Automatic Microdensitometer for Image Evaluation

The aim of the present work is to determine the conditions of high resolution and precise application of the classical microdensitometers to the evaluation of autoradiographic images. The conclusions have been materialized in the improvement of the mechanical microdensitometer developed in our laboratory some years ago. The original model of this instrument was introduced at the VII. International Symposium on Autoradiography in Zakopane 1974. Since then some modifications have been made on the instrument in order to reach optimum performance.     

Optical Resolution of 2-(3-Chloro-phenyl)-3,4a,5,6,7,7a-hexahydro-cyclopentapyrimidin-4-one with O,O′-Dibenzoyl-2R,3R-tartaric Acid in Water-Chloroform Two Phase Solvent System

Optical resolution of racemic 2-(3-chloro-phenyl)-3.4a. 5.6.7.7a-hexahydrocyclopentapyrimidin-4-one with O.O′-dibenzoyl-2R,3R-tartaric acid in an unusual solvent combination, in water-chloroform two phase solvent system was accomplished. During enantiomeric enrichment of the resulted raw base the optically active base can be recovered from the ethanolic mother liquor.     

Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

We study the basis property of systems of exponentials with frequencies belonging to ‘simple quasicrystals’. We show that a diophantine condition is necessary and sufficient for such a system to be a Riesz basis in L ² on a finite union of intervals. For the proof we extend to BMO a theorem of Kesten about the discrepancy of irrational rotations of the circle.     

A Novel Route to trans-Epoxidation of Terpinen-4-ol

Pure (1S,2R,4S)-1,2-epoxy-p-menthan-4-ol and (1R,2S,4R)-1,2-epoxy-p-menthan-4-ol (trans-epoxides of (4S)-terpinen-4-ol and (4R)-terpinen-4-ol) were prepared and certain reactions of these compounds with nucleophilic reagents were studied. It was shown that the Fürst-Plattner rule regarding the trans-diaxial opening of cyclohexene epoxides predicts the predominant products in all cases studied.     

Scaling in small-world resistor networks

We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards–Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged two-point resistance in the large system-size limit. We find that the small-world structure suppresses large network resistances: both the average resistance and its standard deviation approaches a finite value in the large system-size limit for any non-zero density of random links. We also consider a scenario where the link conductance decays as a power of the length of the random links, l⁻. In this case we find that the average effective system resistance diverges for any non-zero value of .     

The scaling limit of loop-erased random walk in three dimensions

We show that the scaling limit exists and is invariant under dilations and rotations. We give some tools that might be useful to show universality.     

Study of the mechanism of optical resolutions via diastereoisomeric salt formation

Racemic malic acid (I) was resolved by R-α-phenylethylamine(II). The S-(?)-I.R-(+)-II diastereoisomer was in excess in the precipitated salt. DSC curves and X-ray powder diffractograms proved that the diastereoisomeric salt mixture precipitated during the resolution was isomorphous with the optically pure S-(?)-I.R-(+)-II salt. The diastereoisomeric salt mixture containing the R-(?)-I.R-(+)-II salt in abundance bound crystal solvate (water or methanol) when produced by the total evaporation of the mother liquor, while the optically pure R-(?)-I.R-(+)-II salt crystallized without solvate. It is generally assumed that solid solution formation takes place when the two diastereoisomers are alike and the high similarity results in less efficient enantiomer separation. This paper demonstrates that efficient resolution can be accomplished in case of solid solution formation too. The diastereoisomeric salt mixtures can crystallize in isomorphic form even when the physico-chemical properties of the optically pure diastereoisomeric salts are quite different.     

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=\frac43d_{s}=\frac{4}{3} , that is, p _t (x,x)=t ^−2/3+o(1). This establishes a conjecture of Alexander and Orbach (J. Phys. Lett. (Paris) 43:625–631, 1982). En route we calculate the one-arm exponent with respect to the intrinsic distance.     

Study of the mechanism of optical resolutionsvia diastereoisomeric salt formation

The products obtained in the optical resolution of the N-methylamphetamine by the Pope-Peachy method, using half equivalent R, R-tartaric acid and half equivalent hydrochloric acid in absolute ethanol were investigated by thermoanalytical methods. The DSC measurements of the precipitated salts provide sufficient information for following the progress of the resolution. In this way, the results of the resolution can be estimated with the precision of about 5% optical purity.