One and multidimensional sampling theorems associated with Dirichlet problems

We use the eigenfunction expansion of Green's function of Dirichlet problems to obtain sampling theorems. The analytic properties of the sampled integral transforms as well as the uniform convergence of the sampling series are proved without any restrictions on the integral transforms. We obtain a one- and multi-dimensional versions of sampling theorems. In both cases the sampling series are written in terms of Lagrange-type interpolation expansions. Some examples and the truncation error as well as the stability of the obtained sampling expansions are discussed at the end of the paper. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Synthesis and cytotoxic activity of some novel benzocoumarin derivatives under solvent free conditions

In the present study, a rapid, less expensive, clean and environmental friendly route to synthesis new pyrazoles, pyrazolopyridazines and condensed pyrimidines was developed via grinding of 2-(3-(dimethylamino)acryloyl)-3H-benzo[f]chromen-3-one (1) with different reagents. All the new compounds were characterized and established using elemental analysis and spectral data. Eight compounds were selected for in vitro antiproliferative against different human cancer cell lines entitled melanoma, cancers of the lung, leukemia, breast, brain, colon, prostate, ovary and kidney by the USA NCI.     

Recent advances in nanocollision electrochemistry

Ensemble averaging measurements obscure the link between the electrochemical performance and the specific properties of an individual because of the interplay of inhomogeneity and heterogeneity. Nanocollision electrochemistry has attracted increasing interest because of its extremely high sensitivity, revealing the intrinsic properties of individual entities that are masked in the traditional ensemble measurements. In this perspective review, we summarized the recent developments in nanocollision-based single entity electrochemistry and photoelectrochemistry, the combined nanocollision electrochemistry with the other complementary techniques, as well as accurate data process. In closing, future challenges, opportunities, and destinations related to nanocollison electrochemistry were discussed.     

Identification and quantification of diethylene glycol contamination in glycerine raw material

Fourier-transform infrared spectroscopy (FTIR) was successfully used for quantitative determination of diethylene glycol in glycerin raw material. In addition to the pure samples of both diethylene glycol and glycerin, nine binary mixtures of the two components with mixing ratios ranging from (70 to 98)%wt were created and studied as a training set. Glycerine showed, thereby, characteristic infrared bands at 1110, 992, 974, and 922?cm^?1 while those of diethylene glycol appear at 1085, 887, and 881?cm^?1. The quantitative determination of diethylene glycol in binary mixtures with glycerin was achieved upon using the absorbance difference between the 992?cm^?1 and the 881?cm^?1 as well as between 1110 and 1085?cm^?1 bands. With an average %error of 0.60 and 1.74, respectively and a limit of detection down to 0.85%, the created calibration curves from the training set were applied successfully to determine the composition of another eight binary mixtures of the two materials representing a validation set. The method was also applied to aqueous solutions of diethylene glycol and glycerin that contains (25 and 50)%wt water. Once more, training and validation sets of mixtures with different diethylene glycol and glycerin ratios at the two water percentages were prepared and measured. Again, successful determination of diethylene glycol in these aqueous solutions was achieved with an average %error of 0.92 and 0.47, respectively.     

Evaluation of spectral dispersion of optical constants of a-Se films from their normal-incidence transmittance spectra using Swanepoel algebraic envelope approach

Spectral dispersions of index of refraction \({n(\lambda )}\) and extinction coefficient \({\kappa (\lambda )}\) of undoped amorphous selenium (a-Se) films of three thicknesses (d?≈?0.5, 0.75, and 1.0 µm) were evaluated by analyzing experimental room-temperature normal-incidence transmittance-wavelength (\({{T_{{\text{exp}}}}(\lambda )} - \lambda\)) data (λ =?400–1100 µm) of their air-supported {a-Se film/thick glass slide}-stacks using Swanepoel’s transmission envelope theory of uniform films. Above a wavelength \({{\lambda _c}\,\, \approx \,\,640\;{\text{nm}}}\), as-measured \({{T_{{\text{exp}}}}(\lambda )}\,\, - \,\lambda\) spectra display well-resolved maxima and minima, with minor shrinkage in transparent and weak absorption regions (750–1100 nm). Below \({\lambda _{\text{c}}}\), a smeared sharp decline of \({{T_{{\text{exp}}}}(\lambda )}\) with decreasing λ, signifying strong absorption in a-Se films and existence of band-tail localized states. For λ > λ _c, the \({n\,(\lambda )}\, - \,\lambda\) data retrieved from algebraic envelope procedures followed a Sellmeier-like dispersion relation, with the best-fit values of high-frequency dielectric constant \({{\varepsilon _\infty }\, \approx \,\,{\text{4.9}}}\), static index of refraction \({{n_{\text{0}}} = n\left( {E\, \to \,{\text{0}}} \right)\,\, \approx \,\,{\text{2.43}}}\), and resonance wavelength \({{\lambda _0}\, \approx \,490\,\,{\text{nm}}}\), which may be assigned to onset of photogeneration in a-Se. Urbach-like dependency of absorption coefficient \({\alpha (h{{\nu }})}\) of a-Se films on photon energy \({h{{\nu }}}\) was realized with an Urbach-tail breadth of 85 meV. All achieved optical parameters were found to be slightly dependent on film thickness. Findings of present algebraic analysis are consistent with reported literature results obtained on the basis of other optical analytical approaches.     

Grand canonical Monte Carlo simulation of isotherm for hydrogen adsorption on nanoporous siliceous zeolites at room temperature

Zeolites belong to a most prominent class of nanoporous materials which have been considered as potential sorbents for hydrogen storage. The adsorption of hydrogen molecules on purely siliceous zeolites such as ACO, MEP, ASV, ANA, RWY, and RHO, which encompass a range of different pore structures and their chemical compositions has been simulated employing Grand Canonical Monte Carlo (GCMC) procedure for a temperature range of 250-325 K, and a pressure range of 0-10 kbar. The effects of pore structure of zeolites, temperature and pressure on the hydrogen adsorption has been examined. The results clearly show that the number of adsorbed hydrogen molecules at high pressure, only depends on pore diameter, and the temperature effect on the adsorption decreases with decrease in the number of adsorbed of hydrogen molecules.     

FeCl3-SiO2 as a reusable heterogeneous catalyst for the synthesis of 5-substituted 1H-tetrazoles via [2+3] cycloaddition of nitriles and sodium azide

An efficient method for the preparation of 5-substituted 1H-tetrazole derivatives is reported using FeCl₃-SiO₂ as an effective heterogeneous catalyst. This method has the advantages of high yields, simple methodology, and easy work-up. The catalyst can be recovered by simple filtration and reused delivering good yields.     

Prednisone/Cyclodextrin Inclusion Complexation: Phase Solubility,Thermodynamic, Physicochemical and Computational Analysis

Guest–host interaction of prednisone (PN) with cyclodextrins (CDs) have been investigated using phase solubility diagrams (PSD), differential scanning calorimetry (DSC), X-ray powder diffractometry (XRPD), scanning electron microscopy (SEM) and molecular mechanical modeling (MM). Estimates of the complex formation constant (K ₁₁) show that the tendency of PN to complex with CDs follows the order: β-CD>γ-CD>HP-β-CD>α-CD. At the same pH of 7.0, β-CD forms soluble 1:1 and insoluble 1:2 PN/CD complexes (B_S-type PSDs). The thermodynamic functions for 1:1 PN/β-CD estimated at pH = 7.0 (ΔG ₁₁^o=−20.8 kJ⋅mol⁻¹) show that complexation is driven by enthalpy (−30.7 kJ⋅mol⁻¹) but retarded by entropy (ΔS ₁₁^o=−33.1 J⋅mol⁻¹⋅K⁻¹) changes. The MM modeling study indicates the formation of different isomeric 1:1 complexes with CDs. PSD, DSC, XRPD, SEM and MM studies established the formation of inclusion complexes in solution and the solid state.     

Quantum mechanical studies of the protonation and NBr bond dissociation of the biologically important N-bromosuccinimide

N-Bromosuccinimide (NBS) is a brominating and oxidizing agent that is used as a source of bromine. The proton affinities, the tautomeric forms and NBr bond dissociation of NBS have been computed using the B3LYP functional as implemented in the density functional approach. The electronic structures of all possible tautomeric forms of NBS have been thoroughly investigated. The keto form of NBS has been shown to be more stable than any other tautomeric forms. The geometries and relative energies for various stationary structures were determined. The results indicate clearly that O-site protonation is strongly favored over N-site protonation for the studied compound in case of mono- and di-protonation. The bond dissociation energies (BDEs), involving the formation of the bromine radical, cation, and anion, of the NBr bond have been investigated. The NBr BDE of the Br radical formation is lower than that of the Br anion or cation. These conclusions are in good agreement with the experimental results.     

Enhancement of immune response and protection in BALB/c mice immunized with liposomal recombinant major surface glycoprotein of Leishmania (rgp63): The role of bilayer composition

Development of new generation vaccines requires adjuvants to elicit the type and intensity of immune response needed for protection. Liposomes have been shown to be an effective adjuvant formulation. In this study, the role of liposome bilayer composition with different phase transition temperature (T_c) to induce a T helper 1 (Th1) type of immune response and protection against leishmaniasis in BALB/c mice was assessed. Liposome formulations with different bilayer compositions consisting of egg phosphatidylcholine (EPC, T_c < 0 °C), dipalmitoylphosphatidylcholine (DPPC, T_c 41 °C), or distearoylphosphatidylcholine (DSPC, T_c 54 °C) were prepared. All liposomes were contained rgp63 as a recombinant antigen and used to immunize mice subcutaneously 3 times in 3-week intervals. Evaluation of lesion development and splenic parasite burden after challenge with L. major, evaluation of Th1 cytokine (IFN-γ) and Th2 cytokine (IL-4), and titration of IgG isotypes were carried out to assess the type of generated immune response and extent of protection. The results indicated the generated immune response in mice was influenced by the bilayer composition of liposomes, so that mice immunized with liposomes consisting of EPC induced a Th2 type of immune response while liposome consisting of DPPC or DSPC induced Th1 type of immune response. It seems that liposomes prepared with higher Tm phospholipids are suitable formulation to induce Th1 type of immune response and protection, and so might be used for further investigations to develop an effective vaccine against leishmaniasis.