On the connectivity of graphs generated by a sum of random mappings

We consider four models of random directed multigraphs with n labeled vertices of out-degree d. First we establish formal relationships between our models with respect to exact and asymptotic (as n → ∞) probabilities of possessing a graph monotone property. We also study the asymptotic behavior of the strength of connectivity of the underlying simple graphs when d = o(n). © 1993 John Wiley & Sons, Inc.     

Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains

We introduce a notion of an asymptotically compact (AC) random dynamical system (RDS). We prove that for an AC RDS the -limit set of any bounded set is nonempty, compact, strictly invariant and attracts the set . We establish that the D Navier Stokes Equations (NSEs) in a domain satisfying the Poincaré inequality perturbed by an additive irregular noise generate an AC RDS in the energy space . As a consequence we deduce existence of an invariant measure for such NSEs. Our study generalizes on the one hand the earlier results by Flandoli-Crauel (1994) and Schmalfuss (1992) obtained in the case of bounded domains and regular noise, and on the other hand the results by Rosa (1998) for the deterministic NSEs.

     

Comparative PIV and LDA studies of Newtonian and non-Newtonian flows in an agitated tank

The paper presents results of an experimental study of the fluid velocity field in a stirred tank equipped with a Prochem Maxflo T (PMT) type impeller which was rotating at a constant frequency of N = 4.1 or 8.2 s^?1 inducing transitional (Re = 499 or 1307) or turbulent (Re = 2.43 × 10⁴) flow of the fluid. The experiments were performed for a Newtonian fluid (water) and a non-Newtonian fluid (0.2 wt% aqueous solution of carboxymethyl cellulose, CMC) exhibiting mild viscoelastic properties. Measurements were carried out using laser light scattering on tracer particles which follow the flow (2-D PIV). For both the water and the CMC solution one primary and two secondary circulation loops were observed within the fluid volume; however, the secondary loops were characterized by much lower intensity. The applied PMT-type impeller produced in the Newtonian fluid an axial primary flow, whilst in the non-Newtonian fluid the flow was more radial. The results obtained in the form of the local mean velocity components were in satisfactory agreement with the literature data from LDA. Distribution of the shear rate in the studied system was also analyzed. For the non-Newtonian fluid an area was computed where the elastic force dominates over the viscous one. The area was nearly matching the region occupied by the primary circulation loop.     

Syntheses of potassium 1,1‐dioxopyrido[4,3‐e]‐1,4,2‐dithiazine‐3‐thiolate and its application to the synthesis of novel sulfonamides with potential biological activity

Potassium 1,1‐dioxopyrido[4,3‐e]‐1,4,2‐dithiazine‐3‐thiolate 2 has been synthesized and applied to the syntheses of 7H‐1,1‐dioxopyrido[4,3‐e]‐1,4,2‐dithiazolium‐3‐thiolate 3 and 3‐methylthiopyrido[4,3‐e]‐1,4,2‐dithiazine 1,1‐dioxide 4 which provided easy access to a variety of its 3‐amino derivatives 5‐10 . Hydrazinolysis of 7, 8 and 10 afforded the corresponding 3‐amino‐2‐(1,4‐dihydro‐4‐thioxopyrid‐3‐ylsulfonyl)guanidines 11‐13 . Subsequent reaction of 12 with 4‐chlorobenzaldehyde gave condensation product 14 . 1,4‐Dihydro‐2‐thioxopyridine‐3‐sulfonamide 15 was also prepared from the potassium salt 2 upon alkaline hydrolysis, whereas alkylation of 15 gave the appropriate S‐substituted derivatives 16‐19 or S,N‐disubstituted compounds 20‐21 .     

Benefiting from information-rich multi-frequency AC voltammetry coupled with chemometrics on the example of on-line monitoring of leveler component of electroplating bath

Simultaneous application of multiple sinusoidal waveforms perturbations superimposed onto DC staircase step significantly enriches current response. The measured current is characterized by a matrix of data rather than a conventional voltammetric output in a form of a vector. This increase of the dimensionality of the current response and therefore the wealth of analytical information is achieved without compromising the time of analysis. The natural approach for compression of such data and extraction of relevant information is by utilizing multi-way chemometric decomposition techniques. An electroplating solution presents a very challenging analyte for electroanalysis as its constituents interact synergistically with each other during both the plating process and its simulation during electroanalysis. For some components the mechanism is not entirely understood. Therefore, the only way to benefit from the analytical data is by employing soft modeling. The electrode processes involving additives rely heavily on adsorption and, indirectly, on electron transfer kinetics for which AC voltammetry is an analytical technique capable of delivering informative signals. This paper presents a rigorous universal method for calculating and validating an exemplary multi-way calibration of a leveler component in a copper electroplating bath used in the semiconductor industry. The method presented employs comparatively Parallel Factor Analysis coupled with Inverse Least Squares Regression and multi-linear Partial Least Squares. The calibration training set consists of multi-frequency AC voltammetric data subjected to pretreatments aiming to select informative independent variables and exclude outliers.     

CycloSiFA: The Next Generation of Silicon-Based Fluoride Acceptors for Positron Emission Tomography (PET)

The ring-opening Si-fluorination of a variety of azasilole derivatives cyclo-1-(iPr₂Si)−4-X−C₆H₃−2-CH₂NR ( 4 : R=2,6-iPr₂C₆H₃, X=H; 4 a : R=2,4,6-Me₃C₆H₂, X=H; 9 : R=2,6-iPr₂C₆H₃, X=tBuMe₂SiO; 10 : R=2,6-iPr₂C₆H₃, X=OH; 13 : R=2,6-iPr₂C₆H₃, X=HCCCH₂O; 22 : R=2,6-iPr₂C₆H₃, X=tBuMe₂SiCH₂O) with different ¹⁹F-fluoride sources was studied, optimized and the experience gained was used in a translational approach to create a straightforward ¹⁸F-labelling protocol for the azasilole derivatives [¹⁸F] 6 and [¹⁸F] 14 . The latter constitutes a potential clickable CycloSiFA prosthetic group which might be used in PET tracer development using Cu-catalysed triazole formation. Based on our findings, CycloSiFA has the potential to become a new entry into non-canonical labelling methodologies for radioactive PET tracer development.     

Rapid measurement of sphingolipids from Arabidopsis thaliana by reversed-phase high-performance liquid chromatography coupled to electrospray ionization tandem mass spectrometry

Changes in sphingolipids have been associated with profound effects in cell fate and development in both plants and animals. Sphingolipids as a group consist of a large number of different compound classes of which numerous individual species may vary in response to environmental stimuli to affect cellular responses. The ability to measure all sphingolipids simultaneously is, therefore, essential to an understanding of the biochemical regulation of sphingolipid metabolism and signaling molecules derived from it. In the model plant Arabidopsis thaliana, the major sphingolipid classes are glycosylinositolphosphoceramides, glucosylceramides, hydroxyceramides and ceramides. Other minor but potentially important sphingolipids are free long-chain bases and their phosphorylated derivates. By using a single solvent system with reversed-phase high-performance liquid chromatography coupled to electrospray ionization tandem mass spectrometry detection we have been able to separate and measure 168 sphingolipids from a crude sample. This greatly speeds up and simplifies the analysis of plant sphingolipids and should pave the way for a better understanding of their role in plant performance.