Stable blow-up dynamics in the -critical and -supercritical generalized Hartree equation

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: First, we consider the -critical case in dimensions and obtain that a generic blow-up has a self-similar structure and exhibits not only the square root blowup rate , but also the log-log correction (via asymptotic analysis and functional fitting), thus, behaving similarly to the stable blow-up regime in the -critical nonlinear Schrödinger equation. In this setting, we also study blow-up profiles and show that generic blow-up solutions converge to the rescaled , a ground state solution of the elliptic equation . We also consider the -supercritical case in dimensions . We derive the profile equation for the self-similar blow-up and establish the existence and local uniqueness of its solutions. As in the NLS -supercritical regime, the profile equation exhibits branches of nonoscillating, polynomially decaying (multi-bump) solutions. A numerical scheme of putting constraints into solving the corresponding ordinary differential equation is applied during the process of finding the multi-bump solutions. Direct numerical simulation of solutions to the generalized Hartree equation by the dynamic rescaling method indicates that the is the profile for the stable blow-up. In this supercritical case, we obtain the blow-up rate without any correction. This blow-up happens at the focusing level , and thus, numerically observable (unlike the -critical case). In summary, we find that the results are similar to the behavior of stable self-similar blowup solutions in the corresponding settings for the nonlinear Schrödinger equation. Consequently, one may expect that the form of the nonlinearity in the Schrödinger-type equations is not essential in the stable formation of singularities.     

The secondary X-ray fluorescence and absorption near the interface of multi-material: Case of EDS microanalysis

A simple model is proposed to take into account secondary X-ray fluorescence and absorption effects near the interface. This model is based on the investigation of the shape change of the first derivative equation that can fit the sigmoidal EDS profile obtained when a high vacuum electron beam passes through the interface of two adjacent materials. The contribution of the photoelectric absorption of primary X-rays (characteristic and Bremsstrahlung) and the secondary fluorescence on the degradation of the X-ray spatial resolution can be easily quantified. The close agreement between the simulated (Monte Carlo simulation using the Casino software) and the experimental data serves to assess the reliability of this developed model.     

Cross section of the impact single ionization of B2＋ by H＋

The ionization process of B2+ by H+ impact is studied using the continuum-distorted-wave eikonal-initial-state (CDW-EIS) method and the modified free electron peak approximation (M-FEPA), respectively. Total, single-, and double- differential cross sections from 1s and 2s orbitals are presented for the energy range from 10 keV/u to 10 MeV/u. Comparison between the results from the two methods demonstrates that the total and single-differential cross sections for the high-energy incident projectile case can be well evaluated using the simple M-FEPA model. Moreover, the M-FEPA model reproduces the essential features of the binary-encounter (BE) bump in the double-differential cross sections. Thus, the BE ionization mechanism is discussed in detail by adopting the M-FEPA model. In particular, the double- and single-differential cross sections from the 2s orbital show a high-energy hip, which is different from those from the 1s orbital. Based on Ref. [1], the Compton profiles of B2+ for 1s and 2s orbitals are given, and the hips in DDCS and SDCS from the 2s orbital are explained.     

Molecular phylogenetic study and expression analysis of ATP-binding cassette transporter gene family in Oryza sativa in response to salt stress

ATP-binding cassette (ABC) transporter is a large gene superfamily that utilizes the energy released from ATP hydrolysis for transporting myriad of substrates across the biological membranes. Although many investigations have been done on the structural and functional analysis of the ABC transporters in Oryza sativa, much less is known about molecular phylogenetic and global expression pattern of the complete ABC family in rice. In this study, we have carried out a comprehensive phylogenetic analysis constructing neighbor-joining and maximum-likelihood trees based on various statistical methods of different ABC protein subfamily of five plant lineages including Chlamydomonas reinhardtii (green algae), Physcomitrella patens (moss), Selaginella moellendorffii (lycophyte), Arabidopsis thaliana (dicot) and O. sativa (monocot) to explore the origin and evolutionary patterns of these ABC genes. We have identified several conserved motifs in nucleotide binding domain (NBD) of ABC proteins among all plant lineages during evolution. Amongst the different ABC protein subfamilies, ‘ABCE’ has not yet been identified in lower plant genomes (algae, moss and lycophytes). The result indicated that gene duplication and diversification process acted upon these genes as a major operative force creating new groups and subgroups and functional divergence during evolution. We have demonstrated that rice ABCI subfamily consists of only half size transporters that represented highly dynamic members showing maximum sequence variations among the other rice ABC subfamilies. The evolutionary and the expression analysis contribute to a deep insight into the evolution and diversity of rice ABC proteins and their roles in response to salt stress that facilitate our further understanding on rice ABC transporters.     

Organotin(IV) Complexes of 2-[(2′,4′,6′- Trichlorophenylamido)]benzoic Acid: Synthesis,Coordination Chemistry,and Semi-Empirical Study

A new series of organotin(IV) complexes of aniline derivatives, R₂SnL₂ and R₃SnL [where R = Me, n-Bu, n-Oct, and Ph], have been synthesized by the reaction of ligand acid with respective organotin halides in the presence of triethylamine as base or dioctyltin oxide using a Dean–Stark trap for the removal of water under reflux conditions. Experimental details for the preparation and characterization, including elemental analysis, IR, semi-empirical study, multinuclear NMR (¹H, ¹³C, and ¹¹⁹Sn spectra and EI mass spectral studies) of all reported complexes are provided. The IR data indicate that in both di- and triorganotin(IV) carboxylates, the ligand moiety ?COO acts as a bidentate group in the solid state. Multinuclear NMR data show that triorganotin complexes exhibits a four-coordinated geometry, while diorganotin(IV) complexes show a coordination number greater than four, probably five or six, in solution state.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Thiosemicarbazone Complexes of Ruthenium(II) and Rhodium(I) Containing Triphenylphosphine

Several new hexa-coordinated ruthenium(II) and penta-coordinated rhodium(I) complexes of the types [RuCl(CO)(PPh ₃ ) ₂ (TSC)], [RuH(CO)(PPh ₃ ) ₂ (TSC)], and [Rh(PPh ₃ ) ₃ (TSC)] (where TSC = anion of thiosemicarbazone Schiff bases) have been prepared by the reactions of [RuHCl(CO)(PPh ₃ ) ₃ ], [RuH ₂ (CO)(PPh ₃ ) ₃ )], and [RhH(PPh ₃ ) ₄ ] with thiosemicarbazones of 2-furaldehyde (H-FTSC), thiophene-2-carboxaldehyde (H-TCTSC), p-anisaldehyde (H-ATSC), piperonaldehyde (H-PTSC), and cyclohexanone (H-CTSC). All the new complexes obtained have been characterized on the basis of elemental analysis, IR, ¹ H NMR, ³¹ P NMR, and electronic spectral data.     

Synthesis,Spectroscopic Studies,and Biological Activity of Organosilicon(iv) Complexes of Ligands Derived from 2-Aminobenzothiazole Derivatives and 2-Hydroxy-3-Methoxy Benzaldehyde

Abstract

The Schiff bases derived from the condensation of 2-aminobenzothiazole derivatives and 2-hydroxy-3-methoxybenzaldehyde and their silicon(IV) complexes with the general formula R₂Si(L)Cl (R = Et, Bu, Ph, L = 2-(2-hydroxy-3-methoxy) benzylideneaminobenzo-thiazole) have been synthesized. These complexes have been characterized by elemental analysis, molar conductance, and spectroscopic studies including IR and NMR (¹H, ¹³C, and ²⁹Si) spectroscopy. The analytical data suggest trigonal bipyramidal geometry around the silicon atom in the resulting complexes. The ligands and their organosilicon complexes have also been evaluated for in vitro antimicrobial activity against bacteria (Staphylococcus aureus, Bacillus subtilis, and Escherichia coli) and fungi (Aspergillus niger and Candida albicans). The complexes were found to be more potent as compared to the ligands.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.