Microstructure determination of poly-(1,3-pentadiene) by a combination of infrared, 60-MHz NMR, 300-MHz NMR,and X-ray diffraction spectroscopy

A quantitative procedure has been developed for characterizing the complete microstructure of polymers of 1,3-pentadiene, including the tacticity of any crystalline component. This can be accomplished by a combination of infrared spectroscopy, X-ray crystallinity, and 300-MHz NMR spectroscopy. A series of high structural purity polymers were synthesized with a series of previously unreported mixed microstructures. These samples were characterized by using the three techniques mentioned, including the previously unreported 300-MHz NMR data. With those results a 60-MHz NMR/IR method of spectroscopy was developed to determine the composition of poly(1,3-pentadiene)s in terms of percent cis-1,2-, cis-1,4-, trans-1,4-, and 3,4-pentadiene units.     

A noncommutative geometric approach to left-right symmetric weak interactions

By combining the generalized exterior algebra of forms over a noncommutative algebra with the gauging of discrete directions and the associated Higgs fields, we consider the construction of the bosonic sector of left-right symmetric models of the form SU(2) _L SU(2) _R U(1). We see that within this formalism maximal use can be made of the gauge connection associated with the noncommutative graded algebra.     

Metallic reflectance of AsF5-graphite intercalation compounds

Room temperature measurements of the 0.07–2.0 eV optical reflectance of carefully prepared stage 1–4 AsF₅-graphite intercalation compounds have been performed. Stages 1–3 show simple metallic behavior with a well-defined plasma edge. Curve fits to the data give good agreement between dc and optical conductivities for stage 1 and 2. Comparison between stage 2 data for AsF₅ and HNO₃ compounds suggests that the higher conductivity of the former arises from a longer carrier relaxation time rather than from a greater carrier density.     

Correlations in the final states ppπ+π−π+π− and ppπ+π−π+π−π+π− from 28.5 GeV/c pp collisions

We compare various invariant mass and angular distributions from the final states ppπ⁺π^?π⁺π^? and ppπ⁺π^?π⁺π^?π⁺π^? with the predictions of two models. The essential input to these models is the correct single-particle distributions with energy and momentum conservation constraints taken into account. The data is from 28.5 GeV/c pp interactions in the BNL 80-inch bubble chamber. Substantial agreement between the data and the models is obtained inferring that the kinematic constraints of energy and momentum conservation play a strong role in determining correlations between particles in these high multiplicity final states.     

Counting bridgeless graphs

Methods are developed for finding the number of unlabeled bridgeless or 2-line-connected graphs of any order. These methods are based on cycle index sums, but it is shown how to avoid explicit compution with cycle index sums by using suitable inversion techniques. Similar results are obtained for unlabeled bridgeless graphs by numbers of points and lines, and connected graphs by numbers of points and bridges. Corresponding results for labeled graphs are found as corollaries. When lines or bridges are required as enumeration parameters in the labeled case it is also shown how to obtain improved recurrence relations. The latter appear to have no analog for unlabeled graphs.     

Order and disorder in algebraic combinatorics

Text of a plenary address given to the Canadian Mathematical Society at their annual meeting at the University of Waterloo in December 1990. The author’s work is partially supported by grants from the National Science Foundation.     

Evidence for strong clustering effects in high-multiplicity final states at 30 GeV

A statistical analysis of the event-to-event fluctuations of the langitudinal-momentum distributions is applied to 2-, 3-, 4- and 6-pion production data in $\text{28}\text{GeV}\text{c}$ proton-nucleon collisions, as well as to several models. The results indicate that a dominant feature of these final states is the formation of high-multiplicity clusters of particles.     

Scattering differentiates Alzheimer disease in vitro

The molecular bases of Alzheimer disease and related neurodegenerative disorders are becoming better understood, but the means for definitive diagnosis and monitoring in vivo remain lacking. Near-infrared optical spectroscopy offers a potential solution. We acquired transmission and reflectance spectra of thin brain tissue slabs, from which we calculated wavelength-dependent absorption and reduced scattering coefficients from 470-1000 nm. The reduced scattering coefficients in the near infrared clearly differentiated Alzheimer from control specimens. Diffuse reflectance spectra of gross brain tissue in vitro confirmed this observation. These results suggest a means for diagnosing and monitoring Alzheimer disease in vivo, using near-infrared optical spectroscopy.     

Tractable Partially Ordered Sets Derived from Root Systems and Biased Graphs

We study new posets Q obtained by removing from a geometric lattice L ofa biased graph certain flats indexed by a simplicial complex . (One example of L is the lattice of flats of thevector matroid of a root system B _n .) We study the structureand compute the characteristic polynomial of Q. With certainchoices of L and , including ones for which Q is alattice interpolating between those of B _n and D _n , we observe curious relationships among the roots of thecharacteristic polynomials of Q, L, and .     

A -deformation of a trivial symmetric group action

Let be the arrangement of hyperplanes consisting of the reflecting hyperplanes for the root system . Let be the Varchenko matrix for this arrangement with all hyperplane parameters equal to . We show that is the matrix with rows and columns indexed by permutations with entry equal to where is the number of inversions of . Equivalently is the matrix for left multiplication on by

Clearly commutes with the right-regular action of on . A general theorem of Varchenko applied in this special case shows that is singular exactly when is a root of for some between and . In this paper we prove two results which partially solve the problem (originally posed by Varchenko) of describing the -module structure of the nullspace of in the case that is singular. Our first result is that

in the case that where Lie denotes the multilinear part of the free Lie algebra with generators. Our second result gives an elegant formula for the determinant of restricted to the virtual -module with characteristic the power sum symmetric function .