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.     

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.     

Perturbative and nonperturbative correspondences between compact and noncompact sigma-models

Compact (ferro- and antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions d?2$d?2$. While the ferro- and antiferromagnetic models are essentially equivalent, the qualitative difference to the noncompact models is highlighted. The perturbative and the large N expansions are studied in both types of models and are argued to be asymptotic expansions on a finite lattice. An exact correspondence between the expansion coefficients of the compact and the noncompact models is established, for both expansions, valid to all orders on a finite lattice. The perturbative one involves flipping the sign of the coupling and remains valid in the termwise infinite volume limit. The large N correspondence concerns the functional dependence on the free propagator and holds directly only in finite volume.     

Atomic subspaces of {L_1}-martingale spaces

In Part I of the present paper the following problem was investigated. Let G be a finite simple graph, and S be a finite set of primes. We say that G is representable with S if it is possible to attach rational numbers to the vertices of G such that the vertices v₁, v₂ are connected by an edge if and only if the difference of the attached values is an S-unit. In Part I we gave several results concerning the representability of graphs in the above sense.     

Characterization of peptide-pyrazole interactions in solution by low-temperature NMR studies

Complexation of the amino- and carboxyl-protected tripeptide Piv-L-Val-L-Val-L-Val-tBu with 3-methylpyrazole and 3-amino-5-methylpyrazole was studied by low-temperature NMR experiments in a freonic solvent. The peptide forms an extended beta-type structure at all temperatures and associates through hydrogen bonding with the two pyrazole-based beta-sheet ligands. A detailed structural characterization of the formed complexes by one- and two-dimensional NMR experiments under slow exchange conditions was made possible by employing very low temperatures. The tripeptide associates to stable antiparallel dimers that are symmetrically capped on both sides by two pyrazole receptors to form 2:2 complexes. Amide groups of two neighboring residues in an extended conformation are involved in cyclic hydrogen bonds to the pyrazole. Based on amide chemical shift changes, the relative strength of intermolecular hydrogen bonds can be assessed and correlated with the electronic effects of the substituents on the pyrazole.     

Abnormal resting-state cortical coupling in chronic tinnitus

Background  

Subjective tinnitus is characterized by an auditory phantom perception in the absence of any physical sound source. Consequently, in a quiet environment, tinnitus patients differ from control participants because they constantly perceive a sound whereas controls do not. We hypothesized that this difference is expressed by differential activation of distributed cortical networks.     

Weak coupling perturbative calculations of the Wilson loop for the standard action

Wilson loops of size m × n with m, n≤6 are evaluated to second order in weak coupling perturbation theory. The results are compared with earlier estimates by Hattori and Kawai.