On the Long-Time Behavior of the Quantum Fokker-Planck Equation

We analyze the long-time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type diffusion operator, subject to confining potentials of harmonic oscillator type. We establish the existence and uniqueness of a non-equilibrium steady state for the corresponding dynamics. Further, using a (classical) convex Sobolev inequality, we prove an optimal exponential rate of decay towards this state and additionally give precise dispersion estimates in those cases, where no stationary state exists.     

Carousels,Zindler curves and the floating body problem

A carousel is a dynamical system that describes the movement of an equilateral linkage in which the midpoint of each rod travels parallel to it. They are closely related to the floating body problem. We prove, using the work of Auerbach, that any figure that floats in equilibrium in every position is drawn by a carousel. Of special interest are such figures with rational perimetral density of the floating chords, which are then drawn by carousels. In particular, we prove that for some perimetral densities the only such figure is the circle, as the problem suggests.     

Assessing Investigative Skill Development in Inquiry‐Based and Traditional College Science Laboratory Courses

A laboratory practical examination was used to compare the investigative skills developed in two different types of general‐chemistry laboratory courses. Science and engineering majors (SEM) in the control group used a traditional verification approach (SEM‐Ctrl), whereas those in the treatment group learned from an innovative, inquiry‐based approach (SEM‐Trt). A scoring rubric was developed from their examination sheets to assess six component investigative skills. Results indicated that SEM students in the SEM‐Trt group scored significantly higher than those in SEM‐Ctrl for all six skills. Furthermore, nursing and applied science majors (NonSEM) in the inquiry‐based group (NonSEM‐Trt) wrote significantly better discussions than did SEM students in SEM‐Ctrl group. Overall, competency at the mid‐range level of laboratory skills was attained by most SEM‐Trt students (72.5%) but by only 30.5% of SEM‐Ctrl and 28.6% of NonSEM‐Trt students. Apparently, during the semester students in the SEM‐Trt group were able to use the inquiry‐based method effectively to combine chemical tasks with writing tasks and postlaboratory discussions. One implication of this study for science instructors is that practical examinations can provide useful feedback regarding the quality of the laboratory experience. Another implication is that this study provides evidence for the use of the innovative inquiry‐based laboratory approach to support student learning of high‐level investigative skills. However, students' requisite background knowledge must match the level of these skills.     

A flexible and generic approach to dynamic modelling of supply chains

In this paper, we present a new modelling approach for realistic supply chain simulation. The model provides an experimental environment for informed comparison between different supply chain policies. A basic simulation model for a generic node, from which a supply chain network can be built, has been developed using an object-oriented approach. This generic model allows the incorporation of the information and physical systems and decision-making policies used by each node. The object-oriented approach gives the flexibility in specifying the supply chain configuration and operation decisions, and policies. Stochastic simulations are achieved by applying Latin Supercube Sampling to the uncertain variables in descending order of importance, which reduces the number of simulations required. We also present a case study to show that the model is applicable to a real-life situation for dynamic stochastic studies.     

Allocating electricity transmission costs through tracing: a game-theoretic rationale

Tracing is a method of assigning flows in an electricity network to particular generators and loads, assuming perfect mixing at each node. It can be used to assign costs to transmission users. We show that the resulting allocation is equal to the Shapley value of an equivalent co-operative game.     

Polynomial Quantization on Rank One Para-Hermitian Symmetric Spaces

We construct the polynomial quantization on the space G/H where G=SL(n,R),H=GL(n–1,R). It is a variant of quantization in the spirit of Berezin. In our case covariant and contravariant symbols are polynomials on G/H. We introduce a multiplication of covariant symbols, establish the correspondence principle, study transformations of symbols (the Berezin transform) and of operators. We write a full asymptotic decomposition of the Berezin transform.     

Gauss Algebras

A special class of associative algebras is introduced and studied. A criteria of semisimplicity for suitable category of modules is obtained.     

Some Problems of Harmonic Analysis on Reductive Groups

An algebraic approach to harmonic analysis on reductive Lie groups is proposed. The case of complex semisimple Lie groups is considered in details. Some problems for real reductive Lie groups are discussed.