A mean value theorem on bounded symmetric domains

Let be a Cartan domain of rank and genus and , , the Berezin transform on ; the number can be interpreted as a certain invariant-mean-value of a function around . We show that a Lebesgue integrable function satisfying , , must be -harmonic. In a sense, this result is reminiscent of Delsarte's two-radius mean-value theorem for ordinary harmonic functions on the complex -space , but with the role of radius played by the quantity .

     

Solution of a class of kinetic equations

The kinetic equation of the weakly ionized plasma is reduced to the canonical form of parabolic equation. Analytical solution for some practically important cases can easily be found.Dedicated to Professor Ivan Úlehla on the occasion of his sixtieth birthday.     

Geometry of the numerical range of matrices

Some techniques for the study of the algebraic curve C(A) which generates the numerical range W(A) of an n×n matrix A as its convex hull are developed. These enable one to give an explicit point equation of C(A) and a formula for the curvature of C(A) at a boundary point of W(A). Applied to the case of a nonnegative matrix A, a simple relation is found between the curvature of the function Φ(A)=p((1?α)A+ αA^T) (pbeingthePerronroot) at $\text{α=}\text{1}\text{2}$ and the curvature of W(A) at the Perron root of $\text{1}\text{2}\text{(A+A}{}^{\mathrm{T}}\text{)}$. A connection with 2-dimensional pencils of Hermitian matrices is mentioned and a conjecture formulated.     

Applications of NMR spectroscopy of chiral association complexes. 6. rotation about the C(sp2)—C(aryl) bond in 2,6-disubstituted pivalophenones

For the investigation of the barrier to rotation about the C(sp²)—C(aryl) bond in non-planar pivalophenones five derivatives were prepared and their ¹H and ¹³C NMR spectra assigned. Methyl and bromine groups in the 3-position have opposite substituent effects on the chemical shifts of the ¹H and ¹³C signals of Me² and Me⁴. The ΔG values were determined from the coalescence temperatures of the signal splittings generated by the addition of optically active shift reagents. The accuracy of this method was estimated by using different signals of 3-bromo-2,4,6-trimethylpivalophenone and by computer simulation of the line shape. A buttressing effect of substituents in the aromatic ring was observed. A change of the twist angle by the substitution of methyl by bromine in the tert-butyl group was suggested in order to explain the changes in ΔG and the chemical shifts.     

Wetting films of lipids in the development of sensitive interfaces. An electrochemical approach

Solid-supported thin liquid films of lipids, contacting an electrolyte phase, turned out to be a dependable system in the field of bosensors. The investigations of these objects during the past decade reveal some of their intriguing features enabling the application in constructions of receptor part with 'two-dimensional' arrangement. As a model system, complementary to the other artificial analogs of biomembranes, the wetting films of lipids offer certain advantages concerning the compromise between the stability and flexibility of the molecular structures involved in sensing. The basic principles underlaying the techniques of formation, as well as the conditions of the films stability are emphasized in the present consized review. While no limitations are imposed by the way of preparation, the films seem especially profitable in conjunction with methods for electrochemical signal transduction. In this regard some prominent examples are discussed.     

Congruence-preserving functions on Stone and Kleene algebras

We investigate local polynomial functions on Stone algebras and on Kleene algebras. We find a generating set for the clone of all local polynomial functions. We also represent local polynomial functions on a given algebra by polynomial functions of some canonical extension of this algebra.     

Lineshapes of spin exchange broadened EPR spectra

An unexplained residual in the fits of theoretical and experimental spectra of exchange broadened nitroxide spin probes reported by Robinson et al. [J. Magn. Reson. 138 (1999) 199] is shown to be understood by inclusion of theoretically predicted lineshape changes into the fitting routine. These lineshape changes provide an additional estimate of the spin exchange frequency that is independent of linewidth methods.     

A general synthesis of water soluble upper rim calix[n]arene guanidinium derivatives which bind to plasmid DNA

The reaction of O-alkylated p-aminocalix[n]arenes (n=4, 6, 8) with N,N′-di(tert-butoxycarbonyl)thiourea in the presence of HgCl₂ and subsequent removal of the protective groups with hydrochloric acid led to the new water soluble calix[n]guanidinium derivatives (p-guanidiniumcalix[n]arenes) 20-23. With the exception of tetraoctyl-p-guanidiniumcalix[4]arene 21, which forms a macroscopic gelatinous aggregate even at very low concentration, all the synthesised guanidinium calixarenes show good solubility in water and sharp NMR signals. Moreover, these compounds are not cytotoxic and bind to plasmid DNA.     

A modified HPLC method for the determination of aspartic acid racemization in collagen from human dentin and its comparison with GC

The D/L ratio of aspartic acid enantiomers in proteins of low turnover is generally accepted as a reliable procedure for age determination. In our study, twelve samples of eyetooth dentin were analyzed for age determination. The pure insoluble collagen isolated from eyetooth dentin was obtained by an EDTA demineralization process. Free amino acids obtained after collagen hydrolysis were converted into o-phthaldialdehyde-N-acetyl-L-cysteine (OPA-NAC) derivatives for HPLC analysis under modified conditions and into trifluoroacetic acid isopropyl esters for GC analysis, respectively. The modified HPLC procedure used phosphate buffer and acidified sample matrix prior to injection which resulted in suppression of peak tailing of both diastereomers, thus allowing achievement of both good selectivity and good resolution. To ensure the high accuracy of the developed method the other parameters, i.e. specificity, precision, linearity, LOD, and LOQ, were also determined. Nine collagen samples covering the age range of 18 to 84 years were used for the determination of coefficient of racemization (KR) and calculation of parameters for age estimation. The regression equations for the data set analyzed were as follows: KR= 0.0005 x age + 0.0262 (R2 = 0.9639) for HPLC, and KR= 0.0006 x age + 0.0319 (R2 = 0.9374) for GC, respectively.     

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.