Newton's method for a class of nonsmooth functions

This paper presents and justifies a Newton iterative process for finding zeros of functions admitting a certain type of approximation. This class includes smooth functions as well as nonsmooth reformulations of variational inequalities. We prove for this method an analogue of the fundamental local convergence theorem of Kantorovich including optimal error bounds.The research reported here was sponsored by the National Science Foundation under Grants CCR-8801489 and CCR-9109345, by the Air Force Systems Command, USAF, under Grants AFOSR-88-0090 and F49620-93-1-0068, by the U. S. Army Research Office under Grant No. DAAL03-92-G-0408, and by the U. S. Army Space and Strategic Defense Command under Contract No. DASG60-91-C-0144. The U. S. Government has certain rights in this material, and is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.     

Detecting shifts in the mean of a simulation output process

The application of the correct simulation output analysis technique requires a knowledge of the model's behaviour. Traditionally, only two types of model behaviour are discussed for discrete event simulations: transient and steady state. In this paper, a third type of behaviour, denoted shifting steady state, is considered in which the model passes through successive periods of different steady states. A heuristic technique for identifying the shifts in the mean of a time series is applied to the output data from simulation models with known shifting steady-state behaviour in order to test its effectiveness in detecting the shifts. The heuristic performs well, indicating that it may be a valuable additional technique for output analysis.     

Stability of random attractors under perturbation and approximation

The comparison of the long-time behaviour of dynamical systems and their numerical approximations is not straightforward since in general such methods only converge on bounded time intervals. However, one can still compare their asymptotic behaviour using the global attractor, and this is now standard in the deterministic autonomous case. For random dynamical systems there is an additional problem, since the convergence of numerical methods for such systems is usually given only on average. In this paper the deterministic approach is extended to cover stochastic differential equations, giving necessary and sufficient conditions for the random attractor arising from a random dynamical system to be upper semi-continuous with respect to a given family of perturbations or approximations.     

A permutational property of groups

Ohne ZusammenfassungHelmut Wielandt zum 75. Geburstag am 19. Dezember 1985 gewidmet     

Critical phenomena in a mixture of methane,carbon dioxide and hydrogen sulfide

Ng, H.-J., Robinson, D.B. and Leu, A.-D., 1985. Critical phenomena in a mixture of methane, carbon dioxide and hydrogen sulfide. Fluid Phase Equilibria, 19:273-286.The two- and three-phase boundaries for a mixture containing nominally 0.50 mole fraction methane, 0.10 mole fraction carbon dioxide and 0.40 mole fraction hydrogen sulfide were determined experimentally for a range of temperatures from c. 29 to – 83°C at pressures up to c. 13 MPa.The two-phase boundary curve commences with a conventional hydrogen-sulfide-rich liquid dew point locus which passes through an upper retrograde region and terminates at a vapor-hydrogen-sulfide-rich liquid critical point at ? 16.9°C and 11.03 MPa. The phase boundary then follows a bubble point locus which terminates at a hydrogen-sulfide-rich liquid-methane-rich liquuid critical point at ?45.6°C and 8.79 MPa. After this the boundary turns sharply upwards to higher pressures at lower temperatures. This separates the single phase from a second retrograde-like two-liquid region.The three-phase boundary enclosing a hydrogen-sulfide-rich liquid-methane-rich liquid—vapor region terminates when the methane-rich liquid dew point locus and the three-phase bubble point locus meet at a third critical point occurring at ?57.5°C and 6.62 MPa.The measurements and observations were made using a sapphire cylinder as an equilibrium cell. Phase compositions and phase volume percentages were measured under a number of selected conditions in both the two- and three-phase regions.     

Boron trifluoride promoted reactions of n-haloelectrophiles with alkenes

N-Haloelectrophiles react with alkenes in the presence of boron rifluoride etherate to give halofluorides and N-halo adducts.     

The rearrangement of some 2-substituted-4-bromo-2,5-dinitro-6-hydroxy-3,6-dimethylcyclohex-3-en-1-ones

In chloroform at 20°, or in tetrachloroethylene at 120°, the title compounds (1) rearrange to give the α-diketone(2), the structure of which was determined by X-ray crystal structure analysis; a possible rearrangement mechanism is outlined.