Convergence of path measures arising from a mean field or polaron type interaction

Summary We discuss the limiting path measures of Markov processes with either a mean field or a polaron type interaction of the paths. In the polaron type situation the strength is decaying at large distances on the time axis, and so the interaction is of short range in time. In contrast, in the mean field model, the interaction is weak, but of long range in time. Donsker and Varadhan proved that for the partition functions, there is a transition from the polaron type to the mean field interaction when passing to a limit by letting the strength tend to zero while increasing the range. The discussion of the path measures is more subtle. We treat the mean field case as an example of a differentiable interaction and discuss the transition from the polaron type to the mean field interaction for two instructive examples.Research supported by the Swiss National Foundation (21-29833.90)This article was processed by the authors using the Springer-Verlag T_EX ProbTh macro package 1991.     

A Pilot Survey of Vocal Health in Young Singers

The objective of this study was to determine the incidence of vocal problems in young choir singers and to correlate vocal problems with demographic and behavioral information. A questionnaire addressing vocal habits and hygiene was offered to 571 young choir singers, up to 25 years of age, who sing at least weekly; 129 (22.6%) responded. More than one-half of the respondents had experienced vocal difficulty, particularly older adolescents. Detrimental behaviors and circumstances surveyed were not reflective of the incidence of vocal difficulty, except for morning hoarseness, chronic fatigue, insomnia, and female gender after puberty. Voice care professionals should be aware that self-reported voice difficulties are common among young choral singers, especially postpubescent girls, and children with symptoms consistent with reflux (morning hoarseness) and emotional stress (insomnia). Laryngologists should communicate with choral conductors and singing teachers to enhance early identification and treatment of children with voice complaints, and to develop choral educational strategies that help decrease their incidence.     

Approximating weak Chebyshev subspaces by Chebyshev subspaces

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties.     

Optimized analysis of the critical behavior in polymer mixtures from Monte Carlo simulations

A complete outline is given for how to determine the critical properties of polymer mixtures with extrapolation methods similar to the Ferrenberg-Swendsen techniques recently devised for spin systems. By measuring not only averages but the whole distribution of the quantities of interest, it is possible to extrapolate the data obtained in only a few simulations nearT _c over the entire critical region, thereby saving at least 90% of the computer time normally needed to locate susceptibility peaks or cumulant intersections and still getting more precise results. A complete picture of the critical properties of polymer mixtures in the thermodynamic limit is then obtained with finite-size scaling functions. Since the amount of information extracted from a simulation in this way is drastically increased as compared to conventional methods, the investigation of mixtures with long chains or built-in asymmetries is now possible. As an example, the critical points, exponents, and amplitudes of dense, symmetric polymer mixtures with chain lengths ranging fromN=16 up toN=256 are determined within the framework of the 3D bond fluctuation model using grand canonical simulation techniques. As an example for an asymmetry, the generalization of the method to asymmetric monomer potentials is briefly discussed.     

Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer

The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer.     

WITCH: A Penning Trap Retardation Spectrometer Combination for Precision Studies of the Weak Interaction

We present data from three seasons of experimental field work designed to recreate ancient Andean coastal ceramic firing techniques. Based on the recent discovery of two different archaeological ceramic production sites in the La Leche river valley of northern coastal Peru, the opportunity arose to apply Mössbauer spectroscopy and other analytical methods to reconstruct ancient firing procedures. Two sets of firings took place in 1993 and 1997 in Batán Grande using a partially restored Formative kiln from about 800 BC, local hardwood and cow dung as fuel. A third experiment followed in 2000 after the discovery of a Middle Sicán ceramics workshop in use between ca. AD 950 and 1050 at Huaca Sialupe, where an exact replica of an ancient kiln was built from local clay, and fired with local wood and cow dung. Additionally, inverted urns found at Huaca Sialupe were tested for their potential use as furnaces for metal working. Mössbauer spectroscopy was used to compare the physical and chemical state of specimens produced in the field experiments with ancient ceramics and with specimens produced in controlled laboratory experiments.     

A selective synthesis of 4‐bromo‐2‐furancarboxaldehyde and its pinacolborane derivative

A selective synthesis of ethylene acetal of 4‐bromo‐2‐furancarboxaldehyde ( 4 ) and its pinacolborane derivative ( 5 ) is described. The synthesis was carried out using 2‐furancarboxaldehyde ( 1 ) that was bromi‐nated to 4,5‐dibromo‐2‐furancarboxaldehyde ( 2 ) in an emulsion of aluminum chloride and methylene chloride. The product was isolated, protected as ethylene acetal, and selectively debrominated to the ethylene acetal of 4‐bromo‐2‐furancarboxaldehyde ( 4 ) in one step. This moiety was reacted with pinacolborane to give a reactive reagent of Suzuki coupling.     

On self-repellent one dimensional random walks

Summary We consider an ordinary one dimensional recurrent random walk on. A self-repellent random walk is defined by changing the ordinary law of the random walk in the following way: A path gets a new relative weight by multiplying the old one with a factor 1– for every self intersection of the path. 0<<1 is a parameter.It is shown that if the jump distribution of the random walk has an exponential moment and if is small enough then the displacement of the endpoint is asymptotically of the order of the length of the path.Partially supported by the Deutsche Forschungsgemeinschaft and the Akademie der Wissenschaften zu Berlin