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.     

The determination of the past and the future of a physical system in quantum mechanics

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using unsharp measurements.This work was partly supported by the Bundesministerium für Forschung und Technologie, Bonn, the Research Institute for Theoretical Physics, Helsinki, and the University of Turku Foundation, Turku.     

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).     

Coherent States and Number-Phase Uncertainty Relations

The number-phase uncertainty relations arerevisited in view of the recent discovery of a propercovariant phase observable. The high-amplitude limits ofthe coherent-state expectations of the moment operators of the phase observable are determined and thebehavior of the number-phase uncertainty product in thatlimit is investigated.     

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.