Geometric visualization of the Brewster angle from dielectric-magnetic interface

A geometric visualization is presented for the Brewster angle for a plane wave reflecting from an interface. The surface is assumed to be isotropic but it is allowed to display both dielectric and magnetic susceptibility, and hence the Brewster (polarizing) angle can attain any value between 0 and 90^°, and can exist for both parallel and perpendicular polarizations. The geometric construction (a tetrahedron) is spanned by the basic material parameters of the surface. The Brewster angle appears in one of the faces of the tetrahedron.     

Relativistic Notion of Mass and a Resolution of a Conflict Between Schopenhauer and Hegel

We discuss a mass change that has its origin in the action of forces on an object. This phenomenon, well-known in the context of quantum field theory (mass renormalization), can be discussed systematically in both classical and quantum mechanics in a framework given by Stückelberg. We employ this framework to resolve an interesting conflict of opinions between Schopenhauer and Hegel in the mid-19th century. We show that Hegel, Kant, and Schopenhauer demonstrated remarkable prescience in their views as seen from a modern perspective.     

Equilibrium in Queueing Systems with Complementary Products

We study a model of a queueing system with two complementary products/services. In our model, there is one M/M/1 system and another facility that provides instantaneous service. The two services are complementary and the customer has no benefit from obtaining just one of them. We investigate the model under various price structures and ownership assumptions.AMS subject classification: 90B22, 91A10The authors are equal in their contribution to this paper. This paper is submitted by the first author to the Tokyo Institute of Technology as partial fulfillment of the requirements for the Ph.D. program in the Department of Value and Decision Sciences, and the order of names was chosen in compliance with program conditions. This research was supported by the Israel Science Foundation (grant No. 237/02).     

Weighted extended b-splines for one-dimensional electromagnetic problems

This paper considers the weighted extended b-splines as basis function for finite element method in electromagnetics and compares with the standard finite element method applied to the two-point boundary value problems with different boundary conditions. This new approach, which provides more accurate results than standard finite element method, is presented to compare other numerical techniques and applied to one-dimensional electromagnetic problems. Computed results are compared with other numerical results in literature.     

The Effect of Boundary Conditions on Gas-phase Synthesised Silver Nanoparticles

We have prepared spherical non-agglomerated silver nanoparticles by an evaporation–condensation–dilution/cooling technique. Silver was evaporated from a crucible in a tubular flow reactor. A porous tube diluter was used to quench the carrier gas at the outlet of the reactor to enhance the formation of small particles and to suppress agglomeration and other particle growth mechanisms. The number size distribution of the prepared particles was measured with a differential mobility analyser–condensation nucleus counter combination and the size and the shape of the particles were analysed with transmission electron microscope. The system was modelled using a sectional aerosol dynamics computer code to estimate the importance of different aerosol processes. In all conditions the particles obtained were non-agglomerated and spherical. The mean particle diameter varied from 4 to 10-nm depending on boundary conditions. From the modelling studies it can be concluded that the nucleation rate is the most important parameter controlling the final particle size.     

Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.     

Indoloquinolizidine synthesis : Stereochemistry and mechanism of cyclisation

A stereocontrolled cyclisation of suitably substituted indole derivatives can be explained by the revised Pictet-Spengler reaction mechanism.     

Quantum-chemical gas-phase calculations on the protonation forms oftrans- andcis-urocanic acid

The neutral, cationic, and anionic structures of both prototropic tautomers oftrans- andcis-urocanic acid [(E)- and (Z)-3-(1H-imidazol-4(5)-yl)propenoic acid, respectively] were studied by using semiempirical andab initio gas-phase calculations. Potential energy surfaces of the structures were calculated by using the semiempirical AM1 method, and the geometries corresponding to global minima on these surfaces were optimized up to the MP2/6-31G^* level of theory. The calculated protonation forms of each urocanic acid isomer have a planar molecular structure due to a delocalized -electron system, and all of them prefer thes-trans conformation with respect to the bond between the imidazole and the propenoic acid moieties. Thecis-urocanic acid structures are stabilized by an intramolecular hydrogen bond. The chargedcis-urocanic acid isomers have a lower molecular energy than the correspondingtrans-isomers, whereas the neutral molecules have, after inclusion of thermodynamic corrections, approximately the same energy. The cationic urocanic acid structures have about 2500 kJ mol^–1 lower energy than the anionic ones and about 1000 kJ mol^–1 lower energy than the neutral ones. The nonzwitterionic forms of the neutral urocanic acid isomers have about 200 kJ mol^–1 lower energy than the zwitterionic ones. These energy differences are explained by the proton affinities of the imidazole and the propenoic acid moieties of the urocanic acid structures.     

Thermal degradation studies of alkyl-imidazolium salts and their application in nanocomposites

Increasing the thermal stability of organically-modified layered silicates is one of the key points in the successful technical application of polymer-layered silicate nanocomposites on the industrial scale. To circumvent the detrimental effect of the lower thermal stability of alkyl ammonium-treated montmorillonite, a series of alkyl-imidazolium molten salts were prepared and characterized by elemental analysis, thermogravimetry (TGA) and thermal desorption mass spectroscopy (TDMS). The effect of counter ion, alkyl chain length and structural isomerism on the thermal stability of the imidazolium salts was investigated. Alkyl-imidazolium-treated montmorillonite clays were prepared by ion exchange of the imidazolium salts with Na-montmorillonite. These organically-modified clays were characterized by X-ray diffraction (XRD), TDMS and thermogravimetry coupled with Fourier transform infrared spectroscopy (TGA-FTIR), and compared to the conventional quaternary alkyl ammonium montmorillonite. Results indicate that the counter ion has an effect on the thermal stability of the imidazolium salts, and that imidazolium salts with PF₆⁻, N(SO₂CF₃)₂⁻ and BF₄⁻ anions are thermally more stable than the halide salts. A relationship was observed between the chain length of the alkyl group and the thermo-oxidative stability; as the chain length increased from propyl, butyl, decyl, hexadecyl, octadecyl to eicosyl, the stability decreased. The results also show that the imidazolium-treated montmorillonite has greater thermal stability compared to the imidazolium halide. Analysis of the decomposition products by FTIR provides an insight about the decomposition products which are water, carbon dioxide and hydrocarbons.