On Gårding's inequality

In this paper we prove Gårding's inequality for linear differential operators in generalized divergence form which satisfy a generalized Ehrling inequality, an ellipticity condition and a condition on the coefficients. Using a compact imbedding between certain anisotropic Sobolev spaces we substitute the first condition (Ehrling's inequality) by a simple condition on a set of multi-indices.     

Abrupt increase in thermal diffusion belowT c in YBa2Cu3O7−δ

We report the variation of the thermal diffusivity in the high temperature superconductor YBa₂Cu₃O_7−δ below the transition temperature measured using photo-acoustic technique α is found to increase sharply belowT _c. Qualitative explanations are given.     

Low-Temperature Localisation for Continuous Spin-Systems

We study the free energy of continuous spin-systems on Z ^d , in the framework of Laplace integrals and transfer operators. Under a weak coupling condition, we show that the free energy in the low-temperature limit is determined, up to an exponentially small error, by the restriction to a neighbourhood of global minima of the energy. We have results for some single- and double-well problems.     

Application of ion pair high performance liquid chromatography to the analysis of porphyrins in clinical samples

Reversed phase ion pair chromatography is a highly selective separation technique for the determination of free porphyrin carboxylic acids from human materials. Isocratic and gradient elution methods can be used to analyse porphyrin isomers and to establish porphyrin profiles for the biochemical diagnosis of porphyrias. Ion pair high performance liquid chromatography led to the discovery of the atypical isomers II and IV of uroporphyrin and coproporphyrin in human urine. Advantages and limitations of the ion pair technique are discussed.     

Thermal diffusion near glass transition in Ge-Se glasses measured by photoacoustics

The glass transition in Ge _x Se_1−x ) (0·1 ⩽x ⩽ 0·25) glasses has been investigated using the photoacoustic (PA) technique. It is found that the PA amplitude and phase undergo anomalous changes at the glass transition temperatureT _g. The amplitude has critical minimum and phase has maximum values atT _g. The variation of the thermal diffusivity, determined by measuring the frequency dependence of the PA amplitude and phase, with temperature shows sharp decrease near the glass transition temperature. The temperature dependence of the optical energy gap also has been measured and it shows a decrease with temperature for all compositions, the rate of decrease being higher for temperatures greater thanT _g.     

On the “piano movers'” problem I. The case of a two-dimensional rigid polygonal body moving amidst polygonal barriers

We present an algorithm that solves a two-dimensional case of the following problem which arises in robotics: Given a body B, and a region bounded by a collection of “walls”, either find a continuous motion connecting two given positions and orientations of B during which B avoids collision with the walls, or else establish that no such motion exists. The algorithm is polynomial in the number of walls (O(n⁵) if n is the number of walls), but for typical wall configurations can run more efficiently. It is somewhat related to a technique outlined by Reif.     

Beitrag zur Pfropf-copolymerisation der Cellulose mit polymerisierbaren Monomeren im Wege der Kettenübertragung

Zusammenfassung Die Pfropfung der Cellulose mit Styrol im Wege der Kettenübertragung wird bei Abwandlung der Menge des Initiators, der Konzentration des Monomeren, der Reaktionsdauer und der Reaktionstemperatur untersucht. Die Verwendung von anderen Initiatoren wie auch der Einsatz anderer Monomeren (Acrylnitril, Methylacrylat) werden einer kurzen Prüfung unterzogen.

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Grafting of cellulose with styrene by means of chain transfer has been investigated by varying the amount of initiator, concentration of monomer, reaction time and temperature. The use of other initiators and other monomers (acrylonitrile, methylacrylate) has been tested.

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Mit 2 Abbildungen

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Herrn Prof. Dr.Anton v. Wacek zu seinem 70. Geburtstag gewidmet.     

Utilisation de l'ultracentrifugeuse pour la mesure des masses et pour l'etude de la polydispersite des polymeres de synthese

After a review of the two techniques based on sedimentation rate and equilibrium in binary medium, more recent methods involving the presence of a second non-macromolecular solute are described. Application of these methods to synthetic polymers is still rare but of increasing interest. The use of computers simplifies the exploitation of the measurements.     

A comparison between simula and fortran

The general purpose simulation language SIMULA is compared with the ordinary scientific programming language FORTRAN. A typical military simulation model is programmed in both SIMULA and FORTRAN.The SIMULA program is found to be 24% shorter than the FORTRAN version. The SIMULA version is also more straightforward and gives a better picture of the simulated model. On the other hand, execution time for production runs is 64% longer with SIMULA. Weighing pros and cons shows that SIMULA will be more and more profitable, with higher personnel costs and lower computer costs to be expected in the future.     

Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents

Our objective is to explain the phenomenon of permanent currents within the context of the Ginzburg-Landau model for superconductors. Using variational techniques we make a connection between the formation of permanent currents and the topology of the superconducting sample.Research supported in part by the Fund for the Promotion of Research at the Technion.Research supported in part by a grant from the National Science Foundation.