Moments of partitions and derivatives of higher order

Journal of Algebraic Combinatorics - We define moments of partitions of integers, and show that they appear in higher-order derivatives of certain combinations of functions.     

Tobramycin and Nebramine as Pseudo‐oligosaccharide Scaffolds for the Development of Antimicrobial Cationic Amphiphiles

Antimicrobial cationic amphiphiles derived from aminoglycoside pseudo‐oligosaccharide antibiotics interfere with the structure and function of bacterial membranes and offer a promising direction for the development of novel antibiotics. Herein, we report the design and synthesis of cationic amphiphiles derived from the pseudo‐trisaccharide aminoglycoside tobramycin and its pseudo‐disaccharide segment nebramine. Antimicrobial activity, membrane selectivity, mode of action, and structure–activity relationships were studied. Several cationic amphiphiles showed marked antimicrobial activity, and one amphiphilic nebramine derivative proved effective against all of the tested strains of bacteria; furthermore, against several of the tested strains, this compound was well over an order of magnitude more potent than the parent antibiotic tobramycin, the membrane‐targeting antimicrobial peptide mixture gramicidin D, and the cationic lipopeptide polymyxin B, which are in clinical use.     

Two-dimensional adaptive Eulerian-Lagrangian method for mass transport with spatial velocity distribution

A Eulerian-Lagrangian scheme is used to solve the two-dimensional advection-dispersion equation. Concentration and its partial differential operator are decomposed into advection and dispersion terms. Thus, advection is formally decoupled from dispersion and solved by continuous forward particle tracking. Dispersion is handled by implicit finite elements on a fixed Eulerian grid. Translation of steep gradients of concentration in advection-dominated flow regimes, is done without numerical distortion. Continuous spatial distribution of velocities are evaluated by using Galerkin's approach in conjunction with Darcy's law based on hydraulic input data from each element. The method was implemented on coarse FE grid with linear shape functions, demonstrating no over/under shooting and practically no numerical dispersion. Simulations, covering a wide range of Peclet numbers, yield high agreement with analytic and practical results.     

Shock waves in saturated thermoelastic porous media

The objective of this paper is to develop and present the macroscopic motion equations for the fluid and the solid matrix, in the case of a saturated porous medium, in the form of coupled, nonlinear wave equations for the fluid and solid velocities. The nonlinearity in the equations enables the generation of shock waves. The complete set of equations required for determining phase velocities in the case of a thermoelastic solid matrix, includes also the energy balance equation for the porous medium as a whole, as well as mass balance equations for the two phase. In the special case of a rigid solid matrix, the wave after an abrupt change in pressure propagates only through the fluid.     

Anionic Oligomerization of Methyl Methacrylate by Alkali Metal Alkoxides

Abstract

The kinetics of the oligomerization of methyl methacrylate (MMA) by methoxide/methanol solutions was studied using gas chromatography techniques. The effects of the type of the alkali metal, [CH OH]/[monomer] ratio, solvent, and initiator concentration were investigated. The rate of conversion using different alkali metal alkoxides was in the order CH₃OLi < CH₃ONa < CH₃OK, but no oligomers higher than the addition product, RO—MMA (n=1), could be obtained by CH₃OLL DP_n decreased with increasing the [CH₃OH]/[monomer] ratio and with lowering of the initiator concentration. Using DMSO as solvent increased the yields of the higher oligomers. The formation of n=1 was reversible, contrary to the formation of the higher oligomers. Some of the rate constants of the various steps of the oligomerization were estimated by taking into account the reversibility of the initiation reaction and assuming steady-state conditions in the concentration of the various anions present in the system.     

Modified Eulerian–Lagrangian formulation for hydrodynamic modeling

We present the modified Eulerian–Lagrangian (MEL) formulation, based on non-divergent forms of partial differential balance equations, for simulating transport of extensive quantities in a porous medium. Hydrodynamic derivatives are written in terms of modified velocities for particles propagating phase and component quantities along their respective paths. The particles physically interpreted velocities also address the heterogeneity of the matrix and fluid properties. The MEL formulation is also implemented to parabolic Partial Differential Equations (PDE’s) as these are shown to be interchangeable with equivalent PDE’s having hyperbolic – parabolic characteristics, without violating the same physical concepts. We prove that the MEL schemes provide a convergent and monotone approximation also to PDE’s with discontinuous coefficients. An extension to the Peclet number is presented that also accounts for advective dominant PDE’s with no reference to the fluid velocity or even when this velocity is not introduced.In Sorek et al. [27], a mathematical analysis for a linear system of coupled PDE’s and an example of nonlinear PDE’s, proved that the finite difference MEL, unlike an Eulerian scheme, guaranties the absence of spurious oscillations. Currently, we present notions of monotone interpolation associated with the MEL particle tracking procedure and prove the convergence of the MEL schemes to the original balance equation also for discontinuous coefficients on the basis of difference schemes approximating PDE’s. We provide numerical examples, also with highly random fields of permeabilities and/or dispersivities, suggesting that the MEL scheme produces resolutions that are more consistent with the physical phenomenon in comparison to the Eulerian and the Eulerian–Lagrangian (EL) schemes.     

Spectroscopic techniques in medicine: The future of diagnostics

Spectroscopic techniques have been finding increasing applications in the field of biomedicine especially in the field of disease diagnosis and monitoring in spite of the rapid emergence of several molecular biology based techniques. The significance of spectroscopy techniques and the possibility of using some of the underutilized regions of the electromagnetic radiations are discussed in this review. While previous reviews have already dealt with the potential of Fourier transform infrared spectroscopy-based (FTIR) techniques for clinical applications, the present review addresses the lacunae of the techniques along with its future trends that may make it a technique routinely applied in clinical settings.