Anomalies of the free loop wave equation in the WKB approximation

We derive a well-defined, reparametrization invariant expression for the next to leading term in the small ? expansion of the euclidean loop Green functional ψ($\text{C}$). To this order in ?, we then verify that ψ($\text{C}$) satisfies a renormalized loop wave equation, which involves a number of local, but non-harmonic anomalous terms. Also, we find that the quantum fluctuations of the string give rise, in 3 + 1 dimensions, to a correction of the static quark potential by an attractive Coulomb potential of universal strength $\text{α}{}_{\mathrm{<mtext>string</mtext>}}\text{=}\text{1}\text{12}\text{π}$.     

Beiträge zu kinetisch-katalytischen analysenmethoden unter verwendung offener systeme

Three basic possibilities for the application of “open systems” in catalytic-kinetic analytical methods are discussed: steady-state, stat and continuous-flow methods. Two further possibilities for such methods are reported: (1) the simultaneous addition of one reactant and the catalyst at constant speed; (2) the simultaneous addition of one reactant and the catalyst at a speed, regulated by the system itself, necessary to keep constant a preset potential or absorbance. Some examples of both methods are described.     

Spectrochemical and Thermal Behaviour of the 5-chloro-2-nitrobenzoates of Rare Earth Elements

The conditions of the formation of yttrium and lanthanide 5-chloro-2-nitrobenzoates were studied and their quantitative composition and solubilities in water at 298 K were determined. They are anhydrous or hydrated complexes and their solubilities are of the order of 10-3 mol dm-3. The IR and X-ray spectra for the complexes were recorded. All complexes are crystalline compounds. Their thermal decomposition was studied. It was found that on heating above 523 K the complexes decompose explosively. Therefore their thermal decomposition was carried out in the temperature range 273-523 K. Hydrated complexes lose crystallization water molecules in one step. From the results it appeared that during dehydration process no transformation of nitro group to nitrito took place. Some of physico-chemical properties of rare earth element 5-chloro-2-nitrobenzoates were compared with 2-nitro- and 3-chlorobenzoates of those elements. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solution-phase parallel synthesis of a pyridinium pyrazol-3-olate inner salt library using a three-component reaction

We present here the discovery of a novel, versatile, multicomponent reaction leading to various 4-[4-(pyridinium-1-yl)-2,5-dioxo-2,5-dihydro-1H-pyrrol-3-yl]-2H-pyrazol-3-olate inner salts. The structure of the unusual zwitterionic inner salts was elucidated, and the scope of the novel reaction was investigated. After rapid optimization, the reaction was adapted to parallel synthesis, and an 800-membered compound library was produced.     

The Segal Algebra {\bf S}_0({\Bbb R}^d) and Norm Summability of Fourier Series and Fourier Transforms

A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier series. Equivalent conditions are derived for the uniform and L ₁-norm convergence of the θ-means σ _n ^θ f to the function f. If f is in a homogeneous Banach space, then the preceeding convergence holds in the norm of the space. In case θ is an element of Feichtinger’s Segal algebra , then these convergence results hold. Some new sufficient conditions are given for θ to be in . A long list of concrete special cases of the θ-summation is listed. The same results are also provided in the context of Fourier transforms, indicating how proofs have to be changed in this case. This research was supported by Lise Meitner fellowship No M733-N04 and the Hungarian Scientific Research Funds (OTKA) No T043769, T047128, T047132.     

Universal method for synthesis of artificial gel antibodies by the imprinting approach combined with a unique electrophoresis technique for detection of minute structural differences of proteins, viruses, and cells (bacteria): II. Gel antibodies against virus (Semliki Forest Virus)

Artificial and highly selective antibodies (in the form of gel granules) against proteins can easily be synthesized by a simple, cost-effective imprinting technique [Liao, J.-L. et al., Chromatographia 1996, 42, 259-262]. Using the same method for synthesis of gel antibodies against viruses in combination with analysis by free zone electrophoresis in a rotating narrow bore tube we have shown that artificial gel antibodies against Semliki Forest Virus (wild type) can sense the difference between this virus and a mutant, although they differ in their chemical composition only by three amino acids in one of the three proteins on the surface of the virus particle. The reason for this extremely high resolution is explained by the fact that we use three types of selectivity: (i) shape selectivity (created by the close fit between the antigen and its imprint in the gel), (ii) bond selectivity in the contact area between the antigen and its imprint in the gel antibody, and (iii) charge selectivity, originating from slightly different structures or/and conformations of the antigens.     

Simulated vibrational spectra of aflatoxins and their demethylated products and the estimation of the energies of the demethylation reactions

The structure of four natural mycotoxins, the aflatoxin B1, B2, G1 and G2 and their demethylated products were optimized with quantum chemical method. The energies and the thermodynamic functions of the molecules were calculated and applied to calculation of the reaction energies of the demethylations. Further results of the calculations are the vibrational force constants, the infrared spectra of the molecules and the assignments of the spectral bands.