Total syntheses of four stereoisomers of 4alpha-hydroxy-1beta,7beta-peroxy- 10betaH-guaia-5-ene

[reaction: see text]. The first total syntheses of four stereoisomers of 4alpha-hydroxy-1beta,7beta-peroxy-10betaH-guaia-5-ene are reported starting from the readily available (+)-dihydrocarvone. These compounds have been synthesized from dienes (-)-isoguaiene and (-)-10-epi-isoguaiene by tandem ene hydroperoxylation-[4 + 2] cycloaddition with O(2) followed by selective reduction. The structure of the natural 4alpha-hydroxy-1beta,7beta-peroxy-10betaH-guaia-5-ene isolated from Liabum floribundum has been confirmed.     

One-pot four-component reaction: aqueous TiCl3/PhN2+-mediated alkyl radical addition to imines generated in situ

Ti(III)-induced free-radical decomposition of a phenyldiazonium salt, followed by phenyl radical iodine-atom abstraction from alkyl iodides, leads to a one-pot selective alkyl radical addition to the C-atom of imines generated in situ under aqueous acidic conditions. [reaction: see text]     

Finite multidimensional behaviors

We study finitely generated and finite systems defined by linear partial difference equations with constant coefficients in a Noetherian ring. The two notions coincide for finite rings, and we show that all finite systems exhibit certain periodicity properties. For the particular case of systems over the ring of integers modulo m?>?1, which is important in coding theory, a method is given for determining the number of trajectories, using Gr?bner basis techniques.     

Heterotrimeric liquid crystalline thiadiazole derivatives

Abstract

Various trimeric co-oligomers combining 2-phenyl-1,3,4-thiadiazole mesogenic moieties with a biphenyl mesogenic moiety were synthesized and their mesomorphic behaviour investigated by polarizing microscopy, calorimetry and X-ray scattering. Such co-oligomeric structures provide an opportunity to combine different mesogenic units. Thus readily accessible homochiral biphenyl mesogenic units were connected with thiadiazole mesogenic units leading to an oligomeric liquid crystal material with ferroelectric properties.     

Mean fluorescence lifetime and its error

Mean excited-state lifetime is one of the fundamental fluorescence characteristics and enters as an important parameter into numerous calculations characterizing molecular interactions, such as e.g. FRET or fluorescence quenching. Our experiments demonstrated that the intensity-weighted mean fluorescence lifetime is very robust characteristic, in contrast to the amplitude-weighted one, which value is dependent on the data quality and particularly on the used fitting model. For the first time, we also report the procedure for the error estimation for both the intensity- and amplitude-weighted mean fluorescence lifetimes. Furthermore, we present a method for estimation of the mean fluorescence lifetime directly from the fluorescence-decay curve recorded by TCSPC (Time-Correlated Single-Photon Counting) method. For its simplicity and low computational demands, it could be a useful tool in the high-throughput applications, such as FACS, FLIM-FRET or HPLC detectors.     

Automatic generation of linear programming problems for computer aided instruction

The paper presents a method for generating random linear programming problems with a previously selected type of solution. The user can choose a problem whose solution is unbounded, bounded for minima, maxima or both, unique or multiple, with given structure, at wish. Initially, the feasible solution of the LPP is generated as the sum of a linear space, a cone, and a polytope, depending on the desired properties of the solution. With the aim of obtaining a simple set of constraints, the generators of these three structures are selected as random vectors with integer simple components, the range of which can be given. Next, an objective function that satisfies the required conditions, i.e. leads to a solution of the desired type, is obtained. The generating algorithms have been implemented in Mathematica and some illustrative examples are given to clarify the generation process. With this tool, a LPP can be generated, according to the instructor requirements, where this is a human or an expert system. They can control student progress and generate a sequence of problems covering all possible cases, in steps of increasing difficulty. Combining this tool with another (also produced by the same authors) that solves the problems and explains the whole process, step by step, a computer aided module for learning LPP, which is completely autonomous, can be easily obtained.