A note to the paper “An efficient algorithm for linear programming” of V Ch Venkaiah

In Venkaiah [1] an algorithm for solving linear optimization problems based on the idea of the projective algorithm of Karmarkar, is proposed. The essential simplification in the new algorithm is the use of a fixed projection operator. In this way the algorithm requires onlyO(n ² ) operations to obtain a sufficient exact solution. In this note it is shown that in some special cases the algorithm of Venkaiah yields a feasible solution that is far from the optimal one.     

Theory of Non-Equilibrium Stationary States as a Theory of Resonances

We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized by two numbers, T ₁ and T ₂ (‘reservoir temperatures’). If T ₁ ≠ T ₂, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T ₁ and T ₂, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T ₁,T ₂) > g ^{2 + α}, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions. Submitted: March 20, 2006. Revised: March 19, 2007. Accepted: May 11, 2007. Marco Merkli: Partly supported by an NSERC PDF, the Institute of Theoretical Physics of ETH Zürich, Switzerland, the Departments of Mathematics of McGill University and the University of Toronto, Canada. Matthias Mück: Supported by DAAD under grant HSP III. Israel Michael Sigal: Supported by NSERC under grant NA7901.     

The first <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-cohomology of some groups with one end

Let p be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first L ^p -cohomology space of some groups that have one end. We also make a connection between the first L ^p -cohomolgy space and the Floyd boundary of the Cayley graph of a group. We apply the result about Floyd boundaries to show that there exists a real number p such that the first L ^p -cohomology space of a nonelementary hyperbolic group does not vanish. Received: 4 August 2006 Revised: 2 November 2006     

Altered protein synthesis in rat kidney cells exposed to semiconductor materials

It is thought that the extensive industrial use of arsenic, gallium and indium, which have applications as the materials for III–V semiconductors, will increase human exposure to these compounds in the near future. We have undertaken the development of new biological indicators for assessing exposure to these elements. Element-specific alterations in protein synthesis patterns were expected to occur following exposure to arsenic compounds. We examined alterations in protein synthesis in primary cultures of rat kidney proximal tubule epithelial cells by sodium arsenite, gallium chloride and indium chloride, utilizing two-dimensional gel electrophoresis. After incubation with the chemicals for 20 h, newly synthesized proteins were labeled with [³⁵S]methionine. A protein with a molecular weight (M_r) of 30 000 was markedly induced on exposure to 10 μM arsenite or 300 μM gallium chloride, and synthesis of proteins with M_r values of 85 000, 71 000, 65 000, 51 000, 38 000 and 28 000 were also increased by exposure to arsenite and gallium chloride. No significant changes were observed upon exposure to indium. Some of these increased proteins could be heat-shock proteins.     

Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.