Some new proofs of modular relations for the Göllnitz-Gordon functions

In this paper, we find new proofs of modular relations for the Göllnitz-Gordon functions established earlier by S.-S. Huang and S.-L. Chen. We use Schröter’s formulas and some simple theta-function identities of Ramanujan to establish the relations. We also find some new modular relations of the same nature.     

Enhanced ionic conductivity in novel nanocomposite gel polymer electrolyte based on intercalation of PMMA into layered LiV3O8

In the present work, a novel polymer electrolyte based on poly(methyl methacrylate) (PMMA)/layered lithium trivanadate (LiV₃O₈) nanocomposite has been investigated. X-ray diffraction (XRD) study shows that d-spacing is increased from 6.3?±?0.1 Å to 12.8?±?0.1 Å upon intercalation of the polymer into the layered LiV₃O₈. Room temperature ionic conductivity of the obtained nanocomposite gel polymer electrolyte is found to be superior to that of conventional PMMA-based gel polymer electrolyte. Enhancement in ionic conductivity of the nanocomposite gel electrolyte is attributed to the formation of a two-dimensional channel as a result of decreased interaction between Li⁺ and V₃O ₈ ^? layers as confirmed by FTIR. SEM results show aggregation of nanocomposite particles resulting from extension of some of the polymer chains from interlayer to the edge providing paths for Li⁺ ion transport. Interfacial stability of nanocomposite gel electrolyte is also found to be better than that of the conventional PMMA-based gel polymer electrolyte.     

Theoretical insight of nitric oxide adsorption on neutral and charged Pdn (n = 1–5) clusters

Density functional theory (DFT) calculations within the framework of generalized gradient approximation have been used to systematically investigate the adsorption of nitric oxide (NO) molecule on neutral, cationic, and anionic Pd_n (n = 1–5) clusters. NO coordinate to one Pd atom of the cluster by the end‐on mode, where the tilted end‐on structure is more favorable due to the additional electron in the π* orbital. On the contrary, in the neutral and cationic Pd₂ system, NO coordinates to the bridge site of cluster preferably by the side‐on mode. Charge transfer between Pd clusters and NO molecule and the corresponding weakening of N? O bond is an essential factor for the adsorption. The N? O stretching frequency follow the order of cationic > neutral > anionic. Binding energy of NO on anionic clusters is found to be greater than those of neutral and cationic clusters. © 2015 Wiley Periodicals, Inc.     

Subnanosecond mid-infrared laser pulse generation by synchronous mode-locked CO2 laser pumping

An injection mode-locked CO₂ laser has been used to synchronously pump NH₃ and C₂D₂ mid-infrared lasers resulting in the generation of short (? 1 ns) and powerful (> 1 MW) pulse trains.     

Identities and congruences for the general partition and Ramanujan’s tau functions

We present some identities and congruences for the general partition function p _r (n). In particular, we deduce some known identities for Ramanujan’s tau function and find simple proofs of Ramanujan’s famous partition congruences for modulo 5 and 7. Our emphasis throughout this paper is to exhibit the use of Ramanujan’s theta functions to generate identities and congruences for general partition function.     

Stability of Taylor–Couette and Dean flow: A semi-analytical study

An alternative method is presented for solving the eigenvalue problem that governs the stability of Taylor–Couette and Dean flow. The eigenvalue problems defined by the two-point boundary value problems are converted into initial value problems by applying unit disturbance method developed by Harris and Reid [27] in 1964. Thereafter, the initial value problems are solved by differential transform method in series and the eigenvalues are computed by shooting technique. Critical wave number and Taylor number for Taylor–Couette flow are computed for a wide range of rotation ratio (μ), −4 ? μ ? 1 (first mode) and −2 ? μ ? 1 (second mode). The radial eigenfunction and cell patterns are presented for μ = −1, 0, 1. Also, we have computed critical wave number and Dean number successfully.     

Replacement of an Indole Scaffold Targeting Human 15‐Lipoxygenase‐1 Using Combinatorial Chemistry

Human 15‐lipoxygenase‐1 (15‐LOX‐1) belongs to the class of lipoxygenases, which catalyze oxygenation of polyunsaturated fatty acids, such as arachidonic and linoleic acid. Recent studies have shown that 15‐LOX‐1 plays an important role in physiological processes linked to several diseases such as airway inflammation disease, coronary artery disease, and several types of cancer such as rectal, colon, breast and prostate cancer. In this study, we aimed to extend the structural diversity of 15‐LOX‐1 inhibitors, starting from the recently identified indolyl core. In order to find new scaffolds, we employed a combinatorial approach using various aromatic aldehydes and an aliphatic hydrazide tail. This scaffold‐hopping study resulted in the identification of the 3‐pyridylring as a suitable replacement of the indolyl core with an inhibitory activity in the micromolar range (IC₅₀=16±6 μm ) and a rapid and efficient structure–activity relationship investigation.     

Cu‐Based Nanoparticles as Emerging Environmental Catalysts

This account provides an overview of current research activities on nanoparticles containing the earth‐abundant and inexpensive element copper (Cu) and Cu‐based nanoparticles, especially in the field of environmental catalysis. The different synthetic strategies with possible modification of the chemical/ physical properties of these nanoparticles using such strategies and/or conditions to improve catalytic activity are presented. The design and development of support and/or bimetallic systems (e. g., alloys, intermetallic, etc.) are also included. Herein, we report synthetic approaches of Cu and Cu‐based nanoparticles (monometallic copper, bimetallic copper and copper (II) oxide nanoparticles/nanostructures) and impregnation of such nanoparticles onto support material (e. g., Co₃O₄ nanostructure), along with their applications as environmental catalyst for various oxidation and reduction reactions. Finally, this account provides necessary advances and perspectives of Cu‐based nanoparticles in the environmental catalysis.     

Magnetic and Mössbauer spectroscopic studies of NiZn ferrite nanoparticles synthesized by a combustion method

The properties of nanocrystalline Ni_0.5Zn_0.5Fe₂O₄ synthesized by an auto-combustion method have been investigated by magnetic measurements and Mössbauer spectroscopy. The as-synthesized single phase nanosized ferrite powder is annealed at different temperatures in the range 673–1,273 K to obtain nanoparticles of different sizes. The powders are characterized by powder X-ray diffraction, vibrating sample magnetometer, transmission electron microscopy and Mössbauer spectroscopy. The as-synthesized powder with average particle size of ~9 nm is superparamagnetic. Magnetic transition temperature increases up to 665 K for the nanosized powder as compared to the transition temperature of 548 K for the bulk ferrite. This has been confirmed as due to the abnormal cation distribution, as evidenced from room temperature Mössbauer spectroscopic studies.