Toeplitz Operators and Group Representations

Toeplitz operators on the Bergman space of the unit disc can be written as integrals of the symbol against an invariant operator field of rank-one projections. We consider a generalization of the Toeplitz calculus obtained upon taking more general invariant operator fields, and also allowing more general domains than the disc; such calculi were recently introduced and studied by Arazy and Upmeier, but also turn up as localization operators in time-frequency analysis (witnessed by recent articles by Wong and others) and in representation theory and mathematical physics. In particular, we establish basic properties like boundedness or Schatten class membership of the resulting operators. A further generalization to the setting when there is no group action present is also discussed, and the various settings in which similar operator calculi appear are briefly surveyed.     

Nil-extensions of unions of groups induced by identities

This paper is a continuation of [11]. Here we study all identities which induce decompositions into nil-extensions of a union of groups and identities which induce various special types of these decompositions. Supported by Grant 0401A of SF Servia through Math. Inst. SANU.     

Productive Coreflective Classes in Top

If sequential cardinals do not exist then every topological space is generated from a converging sequence by using finite products, disjoint sums and quotients. The author acknowledges the support of the grants MSM 0021620839 and GAČR 201/06/0933 of Czech Republic.     

Switching of chirality from racemic to homochiral state in new liquid crystalline monomers with bent-core molecules

The synthesis and physical properties of bent-shaped molecules with ester linkages and methoxy substitution on a non-central ring are presented. Terminal chains of most mesogens contain a group with double bond, which promotes polymerization. In all the compounds studied a B₂ phase just below the isotropic phase has been found. Polarization current profiles indicate that this phase is antiferroelectric, and dielectric spectroscopy data with a pronounced high frequency mode support this fact. For several compound chirality switching from racemic to the homochiral state was seen after application of a low frequency a.c. field. Another phase, which could be assigned to the B₇ family, appears below the B₂ phase on cooling.     

The Mixed Norm Spaces of Polyharmonic Functions

Let be a bounded domain with C ² boundary. And let H _k be the set of all polyharmonic functions f with order k on Ω. For 0<p, q≤∞ and ϕ a normal weight, the mixed-norm space consists of all function f in H _k for which the mixed-norm ||·|| _{p, q, ϕ} <∞. The main result of the paper is the norm equivalence:

High Performance Liquid Chromatography/Electrochemistry/High Resolution Electrospray Ionization‐Mass Spectrometry (HPLC/EC/HR ESI‐MS) Characterization of Selected Cytokinins Oxidation Products

Electrochemistry combined with mass spectrometry represents an emerging analytical technique used to study the oxidation pathway of various drugs and in vivo occurring compounds, continuously showing a capability to generate many known metabolites or new oxidation products. An on‐line HPLC/EC/HR ESI‐MS method had been used to investigate the oxidation of selected cytokinin compounds. This setup allowed rapid identification and general structure elucidation of the obtained products. An electrochemical oxidation of isopentenyladenine resulted in five products, including hydroxylated and dehydrogenated products, which correlates very well with its in vivo metabolism. Electrochemical conversion of trans‐zeatin revealed six products, with two dehydrogenation products corresponding to its in vivo occurring metabolites. cis‐Zeatin oxidation in the electrochemical cell gave rise to eight products, resembling similarity to trans‐zeatin oxidation. All three compounds underwent a complete turnover mainly through two oxidation reactions occurring in the electrochemical cell? dehydrogenation and a less typical aliphatic hydroxylation. The resulting products are in correlation with their known in vivo metabolism.     

Detection of p53 Gene by Using Genomagnetic Assay Combined with Carbon Nanotube Modified Disposable Sensor Technology

Electrochemical monitoring of DNA hybridization related to p53 gene sequence was investigated using genomagnetic assay combined with single walled carbon nanotube (SWCNT) modified pencil graphite electrodes (PGEs). The hybridization was performed either at magnetic beads (MB) surface or in solution. The enhanced guanine signal was obtained using SWCNT‐PGEs compared to one obtained by unmodified PGEs. The selectivity of genomagnetic assay was tested under optimum conditions. The DLs were calculated as 0.88 µM and 0.11 µM for hybridization performed at MB surface and solution, respectively. This selective, practical and cost effective genomagnetic assay combined with SWCNT‐PGEs is reported herein for the first time.     

Electrochemical Activity of Wedelolactone and Probing its Interaction with DNA Using Voltammetry at a Carbon Electrode

Wedelolactone (WLA) is a polyphenolic coumestan derivative found in extracts of plants used in traditional medicine. Due to its cytostatic activity, WLA is one of natural compounds tested as potential anticancer drugs. In this work we for the first time studied electrochemical properties of WLA using cyclic (CV) and square‐wave (SWV) voltammetry at the basal‐plane pyrolytic graphite electrode. A reversible pair of peaks, corresponding to catechol/o‐benzoquinone redox system, was observed using CV around 0.275 V vs. Ag|AgCl|3 M KCl reference electrode. Measurements of SWV signal of WLA in the presence of single‐ or double‐stranded DNA suggested a weak interaction without evident preference for double‐stranded DNA. An indirect assay, employing electroactive DNA intercalator doxorubicin as competitor, confirmed absence of intercalative DNA binding of WLA.