1.

Neighborhoodfollowing algorithms for linear programming





Al WenbaoSchool of Science Beijing University of Posts and Telecommunications Beijing 100876 China《中国科学A辑(英文版)》,2004年第47卷第6期


In this paper, we present neighborhoodfollowing algorithms for linear programming. When the neighborhood is a wide neighborhood, our algorithms are wide neighborhood primaldual interior point algorithms. If the neighborhood degenerates into the central path, our algorithms also degenerate into pathfollowing algorithms. We prove that our algorithms maintain the O(n~(1/2)L)iteration complexity still, while the classical wide neighborhood primaldual interior point algorithms have only the O(nL)iteration complexity. We also proved that the algorithms are quadratic convergence if the optimal vertex is nondegenerate. Finally, we show some computational results of our algorithms.

2.

A FAST SINE TRANSFORM ALGORITHM FOR TOEPLITZ MATRICES AND ITS APPLICATIONS





汪祥 卢琳璋《高等学校计算数学学报(英文版)》,2005年第14卷第2期


In this paper, a fast algorithm for the discrete sine transform(DST) of a Toeplitz matrix of order N is derived. Only O(N log N) O(M) time is needed for the computation of M elements. The auxiliary storage requirement is O(N). An application of the new fast algorithm is also discussed.

3.

Fast rectangular matrix multiplication and some applications





Ke ShanXue Zeng BenSheng Han WenBao Victor Y. Pan《中国科学A辑(英文版)》,2008年第51卷第3期


We study asymptotically fast multiplication algorithms for matrix pairs of arbitrary di mensions, and optimize the exponents of their arithmetic complexity bounds. For a large class of input matrix pairs, we improve the known exponents. We also show some applications of our results:(i) we decrease from O(n~2 n~(1 o)(1)logq)to O(n~(1.9998) n~(1 o(1))logq)the known arithmetic complexity bound for the univariate polynomial factorization of degree n over a finite field with q elements; (ii) we decrease from 2.837 to 2.7945 the known exponent of the work and arithmetic processor bounds for fast deterministic(NC)parallel evaluation of the determinant, the characteristic polynomial, and the inverse of an n×n matrix, as well as for the solution to a nonsingular linear system of n equations; (iii)we decrease from O(m~(1.575)n)to O(m~(1.5356)n)the known bound for computing basic solutions to a linear programming problem with m constraints and n variables.

4.

GAUSSIAN PIVOTING METHOD FORSOLVING LINEAR COMPLEMENTARITY PROBLEM 被引次数：4





L1DONGHUI ZengJinping Zhangzhongzhi《高校应用数学学报(英文版)》,1997年第12卷第4期


In this paper, a new direct algorithm for solving linear complementarity problem with Zmatrix is proposed. The algorithm exhibits either a solution or its nonexistence after at most n steps (where n is the dimension of the problem) and the computational complexity is at most 1/3n^2 O(n^2)

5.

Synthesis and Structure of the Hexanuclear Diazenido－oxomolybdate ［（n－C_4H_9）_4N］_3［Mo_6O_（18）（N_2C_6H_4－p－NO_2）］





Li HaiLian You XiaoZeng Xu XueXiang《结构化学》,1994年第2期


ＳｙｎｔｈｅｓｉｓａｎｄＳｔｒｕｃｔｕｒｅｏｆｔｈｅＨｅｘａｎｕｃｌｅａｒＤｉａｚｅｎｉｄｏ－ｏｘｏｍｏｌｙｂｄａｔｅ［（ｎ－Ｃ_４Ｈ_９）_４Ｎ］_３［Ｍｏ_６Ｏ_（１８）（Ｎ_２Ｃ_６Ｈ_４－ｐ－ＮＯ_２）］ＬｉＨａｉ－Ｌｉａｎ；ＹｏｕＸｉａｏ－Ｚｅｎｇ；...

6.

A MehrotraType PredictorCorrector Algorithm for P*(κ) Linear Complementarity Problems





Weihua LI Mingwang ZHANG Yiyuan ZHOU《数学研究与评论》,2012年第32卷第3期


Mehrotratype predictorcorrector algorithm,as one of most efficient interior point methods,has become the backbones of most optimization packages.Salahi et al.proposed a cut strategy based algorithm for linear optimization that enjoyed polynomial complexity and maintained its efficiency in practice.We extend their algorithm to P_{*}（κ）linear complementarity problems.The way of choosing corrector direction for our algorithm is different from theirs. The new algorithm has been proved to have an ο(（1+4κ）（17+19κ） √（1+2κn）^{3/2}log[（x^{0}）^{T}s^{0}/ε] worst case iteration complexity bound.An numerical experiment verifies the feasibility of the new algorithm.

7.

$P_*(\kappa)$线性互补问题的Mehrotra型预估校正算法





李卫滑 张明望 周意元《数学研究及应用》,2012年第32卷第3期


Mehrotratype predictorcorrector algorithm,as one of most efficient interior point methods,has become the backbones of most optimization packages.Salahi et al.proposed a cut strategy based algorithm for linear optimization that enjoyed polynomial complexity and maintained its efficiency in practice.We extend their algorithm to P_{*}（κ）linear complementarity problems.The way of choosing corrector direction for our algorithm is different from theirs. The new algorithm has been proved to have an ο(（1+4κ）（17+19κ） √（1+2κn）^{3/2}log[（x^{0}）^{T}s^{0}/ε] worst case iteration complexity bound.An numerical experiment verifies the feasibility of the new algorithm.

8.

Studies on OrganoPhosphorus, Arsenic and Antimony Polytungstates and Polymolybdates (Ⅶ)——Preparation and Properties of pAminophenylarsenic Polymolybdates





Liu Benyao Gong Ziqiu Gu Yidong《高等学校化学研究》,1989年第3期


In order to investigate the influence of organic groups on the types of organoarsenic polymolybdates, the reations of paminophenylarsonic acid with sodium molybdate were tested at pH=35. Six salts were prepared and characterized. (1) (CN3H8)4 [(pNH3C6H4As)2Mo6O25] · H2O, (2) (CN3H6)4 [(p, NH3C6H4As )2Mo6O25 ] · 6H20, (3) Cs4 [(pNH3C6H4As)2Mo6O25] · 4H2O, (4) C(CH3)4N]4[(pNH3C6H4As)2Mo6O25] · 5H2O, (5) [(nC4H9)4N]3Na[(pNH3C6H4As)2Mo6O25] · 2H2O, (6) Ba2 NH3C6H4As)2Mo6O25] · 10H2O. The IR, UV spectra, and electrochemical behavior are reported and discussed. They should belong to the same type as that for phenyl derivative or the nitrophenyl derivatives. But the ammo groups can accept protons, so that the anion' s charge decreases. Very similar to the tungsten congener (CN3H6)4[(pNH3C,H4As)2W6O25] · 4H2O, [(RAs)2Mo6O25]4 type of complexes are formed.

9.

ON THE COMPLEXITY OF A PL HOMOTOPY ALGORITHM FOR ZEROS OF POLYNOMIALS





高堂安 王则柯《应用数学学报(英文版)》,1993年第2期


A PL homotopy algorithm is modified to yield a polynomialtime result on its computational complexity.We prove that the cost of locating all zeros of a polynomial of degree n to an accuracy of ε(measured by the number of evaluations of the polynomial)grows no faster than O(max{n~4,n~3log_2(n/ε)}).This work is in response to a question raised in a paper by S.Smale as to the efficiency of piecewise linear methods in solving equations.In comparison with a few results reported,the algorithm under discussion is the only one providing correct multiplicities and the only one employing vector labelling.

10.

Scheme for Implementing Quantum Search Algorithm in a Cluster State Quantum Computer





WANG YanHui ZHANG Yong《理论物理通讯》,2008年第49卷第6期


Using cluster state and single qubit measurement one can perform the oneway quantum computation. Here we give a detailed scheme for realizing a modified Grover search algorithm using measurements on cluster state. We give the measurement pattern for the clusterstate realization of the algorithm and estimated the number of measurement needed for its implementation. It is found that O（2^3n/^2n^2） number of single qubit measurements is required for its realization in a clusterstate quantum computer.

11.

Homogenization of Elliptic Problems with Neumann Boundary Conditions in Nonsmooth Domains





Jun Geng《数学学报(英文版)》,2018年第34卷第4期


We consider a family of secondorder elliptic operators {L_ε} in divergence form with rapidly oscillating and periodic coefficients in Lipschitz and convex domains in R~n. We are able to show that the uniform W~(1,p) estimate of second order elliptic systems holds for 2n/(n+1)δ p 2n/(n1)+ δ where δ 0 is independent of ε and the ranges are sharp for n = 2, 3. And for elliptic equations in Lipschitz domains, the W~(1,p) estimate is true for 3/2δ p 3 + δ if n ≥ 4, similar estimate was extended to convex domains for 1 p ∞.

12.

A quantum search algorithm of two entangled registers to realize quantum discrete Fouriertransform of signal processing





庞朝阳 胡本琼《中国物理 B》,2008年第17卷第9期


The discrete Fourier transform （DFT） is the base of modern signal processing. 1dimensional fast Fourier transform （1D FFT） and 2D FFT have time complexity O（N log N） and O（N^2 log N） respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover＇s iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. Onedimensional quantum DFT （1D QDFT） and twodimensional quantum DFT （2D QDFT） are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, 1D and 2D QDFT have time complexity O（v/N） and O（N） respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible.

13.

The Bergman Kernels and Comparison Theorem on Hua Domain of the Third 被引次数：1





殷慰萍 赵晓霞《数学进展》,2000年第29卷第5期


1 The Bergman Kernel Function The Bergman Kernel function plays an important role in several complexvariables. L.～K. Hua［1］ obtained the Bergmankernel, Cauchy kernel and Poisson Kernel on four types of Cartan domains.So the basic theory of several complex variables was built on such domains.Yin Weiping［2］ computed such three types of kernels on two exceptional Cartandomains. The Cartan domains are bounded symmetric domain (homogeneous domainalso). For the bounded nonsymmetric domainwe can get the explicit formulas of Bergman kernel function by using theL.～K. Hua's method［3,4］ if the holomorphic transitivegroup is given. Except the bounded homogeneous domains, we have known theexplicit formulas of Bergman kernelfunction on egg domain E(p1, p2,,pn) defined by the inequality z12p1)++zn2)/(pn)< 1 in some cases. For example, Bergman［5］computed the Bergman kernel of E(1,p) in C2.D'Angelo used a method to sum an infinite series to get the explicit formulaof Bergman kernel forE(1,2,,1, pn). Where the z C［6］ or z Cm［7］. When p1, p2,, pn are positive integers,the explicit formula of the Bergman for E(p1,p2,,pn) was first computedby Zinov'ev［8］. If p1,p2,,pn1 are positive integers and pn is apositive real number. The explicit formula of Bergman kernel ofE(p1,, pn) is given by Francsics and Hanges［9］. Recently, H.～Boas,Siqi Fu and J. Straube［10］ proved two principles to compute the Bergman kernelsin a simple way.

14.

A fast and practical method to pack spheres for mesh generation





Jianfei Liu Shuixiang Li Yongqiang Chen《Acta Mechanica Sinica》,2008年第24卷第4期


Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents an efficient sphere packing algorithm which is much faster and appears to be the most practical among all sphere packing methods presented so far for mesh generation. The algorithm packs spheres inside a domain using advancing front method. High efficiency has resulted from a concept of 4R measure, which localizes all the computations involved in the whole sphere packing process.

15.

一种基于正则参数化的降维细分算法(英文)





姜政毅 关玉景《东北数学》,2008年第24卷第1期


In our previous work, we have given an algorithm for segmenting a simplex in the ndimensional space into rt n＋ 1 polyhedrons and provided map F which maps the ndimensional unit cube to these polyhedrons. In this paper, we prove that the map F is a one to one correspondence at least in lower dimensional spaces （n _〈 3）. Moreover, we propose the approximating subdivision and the interpolatory subdivision schemes and the estimation of computational complexity for triangular Bézier patches on a 2dimensional space. Finally, we compare our schemes with Goldman＇s in computational complexity and speed.

16.

红黑排序混合算法收敛速度分析 被引次数：6





杭旭登 刘兴平 袁光伟 宋杰《计算数学》,2003年第25卷第4期


The algorithm of applying the block Gauss elimination to the RedBlack ordering matrix to reduce the order of the system then solve the reduced system byiterative methods is called Hybrid RedBlack Ordering algorithm.In this paper,we discuss the convergence rate of the hybrid methods combined with JACOBI,CG,GMRES(m).Theoretical analysis shows that without preconditioner thesethree hybrid methods converge about 2 times as fast as the corresponding natural ordering methods.For the case that all the eigenvalues is near the real axis, the GMRES(m) algorithm converges about 3 times faster than the natural ordering GMRES(m).Various numerical experiments are presented.For large scale problem with preconditioners, numerical experiments show that the GMRES(m) hybrid methods converge from about 3 times to even 5 times as fast as the natural ordering methods and the computing time is reduced to about 1/3 even 1/6 of that of the natural ordering methods.

17.

The exceptional set for sums of unlike powers of primes





Li Lu Zhao《数学学报(英文版)》,2014年第30卷第11期


It is established that all even positive integers up to N but at most O（N15/16＋ε） exceptions can be expressed in the form p1^2＋ p2^3＋ p3^4＋ p4^5,where p1,p2,p3 and p4 are prime numbers.

18.

Spatially Resolved N2（A3Σ＋u, ν=0） Decay Studies in the Pulsed DirectCurrent Nitrogen Discharge using the LaserInducedFluorescence Technique





FENG ChunLei YANG HongLiang GAO Liang DING Hongbin《中国物理快报》,2014年第3期


We focus on the investigation of the spatial distribution and temporal evolution of N2（A3Σ＋u, ν=0） in a very early afterglow of a pulsed dc nitrogen discharge. The results indicate that a fast quenching process of N2（A3Σ＋u, ν=0） exists in the very early afterglow. We study the dependence of this fast quenching process on the discharge pressure 20–40 torr. It seems that this fast quenching behavior of N2（A3Σ＋u, ν=0） found in our experiment can be ascribed to the combined action of pooling reaction and collisions with N atoms through N2（A3Σ＋u）＋N2（A3Σ＋u）→ N2＊＋N2（N2＊=N2（B3Πg, C3Πu, C＇3Πu, C＂5Πu）） and N2（A3Σ＋u）＋N（4S）→N（2P）＋N2, respectively. Meanwhile, the decay studies of N2（A3Σ＋u, ν=0） near the anode and cathode infer that the production of N（4S） atoms does not distribute uniformly along the axis of the discharge gap at relatively low pressure, and this effect becomes gradually inconspicuous with the increasing discharge pressure.

19.

反相高效液相色谱法测定尿中对氨基苯酚





梁力 蔡伯祥 陶俊强 杨春英《色谱》,1995年第13卷第3期


In this paper, paminophenol in urine was separated from its matrix and determined bv RPHPLC witha fast column of Spherisorb C(18), 3μm, 50×4.6mm i.d.and mobile ohase of MeOH: H2O: H3PO4(22: 78:0.1, V/V/V). The sample was previously undergone hydrolysis,extraction and filtration through 0. 22μm membrane.

20.

Cocrystal Phenomena of DABCO with Phenol Derivatives





《高等学校化学研究》,1993年第3期


It has been reported that 1,4diazabicyclo[2,2,2] octane(DABCO) can form complexed crystals with lithium alkals. Our experimental results show that DABCO can also form cocrystals with phenol derivatives such as phenol(2), ocresol(3), mcresol(4), pcresol(5), pchlorophenol(6), and pnitrophenol(7). The separa
