Acoustic Doppler shifts in medicine

This is a brief discourse on the history of the uses of acoustic Doppler frequency shifts in modern medicine. The Doppler effect and the Doppler equation are discussed. The technological developments over the last half century are covered, as well as their applications in diagnostic medical sonography. A limited discussion of the pathologies that may be diagnosed using the Doppler effect is also presented.     

Classical chemical concepts from ab initio SCF calculations

Alternative definitions of bond order, valency, gross orbital populations and total atomic charge for SCF wavefunctions are compared. It is found that there are sound theoretical and numerical reasons for preferring definitions based on the Löwdin density matrix.     

An experimental investigation of the onset of theL 2-L 3 M 4 andL 2-L 3 M 5 Coster-Kronig transitions forZ>90

L-M coincidence measurements were made on x rays from the radioactive decays of ₉₆ ²⁴⁴ Cm, ₉₄ ²³⁸ Pu, and ₉₂ ²³² U. The observation ofM x rays in coincidence with theL ₃ N _{4, 5} transition indicates that the onset of theL ₂-L ₃ M ₅ Coster-Kronig transition takes place atZ=91 or 92. The measured ratio of theM x-ray counting rates, coincident with theL ₃ N _{4, 5} andL ₂ M ₄ transitions, establishes that both theL ₂-L ₃ M ₄ and theL ₂-L ₃ M ₅ transitions are energetically possible forZ≧94, but the results do not rule out the possibility that these transitions begin as low asZ=92. The measurement ofL-M x-ray coincidences, together with relative Coster-Kronig electron intensities from theory or experiment, provides a new way to measure the totalL ₂-L ₃ Coster-Kronig transition probability,f ₂₃, at highZ for radioactive sources where the primary vacancies are created primarily in theL ₂ andL ₃ subshells. The present result atZ=94 indicates that the theoretical calculations of McGuire of the relative partial Coster-Kronig transition rates forL ₂-L ₃ M _4,5 are accurate to within 10 percent.     

Simple automated gas chromatographic analysis of amino acids and its application to brain tissue and urine

The separation of 21 free amino acids as their isobutyl N(O,S)-pentafluorobenzoyl derivatives by capillary gas chromatography with electron-capture detection is described. This method has been successfully applied to routine analysis of most of these amino acids in brain tissue and urine. The amino acids are converted to their isobutyl N(O,S)-pentafluorobenzoyl derivatives by acid-catalysed esterification followed by aqueous extractive pentafluorobenzoylation. The 21 amino acids can be separated on a single capillary column in 21 min. The high sensitivity permits analysis in minute quantities of sample and the high stability permits the use of an automatic sample injector at ambient temperatures. Thus, over 50 samples can be readily analyzed in a single day.     

Structural resolution of the stereochemistry of a spirooxirane derived from an α-arylidene heterocyclic carbonyl. The crystal and molecular structure of 2-(p-chlorophenyl)-5-phenyl-7-methyl-1-oxa-5,6-diazaspiro[2.4]hept-6-en-4-one

The stereochemical assignment of molecular geometry for α-arylidene carbonyl compounds and spirooxirane derived from them have continued to be a challenging problem for which the most satisfactory solution continues to be an x-ray diffraction structure determination. In that regard, the title compound (a spirooxirane) has been found to crystallize in the monoclinic space group P2_1/c with cell dimensions of a = 5.989(1)Å, b = 27.625(4)Å, c = 9.374(2)Å, β = 99.06(1)°. The structure of the compound has been determined, with the refinement to R = 0.059. The previous, tentative assignment of structure has been confirmed substantiating our prediction that the oxidation of the enone system proceeds with rotation of the phenyl group on the β-carbon away from the carbonyl group, minimizing adverse steric interactions and allowing orbitals of the carbonyl group to overlap with those of the carbanionic center during the closure of the oxirane ring. The agreement between predictions based on nmr data and the x-ray diffraction determination will support a stronger reliance on the nmr data predictions in subsequent studies.     

Orthogonal line packings of PG2m − 1(2)

Baker (Discrete Math., 15 (1976), 205–211) has shown that there exists a packing of the lines of each odd dimensional projective space over the field of two elements as a corollary to a theorem asserting the existence of a 2-resolution of the Steiner quadruple system of planes in an even dimensional affine space over the field of two elements. Two packings are orthogonal if any two of their spreads have at most one line in common. A variation of the previous construction gives alternate packings so that, for example, the existence of orthogonal packings of PG_{2m ? 1}(2) when three does not divide 2m ? 1 can be demonstrated.