Stability of control systems with a moving optimization interval for a class of nonlinear plants

We investigate the stability of the control system with a moving optimization interval for a nonlinear discrete dynamic plant with additive controls. Sufficient stability conditions are derived for a control system with an arbitrary finite lookahead interval.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 116–118, 1987.     

Determination of low level85Kr and133Xe concentrations in the environment

This study was performed under the joint TRMC/INER program for the determination of low level⁸⁵Kr and¹³³Xe concentrations in the environmental air samples. Based on cryogenic adsorption of krypton and xenon on charcoal followed by chromatographic separation from other gases, the⁸⁵Kr and¹³³Xe recovered from 200 liters of atmospheric air can be determined by either on-line gas flow proportional counter or liquid scintillation counting. The recovery yields of krypton and xenon examined by using⁸⁵Kr and¹³³Xe tracers were nearly 100%. The minimum detectable activity of⁸⁵Kr and¹³³Xe by gas flow proportional counting is about 7.40 Bq. The method is satisfactory for environmental monitoring applications under abnormal conditions of nuclear facilities. However, for lower level environmental⁸⁵Kr and¹³³Xe measurements, the liquid scintillation counting method can be applied due to their extremely low detection limits (i.e. 0.107 Bq and 0.093 Bq for⁸⁵Kr and¹³³Xe, respectively). Using this method, the measurable limits of concentrations are 0.535 Bq/m³ and 0.466 Bq/m³ for⁸⁵Kr and¹³³Xe, respectively.     

Independence and graph homomorphisms graph homomorphisms

A graph with n vertices that contains no triangle and no 5-cycle and minimum degree exceeding n/4 contains an independent set with at least (3n)/7 vertices. This is best possible. The proof proceeds by producing a homomorphism to the 7-cycle and invoking the No Homomorphism Lemma. For k ≥ 4, a graph with n vertices, odd girth 2k+1, and minimum degree exceeding n/(k+1) contains an independent set with at least kn/(2k+1) vertices; however, we suspect this is not best possible. © 1993 John Wiley & Sons, Inc.     

Time‐integrated energy domain measurements with synchrotron radiation

A new time integrated method for the study of resonant nuclear scattering of synchrotron radiation in the forward direction or in Bragg directions is introduced. This method gives in principle similar information as the well known time differential method. A brief comparison of both methods is presented. The idea is to excite coherently the nuclei incorporated in two absorbers, one moving with respect to the other. The fields radiated by the nuclei from both absorbers interfere and each time the nuclear energy in one absorber matches, by Doppler modulation, the nuclear energy of the other, an extremum in the time integrated intensity is observed. The results of the first experiments at the Advanced Photon Source at the Argonne National Laboratory will be presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

On Improvements to the Analytic Center Cutting Plane Method

In this paper, we explore a weakness of a specific implementation of the analytic center cutting plane method applied to convex optimization problems, which may lead to weaker results than Kelley's cutting plane method. Improvements to the analytic center cutting plane method are suggested, and tested on some example problems.     

Chaotic Maps, Control Parameter, and Liapunov Exponent

We describe a one-dimensional chaotic map wherethe Liapunov exponent is a smooth function of a controlparameter.     

Induced smectic C* phases

Induced ferroelectric S*_C phases are formed by non-chiral S_C host phases doped with chiral dipolar guest molecules. In those mixtures the spontaneous polarization P_s and the tilt angle Θ has been investigated as a function of the mole fraction x_G of the chiral dopant. In most cases the reduced polarization P₀ = P_S/ sin Θ has been found to depend linearly on x_G. The polarization power which is defined by δ_P=(∂P₀/∂x_G)ΔT is discussed in terms of the molecular structure of the chiral dopants. There are systems in which P₀(x_G) deviates positively from linearity. This behaviour can be understood by considering a local field correction to P₀. By assuming a local field of Lorentz type a theoretical relation for P₀(x_G) has been derived which explains the experimental results. The effect of a local field is considerable if the transverse dipole moment and the polarizability of the chiral dopant are large.