Convergence of algebraic multigrid based on smoothed aggregation

Summary. We prove an abstract convergence estimate for the Algebraic Multigrid Method with prolongator defined by a disaggregation followed by a smoothing. The method input is the problem matrix and a matrix of the zero energy modes of the same problem but with natural boundary conditions. The construction is described in the case of a general elliptic system. The condition number bound increases only as a polynomial of the number of levels, and requires only a uniform weak approximation property for the aggregation operators. This property can be a-priori verified computationally once the aggregates are known. For illustration, it is also verified here for a uniformly elliptic diffusion equations discretized by linear conforming quasiuniform finite elements. Only very weak and natural assumptions on the hierarchy of aggregates are needed. Received March 1, 1998 / Revised version received January 28, 2000 / Published online: December 19, 2000     

Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

Recovering Invisible Signals by Two‐Field NMR Spectroscopy

Nuclear magnetic resonance (NMR) studies have benefited tremendously from the steady increase in the strength of magnetic fields. Spectacular improvements in both sensitivity and resolution have enabled the investigation of molecular systems of rising complexity. At very high fields, this progress may be jeopardized by line broadening, which is due to chemical exchange or relaxation by chemical shift anisotropy. In this work, we introduce a two‐field NMR spectrometer designed for both excitation and observation of nuclear spins in two distinct magnetic fields in a single experiment. NMR spectra of several small molecules as well as a protein were obtained, with two dimensions acquired at vastly different magnetic fields. Resonances of exchanging groups that are broadened beyond recognition at high field can be sharpened to narrow peaks in the low‐field dimension. Two‐field NMR spectroscopy enables the measurement of chemical shifts at optimal fields and the study of molecular systems that suffer from internal dynamics, and opens new avenues for NMR spectroscopy at very high magnetic fields.     

N-Endaminos?urensequenz von 55 Resten des Schweinepepsins

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Fuzzy Horn logic II

The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general implicational theories, finitary implicational theories, and Horn theories by means of closedness under suitable algebraic constructions.     

Vitamin a derivatives labelled with 131I — Potential agents for liver scientigraphy

Two retinol derivatives, 4-[(¹³¹I)-4-iodobenzoyloxy]retinol propionate and 4-[(¹³¹I)-3-iodobenzylcarbamoyl]retinol propionate, were synthesized and their biodistribution in rats was studied in vivo by the whole body scintigraphy.     

Fuzzy Horn logic I

The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability equals degree of truth) from which we get some particular cases by imposing restrictions on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic.     

Fuzzy equational logic

Presented is a completeness theorem for fuzzy equational logic with truth values in a complete residuated lattice: Given a fuzzy set Σ of identities and an identity p≈q, the degree to which p≈q syntactically follows (is provable) from Σ equals the degree to which p≈q semantically follows from Σ. Pavelka style generalization of well-known Birkhoff's theorem is therefore established. Received: 15 March 2000 / Revised version: 20 September 2000 Published online: 12 December 2001