Iterative solution of some nonlinear differential equations

We propose an iterative method to solve some non-linear ordinary differential equations. Comparing on the Mathieu, van der Pol and Hill equation of fourth order, we see that this method is much more efficient than the well known methods by Lyapunov or Picard.     

Multi-technique Characterization of Self-assembled Carboxylic Acid Terminated Alkanethiol Monolayers on Nanoparticle and Flat Gold Surfaces

Gold nanoparticles (AuNPs) with 14, 25 and 40nm diameters were functionalized with different chain length (C6, C8, C11 and C16) carboxylic acid terminated alkanethiol self-assembled monolayers (COOH-SAMs). X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ion mass spectrometry (ToF-SIMS) were used to examine the changes in surface chemistry as both AuNP diameter and SAM chain length were varied. COOH-SAMs on flat gold surfaces were also examined and compared to the COOH-SAM on AuNP results. For a given surface, as the COOH-SAM chain length increased the XPS C/Au atomic ratio increased due to an increased number of carbon atoms per molecule in the overlayer and an increased attenuation of the Au substrate signal. For the C16 COOH-SAMs, as the size of AuNPs decreased the XPS C/Au atomic ratio and the apparent SAM thickness increased due to the increased curvature of the smaller AuNPs. The C16 COOH-SAMs on the flat Au had the lowest XPS C/Au atomic ratio and apparent SAM thickness of any C16 COOH-SAM covered Au surface. The effective take-off angles of the COOH-SAMs were also calculated by comparing the apparent thickness of COOH-SAMs with literature values. The effective take-off angle for C16 COOH-SAM on 14nm, 25nm and 40nm diameter AuNPs and flat Au were found to be 57°, 53°, 51° and 39°, respectively, for data acquired in a mode that collects a wide range of photoelectron take-off angles. The effective take-off angle for C16 COOH-SAM on 14nm AuNP and flat Au decreased to 52° and 0°, respectively, for data acquired in a mode that collects a narrow range of photoelectron take-off angles. The ToF-SIMS results showed similar changes in surface chemistry with COOH-SAM chain length and AuNP size. For example, the ratio of the sum of the C(1-4)H(x)O(y) positive ion intensities to the sum of the Au-containing positive ions intensities increased with decreasing AuNP size and increasing COOH-SAM chain length. Fourier transform IR spectroscopy in the attenuated total reflectance mode (FTIR-ATR) was used to characterize the crystallinity of the COOH-SAMs. The CH(2) stretching frequencies decreased with increasing COOH-SAM chain length on flat Au. The C16 COOH-SAM on the 14nm AuNPs exhibited a crystalline-like CH(2) stretching frequency. The size, size distribution, shapes and solution stability of AuNPs were investigated with transmission electron microscopy (TEM) and UV/VIS spectroscopy. As the average diameter of the AuNPs decreased the size distribution became narrower and the shape became more spherical.     

On generalized balanced optimization problems

In the generalized balanced optimization problem (GBaOP) the objective value \({\max_{e \in S}{|c(e)-k\max(S)|}}\) is minimized over all feasible subsets S of E = {1, . . . , m}. We show that the algorithm proposed in Punnen and Aneja (Oper Res Lett 32:27–30, 2004) can be modified to ensure that the resulting solution is indeed optimal. This modification is attained at the expense of increased worst-case complexity, but still maintains polynomial solvability of various special cases that are of general interest. In particular, we show that GBaOP can be solved in polynomial time if an associated bottleneck problem can be solved in polynomial time. For the solution of this bottleneck problem, we propose two alternative approaches.     

Densely Functionalized 2-Methylideneazetidines: Evaluation as Antibacterials

Twenty-two novel, variously substituted nitroazetidines were designed as both sulfonamide and urethane vinylogs possibly endowed with antimicrobial activity. The compounds under study were obtained following a general procedure recently developed, starting from 4-nitropentadienoates deriving from a common β-nitrothiophenic precursor. While being devoid of any activity against fungi and Gram-negative bacteria, most of the title compounds performed as potent antibacterial agents on Gram-positive bacteria (E. faecalis and three strains of S. aureus), with the most potent congener being the 1-(4-chlorobenzyl)-3-nitro-4-(p-tolyl)azetidine 22, which displayed potency close to that of norfloxacin, the reference antibiotic (minimum inhibitory concentration values 4 and 1–2 μg/mL, respectively). Since 22 combines a relatively efficient activity against Gram-positive bacteria and a cytotoxicity on eucharyotic cells only at 4-times higher concentrations (inhibiting concentration on 50% of the cultured eukaryotic cells: 36 ± 10 μM, MIC: 8.6 μM), it may be considered as a promising hit compound for the development of a new series of antibacterials selectively active on Gram-positive pathogens. The relatively concise synthetic route described herein, based on widely available starting materials, could feed further structure–activity relationship studies, thus allowing for the fine investigation and optimization of the toxico-pharmacological profile.     

Fast estimation of stable regions in real models

The combined use of periodic orbit computation and Fast Lyapunov Indicator Maps of systems with three degrees of freedom is proposed as a tool for estimating qualitative stability in corresponding real models. Application to spacecraft mission analysis reveals very useful in finding real orbits with very long term stability properties.     

Synthesis and some chemical transformations of 3-ferrocenyl-3-phenylcyclopropene

Crystalline 3-ferrocenyl-3-phenylcyclopropene was obtained by dehydrobromination of 2-bromo-l-ferrocenyl-l-phenylcyclopropane with potassiumtert-butoxide in dimethyl sulfoxide. The compound synthesized undergoes catalytic hydrogenation to l-ferrocenyl-I-phenylcyclopropane, reacts with 1,3-diphenylisobenzofuran to give the expected product of stereospecific [4+2[-cycloaddition and 3-ferrocenylindene, and also undegoes opening of the small ring on treatment with superacids to give 3-ferrocenylindene as the major product. The data of single crystal X-ray diffraction analysis of 1-ferrocenyl-l-phenylcyclopropane and the diene adduct of 3-ferrocenyl-3-phenylcyclopropene with 1,3-diphenylisobenzofuran are given.     

Electro-optic properties of LiKSO4 and LiK1-xRbxSO4 crystals

1-x Rb_xSO₄ for x varying between 0 and 0.50 were investigated by an ac modulation method based upon the Sénarmont arrangement. The electro-optic coefficient r_c, and for the first time the coefficients r₄₁ and r₅₁ were determined with good accuracy in pure LiKSO₄ around room temperature at a wavelength of 633 nm. The frequency dependence of the electro-optic coefficient r_c was measured in the frequency range from 1 kHz up to 1 MHz. The values of the factor of merit n_e ³r_c of the mixed crystals LiK_1-xRb_xSO₄ were obtained for the first time, for the concentrations x=0.05, 0.10, 0.20, and 0.50. The electro-optic properties are shown to be affected by the random presence of the rubidium ions in this disordered system. Received: 16 March 1998/Revised version: 2 June 1998     

Nitroso group transfer in s-nitrosocysteine: evidence of a new decomposition pathway for nitrosothiols

The rate of S-nitrosocysteine decomposition in a pH range between 0.7 < pH < 13 exhibits first- and second-order dependence on total cysteine concentration. The second-order term is only observed for pH values between 6.9 < pH < 12. Both first- and second-order terms show a complex dependence on the acidity of the medium. They increase with increasing pH, reaching a maximum value around pH = 8 and then decrease with further increase in pH. An analysis of the reaction products reveals the absence of nitrite ion and ammonia. No evidence of catalysis by copper ions is observed. These results suggest the existence of a new decomposition pathway for S-nitrosocysteine, which proceeds via an intramolecular nitroso group transfer producing a primary N-nitrosamine that decomposes rapidly to give the corresponding diazonium salt. The nitroso group transfer reaction occurs intermolecularly for the decomposition pathway exhibiting a quadratic dependence on cysteine concentration. Both nitroso group transfer pathways are subject to acid catalysis by cysteine. Kinetic results indicate that the extent of S...NO bond cleavage in the transition state is ahead of protonation of the AH...S sulfur atom. The results obtained show the existence of a new decomposition pathway for the S-nitrosocysteine where NO is not released, and hence, it has a significant biological impact due to the potential use of nitrosothiols as NO donors.     

Passivation of the calcite surface with phenylmalonate and benzylmalonate ions

We explored the affinity of calcite to adsorbed organic molecules as an approach to the conservation of cultural heritage built of marble and limestone. The utilization of phenylmalonic and benzylmalonic acids provided a hydrophobic adsorptive interface, adequate to prevent processes of aqueous weathering. Samples of marble powder (polycrystalline calcite) were impregnated with solutions of phenylmalonic and benzylmalonic acid at three concentrations (5 x 10(-2), 5 x 10(-3), and 5 x 10(-4) M) and different pH values (6.00, 7.00, and 8.00). The surface charge of the calcite suspensions was determined by potentiometric measurements under equilibrium conditions at room temperature in aqueous solution of the dicarboxylic acids, in order to understand the influence of the electrokinetic potential in the surface association. The adsorbed amounts were determined by calculation of the thermodynamic equilibria of solutions. The presence of the organic interface on the mineral surface was corroborated by Raman spectroscopy and small-angle X-ray scattering (SAXS). The results indicate effective adsorption of both dicarboxylic acids as a function of the concentration and pH, and several other conditions that favors coulombic interaction, an absence of electrophoretic mobility or surface electroneutrality related to the solid surface potentials. The coverage of pores by dicarboxylic adsorbate modified the geometrical pore shape and the pore size distribution, filling all the pores of larger than 80 A diameter, giving as a result a mesoporous structure. This change in the surface morphology by organic adsorbates constitutes a modification in the diffusional processes of the environment on the mineral surface.