Julia sets of permutable Holomorphic maps

Let f and g be two permutable transcendental holomorphic maps in the plane. We shall discuss the dynamical properties of f, g and f o g and prove, among other things, that if either f has no wandering domains or f is of bounded type, then the Julia sets of f and f(g) coincide. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Cryogen-free dilution refrigerator for bolometric search of neutrinoless double beta decay (0νβ β) in 124Sn

The feasibility study for searching neutrinoless double beta decay in ¹²⁴Sn using cryogenic bolometer has been initiated. For this purpose, a custom-built cryogen-free dilution refrigerator, having a large cooling power of 1.4 mW at 120 mK, has been installed at TIFR, India. This paper describes the design, installation and performance of a cryogen-free dilution refrigerator (CFDR-1200). The performance of CFDR-1200 has been analysed using Takano’s model developed for conventional (wet) dilution refrigerators.     

Synthesis of phenanthro[a] phenazine derivatives: a novel ring structure forming discotic liquid crystals

Phenanthro[a] phenazine, a new heterocyclic ring structure of both biological and physical interest, has been prepared by coupling 1,2-phenylenediamine with triphenylene-1,2-diquinone derivatives in high yields. 2,3,6,7,10-Penta-alkoxyphenanthro[a] phenazines are mesogenic over a broad temperature range. These novel unsymmetrical, coloured, polar, heteroaromatic discotic mesogens are potential candidates for the study of conducting, photoconducting, electroluminescence, photorefrective, etc. properties.     

Precision two-photon spectroscopy of alkali elements

In this paper, we have briefly reviewed the work on two-photon spectroscopy of alkali elements and its applications. The technique of Doppler-free two-photon spectroscopy is briefly summarized. A review of various techniques adopted for measuring absolute frequencies of the atomic transitions and precision measurements of isotope shifts and hyperfine structures (HFS) is presented. Some of the recent works on precision measurements of HFS constants of 6s ² S _1/2 level of ³⁹K and ⁴¹K, 9s ² S _1/2level and 7d ² D _3/2 level of ¹³³Cs are also discussed.     

Generation of tunable 16 μm radiation from CO2 by cascade lasing

In this paper we propose a scheme to generate tunable 16 μm radiation from CO₂ molecules by cascade lasing. The stimulating 9.5 μm radiation is generated internally by the fast rotating mirror Q-switching technique. The optical scheme proposed by us uses an intracavity prism to separate the 9.5 μm and the 16 μm beams. This facilitates independent tuning of the two beams if required. In the present configuration, only the 16 μm cavity is dispersive. The 9.5 μm beam grows spontaneously in a stable semiconfocal resonator. We have developed a theoretical model to simulate the proposed scheme. The model predicts the energy and power of 16 μm radiation. The calculated values are much higher than the previously obtained experimental values. The results point out the feasibility of developing a laser system based on the theoretical design parameters presented in this paper. Such laser systems can find application in uranium isotope separation studies.     

Higher-Order (F,α,β,ρ,d,E)-Convexity in Fractional Programming

In this paper we define higher order (F,α,β,ρ,d,E)-convex function with respect to E-differentiable function K and obtain optimality conditions for nonlinear programming problem (NP) from the concept of higher order (F,α,β,ρ,d)-convexity. Here, we establish Mond-Weir and Wolfe duality for (NP) and utilize these duality in nonlinear fractional programming problem.