Magnetic properties of xCoO.(1-x)[2B2O3.K2O] glasses

The results of magnetic investigations onxCoO.(1-x)[2B₂O₃.K₂O] glasses are reported. The magnetic properties of these glasses are dependent on the CoO content. For glasses withx > > 10 mol% CoO, the Co²⁺ ions are coupled antiferromagnetically.     

Generalized roughening transition and its effect on the string tension

The well-understood roughening transition of an interface in the d = 3 Ising model implies an essential singularity in the string tension of the dual Z₂ gauge model. The roughening transition corresponds to the delocalization of the string due to strong long-wavelength fluctuations, and this reformulation can be generalized to other gauge groups and to d = 4 also. It is not a deconfining transition - it is expected to occur deep in the confining region - but its presence would raise serious questions about the continuation of strong coupling expansions of the tension beyond this point. In this paper predictions on the roughening transition are confronted with the available information on the string tension for different gauge groups in three dimensions.     

Thermal stability of polyurethanes

Summary The combined application of thermogravimetry reactiongas chromatography and gel-permeation chromatography permits to follow the heat degradation of polyurethane polymers in inert gas, air and water-saturated environment. The examinations give information on the rate of thermal degradation, the individual volatile degradation components, the critical points of the polymer chains and on the change of their molecular-weight distribution. Gas chromatographic examinations also permit the identification of the chain-extending components of different types of polyurethanes.     

Analytical investigation of a four-variable model of the BZ reaction

It is proved analytically that the four-variable model reported in the preceding paper [1] has a unique stationary solution for each set of rate constants. An upper and a lower boundary for the stationary concentrations are established.

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New theta constant identities

The residue theorem is employed to obtain new identities amongpthe powers of theta constants with rational characteristics. The technique is then used to derive some known identities of Ramanujan. Dedicated to John Thompson for his many original contributions to mathematics Research by HMF partially sponsored by the Edmund Landau Center for Research in Mathematical Analysis, supported by the Minerva Foundation (Germany).     

Experiment on the optical tunneling process of electrons from a gold surface induced by mode-locked CO2 laser pulse trains

Using intense mode-locked CO₂ laser pulse trains we verified the occurrence of the laser-induced, new-type dynamic optical tunneling of electrons from a gold surface. The results are in accordance with the theoretical predictions and our previous experiments carried out for both atoms and gold surface using single longer (ns) CO₂ laser pulses. Unknown properties of the development of the CO₂ laser train are revealed based on our higher-order coherence detection of electron emission.     

On Fuglede's Conjecture and the Existence of Universal Spectra

Recent methods developed by Tao [18], Kolountzakis and Matolcsi [7] have led to counterexamples to Fugelde’s Spectral Set Conjecture in both directions. Namely, in Tao produced a spectral set which is not a tile, while Kolountzakis and Matolcsi showed an example of a nonspectral tile. In search of lower dimensional nonspectral tiles we were led to investigate the Universal Spectrum Conjecture (USC) of Lagarias and Wang [14]. In particular, we prove here that the USC and the "tile → spectral" direction of Fuglede’s conjecture are equivalent in any dimensions. Also, we show by an example that the sufficient condition of Lagarias and Szabó [13] for the existence of universal spectra is not necessary. This fact causes considerable difficulties in producing lower dimensional examples of tiles which have no spectra. We overcome these difficulties by invoking some ideas of Révész and Farkas [2], and obtain nonspectral tiles in . Fuglede’s conjecture and the Universal Spectrum Conjecture remains open in 1 and 2 dimensions. The one-dimensional case is closely related to a number theoretical conjecture on tilings by Coven and Meyerowitz [1].