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.     

On some educational and psychological aspects of problem solving

An attempt has been made to present an overview of various learning theories keeping in view the psychological aspect of problem solving behaviours of children and to explain the processes by which problem solving skills are acquired and applied. The four important research variables—as described by Lester (task, subject, process and instructional variables)—have been discussed and some research questions have been formulated for further research investigations in the area of problem solving.     

Dielectric relaxation studies in 5CB nematic liquid crystal at 9 GHz under the influence of external magnetic field using microwave cavity spectrometer

Resonance width, shift in resonance frequency, relaxation time and activation energy of 5CB nematic liquid crystal are measured using microwave cavity technique under the influence of an external magnetic field at 9 GHz and at different temperatures. The dielectric response in liquid crystal at different temperatures and the effects of applied magnetic field on transition temperatures are studied in the present work. The technique needs a small quantity (< 0.001 cm³) of the sample and provides fruitful information about the macroscopic structure of the liquid crystal.     

Energy-dispersive X-ray fluorescence – A tool for interdisciplinary research

Trace elements have been at the focus of attention for decades with considerable emphasis on their role in biology and biomedical sciences, environmental sciences, geology, archaeology and material sciences. They comprise a large number of elements, some having essential physiological functions, whereas others are toxic, mutagenic or carcinogenic. A few even have antiproliferative and anticarciniogenic properties. The advent of various instrumental techniques and sophisticated instrumentations has made their detection to very low limits possible, making this a very important multidisciplinary study. Among these techniques the energy-dispersive X-ray fluorescence (EDXRF) technique is being widely used for trace element detection in various fields of science. Keeping the importance of trace elements in mind, the Kolkata centre of UGC-DAE Consortium for Scientific Research initiated several research schemes in different fields of trace element research using various techniques, EDXRF being one of the main techniques. A Xenemetrix (erstwhile Jordan Valley) EX 3600 EDXRF spectrometer is being used to carry out the research. This presentation aims to highlight some of the very recent applications of EDXRF in the study of the role of trace elements in pre-cancerous tissues, medicinal plants and also in some environmental studies.     

The effect of finite response–time in coupled dynamical systems

The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval τ. A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous (τ?=?0) case. The critical coupling strength at which synchronization sets in is found to increase with τ. The systems explored are the chaotic Rössler and limit cycle (the Landau–Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization.     

Magnetic behaviour of AuFe and NiMo alloys

We study the electronic structure and a mean-field phase analysis based on the pair–pair energies derived from first-principles electronic structure calculations of AuFe and NiMo alloys. We have used the tight-binding linear muffin-tin orbitals-based augmented space recursion (TB-LMTO-ASR) method to do so. We investigate different behaviours of the two alloy systems by mapping the problems onto equivalent Ising models and then discuss the magnetic phase diagrams using the calculated pair energies. All three phases: paramagnetic, random ferromagnetic and spin glass, have been studied.     

Accretion,primordial black holes and standard cosmology

Primordial black holes evaporate due to Hawking radiation. We find that the evaporation times of primordial black holes increase when accretion of radiation is included. Thus, depending on accretion efficiency, more primordial black holes are existing today, which strengthens the conjecture that the primordial black holes are the proper candidates for dark matter.