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.     

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.     

On the Hahn-Banach Extension Property in Hardy and mixed norm spaces on the unit ball

For a nonempty setE of nonnegative integers letH _E ^{p, q, a} andH _E ^p be the closed linear span of

Deterministic solution of the kinetic theory model of colloidal suspensions of structureless particles

A direct modeling of colloidal suspensions consists of calculating trajectories of all suspended objects. Due to the large time computing and the large cost involved in such calculations, we consider in this paper another route. Colloidal suspensions are described on a mesoscopic level by a distribution function whose time evolution is governed by a Fokker–Planck-like equation. The difficulty encountered on this route is the high dimensionality of the space in which the distribution function is defined. A novel strategy is used to solve numerically the Fokker–Planck equation circumventing the curse of dimensionality issue. Rheological and morphological predictions of the model that includes both direct and hydrodynamic interactions are presented in different flows.     

How to confirm identified toxicants in effect-directed analysis

Due to the production and use of a multitude of chemicals in modern society, waters, sediments, soils and biota may be contaminated with numerous known and unknown chemicals that may cause adverse effects on ecosystems and human health. Effect-directed analysis (EDA), combining biotesting, fractionation and chemical analysis, helps to identify hazardous compounds in complex environmental mixtures. Confirmation of tentatively identified toxicants will help to avoid artefacts and to establish reliable cause–effect relationships. A tiered approach to confirmation is suggested in the present paper. The first tier focuses on the analytical confirmation of tentatively identified structures. If straightforward confirmation with neat standards for GC–MS or LC–MS is not available, it is suggested that a lines-of-evidence approach is used that combines spectral library information with computer-based structure generation and prediction of retention behaviour in different chromatographic systems using quantitative structure–retention relationships (QSRR). In the second tier, the identified toxicants need to be confirmed as being the cause of the measured effects. Candidate components of toxic fractions may be selected based, for example, on structural alerts. Quantitative effect confirmation is based on joint effect models. Joint effect prediction on the basis of full concentration–response plots and careful selection of the appropriate model are suggested as a means to improve confirmation quality. Confirmation according to the Toxicity Identification Evaluation (TIE) concept of the US EPA and novel tools of hazard identification help to confirm the relevance of identified compounds to populations and communities under realistic exposure conditions. Promising tools include bioavailability-directed extraction and dosing techniques, biomarker approaches and the concept of pollution-induced community tolerance (PICT). Figure Toxicity confirmation in EDA as a tiered approach     

Small camera as a handheld colorimetric tool in the analytical chemistry

Recently, there is an effort to introduce new types of analytical procedures and handheld assays to provide simple and reliable equipment for the field and household analyses. Development of diagnostic tools for self-diagnosis is another challenge in analytical chemistry. Digital cameras are widely available and cheap, hence they could be the sensor platform for construction of analytical and diagnostic methods. In general, good availability of cameras integrated into smartphones can be easily converted into an analytical tool. This review relates to the use of digital camera in analytical chemistry and there are introduced the facts how digital data can be processed and what the limits of digital photography are. Recent papers in this issue and discussion of development in camera based assays is also provided here.     

Capillary electrophoretic study of interactions of metal ions with crown ethers,a sulfated beta-cyclodextrin,and zwitterionic buffers present as additives in the background electrolyte

Stability constants of K, Na, Ca, and Ba with 18-crown-6, K, Na, Li with sulfated beta-cyclodextrin and K, Li, Ca, Mg, Sr, and Ba ions with ([2-hydroxy-1,1-bis(hydroxymethyl) ethyl]-amino)-1-propanesulfonic acid (TAPS) were determined by capillary electrophoresis and computed using a general least squares minimizing program CELET. The results for 18-crown-6 agreed well with those evaluated by graphical methods or reported in the literature. Previously unknown stability constants of sulfated beta-cyclodextrins and TAPS determined for alkali and alkaline earth metals show that sulfated beta-cyclodextrin interacts with monovalent metals allowing to manipulate their effective mobility. It interacts stronger with divalent metal cations. TAPS, as zwitterionic buffer widely used in various analytical, biochemical and other applications, forms complexes with alkali and alkaline earth cations, and although the stability constants are rather low, the equilibria should be taken into account when TAPS is used and metal cations are present in solution at the same time.