Decomposition of Quasi-regular Representations Induced from Discrete Subgroups of Nilpotent Lie Groups

We describe the direct integral decomposition of a quasi regular representation of a connected and simply connected nilpotent Lie group G, which is induced from a discrete subgroup Γ. The solution is given explicitly in terms of orbital parameters. That is, the spectrum, multiplicity and spectral measure that constitute the decomposition are described completely in terms of natural objects associated to the co-adjoint orbits of G. We conclude with a study of the multiplicity function in certain cases.      

A mechanistic MEDT study of the competitive catalysed [4+2] and [2+2] cycloaddition reactions between 1-methyl-1-phenylallene and methyl acrylate: the role of Lewis acid on the mechanism and selectivity

The selectivity and the nature of the mechanism of the competitive Lewis acid catalysed [4+2]/[2+2] cycloaddition reactions of 1-methyl-1-phenylallene (MPA) with methylacrylate (MA) have been theoretically studied within the Molecular Electron Density Theory using DFT methods at the B3LYP/6-31G(d) theoretical level. DFT reactivity indices indicate that MPA is a strong nucleophile and the LA-MA complex is a strong electrophile. The coordination of LA to MA enhances the reaction rate and increases the asynchronicity of the [4+2] CA reaction, changes the nature of the mechanism from one step to stepwise for the [2+2] CA reaction and increases the polar character of these cycloaddition reactions, which become demands a relatively low activation energy. Analysis of different energy profiles indicates that these competitive LA-catalysed CA reactions favour the formation of a mixture of meta regioisomers in both types of cycloaddition, in which the [4+2] cycloadducts were obtained in majority amount, in agreement with the experiment. Analysis based on Electron Localisation Function topological shows that the favoured [4+2] CA reaction takes place through a non-concerted two-stage one-step mechanism.     

Photoactivated enediynes: targeted chimeras which undergo photo-Bergman cyclization

Chimeric enediynes composed of a photoactivatable warhead coupled either to a porphyrin or spiroalcohol have been prepared. The molecules underwent photoactivation to produce diaryl radicals paving the way for applications in targeted photodynamic therapy.     

Addition of Xanthenyl and Thioxanthenyl Halides to Asymmetric Diarylethylenes and Their 2-Halogeno-Derivatives

Xanthenyl and thioxanthenyl halides added readily to asymmetric diarylethylenes and their 2-halogeno-derivatives to give after dehydrohalogenation 1,1-diaryl-2-[xanthen(orthioxanthen)-9-yl]-ethylenes and 1,1-diaryl-2-halogeno-2-[xanthen(or thioxanthen)-9-yl]-ethylenes. The thioxanthenylethylenes were also obtained by another way. Reactions of these ethylenes with bromine, chlorine or sulfuryl chloride were influenced by the halogen and the nature of the p-substituent. Dehydrohalogenation of the 2-halogenoxanthenyl(or thioxanthenyl) ethylenes gave the corresponding 1,1-diaryl-2-[xanthen(or thioxanthen)-9-ylidene]-ethylenes.     

CFD investigation on mixing in a rapidly mixed tubular flame burner

Computational fluid dynamics is used to simulate a mixing process in a rapidly mixed tubular flame burner (RTFB). The effect of several parameters such as the swirl number (S), the velocity ratio (α) and the injector arrangements (N₁ and N₂) is investigated. The mixing process is identified for a variation of the swirl number (from 0.23 to 5.44) via the Lagrangian discrete phase model. The validation of the numerical results is performed by confronting the predicted particle trajectory, the tangential velocity and the mixing layer thickness results to the experimental data. By means of the validated model, a mathematical correlation between the mixing coefficient and the different geometric parameters characterizing the RTFB is established, enabling the prediction of the mixing time for any RTFB design.     

Calculation of Molecular Weight Distributions in Non‐Linear Free‐Radical Polymerization Using the Numerical Fractionation Technique

Mathematical Modeling of non‐linear polymerization systems subject to gel formation is a challenging endeavor. At the gel point, the second and higher molecular weight moments diverge to infinity making it impossible to obtain the molecular weight distribution (MWD). The numerical fractionation (NF) technique utilizes a refinement of the method of moments to model non‐linear polymerization systems that form gel. Since the method of moments yields results in terms of average quantities, some information is lost when reconstructing the MWD using NF. As a consequence, a broad shoulder appears at the high chain length end of the MWD tail. This study demonstrates that the validity of the gamma distribution deteriorates for the broader branched polymer generations and evaluates the performance of various alternative model distributions. Proper selection of the model distribution enhances the NF‐reconstructed MWD.     

Heterocyclic synthesis with 4‐hydrazinopyridothienopyrimidines: Synthesis of pyridothienotriazolopyrimidines and heterocyclylpyridothienopyrimidines with biological interest

Synthesis of the new 4‐hydrazinopyrido[3′,2′:4,5]thieno[3,2‐d]pyrimidines 7a,b was reported. Their reactivity toward a variety of carbon electrophiles and active methylene reagents was studied to give pyridothienotraizolopyrimidines as well as other substituted phthalazinyl‐ and pyrazolyl‐pyridothienopyrimidine derivatives. The antimicrobial activity of some newly synthesized compounds was evaluated. © 2005 Wiley Periodicals, Inc. 16:298–307, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20126     

Synthesis and antimicrobial evaluation of some 1,2,4‐triazole, 1,3,4‐oxa(thia)diazole,and 1,2,4‐triazolo[3,4‐b]‐1,3,4‐thiadiazine derivatives

3‐Methyl‐2‐benzofurancarboxylic acid hydrazide ( 2 ) reacts with carbon disulfide and pota‐ ssium hydroxide to give the corresponding potassium carbodithioate salt 3 . Treatment of the latter salt with hydrochloric acid, hydrazine hydrate, and with phen‐ acyl bromide afforded the corresponding 1,3,4‐oxadia‐ zole‐5‐thione 4 , 4‐amino‐1,2,4‐triazole‐5‐thione 5 , and thiazolidine‐2‐thione 9 derivatives, respectively. The reaction of either 1,3,4‐oxadiazole‐5‐thione 4 or 4‐amino‐1,2,4‐triazole‐5‐thione 5 with phenacyl bromide resulted in the formation of 1,2,4‐triazolo[3, 4‐b]‐1,3,4‐thiadiazine derivative 8 . Treatment of compounds 3 or 4 with hydrazonoyl halides 10a–d furn‐ ished the same 1,3,4‐thiadiazol‐2‐ylidene derivatives 11a–d . The 7‐arylhydrazono‐1,2,4‐triazolo[3,4‐ b ]‐1, 3,4‐thiadiazine derivatives 12a–d were obtained either by treatment of 4‐amino‐1,2,4‐triazole‐5‐thione 5 with hydrazonoyl halides 10a–d or by coupling of the 1,2,4‐triazolo[3,4‐b]‐1,3,4‐thiadiazine derivative 8 with diazonium salts. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:621–627, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20162     

Utility of a 2‐aminothiophene‐3‐carboxamide in the synthesis of thienopyridines and thienopyrimidines

2‐Amino‐4,5,6,7‐tetrahydrobenzo[b]‐ thiophene‐3‐carboxamide ( 1 ) was prepared according to Gewald procedure. Its reactivity toward a variety of chemical reagents was studied to give thienopyridines and ‐pyrimidines. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 14:459–467, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10179     

Time-Dependent Action in φ6 Potential

The false vacuum decay in field theory from a coherently oscillating initial state is studied for φ⁶ potential. An oscillating bubble solution is obtained. The instantaneous bubble nucleation rate is calculated.