The application of a vehicle routing model to a waste-collection problem: two case studies

In this paper we suggest a unique model for estimating the operating cost of each of three waste-collection systems. Under the traditional system, which is widely used, waste is typically collected in plastic bags and a three-man crew is needed on each vehicle. The other two systems require a one-man crew for vehicle collecting street containers. The side-loader system with fixed body automatically empties street containers into the vehicle body and empties the load at the disposal site. The side-loader system with demountable body allows the separation of the waste collection phase from transport to the disposal site, since the vehicle body can be demounted. We also present two case studies and show how the estimation of operating costs is a critical issue in decisions regarding the type of system to be used for waste collection.     

The study and applications of photochemical-dynamical gravity wave model II

A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime.     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

Polyhedral <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">2</Emphasis></Subscript>

 Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional case provides interesting classes of groups. Received: 13 December 2001 / Revised version: 24 June 2002 The second author was supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107 Mathematics Subject Classification (2000): 14L27, 14M25, 19C09, 52B20     

Singularity conjecture and constructions of Jacobi forms

This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of Rankin-typeL-series.     

Time Evolution of Vibration-Induced Excited State Decay

A simple model consisting of two electronic levels and one vibrational mode (phonon) was theoretically studied. The electronic-vibrational interaction was linear in the vibrational displacement. The vibrational mode was taken in the harmonic approximation and was attached to the thermal bath formed by the ambient environment. The kinetic constants of the vibrational dissipation were of the second order in the vibrational-bath coupling and were taken in the Markovian limit. Although, depending on the parameters of the model, different curves of the non-radiative vibration-induced excited state decay were obtained, in general, three time intervals, corresponding to different physical behaviour, were found. In the short-time interval, small oscillations superimposed on the excited state decay were observed. They were determined by the vibrational frequency and influenced by electronic-vibrational coupling. In the middle-time interval, almost quasi-exponential decay was detected; its rate constant increased with stronger electronic-vibrational interaction and speed of vibrational relaxation. In the long-time interval, the decay was very slow and, under special conditions, even an asymptotic non-zero excited state population was observed. Its value increased with the strength of the off-diagonal electron-vibrational coupling. Links of the parameters of the model with quantum chemical terms were estimated.     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.     

Instability of quark matter core in a compact newborn neutron star with moderately strong magnetic field

It is explicitly shown that if phase transition occurs at the core of a newborn neutron star with moderately strong magnetic field strength, which populates only the electron’s Landau levels, then in the β -equilibrium condition, the quark core is energetically much more unstable than the neutron matter of identical physical condition.