Construction of Approximate Entropy Measure-Valued Solutions for Hyperbolic Systems of Conservation Laws

Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Székelyhidi Jr (Ann Math 170(3):1417–1436, 2009) and Chiodaroli et al. (2013) have demonstrated that entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical schemes need not converge to an entropy solution of systems of conservation laws as the mesh is refined. Combining these two facts, we argue that entropy solutions may not be suitable as a solution framework for systems of conservation laws, particularly in several space dimensions. We advocate entropy measure-valued solutions, first proposed by DiPerna, as the appropriate solution paradigm for systems of conservation laws. To this end, we present a detailed numerical procedure which constructs stable approximations to entropy measure-valued solutions, and provide sufficient conditions that guarantee that these approximations converge to an entropy measure-valued solution as the mesh is refined, thus providing a viable numerical framework for systems of conservation laws in several space dimensions. A large number of numerical experiments that illustrate the proposed paradigm are presented and are utilized to examine several interesting properties of the computed entropy measure-valued solutions.     

The Asymptotic Behavior of Certain Birth Processes

We describe a connection between discrete birth process and a certain family of multivariate interpolation polynomials. This enables us to compute all asymptotic moments of the birth process, generalizing previously known results for the mean and variance. Received July 15, 2004     

New quinoxaline-piperazine-oxazole conjugates: Synthesis,in vitro anticancer,in silico ADMET,and molecular docking studies

In this paper, we describe the synthesis of some new quinoxaline-piperazine-oxazole amide conjugates 6a-n from 3-chloroquinoxaline-2-carbonitrile using well-known reaction sequences. The synthesized compounds were characterized by ¹H NMR,¹³C NMR, and mass spectral analysis. The compounds were tested for their in vitro antiproliferative activity toward four different cancer cell lines such as PC-3, MCF-7, DU-145, and A-549 by MTT method. The compounds, 6c, 6h, 6i , and 6n were found to be more potent than the standard Erlotinib. In vitro tyrosine kinase EGFR inhibition studies using four potent compounds revealed that 6n has double inhibiting tendency with value IC₅₀ of 0.22 μM and 6h with value of IC₅₀ 0.27 μM compared to reference compound. Molecular docking studies of active compounds, 6c , 6h , 6i , and 6n on EGFR receptor suggested that all the compounds have more binding energies than that of Erlotinib. Furthermore, the in silico pharmacokinetic profile was accomplished for the active compounds, 6c , 6h , 6i , and 6n using SWISS/ADME and pk CSM, whereas compounds, 6h , 6i , and 6c followed Lipinski rule, Veber rule, Egan rule and Muegge rule. The remaining compound 6n did not follow Lipinski rule, Ghose rule because one common violation, that is, because of high molecular weight (MW > 350).     

Fundamental solution of steady oscillations in thermoelastic medium with voids

ABSTRACT

The article deals with the study of plane wave propagation in the thermoelastic medium in the presence of voids. The problem is considered in the context of three-phase-lag model of generalized thermoelasticity. There exists three longitudinal waves, namely elastic (E-mode), thermal (T-mode) and volume fraction (V-mode) in addition to transverse waves which get decoupled from the rest of motion and not affected by thermal and volume fraction fields. The fundamental solution of the system of differential equations in case of steady oscillations in terms of the elementary functions has been constructed. The phase velocity and attenuation coefficient of these waves are computed numerically and presented graphically.     

Reversed-phase liquid chromatography of immunoglobulin G molecules and their fragments with the diphenyl column

A diphenyl column was able to resolve two closely related monoclonal IgG2 molecules, while a C8 column failed to separate these IgGs under identical chromatographic conditions. The diphenyl column also showed a better separation of a mixture of two light and two heavy chains than the C8 column. The influence of amino acid side chains from protein sequences in binding to the diphenyl and C8 stationary phases was studied by using a set of synthetic peptides with the sequence GXXLLLKK, where X represents substitution with all of the 20 amino acids. Peptides containing aromatic amino acids showed a greater binding on the diphenyl column than on the C8 column. This increase in retention was attributed to pi-pi interactions between the aromatic amino acid side chains and the diphenyl ligand. Based on the retention of peptides on the diphenyl column, new retention coefficients were assigned for the separation of proteins. A good correlation was observed between the sum of retention coefficients (SigmaRc) for IgGs and their retention time on the diphenyl column. On-column hydrogen-deuterium exchange showed that the diphenyl column had a larger surface of interaction with protein than the C8 column. pi-pi interactions and the large contact surface resulted in improved resolution of IgGs and their fragments on the diphenyl column.     

Regioselective strategies mediated by lanthanide triflates for efficient assembly of oligomannans

Readily prepared mannosyl n-pentenylorthoesters (NPOEs) serve as donors in themselves and as convenient intermediates for other glycosyl donors, such as n-pentenyl glycosides (NPGs), thioglycosides, and trichloroacetimidates. These various donors are activated by different reagents, and are therefore amenable to versatile, discriminate use. Scandium and ytterbium triflates respond very differently to these donors, with the result that chemoselective discrimination between NPOEs, NPGs, trichloroacetimidates as well as ethyl and phenyl thioglycosides can be achieved. Appropriate NPOEs are also able to provide 2,6 and 3,6 diol acceptors via rearrangement or glycoside formation, and these can be used for one-pot, sequential glycosidations based on orthogonal donors, and in situ double differential glycosidations. Thus NPOEs activated by iodonium ion, specifically generated from ytterbium triflate/N-iodosuccinimide, can be used to monoglycosidate the diols rapidly, with exquisite regio, and sometimes chemo, selectivity. The residual NPOE is converted into disarmed NPG, which is refractory to the reaction conditions, and so poses no threat to the free-OH of the monoglycosidation product. Further glycosidation of the latter can then achieved by direct addition of a trichloroacetimidate or ethyl thioglycoside. This basic strategy has been used to prepare a branched chain pentadecamannan. The success is an example of the efficiency of donor/acceptor MATCH concept for regioselective glycosylation.     

Evaporation-induced patterns from droplets containing motile and nonmotile bacteria

In this letter, we report the observations of specific pattern formation from the evaporation of aqueous droplets containing motile and nonmotile bacteria. We found that when motile bacteria were present the droplet evaporated into disclike patterned deposits of bacteria. However, when the bacteria were made nonmotile by treatment with liquid nitrogen, the droplet evaporated into ringlike deposits. We also observed that bacteria with higher motility produced more uniformly deposited disclike patterns. Furthermore, we propose a model with numerical simulations to explain the mechanism of formation of these patterns. The model is based on the advective fluid flow from the center of the droplet toward the edge due to enhanced evaporation from the edge of the pinned droplet in comparison to that from the free surface. For the case of motile bacteria, we have added another velocity parameter toward the axis of the droplet and directed against the fluid flow in order to account for the disclike pattern formation. The numerical simulations match the experimental observations well. The present work, by qualitative and quantitative understanding of the evaporation of bacteria droplets, demonstrates that the inherent bacterial motility is primarily responsible for the formation of these differential patterns.     

Star–block polymers of multiple polystyrene-b-polyisobutylene arms radiating from a polydivinylbenzene core

The synthesis together with mechanical property and rheological characterization of novel star–block copolymers comprising multiple polystyrene (PSt)-b-polyisobutylene (PIB) arms emanating from polydivinylbenzene (PDVB) cores are described. The synthesis strategy involved the preparation of PSt-b-PIB-Cl^t (i.e., diblocks fitted with a tert-chlorine terminus at the PIB end) by sequential living block polymerization of St and IB, ionizing the -Cl^t terminus by TiCl₄ at room temperature, and linking the PSt-b-PIB^⊕ prearms by DVB. Molecular characterization was effected mainly by triple detector GPC including refractive index (RI)-, UV-, and laser light scattering (LLS)-GPC traces. Evidence for intra- and intermolecular reactions between individual star–blocks is presented and a comprehensive mechanism to the final product is proposed. The stress–strain behavior of star–blocks has been studied and is compared with those of linear triblocks (i.e., two-arm stars) of similar arm molecular weights and composition in the 25–70°C range. The mechanical properties of star–blocks are invariably superior to those of the triblocks over the entire temperature range. The rheological behavior of star–blocks and linear triblocks has been compared in terms of dynamic viscosity at various frequencies. Star–blocks exhibit significantly lower melt viscosities than their linear counterparts, which signals improved processing behavior. We have also compared select rheological properties of the commercially available PSt-b-(hydrogenated-1,4-polybutadiene)-b-PSt thermoplastic elastomer (Kraton G 1650) with those of PIB-based linear triblocks and multiarm star–blocks of similar glassy/rubbery compositions. The melt viscosities of PIB-based triblocks and star–blocks were significantly lower than that of Kraton G over the entire frequency range investigated. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2235–2243, 1999