线性代数的教学思路(Ⅴ)——线性变换的矩阵同似理论的教学思路

本文给出非数学专业线性代数线性变换的矩阵同似理论的教学思路,并且应用关系映射反演思想方法简要论述线性变换矩阵同似理论。

A novel similarity measurement approach considering intrinsic user groups in collaborative filtering

To improve the similarity measurement between users, a similarity measurement approach incorporating clusters of intrinsic user groups（ SMCUG） is proposed considering the social information of users. The approach constructs the taxonomy trees for each categorical attribute of users. Based on the taxonomy trees, the distance between numerical and categorical attributes is computed in a unified framework via a proper weight. Then, using the proposed distance method, the nave k-means cluster method is modified to compute the intrinsic user groups. Finally, the user group information is incorporated to improve the performance of traditional similarity measurement. A series of experiments are performed on a real world dataset, M ovie Lens. Results demonstrate that the proposed approach considerably outperforms the traditional approaches in the prediction accuracy in collaborative filtering.

Hardware Optimization Technique of Full-Customized HW/SW Co-Design

The hardware optimization technique of mono similarity system generation is presented based on hardware/software(HW/SW) co design.First,the coarse structure of sub graphs' matching based on full customized HW/SW co design is put forward.Then,a universal sub graphs' combination method is discussed.Next,a more advanced vertexes' compression algorithm based on sub graphs' combination method is discussed with great emphasis.Experiments are done successfully with perfect results verifying all the formulas and the methods above.

Improved random noise attenuation using f-x empirical mode decomposition and local similarity

Conventional f-x empirical mode decomposition（EMD） is an effective random noise attenuation method for use with seismic profiles mainly containing horizontal events.However,when a seismic event is not horizontal,the use of f-x EMD is harmful to most useful signals.Based on the framework of f-x EMD,this study proposes an improved denoising approach that retrieves lost useful signals by detecting effective signal points in a noise section using local similarity and then designing a weighting operator for retrieving signals.Compared with conventional f-x EMD,f-x predictive filtering,and f-x empirical mode decomposition predictive filtering,the new approach can preserve more useful signals and obtain a relatively cleaner denoised image.Synthetic and field data examples are shown as test performances of the proposed approach,thereby verifying the effectiveness of this method.

^106,110Pd （p,nγ）^106,110 Ag reactions at Ep = 6.0 - 7.7 MeV

This paper reports that the experimental excitation functions of reaction （p,n） are measured for ^106pd and ^110pd at proton energy Ep = 6.1 - 7.5 MeV and Ep = 6.0 - 7.7 MeV respectively. The off-resonance excitation functions were compared with calculation values of the statistical model. A new formula used to estimate the peak cross section of isobaric analogue resonance was tested and it was found that calculation values agree reasonably well with the present data within experimental error, which confirms that the excitation strength of isobaric analogue state in （p,n） reaction not only depends on its spin, but also proportionally increases with the projectile proton spatial transmission Tp and the spectroscopic factor S for reaction （d,p） on the same target.

The Multivariate Saddlepoint Approximation to the Distribution of Estimators： A General Approach

We develop the theory of multivariate saddlepoint approximations. Our treatment differs from the one in Barndorff-Nielsen and Cox （1979, equation （4.7）） in two aspects： 1） our results are satisfied for random vectors that are not necessarily sums of independent and identically distributed random vectors, and 2） we consider that the sample is taken from any distribution, not necessarily a member of the exponential family of densities. We also show the relationship with the corresponding multivariate Edgeworth approximations whose general treatment was developed by Durbin in 1980, emphasizing that the basic assumptions that support the validity of both approaches are essentially similar.

Approximate Homotopy Symmetry Reduction Method:Infinite Series Reductions to Kawahara Equation

The Kawahara equation is studied through the approximate homotopy symmetry method. Under this method we get the similarity reduction solutions of the Kawahara equation, leading to the corresponding homotopy series solutions. Furthermore, the similarity solutions of the corresponding reduced linear ordinary differential equations are also considered.

A Numerical Study of One-Dimensional Hyperbolic Telegraph Equation

In this paper, an approximate solution for the one-dimensional hyperbolic telegraph equation by using the q-homotopy analysis method （q-HAM） is proposed.The results shows that the convergence of the q- homotopy analysis method is more accurate than the convergence of the homotopy analysis method （HAM）.

SEED REGION SELECTION AND HOMOGENEITY CRITERION FOR DOORPLATE IMAGE SEGMENTATION IN MOBILE ROBOT NAVIGATION

Focused on the seed region selection and homogeneity criterion in Seeded Region Growing (SRG), an unsupervised seed region selection and a polynomial fitting homogeneity criterion for SRG are proposed in this paper. First of all, making use of Peer Group Filtering (PGF) techniques, an unsupervised seed region selection algorithm is presented to construct a seed region. Then based on the constructed seed region a polynomial fitting homogeneity criterion is applied to solve the concrete problem of doorplate segmentation appearing in the robot navigation along a corridor. At last, experiments are performed and the results demonstrate the effectiveness of the proposed algorithm.

A Note on Fermat Equation＇s Fascination

As former Fermatist, the author tried many times to prove Fermat＇s Last Theorem in an elementary way. Just few insights of the proposed schemes partially passed the peer-reviewing and they motivated the subsequent fruitful collaboration with Prof. Mario De Paz. Among the author＇s failures, there is an unpublished proof emblematic of the FLT＇s charming power for the suggestive circumstances it was formulated. As sometimes happens with similar erroneous attempts, containing out-of-context hints, it provides a germinal approach to power sums yet to be refined.

Synergistic effects of a curcumin analogue and docetaxel on growth inhibition of human prostate cancer cells

Cancer of the prostate gland is a leading cause of death. In the present study, we studied the effects and mechanisms of curcumin analogue E10, docetaxel or their combination on prostate cancer （PC）-3 cells. Treatment of PC-3 cells with El0 or docetaxel resulted in growth inhibition in a concentration-reliant fashion. Combinations of E10 and docetaxel inhibited the growth of PC-3 cells in a synergistic manner. Effects of a combination of E10 and docetaxel were associated with synergistic inhibition of the transcriptional activity of nuclear factor-kappa B （NF-KB）, and robust reductions in the levels of B-cell lymphoma-2 （Bcl-2） were found in PC-3 cells treated with a combination of E10 and docetaxel. Our data indicated that the effects of El0 in combination with docetaxel on PC-3 cells were associated with inhibition of NF-r,B and Bcl-2. Further studies using suitable animal models are necessary to determine the in vivo effect of this combination.

On well posedness of best simultaneous approximation problems in Banach spaces

The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points inE(G) such that the best simultaneous approximation problems are not well posed is a u- porous set inE(G) whenX is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.

Protein sequence analysis based on hydropathy profile of amino acids

Biology sequence comparison is a fundamental task in computational biology.According to the hydropathy profile of amino acids,a protein sequence is taken as a string with three letters.Three curves of the new protein sequence were defined to describe the protein sequence.A new method to analyze the similarity/dissimilarity of protein sequence was proposed based on the conditional probability of the protein sequence.Finally,the protein sequences of ND6(NADH dehydrogenase subunit 6)protein of eight species were taken as an example to illustrate the new approach.The results demonstrated that the method is convenient and efficient.

Gap Property of Bi-Lipschitz Constants of Bi-Lipschitz Automorphisms on Self-similar Sets

For a given self-similar set ERd satisfying the strong separation condition,let Aut(E) be the set of all bi-Lipschitz automorphisms on E.The authors prove that {fAut(E):blip(f)=1} is a finite group,and the gap property of bi-Lipschitz constants holds,i.e.,inf{blip(f)=1:f∈Aut(E)}>1,where lip(g)=sup x,y∈E x≠y(|g(x)-g(y)|)/|x-y| and blip(g)=max(lip(g),lip(g-1)).

ON THE HARISH－CHANDRA HOMOMORPHISM FOR THE CHEVALLEY GROUPS OVER P－ADIC FIELD

The Harish-Chandra homomorphism for the higher congruence spherical functions algebra of Chevalley groups over p-adic fiealds is given in the case of the Levi-component of a (rational)parabolic subgroup. It is a generalization for the Harish-Chandra homomorphism for the higher congurence spherical functions algebra of the groups CLn over p-adic field in the same case.