The radial force on a charged particle in superimposed magnetic fields on Schwarzschild spacetime

Following the approach of optical reference geometry we derive the expression for the total force in the radial direction acting on a charged particle in magnetic fields superimposed on the static Schwarzschild background and show the possible existence of bound orbits for particles in the field of ultra compact objects at distancesr?3m wherein the Lorentz force counterbalances both the gravitational and centrifugal forces.     

Spectroscopic study of rigid-rod polymers. I. Structures of model compounds

Poly(p-phenylene benzbisoxazole) and poly(p-phenylene benzbisthiazole) belong to the class of extended-chain, rigid-rod polymers possessing high modulus, high strength, and good thermal and oxidative resistance. Fibers and films of these polymers are processed from anisotropic solutions in strong acids such as methane sulfonic acid or polyphosphoric acid. The electronic absorption and vibrational spectra of the model compounds have been investigated in order to characterize the structures in the solid state and in nonprotonic solvents. The dramatic intensity differences in the spectra obtained have been interpreted by variations in the dihedral angle between the plane of the phenyl group and the plane of the central heterocyclic ring which affect the resonance configuration between the two rings.     

Magnetic domain behaviour of MgFe2O4-CoFe2O4 system

Ferrites with the composition Mg_1−x CO _x Fe₂O₄(0<x≤0·33) were synthesized by solid state reaction between MgO,α-Fe₂O₃ and CoFe₂O₄ at 1300°C. The compounds were analyzed from the results of x-ray diffraction, magnetic hysteresis and initial susceptibility (χ) studies. All the compounds of the series were found to be monophasic with no appreciable change in their lattice parameter. The saturation magnetization and coercive field (H _c ) values increased with increasing cobalt ferrite content. Similarly, the shapes of theχ-T curves and temperature variations ofH _c values indicated that the magnetic behaviour changes from multi-domain to single domain with increasing cobalt content. The results are similar to those observed for the (MgFe₂O₄)_1−x (Co₃O₄) system.     

Global perspectives for secondary reference materials for analysis of food and related biological samples

Primary, secondary and tertiary reference materials (RM) play an important role in quality controls of analytical measurements. Logistics of preparation and proper use of primary and secondary RMs are presented. Tertiary (i.e. in-house) control materials are useful as substitutes in the absence of recognized primary or secondary RMs. The lack of interdisciplinary interaction during development of RMs (e.g. in specific areas such as foods), has an important impact on limiting the usefulness of certain types of RMs. The abundance of RMs in some countries and regions appears to have little effect on the existing paucity in RMs in other regions, and the underlying causes are outlined. The ability of a laboratory to produce good quality in-house RMs traceable to recognized primary or secondary RMs is a direct measure of its quest for reliable analytical data. Therefore many laboratories should be encouraged to engage in secondary and tertiary RM activities designed to answer specific measurement problems. In this context, assistance (e.g. practical training opportunities) in identifying simple methods of analyses for their efficacy in determining specific analytes is a source of help that can be extended to countries experiencing limitations in laboratory instrumentation.     

Azo-hydrazo Tautomerism and Inclusion Complexation of 1-phenylazo-2-naphthols with Various Solvents and β-cyclodextrin

Spectral characteristics of sudan I (SDI), sudan II (SDII) and mordant violet-5 (MV5) have been studied in various solvents and β-cyclodextrin (β-CD). The inclusion complex of the above molecules with β-CD was analyzed by UV-visible, fluorometry, and DFT methods. The solvent study shows that azo-hydrazo tautomer is present in these molecules. The increase in the fluorescence intensity and a large bathochromic shift in the S₁ state indicate these molecules forms 1:1 inclusion complex with β-CD.     

Leptogenesis from spin-gravity coupling following inflation

The energy levels of the left- and the right-handed neutrinos are split in the background of gravitational waves generated during inflation, which, in presence of lepton-number-violating interactions, gives rise to a net lepton asymmetry at equilibrium. Lepton number violation is achieved by the same dimension five operator which gives rise to neutrino masses after electroweak symmetry breaking. A net baryon asymmetry of the same magnitude can be generated from this lepton asymmetry by electroweak sphaleron processes.     

Switching behaviour of a nonlinear Mach-Zehnder interferometer

In the present paper, a detailed investigation on the switching behaviour of a nonlinear Mach-Zehnder interferometer (NMZI) has been carried out using beam propagation method (BPM). A thorough investigation on input vs. output characteristic has been carried out by varying different parameters like length of the arms, refractive index of the linear/nonlinear arm, wavelength of the input beams and nonlinear coefficient of the material of the nonlinear arm. The input vs. output characteristic has also been investigated by shifting the balance point of the NMZI. The present paper provides a physically intuitive understanding of the effect of change in different parameters of the NMZI on its switching behaviour.     

Unweighted linear congruences with distinct coordinates and the Varshamov–Tenengolts codes

In this paper, we first give explicit formulas for the number of solutions of unweighted linear congruences with distinct coordinates. Our main tools are properties of Ramanujan sums and of the discrete Fourier transform of arithmetic functions. Then, as an application, we derive an explicit formula for the number of codewords in the Varshamov–Tenengolts code \(VT_b(n)\) with Hamming weight k, that is, with exactly k 1’s. The Varshamov–Tenengolts codes are an important class of codes that are capable of correcting asymmetric errors on a Z-channel. As another application, we derive Ginzburg’s formula for the number of codewords in \(VT_b(n)\), that is, \(|VT_b(n)|\). We even go further and discuss connections to several other combinatorial problems, some of which have appeared in seemingly unrelated contexts. This provides a general framework and gives new insight into all these problems which might lead to further work.     

Stability of the generalized quadratic and quartic type functional equation in non-Archimedean fuzzy normed spaces

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of non-Archimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-Archimedean absolute value of $2$ is less than $1$ cannot be omitted in our corollaries. The results improve and extend some recent results.     

Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection

Light scattered from biological tissues can exhibit an inverse power law spectral component. We develop a model based on the Born approximation and von Karman (self-affine) spatial correlation of submicron tissue refractive index to account for this. The model is applied to light scattering spectra obtained from excised esophagi of normal and carcinogen-treated rats. Power law exponents used to fit dysplastic tissue site spectra are significantly smaller than those from normal sites, indicating that changes in tissue self-affinity can serve as a potential biomarker for precancer.