Indexing text using the Ziv–Lempel trie

Let a text of u characters over an alphabet of size σ be compressible to n phrases by the LZ78 algorithm. We show how to build a data structure based on the Ziv–Lempel trie, called the LZ-index, that takes 4nlog₂n(1+o(1)) bits of space (that is, 4 times the entropy of the text for ergodic sources) and reports the R occurrences of a pattern of length m in worst case time O(m³logσ+(m+R)logn). We present a practical implementation of the LZ-index, which is faster than current alternatives when we take into consideration the time to report the positions or text contexts of the occurrences found.     

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.     

Alkylation of nitroaromatics with tetraalkylborate ion via electrochemical oxidation

Aromatic nucleophilic substitution reaction (S(N)Ar) is one of the most thoroughly studied reactions. Alkylation of nitroaromatics with Grignard reagents via chemical oxidation of the sigma(H)-complexes is the most general method to introduce an alkyl group into a nitroaromatic compound. This approach has considerable drawbacks, especially when more than one nitro group are present in the aromatic ring. In this article, we present an electrochemical approach, which offers a new very selective methodology for obtaining alkyl polynitroaromatic compounds. Different strategies based on the use of tetralkylborate anion as nucleophiles are used so as to increase efficiency and to reduce the drawbacks associated with this reaction. A wide list of dinitro- and trinitro-aromatic compounds are studied, the range of yields obtained being from fair (40%) to excellent (85%). The key to improvement in the process is the use of electrochemical techniques for the oxidation of the mixture sigma(H)-complexes/tetrabutylborate ion. The electroactive character of the nucleophile, which can be oxidized to an alkyl radical, means that the S(N)Ar of the hydrogen polar mechanism is not the only mechanism operating during the electroxidation process, since the hydrogen radical S(N)Ar mechanism is running at the same time. Electrochemical mechanistic studies allow the participation of each mechanism in the global product yield obtained to be quantified.     

The Reaction of Triplet State Benzophenone with Acetylacetone

Irradiation of benzophenone in acetic acid containing acetylacetone resulted in regiospecific addition to form cis-2,2-dihpenyl-3-hydroxy-3-methyl-4-acetyloxetane and the rearrangement products therefrom. In the co-presence of copper ions, the regiospecificity is scrambled to give these products and a small amount of 1,1-diphenyl-1-buten-3-one, the secondary decomposition product of the other oxetane arising from the alternative orientation of the addition.     

Photooxygenation of 9-methyl-1,2,3,4-tetrahydrocarbazole: A kinetic study

The reaction of the singlet oxygen with 9-methyl-1,2,3,4-tetrahydrocarbazole has been undertaken to give a benzazonine derivative in good yield. Rose-bengal supported on an anionic resin was used as heterogeneous photosensitizing agent. Kinetic evaluation has been made for the additon of singlet oxygen to the indole ring at room temperature.

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9--1,2,3,4- . , , . .

     

A diastereoselective synthesis 1-trimethylsilyl-(E)-1,3-alkenynes and a simple synthesis of alkyl trimethylsilylethynyl ketones via organoboranes

A convenient, novel diastereoselective synthesis of 1-trimethylsilyl-(E)-1,3-alkenynes and a convenient synthesis of alkyl trimethylsilylethynyl ketones based on Z-1-bromo-1-alkenylboronate esters are developed. α-Bromo-(Z)-1-alkenylboronate esters readily available using literature procedures smoothly undergo a reaction with trimethylsilylethynyllithium (derived from the deprotonation of trimethylsilylethyne with n-butyllithium) in tetrahydrofuran to provide the corresponding ‘ate’ complexes. These ‘ate’ complexes undergo intramolecular nucleophilic substitution reactions to afford the corresponding (E)-1-alkenylboronate esters containing trimethylsilylethynyl moiety which upon protonolysis with acetic acid provide the corresponding 1-trimethylsilyl-(E)-1,3-alkenynes in good yields (70-82%) and in high stereochemical purities (>98%). These intermediates upon oxidation with hydrogen peroxide and sodium acetate afford the corresponding alkyl trimethylsilylethynyl ketones in good yields (66-78%).     

Catalytic Enantioselective Cyclopropylalkynylation of Aldimines Generated In Situ from α-Amido Sulfones

A convenient procedure of synthesis of N-carbamoyl-protected propargylic amines substituted with a cyclopropyl group from α-amido sulfones and cyclopropylacetylene is described. The reaction is catalyzed by a chiral BINOL-type zinc complex and provides the corresponding products in good yields and enantioselectivities.