On the b-Coloring of Cographs and <Emphasis Type="Italic">P</Emphasis><Subscript>4</Subscript>-Sparse Graphs

A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χ _b (G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every . We define a graph G to be b-monotonic if χ _b (H ₁) ≥ χ _b (H ₂) for every induced subgraph H ₁ of G, and every induced subgraph H ₂ of H ₁. In this work, we prove that P ₄-sparse graphs (and, in particular, cographs) are b-continuous and b-monotonic. Besides, we describe a dynamic programming algorithm to compute the b-chromatic number in polynomial time within these graph classes. Flavia Bonomo: Partially supported by ANPCyT PICT-2007-00533 and PICT-2007-00518, and UBACyT Grants X069 and X606 (Argentina). Guillermo Durán: Partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems” (Chile), and ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina). Javier Marenco: Partially supported by ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina).     

Canonical Lévy process and Malliavin calculus

A suitable canonical Lévy process is constructed in order to study a Malliavin calculus based on a chaotic representation property of Lévy processes proved by Itô using multiple two-parameter integrals. In this setup, the two-parameter derivative _Dt,x$D_{t,x}$ is studied, depending on whether x=0$x=0$ or x≠0$x\ne 0$; in the first case, we prove a chain rule; in the second case, a formula by trajectories.     

Ultrasound measurements of cavitation bubble radius for femtosecond laser-induced breakdown in water

A recently developed ultrasound technique is evaluated by measuring the behavior of a cavitation bubble that is induced in water by a femtosecond laser pulse. The passive acoustic emission during optical breakdown is used to estimate the location of the cavitation bubble's origin. In turn, the position of the bubble wall is defined based on the active ultrasonic pulse-echo signal. The results suggest that the developed ultrasound technique can be used for quantitative measurements of femtosecond laser-induced microbubbles.     

Asymptotic Normality of Cross-correlogram Estimates of the Response Function

The problem of estimation of an unknown response function of a time-invariant continuous linear system is considered. Discrete-time sample input–output cross-correlograms are taken as estimates of the response function. The inputs are supposed to be zero-mean stationary Gaussian processes close, in some sense, to a white noise. Both asymptotic normality of finite-dimensional distributions of the estimates and their asymptotic normality in spaces of continuous functions are studied. Our basic tool is a new integral representation for cumulants of the estimate as a finite sum of integrals involving cyclic products of kernels. Some inequalities for these integrals are obtained and their asymptotic behaviour is studied.     

On Torsion of Prismatic Bodies

The method of decaying residual solution is applied to obtain an approximate interior solution for the torsion of slender prismatic elastic bodies under different end conditions. The approximate solution is generally accurate up to terms that are exponentially small in the length-to-cross-sectional-width ratio. For stress end conditions, the result is identical to the classical Saint-Venant torsion solution. Similar types of simple solutions, not known previously, are obtained for different types of mixed end conditions. For displacement conditions at both ends, the corresponding Saint-Venant type result requires an accurate solution of a canonical problem for a semi-infinite prismatic body that is to be obtained once and for all. The solution of the canonical problem is elementary for a circular cross section. The approximate interior solution in that case is identical to the known exact interior solution.     

Adamantyl‐endcapped polyynes

Polyynes spanning from a diyne to a dodecayne with adamantyl endgroups have been synthesized using the Fritsch–Buttenberg–Wiechell rearrangement as a key step to construct the acetylenic framework. Molecular properties as a function of polyyne length have been analyzed by UV–Vis spectroscopy, cyclic voltammetry, differential scanning calorimetry, and X‐ray crystallography. Copyright © 2011 John Wiley & Sons, Ltd.     

Suppression of parasitic lasing in high energy, high repetition rate Ti:sapphire laser amplifiers

Transverse parasitic lasing is well known for limiting the signal gain and the pulse energy that can be extracted from Ti:sapphire petawatt amplifiers. We have developed a technique for suppressing these parasitic lasing modes based on perfect refractive index-matching liquid doped with a broad-bandwidth absorber to suppress the transverse lasing while ensuring proper heat removal from the Ti:sapphire crystal. The 800 nm laser output with a bandwidth of 41 nm (FWHM) and peak energy of 22.7 J at a repetition rate of 1 Hz is demonstrated.     

Quantization of Poisson-Lie groups and applications

LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ^∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras.