Supports of semi-stable probability measures on locally convex spaces

LetE be a locally convex space. Let be an absolutely convexly tight Radom semi-stable probability measure onE with index 1<2 and Lévy measureM. The main result of this paper shows that the closed semigroup generated by the support ofM and the negative of the barycenter ofM restricted to a suitable compact subset ofE is a (closed) linear space ofE, and that the support of is a suitable translate of this linear space. This result complements a few known results concerning the supports of stable and semi-stable probability measures. In particular, it extends an analogous result proved recently for the support of -stable probability measures 1<2 (Ref. 4). Related results concerning the support of Radon semi-stable probability measures onE of index 0<<1 are also discussed.The research of this author was partially supported by AFSOR Grant No. 90-0168The research of this author was supported by KBN Grant, and the University of Tennessee Science Alliance, a State of Tennessee Center of Excellence.     

Sulfuric acid immobilized on silica: an efficient reusable catalyst for selective hydrolysis of the terminal O-isopropylidene group of sugar derivatives

Sulfuric acid immobilized on silica proved to be an efficient catalyst for selective hydrolysis of the terminal O-isopropylidene group of sugar derivatives. The method is very simple and economic for large-scale synthesis in which the catalyst is recovered and reused for several runs. Reactions with di-O-isopropylidene derivatives of d-glucose, d-mannose, d-fructose and l-sorbose led to the formation of the corresponding mono-O-isopropylidene derivatives in good to excellent yields.     

Investigations of the first order magnetic phase transition in dysprosium

The first order magnetic phase transition in polycrystalline sample of dysprosium (Dy) has been investigated in detail by dc-resistance vs. temperature (R-T) measurements. Distinct signature of coexistence of two magnetically ordered phases (i.e. ferromagnetic and antiferromagnetic), originating as a result of the metastable behavior associated with the first order phase transition (FOPT) is found near 90 K. By successfully recording the minor hysteresis loops within the hysteretic R-T regime of Dy, a varying degree of phase coexistence in the FOPT is demonstrated.     

Reduction of wave function associated with electromagnetic fields for imaginary mass system to standard helicity representation of Lorentz group

Reduced expansions for electromagnetic fields associated with spin-1 particles of imaginary mass (tachyons) have been derived in terms of standard helicity representations of inhomogeneous Lorentz group. The effects of wave equation and reality condition on these reduced expansions to satisfy Maxwell’s field equations have been derived. The reduced expansions of charge and current source densities associated with these fields have also been derived and it has been shown that these fields cannot satisfy the Maxwell’s equations in the absence of both the current and charge source densities.     

Preparation of NiFe2O4 nanopowder via EDTA precursor and study of its properties

An ethylene diamine tetra acetic acid (EDTA) precursor-based chemical method is reported for preparing single-phase nickel ferrite (NiFe₂O₄) nanopowder. The synthesized powder was characterized by thermogravimetric analysis, differential scanning calorimetric analysis, X-ray diffraction, particle size analysis and scanning electron microscopy. DC electrical resistivity and magnetic property of the synthesized NiFe₂O₄ were measured by using a two-probe method and a vibrating sample magnetometer respectively. The DC resistivity behaviour of the NiFe₂O₄ nanopowder was correlated with the change of microstructure, during sintering. This EDTA precursor-based method is capable of producing nanostructured single-phase NiFe₂O₄ powder at a comparatively low calcination temperature and offers the potential of a simple and cost-effective route, including the preparation of other ferrite nanoparticles.     

Dual functional novel catalytic Cu1−xZrxFe2O4 (x=0, 0.5, 1) nanoparticles for synthesis of polysubstituted pyridines and sunlight‐driven degradation of methylene blue

The effect of varied zirconium content on the structural, morphological, magnetic, optical, thermal and catalytic properties of nanoparticles of the ferrite Cu_1 ? xZr_xFe₂O₄ (x = 0, 0.5, 1) was investigated. The mixed ferrite was synthesized by the auto‐combustion method using nitrates of respective metals and citric acid as a chelating agent. The as‐prepared nanoparticles showed dual benefits. They were employed as a heterogeneous catalyst for one‐pot synthesis of polysubstituted pyridine derivatives as well as for catalytic degradation of industrial waste dyes such as methylene blue (MB). The highlight of the research reported is the catalytic degradation of industrial waste (MB) with high efficiency in eluent of a wide range of pH (3–13). The proposed nanoparticles arguably offer certain great advantages that include: low cost, facile nature, anti‐leaching property, magnetic recoverability and recyclability. The characterization of the as‐synthesized nanoparticles was done using various techniques. The leaching study was carried out using inductively coupled plasma optical emission spectroscopy. The formation of organic products was confirmed using Fourier transform infrared and ¹H NMR spectroscopies and examination of degradation products of MB dye was carried out using mass spectrometry and UV–visible spectroscopy.     

Blue light emission and amplification in left-handed isotropic Metallo-Semiconductor Photonic Crystal

A new left-handed isotropic design of semiconductor Photonic Crystal with plasmonic (Aluminum) nanorod inclusion is analyzed and proposed to demonstrate All-Angle Negative Refraction (AANR) with blue light amplification. It is shown that the proposed structure provides negative real values of both permeability (μ) and permittivity (?) with extremely low imaginary values for visible light. Phase slope and phase velocity is shown to be negative for blue light for proposed left-handed structure. Index matched to the incident medium and compensated losses due the gain assistance lead the light amplification in the designed structure. Finite Difference Time Domain (FDTD) method is applied to study left-handed transmission and reflection properties. Extremely high Left-Handed Transmission Efficiency is calculated which is found to be more than 99% for the proposed structure. Fabrication tolerance with effect of change in plasmonic nanorod radius by ±10% is also analyzed. Further, left-handed transmission for blue light is confirmed by analyzing the far-field spectrums of the proposed structure obtained by employing 3D FDTD method. Demonstration and study of near-field and far-field resonance reveals the nano-photonic application potential of the proposed structure as directional optical nano-antenna, polarizer and filter.