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.     

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.