On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

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.     

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.     

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.     

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.     

On the Integrability Conditions for Some Structures Related to Evolution Differential Equations

Using the result by D. Gessler, we show that any invariant variational bivector (resp., variational 2-form) on an evolution equation with nondegenerate right-hand side is Hamiltonian (resp., symplectic).     

Non-protein amino acids in peptide design

An overview of the use of non-protein amino acids in the design of conformationally well-defined peptides, based on work from the author’s laboratory, is discussed. The crystal structures of several designed oligopeptides illustrate the useα-aminoisobutyric acid (Aib) in the construction of helices, D-amino acids in the design of helix termination segments and^DPro-Xxx segments for nucleating ofβ-hairpin structures.β- andγ-amino acid residues have been used to expand the range of designed polypeptide structures. Dedicated to Professor C N R Rao on his 70th birthday     

A Clifford algebra approach to real simple Lie algebras,II: The algebras with root system BCr

Received: 14 September 2001 / in final form: 28 April 2002 // Published online: 20 March 2003     

Three-dimensional structure of Saccharomyces cerevisiae inorganic pyrophosphatase complexed with cobalt and phosphate ions

Crystals of Saccharomyces cerevisiae inorganic pyrophosphatase suitable for X-ray diffraction study were grown by cocrystallization of the enzyme with cobalt chloride and imidodiphosphate. Saccharomyces cerevisiae is a metal-dependent enzyme which catalyzes hydrolysis of inorganic pyrophosphate to orthophosphate. The three-dimensional structure of this enzyme was solved by the molecular-replacement method and refined at 1.8 Å resolution to an R factor of 19.5%. Cobalt and phosphate ions were revealed in the active centers of both identical subunits (A and B) of the pyrophosphatase molecule. In subunit B, a water molecule was found between two cobalt ions. It is believed that this water molecule acts as an attacking nucleophile in the enzymatic cleavage of the pyrophosphate bond. It was demonstrated that cobalt ions and a phosphate group occupy only part of the potential binding sites (two chemically identical and crystallographically independent subunits have different binding sites). The arrangement of ligands and the structure of the nucleophile-binding site are discussed in relation to the mechanism of action of the enzyme and the nature of the metal activator.