Practical algorithms for transposition-invariant string-matching

We consider the problems of (1) longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (that is, transposed) to match the second, and (2) transposition-invariant text searching using indel distance. These problems have applications in music comparison and retrieval. We introduce two novel techniques to solve these problems efficiently. The first is based on the branch and bound method, the second on bit-parallelism. Our branch and bound algorithm computes the longest common transposition-invariant subsequence (LCTS) in time O((m²+loglogσ)logσ) in the best case and O((m²+logσ)σ) in the worst case, where m and σ, respectively, are the length of the strings and the size of the alphabet. On the other hand, we show that the same problem can be solved by using bit-parallelism and thus obtain a speedup of O(w/logm) over the classical algorithms, where the computer word has w bits. The advantage of this latter algorithm over the present bit-parallel ones is that it allows the use of more complex distances, including general integer weights. Since our branch and bound method is very flexible, it can be further improved by combining it with other efficient algorithms such as our novel bit-parallel algorithm. We experiment on several combination possibilities and discuss which are the best settings for each of those combinations. Our algorithms are easily extended to other musically relevant cases, such as δ-matching and polyphony (where there are several parallel texts to be considered). We also show how our bit-parallel algorithm is adapted to text searching and illustrate its effectiveness in complex cases where the only known competing method is the use of brute force.     

Second Order Nonlinear Evolution Inclusions Ⅰ： Existence and Relaxation Results

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.     

Local automorphisms of operator algebras on Banach spaces

In this paper we extend a result of Semrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Semrl's paper.

     

Mild and efficient synthesis of propargylamines by copper-catalyzed Mannich reaction

Terminal alkynes undergo mild and efficient aminomethylation with aqueous formaldehyde and secondary amines under CuI catalysis. In most cases high to nearly quantitative yields of tertiary propargylamines are obtained in DMSO solution at room temperature. Aromatic, aliphatic and silylated acetylenes as well as alkynols can be used. Primary amines are less reactive and satisfactory yields of secondary propargylamines are obtained only with phenylacetylene.     

对于工学硕士的《数理统计》教学的研究

工学硕士的《数理统计》教学 ,要根据工学硕士的培养目标和数理统计课程的特点编写教材、确定讲授内容和授课方式 .力求使学员掌握处理随机数据的思考方法 ,培养解决问题、分析问题和善于应用知识的能力 .改革《数理统计》教学 ,实现和普及多媒体教学是时代发展的趋势 .     

New Exact Solutions to the Combined KdV and mKdV Equation

The modified mapping method is developed to obtain new exact solutions to the combined KdV and mKdV equation. The method is applicable to a large variety of nonlinear evolution equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration.