Riesz Fractional Derivatives and Fractional Dimensional Space

The Fourier transform method is used to solve fractional Poisson’s equation with Riesz fractional derivative of order α. It is shown that the solution is given in terms of the fractional dimensional space D. Gauss law for the electrostatic problem is given and the total electric flux is obtained in terms of α and D.     

A generalization of sumset and its applications

Let A be a nonempty finite subset of an additive abelian group G and let r and h be positive integers. The generalized h-fold sumset of A, denoted by \(h^{(r)}A\), is the set of all sums of h elements of A, where each element appears in a sum at most r times. The direct problem for \(h^{(r)}A\) is to find a lower bound for \(|h^{(r)}A|\) in terms of |A|. The inverse problem for \(h^{(r)}A\) is to determine the structure of the finite set A for which \(|h^{(r)}A|\) is minimal with respect to some fixed value of |A|. If \(G = \mathbb {Z}\), the direct and inverse problems are well studied. In case of \(G = \mathbb {Z}/p\mathbb {Z}\), p a prime, the direct problem has been studied very recently by Monopoli (J. Number Theory, 157 (2015) 271–279). In this paper, we express the generalized sumset \(h^{(r)}A\) in terms of the regular and restricted sumsets. As an application of this result, we give a new proof of the theorem of Monopoli and as the second application, we present new proofs of direct and inverse theorems for the case \(G = \mathbb {Z}\).     

PHOTOACOUSTIC SPECTROSCOPIC STUDIES OF POLYCYCLIC AROMATIC HYDROCARBONS: NAPHTHALENE CATION

The photoacoustic (PA) spectrum of naphthalene cation in boric acid glass, in the region 250–400 nm is reported for the first tune and compared with its optical absorption spectrum. The energy levels for the ions are calculated using open shell Wasilewski method with limited configuration interaction and used to interpret the observed PA spectrum.     

Studies on electrical conduction behavior of La1‐3xCaxBaxSrxMnO3 synthesized by chemical route

In the manganite La_1‐xM_xMnO₃ (M = Ca, Ba, Sr) the doping concentration introduces a mixed valency (Mn³⁺, Mn⁴⁺) which governs the magnetic and electrical properties of the compound. The perovskite oxides La_1‐3xCa_xBa_xSr_xMnO₃ (x = 0.00, 0.05, 0.10) were prepared by chemical method. Single‐phase formation is confirmed by XRD studies. The electrical behavior of compositions with x = 0.00, 0.05 and 0.10 in the system La_1‐3xCa_xBa_xSr_xMnO₃ was studied in the temperature range 300‐420 K. It is observed that conductivity decreases with increasing temperature as well as dopants concentration. Metallic behavior of these compositions decreases with increasing dopants concentration (x). The microstructures of these samples have been characterized using scanning electron microscopy (SEM). (© 2007 WILEY ‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Metal-free synthesis of pyridin-2-yl ureas from 2-aminopyridinium salts

An unprecedented base promoted domino approach has been developed for the synthesis of pyridin-2-yl urea derivatives via the reaction of 2-aminopyridinium salts and arylamines. The developed strategy tolerated a wide range of functional groups and afforded pyridin-2-yl ureas in moderate to good yields. The reaction was postulated to involve tandem cyclization, intermolecular nucleophilic addition, ring opening, and demethylation.     

A novel approach for protein identification from complex cell proteome using modified peptide mass fingerprinting algorithm

A unique peptide based search algorithm for identification of protein mixture using PMF is proposed. The proposed search algorithm utilizes binary search and heapsort programs to generate frequency chart depicting the unique peptides corresponding to all proteins in a proteome. The use of binary search program significantly reduces the time for frequency chart preparation to ～2 s for a proteome comprising ～23 000 proteins. The algorithm was applied to a three‐protein mixture identification, host cell protein (HCP) analysis, and a simulation‐generated data set. It was found that the algorithm could identify at least one unique peptide of a protein even in the presence of fourfold higher concentration of another protein. In addition, two HCPs that are known to be difficult to remove were missed by MS/MS approach and were exclusively identified using the presented algorithm. Thus, the proposed algorithm when used along with standard proteomic approaches present avenues for enhanced protein identification efficiency, particularly for applications such as HCP analysis in biopharmaceutical research, where identification of low‐abundance proteins are generally not achieved due to dynamic range limitations between the target product and HCPs.     

Tuning density profiles and mobility of inhomogeneous fluids

Density profiles are the most common measure of inhomogeneous structure in confined fluids, but their connection to transport coefficients is poorly understood. We explore via simulation how tuning particle-wall interactions to flatten or enhance the particle layering of a model confined fluid impacts its self-diffusivity, viscosity, and entropy. Interestingly, interactions that eliminate particle layering significantly reduce confined fluid mobility, whereas those that enhance layering can have the opposite effect. Excess entropy helps to understand and predict these trends.     

A Catalyst and Solvent Free Route for the Synthesis of N-Substituted Pyrrolidones from Levulinic Acid

An efficient, metal-free, catalyst-free and solvent-free methodology for the reductive amination of levulinic acid with different anilines has been developed using HBpin as the reducing reagent. This protocol offers an excellent method to avoid solvents and added catalysts on the synthesis of different kinds of N-substituted pyrrolidones under metal free conditions. It is also the first report for the synthesis of different pyrrolidones by solvent-free as well as catalyst-free methods. The proposed mechanism for the formation of pyrrolidone has been supported by DFT calculations and control experiments.     

Three‐dimensional structure of cyclic antibiotic teicoplanin aglycone using NMR distance and dihedral angle restraints in a DMSO solvation model

The three‐dimensional solution conformation of teicoplanin aglycone was determined using NMR spectroscopy. A combination of NOE and dihedral angle restraints in a DMSO solvation model was used to calculate an ensemble of structures having a root mean square deviation of 0.17 Å. The structures were generated using systematic searches of conformational space for optimal satisfaction of distance and dihedral angle restraints. Comparison of the NMR‐derived structure of teicoplanin aglycone with the X‐ray structure of a teicoplanin aglycone analog revealed a common backbone conformation with deviation of two aromatic side chain substituents. Experimentally determined backbone ¹³C chemical shifts showed good agreement with those computed at the density functional level of theory, providing a cross validation of the backbone conformation. The flexible portion of the molecule was consistent with the region that changes conformation to accommodate protein binding. The results showed that a hydrogen‐bonded DMSO molecule in combination with NMR‐derived restraints together enabled calculation of structures that satisfied experimental data. Copyright © 2015 John Wiley & Sons, Ltd.     

Differential content of secondary metabolites in diploid and tetraploid cytotypes of Siegesbeckia orientalis L.

Siegesbeckia orientalis L. is an annual herb widely distributed throughout the world and has many medicinal properties. In Chinese traditional system, it is popularly known as Xi-Xian and used for its anti-inflammatory properties. In the present study, two cytotypes (diploid and tetraploid) have been investigated for their secondary metabolites. The different plant parts have been explored in terms of total phenolics, total flavonoids, DPPH radical scavenging acitivity and total antioxidant capacity. Out of different plant parts, leaves have the maximum amount of secondary metabolites and antioxidant potential. HPTLC technique has been applied to quantify six marker compounds in the two cytotypes. Tetraploid cytotype has been compared with diploid cytotype, which shows that tetraploid has the maximum amount of studied secondary metabolites with high antioxidant potential.