Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

In-gel deglycosylation of sodiumdodecyl sulfate polyacrylamide gel electrophoresis-separated glycoproteins for carbohydrate estimation by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Mass determination by mass spectrometric methods (electrospray ionization mass spectrometry (ESI-MS), matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS)) of sodiumdodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE)-separated proteins is a well known procedure and reliable protocols are available. In our efforts to use the established methods to determine the molecular mass of the disulfide bridged, heterodimeric glycoprotein GP3 and to determine the carbohydrate content of each protein subunit we developed an in-gel chemical deglycosylation method. For this purpose we established experimental conditions that allow maximum extraction of the high molecular mass protein subunits and developed a routine method to apply the HF-pyridine deglycosylation protocol to proteins isolated from polyacrylamide gel pieces. The novel protocol and extraction procedure described can be used to analyze O-glycosylated proteins up to 150 kDa after SDS-PAGE separation.     

Survey of ligand field parameters of strong field d complexes obtained from the g matrix

Using a newly proposed approach involving an internally consistent set of equations, the ligand field parameters Δ/ξ, V/ξ and k are obtained from literature values of the g matrix for strong field d⁵ systems of various conformations in which |Δ/ξ|≤10. Qualitative analysis of the observed results is done using the Angular Overlap Model, AOM.     

单A直和子空间

引入单直和子空间的概念,证明了线性空间可唯一分解为单直和子空间的直和,并且给出了计算方法.     

Photo-Induced Reactions between Glyoxal and Hydroxylamine in Cryogenic Matrices

In this paper, the photochemistry of glyoxal–hydroxylamine (Gly–HA) complexes is studied using FTIR matrix isolation spectroscopy and ab initio calculations. The irradiation of the Gly–HA complexes with the filtered output of a mercury lamp (λ > 370 nm) leads to their photoconversion to hydroxyketene–hydroxylamine complexes and the formation of hydroxy(hydroxyamino)acetaldehyde with a hemiaminal structure. The first product is the result of a double hydrogen exchange reaction between the aldehyde group of Gly and the amino or hydroxyl group of HA. The second product is formed as a result of the addition of the nitrogen atom of HA to the carbon atom of one aldehyde group of Gly, followed by the migration of the hydrogen atom from the amino group of hydroxylamine to the oxygen atom of the carbonyl group of glyoxal. The identification of the products is confirmed by deuterium substitution and by MP2 calculations of the structures and vibrational spectra of the identified species.     

Secure Direct Communication Using Ensembles with the Same Compressed Density Matrix

In this paper, a quantum secure direct communication protocol using ensembles with the same density matrix is proposed. The two communication parties can realize the message transmission using this method through a quantum channel, each bit of information can be transmitted using an ensemble and read out through global measurement.The eavesdropping behavior can be detected through the channel diagnoses.     

光子四维量子态隐形传输

多维量子纠缠态比二维纠缠态可加载更多的信息,多维量子系统是量子信息处理中一个很重要的资源.本文采用已实现的光子四维纠缠态,给出了光子四维量子态的张量表达式,并描述了四维量子态隐形传输的一般表示方法;通过讨论光子四维量子态系统的量子通道参数矩阵和测量矩阵的特性,得到实现完全传输和非零概率传输的充要条件.最后,本文给出在多种量子通道下的四维态的量子隐形传态方案,这一过程在张量分析表示下十分清晰明了.     

STRUCTURES OF CIRCULANT INVERSE M-MATRICES

In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c（n- 1）] is not a positive matrix and not equal to c0I, then A is an inverse M-matrix if and only if there exists a positive integer k, which is a proper factor of n, such that cjk 〉 0 for j=0,1…, [n-k/k], the other ci are zero and Circ[co, ck,… , c（n-k）] is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices.     

过模慢波结构频率反射特性及谐振腔的影响

利用有限元方法求解:S-参数矩阵,研究了过模慢波结构对圆波导TM01,TM02模的反射特性,分析了在慢波结构末端加入谐振腔后,由于两端口的不对称性而造成的对反射特性影响。结果表明,在TM01的π模频率附近,慢波结构和谐振腔组成的系统对无谐振腔一侧端口入射TM01模的反射增大,而对有谐振腔一侧端口入射TM01模的反射减小。根据计算结果,解释了普通多波切伦柯夫振荡器所用慢波结构周期数较多的原因,说明了在多波切伦柯夫振荡器中引入谐振腔后,不但可以减少所用慢波结构周期数,而且有利于提高微波输出效率。