An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss

A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given.     

Ionic liquids as reagents and solvents in conjunction with microwave heating: rapid synthesis of alkyl halides from alcohols and nitriles from aryl halides

We show that using ionic liquids as reagents in conjunction with microwave heating it is possible to prepare primary alkyl halides from the corresponding alcohols rapidly. Using ionic liquids as solvents in conjunction with microwave heating it is possible to prepare aryl nitriles from the corresponding aryl bromides or iodides. The scope and limitations of using microwave-promotion as a tool in these reactions is discussed.     

Tetrakis(4-N,N-dimethylaminobenzene)porphyrinato]manganese(III) acetate as a novel carrier for a selective iodide PVC membrane electrode.

[5,10,15,20-Tetrakis(4-N,N-dimethylaminobenzene)porphyrinato]Mn(III) acetate (MnTDPAc) was applied as an ionophore for an iodide-selective PVC membrane electrode. The influences of the membrane composition, pH of the test solution and foreign ions on the electrode performance were investigated. The sensor exhibited not only excellent selectivity to iodide ion compared to Cl- and lipophilic anions such as ClO4- and salicylate, but also a Nernstian response with a slope of -59.4 +/- 1.2 mV per decade for iodide ions over a wide concentration range from 1.0 x 10(-2) to 7.5 x 10(-6) M at 25 degrees C. The potentiometric response was independent of the pH of the solution in the pH range of 2 - 8. The electrode could be used for at least 2 months without any considerable divergence in the potential. Good selectivity for iodide ion, a very short response time, simple preparation and relatively long-term stability were the silent characteristics of this electrode. It was successfully used as an indicator electrode in the potentiometric titration of iodide ions, and also in the determination of iodide from seawater samples and drug formulations.     

Visualisation and proof: a brief survey of philosophical perspectives

The contribution of visualisation to mathematics and to mathematics education raises a number of questions of an epistemological nature. This paper is a brief survey of the ways in which visualisation is discussed in the literature on the philosophy of mathematics. The survey is not exhaustive, but pays special attention to the ways in which visualisation is thought to be useful to some aspects of mathematical proof, in particular the ones connected with explanation and justification.     

Texture and electronic activity of grain boundaries in Cu(In,Ga)Se2 thin films

The influence of different film textures on the electronic properties of polycrystalline Cu(In,Ga)Se₂ absorbers is studied by measuring the laterally resolved optoelectronic properties of differently textured Cu(In,Ga)Se₂ films with Kelvin probe force microscopy and cathodoluminescence. The grain boundaries in (112)- and (220/204)-textured films behave differently. The work-function profile measured with the Kelvin probe across a grain boundary in (112)-textured films shows a dip indicating positive charges at the grain boundaries. In panchromatic cathodoluminescence mappings in a transmission electron microscope, such grain boundaries appear dark, i.e. the strongly reduced luminescence indicates that the grain boundaries represent strong non-radiative recombination centers. In contrast, grain boundaries in (220/204)-textured films give rise to a dip or a step in the work function indicating slightly negative charge or neutrality. Cathodoluminescence is reduced at such grain boundaries, but less dramatically than in the (112)-textured case. However, when Na is present in the (220/204)-textured films, the grain boundaries are almost invisible in cathodoluminescence mappings. This strong passivating action of Na occurs only in the (220/204)-textured films, due to a particular grain-boundary population. In (112)-textured films and films without pronounced texture, this passivation effect is much less noticeable. PACS 73.50.Gr; 73.61.Ga; 78.60.Hk; 87.64.Dt     

Teaching proof in the context of physics

This paper describes an application of statics to geometrical proofs in the classroom. The aim of the study was to find out whether the use of concepts and arguments from statics can help students understand and produce proofs of geometrical theorems. The two theorems studied were (1) that the medians in a triangle meet at a single point which is the centre of gravity of the triangle, and (2) the Varignon theorem, that the lines joining the midpoints of successive sides of a quadrilateral form a parallelogram. The classroom experiment showed that most students were successful in using arguments from statics in their proofs, and that they gained a better understanding of the theorems. These findings lend support to the claim that the introduction of statics helps students produce proofs and grasp their meaning.     

Nonlinear electrohydrodynamic instability of a finitely conducting cylinder: Effect of interfacial surface charges

The nonlinear electrohydrodynamic stability of cylindrical interface, supporting surface charge, among two conducting fluids is investigated. The two fluids are subjected to a radial electric field. The analysis based on the multiple scale technique. It is shown that the evolution of the amplitude is governed by two partial differential equations. These equations are combined to yield two alternate Schrödinger equations with cubic nonlinearity. One of which calculates the nonlinear cutoff electric field, separating stable and unstable disturbances, while the other is used to analyze the stability of the system. The stability criteria are analytically discussed and numerically confirmed. Numerical calculations resulted in set of graphs to indicate the stability picture of the considered system.