An Approach to Rotating Boundary Layers Based on Vector Radon Measures

In this paper we develop a new approach to rotating boundary layers via Fourier transformed finite vector Radon measures. As an application we consider the Ekman boundary layer. By our methods we can derive very explicit bounds for existence intervals and solutions of the linearized and the nonlinear Ekman system. For example, we can prove these bounds to be uniform with respect to the angular velocity of rotation which has proved to be relevant for several aspects (see introduction). Another advantage of our approach is that we obtain well-posedness in classes containing nondecaying vector fields such as almost periodic functions. These outcomes give respect to the nature of boundary layer problems and cannot be obtained by approaches in standard function spaces such as Lebesgue, Bessel-potential, Hölder or Besov spaces.     

Scalar-tensor cosmologies with a potential in the general relativity limit: Time evolution

We consider Friedmann–Lemaître–Robertson–Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity. As an illustration we present an example of oscillating dark energy.     

Asymmetric synthesis of the 2,2,3-trisubstituted cyclopentanone,D-ring fragment of 9,11-secosterols

As a part of our studies on the total synthesis of 9,11-secosterols, the possibility of creating a substituted and functionalized D-ring fragment with three consecutive stereocentres, one of which was quaternary, was studied. The simple starting compound 2-methyl-cyclopent-2-ene-1-one was subjected to asymmetric 1,4-addition with (S,S)-crotyl phosphonamide and alkylation with methyl bromoacetate, resulting in a 2,2,3-substituted cyclopentanone in high diastereoselectivity. The covalently bonded chiral auxiliary was removed using oxidative methods. As a result, a stable D-ring fragment was obtained. The relative configuration of the substituents on the cyclopentane ring was assigned by comparison of the experimental with the quantum chemically calculated ¹H–¹H and ¹H–¹³C J-coupling constants.     

Asymmetric oxidation of cyclobutanones: modification of the Sharpless catalyst

Oxidation of prochiral and racemic cyclobutanones with t-BuOOH and Ti-TADDOL-based complexes afforded lactones in up to 44% ee. The enantioselectivity of the reaction clearly depends on the amount of the reagent and the highest enantioselectivities were obtained with stoichiometric amounts of the complex. Modification of the TADDOL structure and use of the mixed complex derived from TADDOL and a tartaric ester led to more reactive but less selective oxidation systems.     

Synthesis and Characterization of Fluorodinitroamine,FN(NO2)2

NF₃ and N(NO₂)₃ are known compounds, whereas the mixed fluoronitroamines, FN(NO₂)₂ and F₂NNO₂, have been unknown thus far. One of these, FN(NO₂)₂, has now been prepared and characterized by multinuclear NMR and Raman spectroscopy. FN(NO₂)₂ is the first known example of an inorganic fluoronitroamine. It is a thermally unstable, highly energetic material formed by the fluorination of the dinitramide anion using NF₄⁺ salts as the preferred fluorinating agent.     

Expression profiling in cancer using cDNA microarrays

Currently there are over 1,000,000 human expressed sequence tag (EST) sequences available on the public database, representing perhaps 50-90% of all human genes. The cDNA microarray technique is a recently developed tool that exploits this wealth of information for the analysis of gene expression. In this method, DNA probes representing cDNA clones are arrayed onto a glass slide and interrogated with fluorescently labeled cDNA targets. The power of the technology is the ability to perform a genome-wide expression profile of thousands of genes in one experiment. In our review we describe the principles of the microarray technology as applied to cancer research, summarize the literature on its use so far, and speculate on the future application of this powerful technique.     

Approximation of multivariate distribution functions

In the paper the unknown distribution function is approximated with a known distribution function by means of Taylor expansion. For this approximation a new matrix operation — matrix integral — is introduced and studied in [PIHLAK, M.: Matrix integral, Linear Algebra Appl. 388 (2004), 315–325]. The approximation is applied in the bivariate case when the unknown distribution function is approximated with normal distribution function. An example on simulated data is also given.      

Horizontal submanifolds of groups of Heisenberg type

We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of dimension half of that of the canonical distribution (“lagrangians”) and illustrate some notable ones of small dimension. An infinitesimal classification of the arbitrary maximal horizontal submanifolds follows as a consequence. This work was supported by CONICET, Antorchas, FONCyT and Secyt (UNC).     

Inhomogeneous symbols, the Newton polygon, and maximal L p -regularity

We prove a maximal regularity result for operators corresponding to rotation invariant symbols (in space) which are inhomogeneous in space and time. Symbols of this type frequently arise in the treatment of half-space models for (free) boundary-value problems. The result is obtained by extending the Newton polygon approach to variables living in complex sectors and combining it with abstract results on the -calculus and -bounded operator families. As an application, we derive maximal regularity for the linearized Stefan problem with Gibbs-Thomson correction. Dedicated to the memory of Leonid Romanovich Volevich     

Synthesis and gas-sensing properties of phenylhydrazine-functionalized single wall carbon nanotubes in polymer matrix

Gas sensor material was prepared by encapsulation of functionalized single-walled carbon nanotubes (SWCNT) into a gas-permeable polymer poly(1-trimethylsilyl-1-propyne) (PTMSP). A phenylhydrazino group was used for the functionalization of SWCNTs to improve their solubility and compatibility with polymers. Syntheses were carried out in aqueous surfactant solutions and in pure phenylhydrazine without surfactant. Two different temperatures (24 and 50°C) and two surfactants (sodium dodecyl sulfate and tricaprylmethylammonium chloride — Aliquat®336) were compared. Functionalized SWCNTs were characterized by X-ray photoelectron (XPS), Raman and Fourier transform infrared (FTIR) spectroscopy. Analyses showed that the synthesis at higher temperature in pure phenylhydrazine resulted in the highest functionalization yield. Phenylhydrazine itself proved to be a good solvent for SWCNTs. The functionalized nanotubes were soluble in organic solvents that under the same conditions were appropriate solvents for polymers. The sensitivity of functionalized SWCNT-PTMSP thin film composite to NO₂ gas at room temperature was significantly higher than that of the similar sensor material containing the pristine SWCNTs.