Electrons magnetic fields and background radio emission in the galaxy

Extensive data now available on the non-thermal background radio emission from different celestial directions, and recent measurements on the energy spectrum of cosmic ray electrons in the vicinity of the earth permit one to deduce information on the mean magnetic fields and cosmic electron spectra needed to exist in different regions of the Galaxy. It is found that in order to explain quantitatively the background radio brightness distributions from the Galaxy one needs (i) the same or nearly same electron spectrum that exists in the near interstellar space, to exist in almost all regions of Galactic space, (ii) a mean magnetic field close to 6×10^?6 Gauss in the Disc in the direction of the Anti-centre, (iii) a mean magnetic field close to 2·5×10^?6 Gauss in the radio Halo and (iv) a mean magnetic field probably close to 9·5×10^?6 Gauss towards the Galactic Ridge in the direction of the Centre. Some inferences are also drawn on the confinement of cosmic rays in the Galaxy.     

High energy photons from the Crab nebula due to the universal microwave field

The flux of high energy photons emanating from the Crab nebula due to inverse Compton scattering of the universal microwave photons from the high energy electrons in the nebula has been calculated. This flux is compared with experimentally obtained values at certain energies and also with the flux calculated due to Compton-synchrotron process. The flux of gamma-rays of about 100 MeV due to the scattering of the microwave photons is found to be of the same order as that due to the Compton-synchrotron process.     

On Stoke's problem in magnetohydrodynamics

Stoke's classic problem involving the impulsive motion of an infinite flat plate in an unbounded viscous incompressible fluid is investigated under the additional specification that the fluid is electrically conducting and the motion is developed in the presence of uniform transverse magnetic field. For the fluids with arbitrary magnetic Prandtl number, the compact expression for the skin friction coefficient at the plate is given in terms of exponential and error functions of complex arguments. For the fluids with unit magnetic Prandtl number, expressions for the induced magnetic field, velocity, current density and induced electric field in the viscous boundary layer region set up near the plate are obtained. The effect of the magnetic field on the skin friction is to make it approach the steady state faster than in nonmagnetic case.     

Electron spin resonance of Cr5+ in CaWO4

Electron Spin Resonance of CaWO₄ with 0·1% of Cr has been investigated at liquid nitrogen and liquid helium temperatures. The observed ESR spectrum is attributed to Cr⁵⁺ ion in the substitutional site of W which has a compressed tetrahedral surroundings. A simple point charge calculation based on this geometry explains the observedg anisotropy and hyperfine anisotropy and places the magnetic electron in a predominantly \(3d_{z^2 } \) orbital. A comparison of these results with those obtained on other isoelectronic systems in similar and different co-ordinations justifies our assignment.     

There exist no Ramanujan congruences mod 6912

Let τ(n) be Ramanujan's function, $$x\prod _{m = 1}^\infty (1 - x^m )^{24} = \sum\nolimits_{n = 1}^\infty {\tau (n)x^n .} $$ In this paper it is shown that the Ramanujan congruence τ(n)=σ_d/nd¹¹ mod 691 cannot be improved mod 691². The following result is proved: for arbitrary r, s mod 691 the set of primes such that p ≡ r mod 691,τ (p) ≡ p¹¹+1+691 · s mod 691² has positive density.     

β-γ Perturbed angular correlation in the decay of124Sb

The β-γ perturbed angular correlation technique is applied to the determination ofg-factor of 603 keV (2⁺) state (τ = 8.5 psec) of¹²⁴Te populated in the decay of¹²⁴Sb. The activity was diffused into a thin iron foil. A small C type electromagnet was used for polarizing the sample. Internal field acting at the Tellurium nucleus in iron was used for perturbing the β-γ angular correlation. Theg-factor extracted isg = 0.28 ± 0.05. This is in good agreement with that obtained by γ-γ perturbed angular correlation method.     

Electrodeposition of copper on copper single crystal (100) face in presence of chloride ions

Observations of copper electrodeposits on to the (100) plane of copper was made from highly purified solutions of copper sulphate containing known concentration of hydrochloric acid from 10^?10 to 10^?1 m/L. In pure solutions at current densities of 5 and 10 mA/cm.² layers and pyramids were noticed. In the presence of hydrochloric acid of concentration 10^?9 to 10^?5 m/L there is a gradual decrease of distance between successive steps. At 10^?4 m/L of HCl there was the breaking of layers giving rise to ridge type of growth. With the increase of concentration to 3·5×10^?3 m/L pyramids appear again. On increasing the concentration of HCl to 10^?2 m/L there was the formation of triangular pyramids of cuprous chloride and on still increasing the concentration, polycrystalline type of deposit was noticed. The transition from layer to ridge, ridge to pyramids and to polycrystalline deposit occurs at all c.d. studied but the critical concentration of HCl needed for the transition depends upon the current density.     

On the global dimension of an algebra

Let algebra R = Λ/P, where Λ is a free algebra over a field w. gl. dim R: = {min n ¦? R-modules X, Y, Tor _n+1 ^R (X, Y)=0}. In order that w. gl. dim R≤2n (w. gl. dim R≤2n+1), it is necessary and sufficient that, for any two ideals of algebra Λ, a left ideal A and a right ideal B, containing ideal P, the following equation holds: $$AP^n \cap P^n B = AP^n B + P^{n + 1} (AP^n B \cap P^{n + 1} = AP^{n + 1} + P^{n + 1} B).$$      

Raman spectrum of dimethyl sulfoxide (DMSO) and the influence of solvents

The Raman spectrum of DMSO is recorded with a Hilger two-prism spectrograph andλ 4358 Å excitation. In addition to all the Raman lines reported earlier, six new lines at 898, 925, 1223, 1309, 2811 and 2871 cm.^?1 are observed and tentative assignments are given. The influence of solvents (CCl₄, CHCl₃, CH₃COOH) on the S=O bond is also studied. A shift from the liquid phase value,i.e., 1043 cm.^?1 to 1054, 1052 and 1009 cm.^?1 in the respective solvents is observed. The possibilities of association effects and hydrogen bonding are discussed.     

Infrared absorption spectra of some lanthanide acetylacetonate complexes

The infrared absorption spectra of 12 lanthanide acetylacetonate complexes were measured in the region 400–2000 cm^?1 and discussed. Assignments of the bands especially those due to metal-oxygen (M—O), C=O and C=C stretching vibration is given. It is found that the band at 530 ± 5 cm^?1 is due mainly to Ln—O stretching vibration. In the carbonyl region, it is confirmed that the band at lower frequency is a C=C stretching vibration while that at higher frequency is due to C=O stretching vibration. Integral intensities for the M—O, C=O and C=C stretching vibrations were calculated in KB₁ and CHCl₃ solutions. The variation of the intensities of the M—O bands witn complexed cation were discussed in terms of crystal field stabilization energy (CFSE).     

Mixed complexes of iron (III)—thiocyanate with some nitrogen and oxygen donors and their analytical applications

Methods for the determination of iron (III) as thiocyanate complex in the presence of neutral donors like isoquinoline and antipyrine have been developed. The two methods are of equal sensitivity (ε=18,000±100 lit. mole^?1 cm^?1) but operate at widely different hydrogen ion concentrations ranging from 10^?5 N(pH 5·0) to 7N. The interference of various foreign substances has been studied in the two methods. The application of these methods in the analysis of alloys and commercial HCl for iron has been explored and the composition of the extracting species established.     

Integrability properties of the maximal operator on partial sums of Fourier series

In the present work we extend a result ofP. Sjölin on the integrability properties of the maximal operator on partial sums of Fourier Series,S ^*. We actually show that the result is applicable to more general operators and could be considered as an abstract extrapolation principle.     

Torsion points on elliptic curves with given j-invariant

Let E be an elliptic curve defined overQ, and let T(E) denote the group ofQ-rational torsion points on E. In this article an explicit method for computing T(E) for all E with a given j-invariant j is given. In particular, if j≠0, 2⁶ 3³ and E is defined by Y²=X³+AD²X+BD³ put into standard form with D its minimal D-factor, then a necessary condition that E possessQ-rational torsion points of order greater than 2 is that D|(2²A³+3³B²).     

γ-rays from discrete radio sources

The fluxes of low energy (～100 MeV) and high energy (～5×10¹² eV)γ-rays from intense radio sources have been calculated under the hypothesis that radio electrons are continuously produced through nuclear collisions. The effect of expansion of the source which gives rise to a decrease in production rate with time has been taken into account in these calculations. It is found that the fluxes expected from nuclear collision process are generally higher than the fluxes from other processes like bremstrahlung and inverse compton scattering by factors of 10 or more. While the calculated fluxes ofγ-rays of energy >100 MeV are less than the observed upper limits for all the processes, the fluxes calculated for nuclear collision process for E>5×10¹² eV, exceed the experimental upper limits for Crab, Cas A and the jet in Virgo A. More sensitive experiments should be able to decide whether the nuclear collision process is ruled out for low energies as well: in this respect Cas A seems to be the most promising source.     

Large time behavior of solutions of a dissipative semilnear heat equation

We study the current of the Pauli operator in a strong constant magnetic field. We prove that in the semi-classical limit the persistent current and the current from the interaction of the spin with the magnetic field cancel, in the case where the magnetic field is very strong. Furthermore we calculate the next term in the asymptotics and estimate the error. Finally, we discuss the connection between this work and the semi-classical estimate of the energy in strong magnetic fields proved by Lieb, Solovej and Yngvason [8] Lieb, E., Solovej, J. P. and Yngvason, J. 1994. Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions. Commun. Math. Phys., 161: 77–124. [Crossref], [Web of Science ®] , [Google Scholar].

     

An OpenMP version of the parallel algorithm for calculation of unsteady gas flow through porous objects with energy sources: Analysis and application

Gas flows in the gravity field through the porous objects with energy sources, which may originate from the natural or man-caused disasters, are investigated. An OpenMP version of the parallel algorithm has been developed for calculating unsteady 2D gas flows through porous self-heating media of complex subsurface geometries. The structure of the sequential algorithm and the transition from it to the OpenMP version are described; the performance and efficiency of parallelization are analyzed. Unsteady gas flows through axisymmetric porous self-heating objects with a partial closure of the object outlet (with a top cover) are investigated by means of the developed parallel algorithm. The influence of the partial closure of the object outlet on the cooling process of the porous objects with a nonuniform distribution of heat sources is analyzed.     

On muons of energy ≥150 Gev in association with EAS

Preliminary results of an investigation on energetic penetrating particles (muons) of energy ≥150 Gev are reported. These particles are recorded at a depth of 580 m.w.e. underground, in association with extensive air showers (EAS) of size 10⁴–10⁵ particles. Neon flash tube technique is being used to study detailed characteristics of these energetic particles. The probability of a muon being accompanied by an electron shower, produced in rock and lead absorber, is compared with the results of other workers. Two cases of large double bursts have been recorded. Some of the possible interpretations have been given. About 16% of the total events observed have more than one particle.     

Infinitesimal CR automorphisms of rigid hypersurfaces in C2

In this paper, we describe the space of infinitesimal CR automorphisms of a rigid, real analytic, real hypersurface in C². We use these results to obtain a geometric characterization of the homogeneous hypersurfaces. Here, a hypersurface is called homogeneous if it is equivalent to one given by an equation of the formIm(w) =p wherep is a homogeneous polynomial inz and \(\bar z\) . This gives an answer in dimension 2 to a problem posed by Linda Rothschild. We give another answer, in terms of a normal form for the defining function, in our paper “A normal form for rigid hypersurfaces in C².”     

Further results on the group inverse of some anti-triangular block matrices

Suppose ? is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ? and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA=C; (ii) , where B ^? exists and BA=BAB ^? B. The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010). Some results in special cases are also generalized to any ring.