Self-healing femtosecond light filaments

A recent experiment [Appl. Phys. Lett. 83, 213 (2003)] indicated that filaments created in femtosecond high-power pulses propagating in air are surprisingly robust when interacting with microscopic water droplets. We present numerical modeling of the dynamics of the filament-droplet interaction. Our simulation results provide further insight into the interplay between the filament's core and the wide transverse pedestal of the pulse. It is shown that the robustness of the filament comes from the transverse low-intensity pedestal that controls the formation of the central hot spot. Implications for penetration of wide, high-power beams through obscurants are discussed.     

Complex Convexity and Vector-Valued Littlewood-Paley Inequalities

Let 2 p > , and let X be a complex Banach space. It is shownthat X is p-uniformly PL-convex if and only if there exists > 0 such that , for all f H^p(X). Applications to embeddings between vector-valued BMOAspaces defined via Poisson integral or Carleson measures areprovided. 2000 Mathematics Subject Classification 46B20, 46L52.     

Analytic models for commuting operator tuples on bounded symmetric domains

For a domain in and a Hilbert space of analytic functions on which satisfies certain conditions, we characterize the commuting -tuples of operators on a separable Hilbert space  such that is unitarily equivalent to the restriction of to an invariant subspace, where is the operator -tuple on the Hilbert space tensor product  . For the unit disc and the Hardy space , this reduces to a well-known theorem of Sz.-Nagy and Foias; for a reproducing kernel Hilbert space on such that the reciprocal of its reproducing kernel is a polynomial in and  , this is a recent result of Ambrozie, Müller and the second author. In this paper, we extend the latter result by treating spaces for which ceases to be a polynomial, or even has a pole: namely, the standard weighted Bergman spaces (or, rather, their analytic continuation) on a Cartan domain corresponding to the parameter in the continuous Wallach set, and reproducing kernel Hilbert spaces for which is a rational function. Further, we treat also the more general problem when the operator is replaced by ,  being a certain generalization of a unitary operator tuple. For the case of the spaces on Cartan domains, our results are based on an analysis of the homogeneous multiplication operators on , which seems to be of an independent interest.

     

Sums and Limits of Generalized Direct Families of Algebras

In this paper we introduce a generalization of direct families of algebras and we study their limits and sums. In the case of generalized direct families of algebras carried by idempotent algebras we investigate some subdirect decompositions of their sums. The results that we obtain generalize various results given by J.L. Chrislock and T. Tamura [2], M. iri and S. Bogdanovi [3-7], H. Mitsch [13], M. Petrich [14-16], B.M. Schein [23-24] and others.Supported by Grant 04M03B of RFNS through Math. Inst. SANU     

A Generalization of Herrlich's Question on Almost Reflective and Coreflective Subclasses of Top and Unif

H. Herrlich asked in Topology Appl. 49 (1993), 251–264, whether there are nontrivial classes of topological spaces that are almost reflective and almost coreflective at the same time. This question was dealt with (in Huek and Tozzi, Appl. Categ. Structures 4 (1996), 57–68) in a more general setting than almost reflective and almost coreflective classes. The present paper investigates a modified question: when a nontrivial generalized reflective class of topological or uniform spaces is equivalent to a generalized coreflective class of spaces.     

The Dynkin system generated by balls in contains all Borel sets

We show that for every each Borel subset of the space with the Euclidean metric can be generated from closed balls by complements and countable disjoint unions.

     

Improving detector signal processing with pulse height analysis in Mössbauer spectrometers

A plenty of different programming techniques and instrument solutions are used in the development of Mössbauer spectrometers. Each of them should provide a faster spectrum accumulation process, increased productivity of measurements, decreased nonlinearity of the velocity scale, etc. The well known virtual instrumentation programming method has been used to design a computer-based Mössbauer spectrometer. Hardware solution was based on two commercially-available PCI modules produced by National Instruments Co. Virtual Mössbauer spectrometer is implemented by the graphical programming language LabVIEW 7 Express. This design environment allows to emulate the multichannel analyzer on the digital oscilloscope platform. This is a novel method based on Waveform Peak Detection function which allows detailed analysis of the acquired signal. The optimal treatment of the detector signal from various detector types is achieved by mathematical processing only. As a result, the possibility of an increase of signal/noise ratio is presented.     

Controlled grafting of cellulose esters using SET‐LRP process

Here, we present the first example of application of single‐electron transfer living radical polymerization (SET‐LRP) process to a controlled grafting of cellulose esters, cellulose diacetate (CDA), and cellulose acetate butyrate (CAB). The cellulose ester macroinitiators with various functionality densities have been prepared by acylation of the backbones with 2‐bromoisobutyryl (BrIB) and dichloroacetyl (DCA) groups, respectively. Methacrylate monomers were polymerized using DCA‐functionalized macroinitiators in the presence of pentamethyldiethylene triamine as a ligand. At 30 °C, the reaction is rather slow, reaching about 10% conversion after 3 to 6 h of polymerization, whereas the higher temperature (60 °C) perceptibly speeds up the polymerization so that methyl methacrylate (MMA) conversion is ～30% after 5 h. Graft copolymers with random‐type and diblock‐type grafts having amphiphilic character were also synthesized. For acrylate grafting (BuA and t‐BuA), BrIB‐functionalized macroinitiators are more convenient in a combination with a low concentration of Cu(0) and Me₆TREN as a ligand and polymerization is detectably faster even at the lower temperature than that of MMA. Kinetic studies show “living” character of both the graftings. Important advantages of SET‐LRP, compared with classic ATRP, are (i) higher polymerization rate, (ii) lower extent of recombination of the growing grafts and (iii) negligible coloration of the products with catalytic residua, so that the prepared polymers do not require additional careful purification. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Cubic β-Fe2O3 as the product of the thermal decomposition of Fe2(SO4)3

Hyperfine Interactions - The thermal decomposition of Fe2(SO4)3 in air has been investigated using transmission Mössbauer spectroscopy, CEMS and X-ray powder diffraction. The hexagonal...     

Bicyclic graphs for which the least eigenvalue is minimum

The spread of a graph is defined to be the difference between the greatest eigenvalue and the least eigenvalue of the adjacency matrix of the graph. In this paper we determine the unique graph with minimum least eigenvalue among all connected bicyclic graphs of order n. Also, we determine the unique graph with maximum spread in this class for each n?28.