Plasma-Maser Instability of Bernstein Mode in Presence of Magnetohydrodynamic Turbulence

A theoretical study is made on the amplification mechanism of electrostatic Bernstein mode wave in presence of kinetic Alfven wave turbulence in a magnetized plasma on the basis of plasma-maser interaction. It is shown that a test high frequency electrostativ Bernstein mode wave is unstable in the presence of low frequency kinetic Alfven wave turbulence. The growth rate of the Bernstein wave vanishes only in an unmagnetized plasma. Because of the universal existence of the kinetic Alfven waves in large scale plasmas, the results have potential importance in space and astrophysical radiation processes.     

The evolution of the resonant mode in plasma-maser interaction

We study the evolution of the resonant waves considering its interaction with the nonresonant waves and the plasma particles due to plasma-maser effect. The nonlinear dielectric function of the resonant wave is calculated and is found to consist of two parts: the direct and the polarization coupling terms. On the other hand, the nonlinear dielectric function of the nonresonant wave consists only of the direct coupling term. The significance of our results is discussed.     

An analysis of a quantum chromodynamic structure function

We obtain an approximate solution of Altarelli-Parisi equations yielding a sample of quantum chromodynamic structure function. The SLAC-MIT data are analysed with it. Possible effects of intrinsic charm and higher twist are also included. Agreement is found to be good forx⩾0.25.     

On the Class-number of the Maximal Real Subfield of a Cyclotomic Field

For any square-free positive integer m, let H(m) be the class-number of the field , where ζ_m is a primitive m-th root of unity. We show that if m = {3(8 g + 5)}² ? 2 is a square-free integer, where g is a positive integer, then H(4 m) > 1. Similar result holds for a square-free integer m = {3(8 g +7)}² ?2, where g is a positive integer. We also show that n|H(4 m) for certain positive integers m and n.     

Highly Dispersed Ce x Zr1−x O2 Nano-Oxides Over Alumina, Silica and Titania Supports for Catalytic Applications

We have been exploring the utilization of supported ceria and ceria–zirconia nano-oxides for different catalytic applications. In this comprehensive investigation, a series of Ce _x Zr_1−x O₂/Al₂O₃, Ce _x Zr_1−x O₂/SiO₂ and Ce _x Zr_1−x O₂/TiO₂ composite oxide catalysts were synthesized and subjected to thermal treatments from 773 to 1073 K to examine the influence of support on thermal stability, textural properties and catalytic activity of the ceria–zirconia solid solutions. The physicochemical characterization studies were performed using X-ray diffraction (XRD), Raman spectroscopy (RS), X-ray photoelectron spectroscopy (XPS), and high-resolution transmission electron microscopy (HREM), thermogravimetry and BET surface area methods. To evaluate the catalytic properties, oxygen storage/release capacity (OSC) and CO oxidation activity measurements were carried out. The XRD analyses revealed the formation of Ce_0.75Zr_0.25O₂, Ce_0.6Zr_0.4O₂, Ce_0.16Zr_0.84O₂ and Ce_0.5Zr_0.5O₂ phases depending on the nature of support and calcination temperature employed. Raman spectroscopy measurements in corroboration with XRD results suggested enrichment of zirconium in the Ce _x Zr_1−x O₂ solid solutions with increasing calcination temperature thereby resulting in the formation of oxygen vacancies, lattice defects and oxygen ion displacement from the ideal cubic lattice positions. The HREM results indicated a well-dispersed cubic Ce _x Zr_1−x O₂ phase of the size around 5 nm over all supports at 773 K and there was no appreciable increase in the size after treatment at 1073 K. The XPS studies revealed the presence of cerium in both Ce⁴⁺ and Ce³⁺ oxidation states in different proportions depending on the nature of support and the treatment temperature applied. All characterization techniques indicated absence of pure ZrO₂ and crystalline inactive phases between Ce–Al, Ce–Si and Ce–Ti oxides. Among the three supports employed, silica was found to stabilize more effectively the nanosized Ce _x Zr_1−x O₂ oxides by retarding the sintering phenomenon during high temperature treatments, followed by alumina and titania. Interestingly, the alumina supported samples exhibited highest OSC and CO oxidation activity followed by titania and silica. Details of these findings are consolidated in this review.     

Stereoselective one-pot, three-component synthesis of 4-amidotetrahydropyran

The reaction of aldehyde with allylsilane in acetonitrile mediated by boron trifluoride etherate generated 4-aminotetrahydropyrans in good yields. The product is highly stereoselective.     

C-C bond cleavage: Metal-free-catalyzed reaction of Betti bases with various heterocycles under microwave irradiation

The reaction of Betti bases with various heterocycles in the presence of p-toluenesulphonic acid (PTSA) under microwave irradiation gives bis(heterocycle)methanes through benzyl transfer. The reaction proceeds via the cleavage of C-N bond followed by C-C bond. The metal-free cleavage of C-C bond, which is in fact a C-dearylation, is rarely reported in the literature.     

Congruences for ℓ-regular overpartition for ℓ ∈ {5, 6, 8}

Let A? _?(n) denote the number of overpartitions of a non-negative integer n with no part divisible by ?, where ? is a positive integer. In this paper, we prove infinite family of congruences for A? ₅(n) modulo 4, A? ₆(n) modulo 3, and A? ₈(n) modulo 4. In the process, we also prove some other congruences.     

Rhodium(I) carbonyl complexes of tetradentate chalcogen functionalized phosphines, [P(X)(CH2CH2P(X)Ph2)3] {X = O, S, Se}: Synthesis, reactivity and catalytic carbonylation reaction

The reaction of [Rh(CO)₂Cl]₂ with 0.5 mol equivalent of the ligands [P^′(X)(CH₂-CH₂P(X)Ph₂)₃](P^′P₃X₄) {where X = O(a), S(b) and Se(c)} affords tetranuclear complexes of the type [Rh₄(CO)₈Cl₄(P^′P₃X₄)] (1a-1c). The complexes 1a-1c have been characterized by elemental analyses, mass spectrometry, IR and multinuclear NMR spectroscopy, and the ligands b and c are structurally determined by single crystal X-ray diffraction. 1a-1c undergo oxidative addition (OA) reactions with CH₃I to generate Rh(III) oxidised products. Kinetic data for the reaction of 1a and 1b with excess CH₃I indicate a pseudo first order reaction. The catalytic activity of 1a-1c for the carbonylation of methanol to acetic acid and its ester show a higher Turn Over Frequency (TOF = 1349-1748 h⁻¹) compared to the well-known species [Rh(CO)₂I₂]⁻ (TOF = 1000 h⁻¹) under the similar experimental conditions. However, 1b and 1c exhibit lower TOF than 1a, which may be due to the desulfurization and deselinization of the ligands in the respective complexes under the reaction conditions.     

Synthesis,Characterization, Properties,and Novel Applications of Fluorescent Nanodiamonds

In the last few years, fluorescent nanodiamonds (FNDs)  have been developed significantly as a new member in the nanocarbon family. The surface of FNDs is embedded with some crystallographic defects containing color centres which surmount the properties of other fluorochromes including up conversion and down conversion nanoparticles, quantum dots, nano tubes, fullerenes, organic dyes, silica etc. Some of the intriguing properties like inevitable photostability, inherent bio-compatibility, outstanding optical and robust mechanical properties, excellent magnetic field, and electric field sensing potentiality make FNDs appealing to some benevolent applications in numerous fields like bio-imaging, delivering drugs, fighting cancer, spin electronics, imaging of magnetic structure at nanoscale and as promising nanometric temperature sensor. The structure of FNDs has certain point defects on the surface among which negatively charged nitrogen vacancy centre (NV^?) is the most investigated color centre. The production of NV^? fluorescence nanodiamonds is the most challenging task as substitution of carbon atoms is required to create vacancies by causing irradiation from an electron beam which is followed by high temperature annealing. Thus, this review points out the relative advantages of FNDs containing negatively charged nitrogen vacancy centres produced from HPHT method or CVD method with those nanodiamonds produced through detonation process or pulsed laser ablation (PLA) method. The steps involved in the fabrication of FNDs are described along with the major challenges and struggles underwent during the process in this review. This review also summarizes the recent developments made in the functionalization and applications predominantly made in the field of biological science and it is understood that depending on the defect color centres they can exhibit different emitted wavelengths ranging from UV–visible to near infrared with broad or narrow bandwidths. This review also highlights some of the fluorescent NDs that emit stable and strong red or green photoluminescence from the defect centers of NV^? which are implanted in the crystal lattice. This critical and extensive review will be useful for the further progress in this futuristic field of FNDs.