A canonical subspace of modular forms of half-integral weight

We characterise the space of newforms of weight k + 1/2 on Γ₀(4N), N odd and square-free (studied by the second and third authors with Vasudevan) under the Atkin-Lehner W(4) operator. As an application, we show that the (±1)-eigensubspaces of the W(4) operator on the space of modular forms of weight k + 1/2 on Γ₀(4N) is mapped to modular forms of weight 2k on Γ₀(N), under a class of Shimura maps. The existence of such subspaces having this mapping property was conjectured by Zagier in a private communication. One of the special features of the (±1)-eigensubspaces is that the (2k + 1)-th power of the classical theta series of weight 1/2 belongs to the +  eigensubspace and hence this gives interesting congruences for r _2k+1(p ²).     

Production of thermostable multiple enzymes from Bacillus amyloliquefaciens KUB29

A strain of Bacillus amyloliquefaciens KUB29 was identified by 16S ribosomal RNA sequencing (Genbank: MF772779.1). Production of thermostable protease, amylase and lipase were done by the isolated strain. The produced enzymes were partially purified by ammonium precipitation followed by dialysis process. Protease and lipase enzymes are effectively used in bio-oil extraction from proteinaceous sample followed by transesterification to produce methyl ester. Amylase enzyme is widely used in food and laundry industry. The produced enzymes are active at thermophilic condition of 55 °C. Use of these enzymes in biofuel production process will make the process cleaner and greener.     

On the Anistropy of the Speed of Light on a Rotating Platform

The paper discusses a recently posed paradox in relativity concerning the speed of light as measured by an observer on board a rotating turn-table. The counter-intuitive problem put forward by F. Selleri concerns the theoretical prediction of an anisotropy in the speed of light in a reference frame comoving with the edge of a rotatiing disc even in the limit of zero acceleration. The paradox not only challenges the internal consistency of the special relativity theory but also undermines the basic tenet of the conventionality of simultaneity thesis of relativity. The present paper resolves the issue in a novel way by recasting the original paradox in the Galilean world and thereby revealing, in a subtle way, the weak points of the reasonings leading to the fallacy. As a background the standard and the non-standard synchronies in the relativistic as well as in the Galilean world are discussed. In passing, this novel approach also clarifies (contrary to often made assertions in the literature) that the so-called desynchronization of clocks cannot be regarded as the root cause of the Sagnac effect. Finally in spite of the flaw in the reasonings leading to the paradox Selleri's observation regarding the superiority of the absolute synchrony over the standard one for a rotation observer has been upheld.     

Exploring the structure,binding mode,flexibility and toxicity nature for Sinefungin molecule: a theoretical approach

Sinefungin (SFN) is an antiviral agent of dengue (DENV) and Zika (ZIKV) viruses with IC₅₀ values of 0.63 and 1.18 µM, respectively. The ADMET properties of SFN revealed that the SFN molecule can be used as an oral drug due to its good solubility nature. The molecular docking analysis of SFN molecule with RNA capping site of DENV and ZIKV NS5 MTase was performed. From this, the SFN-DENV MTase was found to be the best, based on binding energy (??7.56 kcal/mol) and intermolecular interactions. The geometrical parameters of the optimized conformation and docked conformations of SFN molecule are compared which indicated that the intermolecular interactions lead to the modifications of SFN conformation in active site. The molecular electrostatic potential map of SFN depicts the possible nucleophilic and electrophilic locations present in the molecule. The HOMO–LUMO based electronic properties such as electron affinity (A), electrophilicity (ω), electronegativity (χ) and global hardness (η) were calculated to determine the stability and toxicity of SFN molecule. Fukui function and NBO analysis of SFN were also computed.

     

Controlling electrospun nanofiber morphology and mechanical properties using humidity

Electrospinning is a fiber spinning technique used to produce nanoscale polymeric fibers with superior interconnectivity and specific surface area. The fiber diameter, surface morphology, and mechanical strength are important properties of electrospun fibers that can be tuned for diverse applications. In this study, the authors investigate how the humidity during electrospinning influences these specific properties of the fiber mat. Using two previously uninvestigated polymers, poly(acrylonitrile) (PAN) and polysulfone (PSU) dissolved in N,N‐Dimethylformamide (DMF), experimental results show that increasing humidity during spinning causes an increase in fiber diameter and a decrease in mechanical strength. Moreover, surface features such as roughness or pores become evident when electrospinning in an atmosphere with high relative humidity (RH). However, PAN and PSU fibers are affected differently. PAN has a narrower distribution of fiber diameter regardless of the RH, whereas PSU has a wider and more bimodal distribution under high RH. In addition, PSU fibers spun at high humidity exhibit surface pores and higher specific surface area whereas PAN fibers exhibit an increased surface roughness but no visible pores. These fiber morphologies are caused by a complex interaction between the nonsolvent (water), the hygroscopic solvent (DMF), and the polymer. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Carbamic acid 2-trimethylsilylethyl ester as a new ammonia equivalent for palladium-catalyzed amination of aryl halides

Carbamic acid 2-trimethylsilylethyl ester (Teoc-NH₂) serves as an ammonia equivalent in the palladium-catalyzed amination of aryl bromides and aryl chlorides. Anilines with sensitive functional groups can be readily prepared using these amine derivatives.     

Fabrication of nanosized Pt on rutile TiO2 using a standing wave sonochemical reactor (SWSR) – observation of an enhanced catalytic oxidation of CO

Fine particles of rutile TiO₂ supporting nanosized particles of Pt were prepared by a simultaneous in situ sonochemical reduction and deposition method using a standing wave sonochemical reactor (SWSR). The mean diameter of sonochemically obtained Pt particles are of 2 nm. Following this sonochemical technique, rutile TiO₂ was also deposited with different weight percentages of Pt. Catalytic function of the prepared composite catalysts were tested by the oxidation of CO to CO₂. From the catalytic activity results, it has been found out that the catalysts prepared by the sonochemical method exhibited higher catalytic activity for CO oxidation, probably attributed to the higher Pt particle distribution achieved under sonication. Transmission electron microscopy (TEM), X-ray photoelectron spectra (XPS), and diffuse reflectance spectroscopy (DRS) were employed to characterize the resulting material.     

H<Superscript>+</Superscript><Emphasis Type="Bold">and He</Emphasis><Superscript>2+</Superscript> impact single and double ionization of lead

H⁺ and He²⁺ impact single and double ionization cross sections of ground state lead atoms have been calculated in the binary encounter approximation. Calculations of direct double ionization cross sections have been performed in the modified double binary encounter model. The accurate expressions of σ_ΔE (cross-section for energy transfer ΔE) and Hartree-Fock velocity distributions for the target electrons have been used throughout the calculations. Contributions to double ionization from Auger effect following ionization of inner shells have been considered in the present work. Our H⁺ impact single and double ionization cross sections are in good agreement with the experimental observations. In calculations of He²⁺ impact cross sections, the present theoretical approach shows limited success in the experimentally investigated region (50–350 keV amu^-1).