PSL2(59) is a Subgroup of the Monster

A computer construction of the Monster is used to prove thatPSL(2, 59) is a subgroup of the Monster.     

Metric Embeddings—Beyond One-Dimensional Distortion

The extensive study of metric spaces and their embeddings has so far focused on embeddings that preserve pairwise distances. A very intriguing concept introduced by Feige allows us to quantify the extent to which larger structures are preserved by a given embedding. We investigate this concept, focusing on several major graph families such as paths, trees, cubes, and expanders. We find some similarities to the regular (pairwise) distortion, as well as some striking differences.     

Space time-index plots for probing dynamical nonstationarity

We propose a simple method to efficiently probe dynamical nonstationarity in observed time series. In a space time-index plot, the density distributions as a function of normalized time-index are V-shaped due to nonstationarity. We show that this method is workable for short data sets and typical examples are illustrated.     

The Jacobian and the Ginzburg-Landau energy

We study the Ginzburg-Landau functional for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional. Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001     

Miscible blends of modified poly(aryl ether ketones) with aromatic polyimides

The phase behavior of binary blends of poly(ether ether ketone) (PEEK), sulfonated PEEK, and sulfamidated PEEK with aromatic polyimides is reported. PEEK was determined to be immiscible with a poly(amide imide) (TORLON 4000T). Blends of sulfonated and sulfamidated PEEK with this poly(amide imide), however, are reported here to be miscible in all proportions. Blends of sulfonated PEEK and a poly(ether imide) (ULTEM 1000) are also reported to be miscible. Spectroscopic investigations of the intermolecular interactions suggest that formation of electron donoracceptor complexes between the sulfonated/sulfamidated phenylene rings of the PEEKs and the n-phenylene units of the polyimides are responsible for this miscibility. © 1993 John Wiley & Sons, Inc.     

Topics in data assimilation: Stochastic processes

Stochastic models with varying degrees of complexity are increasingly widespread in the oceanic and atmospheric sciences. One application is data assimilation, i.e., the combination of model output with observations to form the best picture of the system under study. For any given quantity to be estimated, the relative weights of the model and the data will be adjusted according to estimated model and data error statistics, so implementation of any data assimilation scheme will require some assumption about errors, which are considered to be random. For dynamical models, some assumption about the evolution of errors will be needed. Stochastic models are also applied in studies of predictability.

The formal theory of stochastic processes was well developed in the last half of the twentieth century. One consequence of this theory is that methods of simulation of deterministic processes cannot be applied to random processes without some modification. In some cases the rules of ordinary calculus must be modified.

The formal theory was developed in terms of mathematical formalism that may be unfamiliar to many oceanic and atmospheric scientists. The purpose of this article is to provide an informal introduction to the relevant theory, and to point out those situations in which that theory must be applied in order to model random processes correctly.     

One-dimensional non-nearest-neighbor random walks in the presence of traps

A one-dimensional lattice random walk in the presence ofm equally spaced traps is considered. The step length distribution is a symmetric exponential. An explicit analytic expression is obtained for the probability that the random walk will be trapped at thejth trapping site.     

Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform acceleration as demonstrated in [12] and [13], we obtain fluid and diffusion limits for the sojourn time of the M_t/M_t/1 processor-sharing queue. Our analysis is enabled by the introduction of a “virtual customer” which differs from the notion of a “tagged customer” in that the former has no effect on the processing time of the other customers in the system. Our analysis generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process are known.     

Latex particles bearing hydrophilic grafted hairs with controlled chain length and functionality synthesized by reversible addition–fragmentation chain transfer

A method is described for synthesizing latex particles with anchored hairs by the grafting of hydrophilic chains, synthesized by reversible addition–fragmentation chain transfer, onto functionalized latex particles. These have the potential to bind biologically active species. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1188–1195, 2003