Algebraic curve in the unit ball in ℂ2 that passes through the origin and all of whose boundary components are arbitrarily short

A negative answer is given to the following question of A.G. Vitushkin: Does there exist a nontrivial lower bound for the length of the maximal component of intersection of the unit sphere and an algebraic curve passing through the origin. Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Vol. 253, pp. 135–157. To the memory of Anatolii Georgievich Vitushkin     

Superior refractive index tailoring properties in composite ZrO2/SiO2 thin film systems achieved through reactive electron beam codeposition process

Composite optical thin-film materials have received a significant amount of interest in order to relieve the material constraints on refractive indices as well as reducing the number of layers required in optical coating design. Amongst others binary zirconia-silica composite thin films have attracted considerable attentions due to their several favorable opto-mechanical properties. In the present studies such a composite system under certain compositional mixings displayed both refractive index and band gap supremacy over pure zirconia films violating the most popular Moss rule. This unexpected evolution has several practical applications one of which can be directly employed in extending the range of tunability of the refractive index. Besides, the probing of such a novel evolution through the analysis of ellipsometric refractive index modeling and morphological correlation functions has revealed several novel as well as superior microstructural properties in the composite thin film systems. All these characterization and analysis techniques distinctly indicate a strong interrelation between the microstructural ordering and superior optical properties of the present zirconia-silica codeposited composites.     

Influence of Cd and Cr substitutions on the magnetization and permeability of magnesium ferrites

Magnetization and permeability of polycrystalline ferrites with general formula Cd_xMg_1−xFe_2−yCr_yO₄ (x=0, 0.2, 0.4, 0.6, 0.8, 1.0; y=0, 0.05 and 0.10) were studied. Study of saturation magnetization reveals that the Neel's two-sublattice model exists upto x=0.4, for y=0, 0.05 and 0.1 and a three-sublattice model (YK-model) is predominant for x>0.4 and y=0, 0.05 and 0.10. The saturation magnetization and magnetic moment were found to decrease with the increase in Cr³⁺ contents, which is attributed to the dilution of B–B site interaction. Variation of initial permeability with temperature revealed the long-range ferromagnetic ordering in the compounds with x=0.4. The sample with x?0.4 and y=0, 0.05 and 0.10 showed peaking behavior near Curie temperature, which is attributed to the decrease of anisotropy constant K₁ to zero. Low-frequency dispersion of initial permeability suggests domain wall displacement. Addition of Cd²⁺ resulted in a sharp decrease in Curie temperature. With the addition of Cr³⁺, initial permeability was found to decrease.     

System dependence of the correlation function of IMFs in Ar + Sn at 35 MeV/u

The inclusive reduced velocity correlation functions of the intermediate mass fragments were measured in the reactions of ³⁶Ar + ^112,124Sn at 35 MeV/u. The anti-correlation is observed to be stronger in ³⁶Ar + ¹²⁴Sn system than that in ³⁶Ar + ¹¹²Sn. The difference of the correlation functions between the two reactions is mainly contributed by the particle pairs with high momenta. A three body Coulomb repulsive trajectory model is employed to calculate the emission time scale of the IMFs for the two systems. The time scale is 150 fm/c in ³⁶Ar + ¹¹²Sn and 120 fm/c in the ³⁶Ar + ¹²⁴Sn, respectively.     

A power-law distribution for tenure lengths of sports managers

We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.     

Students’ Reasoning About One-Object Stochastic Phenomena in an ICT-Environment

This paper focuses on the different ways in which students in lower secondary school (14–16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis was gathered from two interview sessions. The analysis of the interaction is based on constructivist principles on learning; i.e. we adopted a student-oriented perspective, taking into consideration the different ways students try to make sense of chance encounters. Our results show how some students give priority to geometrical and physical concerns, and we discuss how seeking causal explanations of random phenomena may have encouraged this. With respect to numerically oriented models a division strategy appears to stand out as the preferred one.     

A short and efficient synthesis of grisan

A three-step synthesis of grisan (spiro[benzofuran-2(3H)-1′-cyclohexane]), using methoxymethoxybenzene and 1-chloromethylcyclohexene as starting materials, is described.     

Preparation and electrical characterization of (PVC + KBrO3) polymer electrolytes for solid state battery applications

This paper presents results of studies on dc electrical conductivity and transference number measurements on potassium bromate (KBrO₃) complexed polyvinyl chloride (PVC) films prepared by solution cast technique. Temperature dependence of dc electrical conductivity and transference number data indicated the dominance of ion type charge transport in these specimens. The magnitude of conductivity increased with increase in concentration of the salt and temperature. Using this (PVC + KBrO₃) electrolyte, solid-state electrochemical cells were fabricated, and their discharge profiles were studied under a constant load of 100 kΩ. Several cell profiles such as open circuit voltage, short circuit current, power density, and energy density associated with these cells were evaluated and were reported. The features of complexation of the electrolytes were studied by X-ray diffraction and Fourier transform infrared spectroscopy. Paper presented at the Third International Conference on Ionic Devices (ICID 2006), Chennai, Tamilnadu, India, Dec. 7–9, 2006     

Choice of modelling technique for evaluating health care interventions

Economic evaluation, such as cost effectiveness analysis, provides a method for comparing healthcare interventions. These evaluations often use modelling techniques such as decision trees, Markov processes and discrete event simulations (DES). With the aid of examples from coronary heart disease, the use of these techniques in different health care situations is discussed. Guidelines for the choice of modelling technique are developed according to the characteristics of the health care intervention.The choice of modelling technique is shown to depend on the acceptance of the modelling technique, model ‘error’, model appropriateness, dimensionality and ease and speed of model development. Generally decision trees are suitable for acute interventions but they cannot model recursion and Markov models are suitable for simple chronic interventions. It is further recommended that population based models be used in order to provide health care outcomes for the likely cost, health benefits and cost effectiveness of the intervention. The population approach will complicate the construction of the model. DES will allow the modeller to construct more complex, dynamic and accurate systems but these may involve a corresponding increase in development time and expense. The modeller will need to make a judgement on the necessary complexity of the model in terms of interaction of individuals and model size and whether queuing for resources, resource constraints or the interactions between individuals are significant issues in the health care system.