Continuous and discrete Bessel wavelet transforms

Using the theory of Hankel convolution, continuous and discrete Bessel wavelet transforms are defined. Certain boundedness results and inversion formula for the continuous Bessel wavelet transform are obtained. Important properties of the discrete Bessel wavelet transform are given.     

Biosynthesis of silver nanoparticles using <Emphasis Type="Italic">Carissa carandas</Emphasis> berries and its potential antibacterial activities

Metal nanoparticles synthesis using the biological material offers a simple, biocompatible, cost-effective and nontoxic in character. A number of plant materials have been utilized as resource material for the most favorable biosynthesis of active nanomaterials. This study involves the synthesis of active silver nanoparticles (Ag NPs) using the Carissa carandas (Karonda) berry water extract at room temperature. The nanoparticles characterized at several parameters including shape, size, mass and charge with help of electron microscopy (TEM), Fourier transforms IR (FTIR), UV-VIS spectroscopy and Raman spectroscopy which proved the efficient silver nanoparticles to be useful in several practical applications. The UV-visible spectra showed the surface plasmon resonance peak at ~440?nm, which is weel recognized attribute peak in case of silver nanoparticles. Avarage size of the biogenic silver nanoparticles ranged from ~10–60?nm, predominantly spherical in shape. The suggested possible mechanisms for the synthesis of silver nanoparticles relies on reduction of AgNO₃ due to occurrence of carinol (and related resonant compounds) in the berry extract with inductive effect of the proton of methoxy and allyl groups, present at ortho and para positions of the compounds. The biologically synthesized Ag NPs also showed efficient antibacterial activity against different pathogenic and non-pathogenic bacteria at par with the generic antibiotics.

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Synthesis of combinatorial libraries based on terpenoid scaffolds

Triterpenoid-based scaffolds betulinic acid (1a) and ursolic acid (1b), have been used for the generation of combinatorial libraries in parallel format using solid phase organic synthesis method. These templates have the potential for the synthesis and amplification of triterpenoid-based compounds with one and two-point diversity. This has been demonstrated by the synthesis of two small libraries comprising 18 derivatives each of betulinic acid and ursolic acid with structural diversity at C-3 and C-28 positions. The primary screening of antimalarial activity of these libraries against P. falciparum in vitro led to the identification of four compounds with 5 fold increase in the activity compared to betulinic and ursolic acids.     

Heteroleptic Complexes of Zirconium Acetylacetonates: Better Precursors for the Preparation of Zirconia. Structural Characterization of [(acac)2Zr{ONC(Me)py‐2}2]

The reactions of the heteroleptic zirconium diisopropoxide bis(acetylacetonate) in benzene solution with two equivalents of oximes, alkoxyalkanols, triphenylsilanol and trimethylsilyl acetate yield products with the formula [{MeC(O)CHC(O)Me}₂ZrL₂] with L = —ONC(Me)C₅H₄N‐2, —ONC(Me)C₄H₃O‐2, —OCH₂CH₂OR (R = Me, Et, Buⁿ; py = pyridine, fu = furan), —OSiPh₃ and —OSiMe₃. Most of these derivatives are solids, but the [(acac)₂Zr(OSiMe₃)₂] is a viscous oil. They could be purified either by recrystallization or by vacuum distillation; all of these are monomeric in boiling benzene. Their elemental analyses, molecular weight measurements and IR as well as NMR spectra were measured. The oximato complex [(acac)₂Zr{ONC(Me)py‐2}₂] has been shown by single crystal X‐ray crystallography to be monoclinic and mononuclear in the solid state, where zirconium has the coordination number 8; all the ligands are situated in cis‐ position and the oximato ligand binds via N and O in a dihapto (η²‐N, O) manner.     

A concise synthesis of novel naphtho[a]carbazoles and benzo[c]carbazoles

Starting from simple indole precursors the synthesis of naphtho[a]carbazoles and benzo[c]carbazoles is described. Key steps include the use of the Suzuki-Miyaura reaction to afford 2- or 3-aryl substituted indoles, as well as a potassium t-butoxide and light assisted aromatic ring-forming reaction.     

Separation and determination of uranium(VI) with calixarene hydroxamic acids

A new calixarene hydroxamic acid, 5,11,17,23-tetra-(N-p-chlorophenyl hydroxamate c-phenyl-25,26,27,28-tetrahydroxycalix[4]arene (CPCHA) was synthesized and used for the extraction and spectrophotometric determination of uranium(VI). The molar absorptivity of the uranium(VI)-CPCHA-thiocyanate complex was 9.9·10³ 1·mol^–1·cm^–1 at 436 nm. The system obeyed Beer's law in the range of 1.78–23.1 ppm of uranium. The uranium(VI)-hydroxamate-ethyl acetate complex was directly aspirated for graphite furnace atomic absorption spectrometry measurements (GFAAS) which increased the sensitivity by about a factor of fifty. Uranium was determined in various standard and environmental samples.     

The Weierstrass-Jacobi transform

The Weierstrass-Jacobi transform of a function ?, defined by $$f \left( n \right) = \sum\limits_{m = 0}^\infty { h \left( {n, m; 1} \right) \phi \left( m \right) h_{\alpha ,\beta } \left( m \right)} $$ is considered. It is inverted by means of a suitable difference operator e^?∈_n. In terms of Jacobi difference operator ∈_n a theory analogous to that of hormonic functions is presented. A characterization of those functions which are Weierstrass-Jacobi transform of positive functions is given.     

Asymptotic expansions of the Mehler-Fock transform

Asymptotic expansions in the two limitsx → + ∞ andx → 0+ are obtained for the Mehler-Fock transform

The synthesis of angularly fused polyaromatic compounds by using a light-assisted, base-mediated cyclization reaction

The synthesis of substituted polyaromatic compounds that contain at least four benzene rings fused together in an angular fashion is described. Suzuki coupling of 1-bromo-3,4-dihydronaphthalene-2-carbaldehyde with a number of aromatic boronic acids affords products such as 1-(1,4-dimethoxy-3-methyl-2-naphthyl)-3,4-dihydronaphthalene-2-carbaldehyde. Exposure of these dihydronaphthalenes to potassium tert-butoxide and DMF at 80 degrees C yields polyaromatic compounds such as 9,14-dimethoxynaphtho[1,2-a]anthracene.