Synthesis and novel reactivity of halomethyldimethylsulfonium salts

Iodomethyl-, chloromethyl-, and fluoromethyldimethylsulfonium salts, 4b-d, have been synthesized and are observed to be highly reactive molecules that exhibit extraordinary diversity with respect to the nature of their reactivity, undergoing facile direct substitution (S(N)2) reactions, but also being highly susceptible to electron-transfer reactions. Cyclic voltametry experiments indicated that the iodomethyldimethylsulfonium compound, 4b, is a potent electron acceptor, even surpassing the reactivity of perfluoro-n-alkyl iodides in that capacity. The iodo- and chloromethyldimethylsulfonium salts, 4b,c, as well as the analogous iodomethyltrimethylammonium salt, 3a, are shown to be reactive SET acceptors.     

Generalized solitary waves in a finite‐difference Korteweg‐de Vries equation

Generalized solitary waves with exponentially small nondecaying far field oscillations have been studied in a range of singularly perturbed differential equations, including higher order Korteweg‐de Vries (KdV) equations. Many of these studies used exponential asymptotics to compute the behavior of the oscillations, revealing that they appear in the solution as special curves known as Stokes lines are crossed. Recent studies have identified similar behavior in solutions to difference equations. Motivated by these studies, the seventh‐order KdV and a hierarchy of higher order KdV equations are investigated, identifying conditions which produce generalized solitary wave solutions. These results form a foundation for the study of infinite‐order differential equations, which are used as a model for studying lattice equations. Finally, a lattice KdV equation is generated using finite‐difference discretization, in which a lattice generalized solitary wave solution is found.     

Chemical, spectroscopic characterization, DFT studies and initial pharmacological assays of a silver(I) complex with N-acetyl-l-cysteine

A new silver(I) complex with N-acetyl-l-cysteine (NAC) of composition AgC₅H₈NO₃S·H₂O was synthesized and characterized by a set of chemical and spectroscopic measurements. Solid-state ¹³C nuclear magnetic resonance (SSNMR) and infrared (IR) analyses indicate the coordination of the ligand to Ag(I) through the sulfur atom. The Ag-NAC complex is slightly soluble in dimethyl sulfoxide. It is insoluble in water, methanol, ethanol, acetone and hexane. Antibacterial activity of the silver complex with N-acetyl-l-cysteine (Ag-NAC) was evaluated by antibiogram assays using the disc diffusion method. The compound showed an effective antibacterial activity against Staphylococcus aureus (Gram-positive), Escherichia coli and Pseudomonas aeruginosa (Gram-negative) bacterial cells. Biological analysis for evaluation of a potential cytotoxic effect of Ag-NAC was performed using HeLa cells derived from human cervical adenocarcinoma. The complex presented a significant cytotoxic activity, inducing 80% of cell death at a concentration of 200 μmol L⁻¹.     

Palladium(II) complex with S-allyl-L-cysteine: new solid-state NMR spectroscopic measurements, molecular modeling and antibacterial assays

Nuclear magnetic resonance studies, molecular modeling and antibacterial assays of the palladium(II) complex with S-allyl-L-cysteine (deoxyalliin) are presented. Studies based on solid and solution 13C and 15N nuclear magnetic resonance (NMR) spectroscopy confirmed that the palladium(II) complex preserved the same structural arrangement in both states, with no modifications on coordination sphere when dissolved in water. Density functional theory (DFT) studies stated that the trans isomer is the most stable one. Antibacterial activities of S-allyl-L-cysteine and its palladium(II) complex were evaluated by antibiogram assays using the disc diffusion method. The palladium(II) complex showed an effective antibacterial activity against Staphylococcus aureus (Gram-positive), Escherichia coli and Pseudomonas aeruginosa (Gram-negative) bacterial cells.     

Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation

Traveling waves in woodpile chains are typically nanoptera, which are composed of a central solitary wave and exponentially small oscillations. These oscillations have been studied using exponential asymptotic methods, which typically require an explicit form for the leading-order behavior. For many nonlinear systems, such as granular woodpile chains, it is not possible to calculate the leading-order solution explicitly. We show that accurate asymptotic approximations can be obtained using numerical approximation in place of the exact leading-order behavior. We calculate the oscillation behavior for Toda woodpile chains, and compare the results to exponential asymptotics based on previous methods from the literature: long-wave approximation and tanh-fitting. We then use numerical analytic continuation methods based on Padé approximants and the adaptive Antoulas–Anderson (AAA) method. These methods are shown to produce accurate predictions of the amplitude of the oscillations and the mass ratios for which the oscillations vanish. Exponential asymptotics using an AAA approximation for the leading-order behavior is then applied to study granular woodpile chains, including chains with Hertzian interactions—this method is able to calculate behavior that could not be accurately approximated in previous studies.     

The single-mode rate equations for semiconductor lasers with thermal effects

A mathematical model describing the coupling of electrical,optical and thermal effects in semiconductor lasers is introduced.Numerical and asymptotic solutions are derived, including expressionsfor key physical quantities such as the initial time delay,the frequency of spike oscillation and the temperature rise,together with its influence on the photon density, the electronconcentration and the threshold current. The consequences ofthermal effects in reducing efficiency are thus quantified.     

On <Emphasis Type="Italic">g</Emphasis>-functions for Laguerre function expansions of Hermite type

We examine weighted L ^p boundedness of g-functions based on semigroups related to multi-dimensional Laguerre function expansions of Hermite type. A technique of vector-valued Calderón–Zygmund operators is used.