Non-classical law of the iterated logarithm behaviour for trimmed sums

Summary We study the law of the iterated logarithm for the partial sum of i.i.d. random variables when the r _n largest summands are excluded, where r _n=o(log logn). This complements earlier work in which the case log log_n=O(r_n) was considered. A law of the iterated logarithm is again seen to prevail for a wide class of distributions, but for reasons quite different from previously.Research supported in part by NSF Grant DMS-8501732     

Effect of molecular structure on mesomorphism XX. Unsymmetrical dimeric mesogens

A series of unsymmetrical dimeric mesogens was prepared, members of which were composed of a 4'-pentyloxybiphenyl-4-carboxyl core and a 4'-substituted-benzylidene-4-oxyaniline core joined via an alklyene spacer. The structural variants were cyano, nitro and trifluoromethyl. Comparison of mesophase behaviour of the unsymmetrical dimers with that of corresponding monomeric 'halves' and also with that of corresponding symmetrical dimers indicated a tendency for the unsymmetrical dimers to form smectic phases although not as highly ordered as those of some of the monomers corresponding to a relevant core group.     

Atrial activity during thePR segment of the MCG

Summary Sloping signals were observed in thePR segment of normal magnetocardiograms recorded from five dogs. Larger ramps were observed after first-degree AV nodal blockade was induced pharmacologically, and complete atrial repolarization was observed following isolated atrial contractions in two animals with second-degree block. These ramps, ranging up to 6.7 pT in size and arising from the atria, may complicate magnetic detection of His-Purkinje activity. This work was supported by the National Institute of Health under Grant No. HL 23184.     

Anchoring strength coefficient of a monomer and its dimer at a polymer-coated interface

The dialkoxyphenylbenzoate monomer '5005' (C₅H₁₁OC₆H₄COOC₆H₄OC₅H₁₁) and its dimer were aligned parallel to a buffed polyimide-coated glass substrate. A magnetically induced Freedericksz transition in both thick and thin cells was used in conjunction with a capacitance technique to determine the anchoring strength coefficient Was a function of temperature in the nematic phase. It was found that for both monomer and dimer, Wincreases with decreasing temperature. The anchoring coefficient for the dimer, however, was found to be an order of magnitude larger than for the monomer at comparable reduced temperatures. The splay elastic moduli were also determined for both species, and found to be of comparable magnitude, consistent with previous results.