The Measurement of Ultrashort Light Pulses—Simple Devices,Complex Pulses

We review the state of the art of ultrashort-light-pulse measurement using frequency-resolved-optical-gating (FROG). Recent developments have extended the state of the art considerably. FROG devices for measuring the intensity and phase of ultrashort laser pulses have become so simple that almost no alignment is required. In addition, such devices not only operate single shot, but they also yield the two most important spatio-temporal distortions, spatial chirp and pulse-front tilt. With other FROG variations, it is now possible to measure more general ultrashort light pulses (i.e., pulses much more complex than common laser pulses), with time-bandwidth products as large as several thousand and as weak as a few hundred photons, and despite other difficulties such as random absolute phase and poor spatial coherence.     

Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants

In the Laurent expansion

of the Riemann-Hurwitz zeta function, the coefficients are known as Stieltjes, or generalized Euler, constants. [When , (the Riemann zeta function), and .] We present a new approach to high-precision approximation of . Plots of our results reveal much structure in the growth of the generalized Euler constants. Our results when for , and when for (for such as 53/100, 1/2, etc.) suggest that published bounds on the growth of the Stieltjes constants can be much improved, and lead to several conjectures. Defining , we conjecture that is attained: for any given , for some (and similarly that, given and , is within of for infinitely many ). In addition we conjecture that satisfies for 1$">. We also conjecture that , a special case of a more general conjecture relating the values of and for . Finally, it is known that for . Using this to define for all real 0$">, we conjecture that for nonintegral , is precisely times the -th (Weyl) fractional derivative at of the entire function . We also conjecture that , now defined for all real arguments 0$">, is smooth. Our numerical method uses Newton-Cotes integration formulae for very high-degree interpolating polynomials; it differs in implementation from, but compares in error bounding to, Euler-Maclaurin summation based methods.

     

Amalgamation of partitions from multiple segmentation bases: A comparison of non-model-based and model-based methods

The segmentation of customers on multiple bases is a pervasive problem in marketing research. For example, segmentation service providers partition customers using a variety of demographic and psychographic characteristics, as well as an array of consumption attributes such as brand loyalty, switching behavior, and product/service satisfaction. Unfortunately, the partitions obtained from multiple bases are often not in good agreement with one another, making effective segmentation a difficult managerial task. Therefore, the construction of segments using multiple independent bases often results in a need to establish a partition that represents an amalgamation or consensus of the individual partitions. In this paper, we compare three methods for finding a consensus partition. The first two methods are deterministic, do not use a statistical model in the development of the consensus partition, and are representative of methods used in commercial settings, whereas the third method is based on finite mixture modeling. In a large-scale simulation experiment the finite mixture model yielded better average recovery of holdout (validation) partitions than its non-model-based competitors. This result calls for important changes in the current practice of segmentation service providers that group customers for a variety of managerial goals related to the design and marketing of products and services.     

Alignment of liquid crystal and dichroic dye molecules in mixed Langmuir and Langmuir-Blodgett films

A study of dichroic dye-liquid crystal mixtures (guest-host systems) in monolayers formed at a gas-liquid interface (Langmuir films) and at a solid surface (Langmuir-Blodgett films) has been made. As a host 4- n -octyl-4'-cyanobiphenyl (8CB) or 4- n -pentyl-4"-cyano- p -terphenyl (5CT) were chosen, while three dichroic azo dyes with various molecular structures were used as guest species. The dyes were added to the liquid crystal matrices at a concentration corresponding to the whole range of molar fractions and the surface pressure-mean molecular area isotherms for Langmuir films were recorded. On the basis of the isotherms, conclusions about the molecular organization and the miscibility of the components in the ultrathin films were drawn. The Langmuir films were transferred onto the quartz plates at surface pressures below the collapse point. The polarized absorption spectra of the Langmuir-Blodgett films were recorded and information about the alignment and intermolecular interactions in the mixtures of the non-amphiphilic dichroic dyes and the liquid crystals with strongly polar terminal groups were obtained.     

Kinetic features of the carbon erosion of a bulk NiCr alloy during the catalytic decomposition of 1,2-dichloroethane

Kinetic features for the carbon erosion (CE) of bulk NiCr alloy (NiCrA, nichrome wire 0.1 mm in diameter) were studied at 450–750°C under conditions of the catalytic decomposition of 1,2-dichloroethane vapor in a reductive atmosphere (H₂). It was found that the CE process takes place more efficiently in the temperature range from 550 to 720°C, leading to the disintegration of the bulk alloy with the formation of a fibrous carbon product. The apparent activation energy of the process was estimated to be 16.8 ± 0.9 kJ/mol. The realization of CE is hampered outside the optimal temperature range because of chlorination (T < 500°C) or blocking of the alloy’s surface by carbonaceous deposits (T > 720°C). The kinetics of the process is characterized by the existence of an induction period, whose duration decreases with an increasing temperature (from 40 min at 550°C to 6 min at 710°C). According to scanning and transmission electron microscopy data, the submicron metallic particles (0.2–0.4 μm) catalyzing the growth of carbon fibers with disordered structure result from the disintegration of the NiCr alloy.     

Examples of the failure of the local-global principle for similarity of matrices

A cohomological method for computing the set of similarity classes of endomorphisms locally similar to a given endomorphism is presented and several calculations are made.     

Once edge-reinforced random walk on a tree

 We consider a nearest neighbor walk on a regular tree, with transition probabilities proportional to weights or conductances of the edges. Initially all edges have weight 1, and the weight of an edge is increased to $c > 1$ when the edge is traversed for the first time. After such a change the weight of an edge stays at $c$ forever. We show that such a walk is transient for all values of $c \ge 1$, and that the walk moves off to infinity at a linear rate. We also prove an invariance principle for the height of the walk. Received: 6 March 2001 / Revised version: 16 July 2001 / Published online: 15 March 2002     

OBSERVATIONS ON THE SYNTHESIS AND in vivo PHOTODYNAMIC ACTIVITY OF SOME BENZOCHLORINS

An improved synthesis of benzochlorins is reported. Demetallation of the meso-hydroxymethylvinyl derivative of octaethylporphyrin, followed by treatment with sulfuric acid results in cyclization to generate the corresponding octaethylbenzochlorin in high yield. Prolonged treatment with acid generates the sulfonated derivative. These sensitizers were shown to be efficient photodynamic agents in vivo. Animals bearing a transplanted N-[4-(5-nitro-2-furyl)-2-thiazoly]formamide induced urothelial tumor were treated with either the benzochlorin or its sulfonated derivative. Irradiation of tumors 24 h later resulted in a significant tumoricidal effect in a short term assay. We conclude that benzochlorins warrant further examination as potential agents for use in photodynamic therapy.     

Super-Tree Random Measures

We use supercritical branching processes with random walk steps of geometrically decreasing size to construct random measures. Special cases of our construction give close relatives of the super-(spherically symmetric stable) processes. However, other cases can produce measures with very smooth densities in any dimension.