Principal minors, Part I: A method for computing all the principal minors of a matrix

An order O(2ⁿ) algorithm for computing all the principal minors of an arbitrary n × n complex matrix is motivated and presented, offering an improvement by a factor of n³ over direct computation. The algorithm uses recursive Schur complementation and submatrix extraction, storing the answer in a binary order. An implementation of the algorithm in MATLAB® is also given and practical considerations are discussed and treated accordingly.     

Improved high-performance liquid chromatographic method for the determination of 6-N,N,N-trimethyllysine in plasma and urine: biomedical application of chromatographic figures of merit and amine mobile phase modifiers

An internally standardized method for the determination of 6-N,N,N-trimethyllysine in human plasma, human urine, rat plasma, rat urine and hydrolyzed rat urine is described. This methylated amino acid and the procedural internal standard 6-N,N,N-trimethyllysine were isolated from the sample matrices using short ion-exchange columns and detected following high-performance liquid chromatography using a postcolumn reaction (o-phthalic-dicarboxaldehyde-2-mercaptoethanol) and fluorometric detection. The reliable detection limit for 6-N,N,N-trimethyllysine was 0.2 nmol/ml in 200 microliters of human plasma. The chromatographic separation exploits the unique properties of a novel tertiary amine mobile phase modifier, 3-(N,N-dimethylamino)-1,2-propanediol. The capacity factor and "Chromatographic Figures of Merit" (including peak asymmetry and relative system efficiency) were calculated for the chromatographic peak representing 6-N,N,N-trimethyllysine in over 2200 injections made while evaluating 900 biological specimens.     

Special examples of quantized friction

The non-linear velocity potential formulation of quantal friction is studied in several special schematic cases: the spreading of a Gaussian packet, superposition of packets, barrier penetration, and potential resonances. Those features which emerge are unified by the concept of a local fluid velocity to which friction is proportional.     

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.