Minimal logarithmic signatures for finite groups of Lie type

A logarithmic signature (LS) for a finite group G is an ordered tuple α =  [A ₁, A ₂, . . . , A _n ] of subsets A _i of G, such that every element ${g \in G}$ can be expressed uniquely as a product g =  a ₁ a ₂ . . . a _n , where ${a_i \in A_i}$ . The length of an LS α is defined to be ${l(\alpha)= \sum^{n}_{i=1}|A_i|}$ . It can be easily seen that for a group G of order ${\prod^k_{j=1}{p_j}^{m_j}}$ , the length of any LS α for G, satisfies, ${l(\alpha) \geq \sum^k_{j=1}m_jp_j}$ . An LS for which this lower bound is achieved is called a minimal logarithmic signature (MLS) (González Vasco et al., Tatra Mt. Math. Publ. 25:2337, 2002). The MLS conjecture states that every finite simple group has an MLS. This paper addresses the MLS conjecture for classical groups of Lie type and is shown to be true for the families PSL _n (q) and PSp _2n (q). Our methods use Singer subgroups and the Levi decomposition of parabolic subgroups for these groups.     

Modified o-methyl-substituted IBX: room temperature oxidation of alcohols and sulfides in common organic solvents

o-Methyl-substituted Me-IBX is the first modified analog of IBX that oxidizes alcohols in common organic solvents at room temperature, due to a composite of two factors, that is, low solubility and hypervalent twisting-promoted rate enhancement. Furthermore, the reagent is efficient for selective oxidation of sulfides to sulfoxides, a transformation that otherwise occurs only sluggishly with standard IBX. The facile synthetic accessibility and its mild as well as non-hazardous nature render Me-IBX a stable equivalent of Dess-Martin periodinane reagent in organic oxidations.     

Modeling the sorption kinetics of divalent metal ions onto mineral adsorbent using integral method

A mathematical model has been developed that could predict kinetic parameters for the adsorption of divalent cations (lead, copper and zinc) onto low-grade rock phosphate using experimental data. The experiments were conducted with the initial concentrations of metal ions ranging from 10 to 100 mg/L. The mathematical model is based on application of Freundlich isotherm to mass transfer across the film surrounding the adsorbent. A code in C programming is used to numerically integrate the model equation, and to obtain the best simulated values of Freundlich constants K, N, order of reaction n, and film transfer coefficient, alpha. It is observed that the adsorption of metal ions on rock phosphate is more sensitive to N,n, and alpha in comparison to K, and lead is adsorbed more favorably than copper and zinc.     

Exploring the Antibacterial and Antibiofilm Efficacy of Silver Nanoparticles Biosynthesized Using Punica granatum Leaves

The current research work illustrates an economical and rapid approach towards the biogenic synthesis of silver nanoparticles using aqueous Punica granatum leaves extract (PGL-AgNPs). The optimization of major parameters involved in the biosynthesis process was done using Box-Behnken Design (BBD). The effects of different independent variables (parameters), namely concentration of AgNO₃, temperature and ratio of extract to AgNO_3, on response viz. particle size and polydispersity index were analyzed. As a result of experiment designing, 17 reactions were generated, which were further validated experimentally. The statistical and mathematical approaches were employed on these reactions in order to interpret the relationship between the factors and responses. The biosynthesized nanoparticles were initially characterized by UV-vis spectrophotometry followed by physicochemical analysis for determination of particle size, polydispersity index and zeta potential via dynamic light scattering (DLS), SEM and EDX studies. Moreover, the determination of the functional group present in the leaves extract and PGL-AgNPs was done by FTIR. Antibacterial and antibiofilm efficacies of PGL-AgNPs against Gram-positive and Gram-negative bacteria were further determined. The physicochemical studies suggested that PGL-AgNPs were round in shape and of ~37.5 nm in size with uniform distribution. Our studies suggested that PGL-AgNPs exhibit potent antibacterial and antibiofilm properties.     

Angucyclines: Biosynthesis, mode-of-action, new natural products, and synthesis

Covering: 1997 to 2010. The angucycline group is the largest group of type II PKS-engineered natural products, rich in biological activities and chemical scaffolds. This stimulated synthetic creativity and biosynthetic inquisitiveness. The synthetic studies used five different strategies, involving Diels-Alder reactions, nucleophilic additions, electrophilic additions, transition-metal mediated cross-couplings and intramolecular cyclizations to generate the angucycline frames. Biosynthetic studies were particularly intriguing when unusual framework rearrangements by post-PKS tailoring oxidoreductases occurred, or when unusual glycosylation reactions were involved in decorating the benz[a]anthracene-derived cores. This review follows our previous reviews, which were published in 1992 and 1997, and covers new angucycline group antibiotics published between 1997 and 2010. However, in contrast to the previous reviews, the main focus of this article is on new synthetic approaches and biosynthetic investigations, most of which were published between 1997 and 2010, but go beyond, e.g. for some biosyntheses all the way back to the 1980s, to provide the necessary context of information.     

Synthesis and Antiinflammatoryand Anticancer Activity Evaluation of Some Condensed Pyrimidines

Summary.  Upon condensation with 4-isothiocyanato-4-methyl-2-pentanone, 2,3-diaminonaphthalene and N-aminoethyladenosine gave in good yields substituted pyrimidonaphthoimidazole and imidazopyrimidine thione. Refluxing pyrimidobenzthiazole with methanol H₂SO₄ at pH∼1 resulted in S-methyl pyrimidobenzthiazole in moderate yield. Pyrimidobenzimidazole derivatives could be reacted to S-alkylated and N-acylated derivatives by refluxing with ethyl bromoacetate in the presence of anhydrous potassium carbonate in THF and by heating in an acetic acid/acetic anhydride mixture. Heating of pyrimidobenzimidazole with 75% aqueous H₂SO₄ on a water bath ended up in a rearranged product. All compounds gave correct ¹H NMR, IR, and HR mass spectra. Results of antiinflammatory, analgesic, and anticancer activity screening of the new compounds are described. Received October 29, 1999. Accepted (revised) January 13, 2000     

On Wachspress pentagonal patches

Wachspress quadrilateral patches have been recently studied from the point of view of applications to surface modelling in CAGD [1], [3], [4]. Some more applications for defining barycentric coordinates for arbitrary polygons have also been presented in [5] [9]. The purpose of the present paper is to introduce non-negative Wachspress rational basis functions for surface modelling on pentagonal partitions. Interpolation formula for function values and directional derivatives at the vertices of pentagon has been presented. Conditions for C¹– continuity of the composite surface have also been studied in the paper. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inelastic cross sections for pentane isomers by positron impact

ABSTRACT

This work aims at the calculation of various inelastic cross sections for three pentane isomers, namely normal pentane, isopentane and neopentane. The direct ionisation, positronium formation, total ionisation and total inelastic cross section are reported for these targets using modified spherical complex optical potential (mSCOP) and complex scattering potential-ionisation contribution (CSP-ic) method. The cross sections are computed for a wide energy range from their respective thresholds to 5?keV. We have also attempted to probe the isomeric effect in the inelastic scattering of positrons from the pentane isomers. The cross sections for the three isomers were found to overlap for the entire comparative energy range except at the peak region. Hence, in general no appreciable isomeric effect was beheld for the pentane isomers.