数量对合矩阵与数量反对合矩阵的迹与谱

应用相似关系下保持特征值与迹不变的性质,避开了计算特征多项式,得到了数量对合矩阵和数量反对合矩阵的只用迹表示的谱、行列式的计算公式及其相似等价类。作为应用,得到了通常对合矩阵、反对合矩阵、对称正交矩阵和反对称正交矩阵的相关结论。

反对合矩阵的相似对角化

通过证明在复数域上每一个反对合矩阵都可以对角化,指出了全体n阶反对合矩阵按矩阵的相似关系进行分类,一共可以分成n+1类。还证明了,在实数域上不存在奇数阶反对合矩阵,并且每一个偶数阶反对合矩阵都不可对角化,但是每一个2n阶反对合矩阵都相似于diag{J1,J2,…,Jn},这里Jk=(0 -1 1 0),k=1,2,…,n,因而全体2n阶反对合实矩阵按矩阵的相似关系进行分类,只有一种类型。同时,指出了每一个非零偶数维实线性空间上的反对合变换都有无穷多个。

对合矩阵和反对合矩阵的若干性质

在高等代数中矩阵是研究问题很重要的工具,在讨论矩阵的乘法运算时给出了对合矩阵的定义,但对其性质研究很少.对合矩阵和反对合矩阵作为特殊矩阵无论在矩阵理论方面,还是在实际应用方面都有重要的意义.我们在研究矩阵及学习有关数学知识时,经常要讨论这两种特殊矩阵的性质.本文先给出对合矩阵和反对合矩阵的定义,然后讨论了它们的若干性质.

与反对合矩阵可交换的对合矩阵

讨论与反对合矩阵可交换的对合矩阵,主要结果如下:(1)与n阶反对合矩阵可交换的对合矩阵的一种表示;(2)对于2阶反对合矩阵A,如果A≠iI(I是单位矩阵),那么与A可交换的对合矩阵一共有4个,它们是±I和±iA;(3)对于3阶反对合矩阵A,如果A≠iI,那么与A可交换的全体对合矩阵为±I和±iA以及±P11k-1P-1,±P-11k-1P-1,P1k l1-k2l-kP-1,P-1k l1-k2l-kP-1其中k是任意复数,l是任意非零复数;当tr(A)=-i时,P是A与diag{i,-i,-i}这一对相似矩阵之间的一个相似因子;当tr(A)=i时,P是A与diag{-i,i,i}之间的一个相似因子。

与对合矩阵可交换的反对合矩阵

讨论与对合矩阵可交换的反对合矩阵。主要结果如下:(1)给出了与n阶对合矩阵可交换的反对合矩阵的一种表示;(2)对于2阶对合矩阵A,如果A≠±I(I是单位矩阵),那么与A可交换的反对合矩阵一共有4个,它们是±iI和±iA;(3)对于3阶对合矩阵A,如果A≠±I,那么与A可交换的全体反对合矩阵为±iI和±iA,以及■其中k是任意复数,l是任意非零复数;当tr(A)=-1时,P是A与diag{1,-1,-1}这一对相似矩阵之间的相似因子;当tr(A)=1时,P是A与diag{-1,1,1}之间的相似因子。

与四阶对合矩阵可交换的反对合矩阵

讨论与四阶对合矩阵可交换的反对合矩阵。主要结果如下:对于四阶对合矩阵A,如果A≠±I(I是单位矩阵),那么与A可交换的全体反对合矩阵可以分为四类:±i I、±i A、tr(A)=±2和tr(A)=0。

温度对T700/3234反对称铺设圆柱壳结构的双稳态特性影响

讨论温度对T700/3234反对称铺设圆柱壳结构的双稳态特性的影响。通过热压固化成型工艺制备了三种不同铺层层数的试样,采用两点加载的方式,使用在现有的拉伸试验机上改装的实验测试平台驱动反对称铺设圆柱壳结构进行稳态转变,持续捕捉实验过程中的数据,得到在20℃,40℃,60℃和80℃温度下的载荷—位移曲线的变化规律及稳态转变载荷。实验后,通过图像处理技术得到曲率和扭曲率等数据。系统分析稳态转变载荷和稳态曲率变化情况,并对存放时间对壳结构的影响进行了讨论。结果表明,温度对双稳态结构稳态转变影响较大,给出了温度对snap-through和snap-back过程的影响规律。

欧氏空间R_s^n上的三种变换

讨论了R_s^n上的反自共轭变换 。

广义Hamiltonian矩阵反问题及其迭代算法

利用矩阵的分解技术,研究了线性矩阵方程AW=B存在反Hermitian广义Hamiltonian解的充分必要条件,并给出了其解的一般表示形式;然后,给出了该矩阵方程在实数域内反对称广义Hamiltonian解的迭代方法,在不考虑计算误差的情况下,经过有限步迭代,可以得到实反对称广义Hamiltonian解.

保持交换环上两类矩阵运算的映射

主要针对交换环上两类矩阵的保持问题进行展开:(1)刻画了交换环上全矩阵空间和上三角形矩阵空间的保持反对合矩阵映射的形式.(2)研究了交换环上n阶上三角形矩阵空间的保持伴随矩阵映射的形式.

New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay

The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.

Kinetic study on reactive extraction of phenylalanine enantiomers with BINAP-copper complexes

Enantioselective liquid–liquid extraction has attracted considerable attention for its potential use in largescale production. Kinetic data are needed for the reliable scale-up of the process. This paper reports the kinetic study of reactive extraction of phenylalanine(Phe) enantiomers with BINAP–copper complex(BINAP–Cu) as a chiral selector. The theory of extraction accompanied by a chemical reaction was applied.The effects of agitation speed, interfacial area, p H value of aqueous phase, initial concentration of Phe enantiomers and initial concentration of BINAP–Cu on the specific rate of extraction were investigated. The forward rate constants of the reactions in the reactive extraction process are 7.93 × 10-5m5/2·mol-1/2·s-1for D-Phe and 1.29 × 10-4m5/2·mol-1/2·s-1for L-Phe.

Characterization of Bioaerosol Bacterial Communities During Hazy and Foggy Weather in Qingdao, China

This study was conducted to evaluate the impact of hazy and foggy weather on the bacterial communities in bioaerosols, for which samples were collected from the Qingdao coastal region on sunny, foggy, and hazy days in January and March 2013. Bacterial community compositions were determined using polymerase chain reaction denaturing gradient gel electrophoresis(PCR-DGGE). The bacterial community diversity was found to be high on foggy and hazy days, and the dominant species differed during hazy weather. The Shannon-Wiener index revealed that the bacterial community diversity of coarse particles was higher than that of fine particles in the bioaerosols. The bacterial community diversity of fine particles significantly correlated with relative humidity(RH; r^2 = 0.986). The cluster analysis results indicated that the bacterial communities on sunny days differed from those on hazy and foggy days. Compared with sunny days, the bacterial communities in the fine particles during hazy weather exhibited greater changes than those in the coarse particles. Most of the sequenced bacteria were found to be closely affiliated with uncultured bacteria. During hazy weather, members of the classes Bacilli and Gammaproteobacteria(Pseudomonas and Acinetobacter) were dominant. The DGGE analysis revealed that Proteobacteria and Firmicutes were the predominant phyla, and their relative percentages to all the measured species changed significantly on hazy days, particularly in the fine particles. Haze and fog had a significant impact on the bacterial communities in bioaerosols, and the bacterial community diversity varied on different hazy days.

A rapid and sensitive method to detect mycobacterium tuberculosis DNA by fluorescence polarization

Objective: To develop a new high sensitivity, rapid and simple mycobacterium tuberculosis DNA detection method using fluorescence polarization technology. Methods: In our asymmetric PCR protocol, 100 times mole of TB-R primer was added than in the usual symmetric PCR to get enough single strands PCR product. The probe TB-5′-TAMRA and PCR products were mixed in a tube and incubate for 5-15 min at 46 ℃.The polarization (mp) was measured using victor2 Multilabel Plate Reader. Results: Asymmetric and symmetric PCR products were analyzed by the FP method. Asymmetric PCR products are detected more sensitively than symmetric ones. The polarization values of probe associated with asymmetric products were much higher than with symmetric products. Conclusion: This fluorescence polarization assay in conjunction with asymmetric PCR is a powerful and widely applicable method for the rapid and sensitive detection of micro-organisms in clinical laboratories.

Analytical Solutions to the Fundamental Frequency of Arbitrary Laminated Plates under Various Boundary Conditions

In recent years, as the composite laminated plates are widely used in engineering practice such as aerospace, marine and building engineering, the vibration problem of the composite laminated plates is becoming more and more important. Frequency, especially the fundamental frequency, has been considered as an important factor in vibration problem. In this paper, a calculation method of the fundamental frequency of arbitrary laminated plates under various boundary conditions is proposed. The vibration differential equation of the laminated plates is established at the beginning of this paper and the frequency formulae of specialty orthotropic laminated plates under various boundary conditions and antisymmetric angle-ply laminated plates with simply-supported edges are investigated. They are proved to be correct. Simple algorithm of the fundamental frequency for multilayer antisymmetric and arbitrary laminated plates under various boundary conditions is studied by a series of typical examples. From the perspective of coupling, when the number of laminated plates layers N〉8-10, some coupling influence on the fundamental frequency can be neglected. It is reasonable to use specialty orthotropic laminated plates with the same thickness but less layers to calculate the corresponding fundamental frequency of laminated plates. Several examples are conducted to prove correctness of this conclusion. At the end of this paper, the influence of the selected number of layers of specialty orthotropic laminates on the fundamental frequency is investigated. The accuracy and complexity are determined by the number of layers. It is necessary to use proper number of layers of special orthotropic laminates with the same thickness to simulate the fundamental frequency in different boundary conditions.

Expression profiles of antimicrobial peptides (AMPs) and their regulation by Relish

Antimicrobial peptides （AMPs）, as key immune effectors, play important roles in the innate immune system of invertebrates. Different types of AMPs, including Penaeidin, Crustin, ALF （anti- lipopolysaccharide factor） have been identified in different penaeid shrimp; however, systematic analyses on the function of different AMPs in shrimp responsive to different types of bacteria are very limited. In this study, we analyzed the expression profiles of AMPs in the Chinese shrimps, Fenneropenaeus chinensis, simultaneously by real-time RT-PCR （reverse transcription-polymerase chain reaction） when shrimp were challenged with Micrococcus lysodeikticus （Gram-positive, G＋） or Hbrio anguillarium （Gram-negative, G-）. Different AMPs showed different expression profiles when shrimp were injected with one type of bacterium, and one AMP also showed different expression profiles when shrimp were challenged with different bacteria. Furthermore, the expression of these AMPs showed temporal expression profiles, suggesting that different AMPs function coordinately in bacteria-infected shrimp. An RNA interference approach was used to study the function of the Relish transcription factor in regulating the transcription of different AMPs. The current study showed that Relish could regulate the transcription of different AMPs in shrimp. Differential expression profiles of AMPs in shrimp injected with different types of bacteria indicated that a complicated antimicrobial response network existed in shrimp. These data contribute to our understanding of immunity in shrimp and may provide a strategy for the control of disease in shrimp.

Ku80 gene G-1401T promoter polymorphism and risk of gastric cancer

AIM:To evaluate the possible relationship between the Ku80 gene polymorphism and the risk of gastric cancer in China.METHODS:In this hospital-based case-control study of gastric cancer in Jiangsu Province,China,we investigated the association of the Ku80 G-1401T (rs828907) polymorphism with gastric cancer risk.A total of 241 patients with gastric cancer and 273 age-and sexmatched control subjects were genotyped and analyzed by polymerase chain reaction-restriction fragment length polymorphism.RESULTS:The frequencies of genotypes GG,GT and TT were 65.6%,22.8% and 11.6% in gastric cancer cases,respectively,and 75.8%,17.6% and 6.6% in controls,respectively.There were significant differences between gastric cancer and control groups in the distribution of their genotypes (P=0.03) and allelic frequencies (P=0.002) in the Ku80 promoter G-1401T polymorphism.CONCLUSION:The T allele of Ku80 G-1401T may be associated with the development of gastric cancer.

The Asymmetric Response of Older Male Labour Force Participation Rates to Pension Reform and Labour Market Variables

Increasing the labour force participation rates of older workers is a fundamental component of most OECD （Organization for Economic Cooperation and Development） countries＇ response to the fiscal pressures associated with ageing populations. Both pension reform and employment policies are key elements to achieving such increases in participation and reversing the early retirement trends of recent decades. Econometric modeling results from a panel of 12 OECD countries indicate that labour market variables have a greater influence than social security pension value or the standard age of retirement on the labour force participation rates of males aged 55-64 years. Further results from modeling the potential asymmetric response of participation rates to unemployment rates indicate that a decrease in unemployment rates has a greater impact upon increasing the labour force participation rates of older workers compared to the effect of an increase on unemployment rates has on discouraging participation. We found mixed results for the asymmetric response of participation to an increase or decrease in pension value. Findings thus emphasize the importance of labour market oriented policies to reduce unemployment rates in the developed economies in coming years to address ageing population concerns.

Signal transduction mechanism of TRB3 in rats with non-alcoholic fatty liver disease

AIM： To evaluate the possible role of Tribble 3 （TRB3） in a rat model of non-alcoholic fatty liver disease （NAFLD） and its signal transduction mechanism.METHODS： Thirty Sprague-Dawley rats were randomized into three groups： normal control group, non-alcoholic fatty liver group A （fed on a high-fat diet for 8 wk） and group B （fed on a high-fat diet for 16 wk）. To determine the degree of hepatic steatosis in rats of each group, livers were stained with hematoxylin and eosin, and evaluated; real-time fluorescent quantitative reverse transcriptase-polymerase chain reaction was performed to measure the expression levels of TRI33 mRNA, and Western blotting analysis was done to determine the expression levels of protein kinase B （Akt） and phosphorylated protein kinase B （p-Akt-Thr308, p-Akt-Ser473）.RESULTS： Hepatic steatosis was evident in both NAFLD groups： mild to moderate hepatic steatosis occurred in group A, mainly as mild steatosis.Moderate to severe hepatic steatosis occurred in group B, mainly as severe steatosis. The expression level of TRB3 mRNA in group B was significantly higher than in the control group （122.28 ± 95.37 vs 3.06 ± 2.33,P = 0.002） and group A （122.28 ± 95.37 vs 5.77 ± 4.20,P = 0.001）. There was no significant difference in the expression levels of Akt （1.03 ± 0.53 vs 1.12 ± 0.77,P = 0.729） and p-Akt-Thr308 （0.82 ± 0.45 vs 0.92 ± 0.38, P = 0.592） between group A and the control group. The expression level of Akt and p-Akt-Thr308 in group B was significantly lower than in group A （Akt 0.41 ± 0.16 vs 1.12 ± 0.77, P = 0.008; p-Akt-Thr308 0.47 ± 0.19 vs 0.82 ± 0.45, P = 0.036） and the control group （Akt 0.41 ± 0.16 vs 1.03 ± 0.53, P = 0.018;p-Akt-Thr308 0.47 ± 0.19 vs 0.92 ± 0.38, P = 0.010）.The expression level of p-Akt-Ser473 in group A was significantly higher than in group B （1.48 ± 0.50 vs 0.81± 0.39, P = 0.041） as well as the control group （1.48 ± 0.50 vs 0.45 ± 0.26, P = 0.003）.CONCLUSION： TRB3 blocks insulin signaling by inhibiting Akt activation, which contributes to insulin resistance. It may be an important factor in the occurrence and development of NAFLD.

Asymmetric Total Synthesis towards the Simplified Analogs of Antibiotic Elansolid A

Natural product elansolid A belongs to one type of polyketide macrolactone with promising antibiotic activity.Pre-viously,the first total synthesis of elansolid A in 28 longest linear sequence(LLS)and 41 steps in total has been achieved.Herein,the simplified analog of elansolid A,featured with a cyclohexyl-fused 19-memebered macrolactone,was proposed,and its asymmetric total synthesis based on a convergent strategy and key reactions exemplified by desymmetric alcoholysis of anhydride,Pd-catalyzed Stille coupling,Suzuki-Miyaura coupling as well as Mukaiyama macrolactonization was finished.