle, we propose a class of methods of using a supercomputer which consists of thousands of "microprocessors" (more exactly, the "cells").The system presented also has such features: from the view of physical organization it appears as a multidimentional array processor system, but from the view of function (i.e. the view of users) it is a vector computer. The memory is distributed physically, but is concentrated from the viewpoint of users.The following problems of this new type of supercomputer system are also discussed: language, principal algorithms, corresponding principal instructions, principal functions of the cell, '' Common Memory'', synchronizing, the number of data transmission lines, the number of transmission steps, and so on.Finally, we consider a simplified system, the language of which is completely consistent with the "High Level Vector Language" of a normal vector computer.The system we propose in this paper may constitute a series of computer complex of various sizes.  本文从中小规模集成电路为基础的纵横加工向量机(m×n_p型)出发,简略地介绍了由于“超大规模集成电路”的发展趋势而引入的共存细胞结构纵横加工向量机(m×n型,m×n_p型)。 在此基础上,为了用大幅度扩大台数的办法来大幅度提高解题速度,本文重点介绍一种新型通用巨型机,即可以多达成千上万个细胞单元的“虚共存加共存”式的细胞结构纵横加工向量机。它提出了所谓用“微处理机”组合巨型机的一种有效算法和结构,其子系统与多维阵列机等价。本系统可构成一个规模大小不同的组合机系列,如进一步简化,也可以成阵列部件系列。 本文还讨论了这类新型巨型机的语言,主要算法,对应的主要指令,细胞单元的主要功能,以及“共存”、同步、数据传输等问题。 本系统具有如下特点:从物理结构的观点看,它接近于多维阵列机,且是分散存储;但从功能的角度(即用户的角度)看,它是向量机,且是集中、公共存储。   << 更多相关文摘 



