An alternative approach to determine the spot-size of a multi-mode laser beam and its application to diode laser beams

An alternative approach is suggested to determine the spot-size of a multi-mode laser beam. It has been shown by simulations that the suggested approach can give the beam quality factor and characteristic radius with less than 5% error. Unlike the power content method, the proposed method is applicable to the beams even with diameter one tenth of the CCD size. The new approach has been applied to a multi-mode diode laser output and it is shown that the ABCD matrix analysis can be used for beam propagation, with the measured parameters of the laser.     

Crystal base andq-vertex operators

Theq-deformed vertex operators of Frenkel and Reshetikhin are studied in the framework of Kashiwara's crystal base theory. It is shown that the vertex operators preserve the crystal structure, and are naturally labeled by the global crystal base. As an application the one point functions are calculated for the associated elliptic RSOS models, following the scheme of Kang et al. developed for the trigonometric vertex models.Dedicated to Huzihiro Araki     

An example of an iron (III) porphyrin with spin mixed ground state

The paper reports synthesis and physical characterisation of a new iron(III) porphyrin which shows unusual features of quantum mechanically mixed ground state in its magnetic properties. Magnetic susceptibility (300−3·6 K) and M?ssbauer spectroscopy (300−77 K) studies of the compound are described and discussed with reference to some bacterial ferricytochromeC' exhibiting similar spin-mixed ground state.     

Preparation and characterization of MgB2 superconductor

The MgB₂ superconductor, synthesized using solid-state and liquid-phase sintering methods, have been characterized for various properties. The upper critical field, irreversibility line and critical current density have been determined using magnetization data. The current-voltage characteristics recorded under an applied magnetic field revealed the existence of vortex glass transition. The surface analysis using X-ray photoelectron spectroscopy shows that MgB₂ is sensitive to atmospheric degradation.     

The algebraic structure of the Onsager algebra

We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the finite-dimensional representations. We also discuss the solvable algebra aspect of the Onsager algebra through the formal theory.     

Nuclear orbiting and anomalies in nuclear reactions

In this paper, we report our measurements of back-angle oxygen and carbon particle yields from ¹⁶O+⁸⁹Y, ¹²C+⁹³Nb reactions forming the same compound nucleus ¹⁰⁵Ag at the same excitation energy and spin distribution. We find anomalously large oxygen yield and entrance channel dependence at high excitation energies from ¹⁶O+⁸⁹Y reaction implying formation of a dinuclear orbiting complex. Possible connection between nuclear orbiting and fast fission is also discussed.     

One-dimensional configuration sums in vertex models and affine Lie algebra characters

We study the local state probabilities of the vertex models in the face formulation associated with the simple Lie algebras X _n =A _n, B _n, C _n, D _n. The corner transfer matrix method expresses them in terms of one-dimensional configuration sums. We show that the latter are the string functions of X _n ⁽¹⁾ modules. We also present similar results for the restricted face models of types B _n ⁽¹⁾, C _n ⁽¹⁾, D _n ⁽¹⁾.     

Influence of magnetic (Fe) and non-magnetic (Ga) ion doping at Mn-site on the transport and magnetic properties of La0.7Ca0.3MnO3

The modifications in electrical and magnetic properties of polycrystalline bulk La_0.7Ca_0.3Mn_1−xT_xO₃ (T=Fe, Ga) samples at relatively higher doping concentration (x=0.08-0.12) are investigated. All the synthesized, single phase samples were subjected to resistivity measurements in the temperature range 50-300 K. No insulator-metal transition (T_P) was observed for Fe doped samples with x=0.12. For all the other samples the transition temperature decreased with increase in doping concentration. The small polaron hoping energy was found to increase, rather slowly, with increase in doping concentration. The effect on magnetic properties is also prominently observed with respect to doping element and doping concentration. Interestingly, with the increase in doping concentration, the Curie temperature (T_C) and T_P separate out significantly indicating decoupling of electric and magnetic properties. Changes in these properties have been analyzed on the basis of magnetic disorder introduced in the system due to the magnetic and nonmagnetic nature of these ions rather than strong lattice effects which is insignificant due to similar ionic radii of Fe⁺³ and Ga⁺³ when compared to that of Mn⁺³.     

A new realization of the basic representation of A n (1)

The basic representation of A _n ⁽¹⁾ is constructed on a space of paths in (n + 1). A q-analogue of this is also presented. Our construction gives a Lie theoretical proof of a combinatorial identity used in the evaluation of the local state probabilities for a class of solvable lattice models.