一种有效缓解数据稀疏问题的协同过滤推荐算法

传统协同过滤推荐算法依据共同评分项目计算用户相似度,进而产生推荐项目。然而,随着用户和商品数量的不断增加,用户共同评分的项目会越来越少,甚至没有,因此传统协同过滤推荐算法对用户之间相似度的衡量将会越来越不准确,从而影响推荐系统的性能。针对这一问题,本文对用户相似度的计算方法进行了改进,提出直接相似度和间接相似度的概念,同时引入关键人物权重,进一步提高推荐系统的准确性。

簧乐器发声原理分析

簧是乐器直接或间接赖以振动发声的弹性体,以金属、塑料或植物为材料。凡以簧为振体之乐器统称簧乐器。虽然簧乐器种类繁多,样式各别,但是根据它们发声原理的共同性质,我认为可以将它们分为单系统发声原理和双系统发声原理两大类。例如我国的笙,西洋的手风琴、风琴、口琴等类乐器乃属于单系统发声原理;我国的唢呐、喉管,西洋的单、双簧管。巴松、管风琴等类乐器属双系统发声原理。

Clarkson-Kruskal Direct Similarity Approach for Differential-Difference Equations

In this letter, the Clarkson-Kruskal direct method is extended to similarity reduce some differentialdifference equations. As examples, the differential-difference KZ equation and KP equation are considered.

Similarity Reductions of(2+1)-Dimensional Multi-component Broer-Kaup System

Painleve property of the （2＋1）-dimensional multi-component Broer-Kaup （BK） system is considered by using the standard Weiss Kruskal approaches. Applying the Clarkson and Kruskal （CK） direct method to the （2＋1）- dimensional multi-component BK system, some types of similarity reductions are obtained. By solving the reductions, one can get the solutions of the （2＋1）-dimensional multi-component BK system.

Similarity Reduction Analysis for a Coupled KdV System

Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations.

Similarity Reductions of Nonisospectral KP Equation by a Direct Method

On bases of the direct method developed by Clarkson and Kruskal [J.Math.Phys.27 (1989) 2201],the(2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1+1)-dimensional partial differential equations.We focus on solving the third type of reduction and dividing them into threesubcases,from which we obtain rich solutions including some arbitrary functions.

Similarity Reductions of Nonisospectral BKP Equation

Basing on the direct method developed by Clarkson and Kruskal,the nonisospectral BKP equation can bereduced to three types of(1+1)-dimensional variable coefficients partial differential equations(PDEs).Furthermore,onthe basis of the idea of the symmetry group direct method by Lou et al.,three types of reduction PDEs are all reducedto the related constant coefficients PDEs by some transformations.

Approximate Similarity Reduction for Perturbed Kaup-Kupershmidt Equation via Lie Symmetry Method and Direct Method

The perturbed Kaup-Kupershmidt equation is investigated in terms of the approximate symmetry perturbationmethod and the approximate direct method.The similarity reduction solutions of different orders are obtainedfor both methods, series reduction solutions are consequently derived.Higher order similarity reduction equations arelinear variable coefficients ordinary differential equations.By comparison, it is find that the results generated from theapproximate direct method are more general than the results generated from the approximate symmetry perturbationmethod.

Two-Dimensional Spatial Solitons in Nematic Liquid Crystals

We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Oaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.