Cobalt π-cations in carbocyclic ring constructions

In a combination of cobalt-mediated cationic and free radical chemistry, treatment of the allyl silane substituted β-hydroxycobaloxime 13 with pTSA led predominantly to the trans-disubstituted cyclopentane 14, which on irradiation with TEMPO produced 15. In a similar manner, the cobaloxime 18 was cyclised to 19 in the presence of pTSA which, on irradiation with a sunlamp then underwent radical mediated cyclisation to the substituted indane 20.     

Weak-1 generators for a class of subalgebras of l1

Let α ? 0 and let $\text{D(}\text{α}\text{) = {f(z) = ∑}{}_0{}^{\mathrm{\infty }}\text{α}{}_{\mathrm{n}}\text{z}{}^{\mathrm{n}}\text{¦ ∑}{}_0{}^{\mathrm{\infty }}\text{(n + 1)}{}^{\mathrm{<mtext>\alpha </mtext>}}\text{¦ a}{}_{\mathrm{n}}\text{¦ < ∞}}$. Then D(α) is a subalgebra of l¹. We discuss the weak-1 generators of D(α). We use some of our techniques to prove that if ? is a weak-1 generator of H^∞ and ∥ ? ∥_∞ ? 1, then the composition operator C_? on the Dirichlet space has dense range.     

The Effects of the Modified Starches on the Melting Flow and Biodegradation of the Starch/Glycerol Blend

Summary: The purpose of this study was to improve the melting flow of starch/glycerol(GA) blends by modified starches. A variety of modified starches, which was treated by hydrolysis and acid hydrolysis, with and without ultrasonic treatment were used. The MFI (melt flow index) of blends increased from 0.5g/10min to 300g/10min when the addition of acid hydrolysis starch (0.3M CA-starch) was 70wt%. Their crystalline behaviors were analyzed by XRD results. The ultrasonic treatment has been proved to have the effect of hydrolysis without acids and synergistic effect on recrystalline. The SEM micrographs of the blend with the ultrasonic treatment starch gave the cleaving surface with comparison to the other blends. The weight loss of the blends with acid hydrolysis starches reached to 60∼80% after one week biodegradation as the ultrasonic treatment was used.     

Quantum Reduction for Affine Superalgebras

We extend the homological method of quantization of generalized Drinfeld–Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.     

A characterization of “rapidity” curve in the chiral Potts model

We study the geometry of high genus curves of rapidity variables in chiral Potts model. In terms of symmetries, we characterize these Rieman surfaces and derive their period matrices. By the theory of prime forms, the temperature-like parameter is expressed by hyperelliptic theta functions.     

On Ricci flat 3-fold

In this paper we study a sub-class of compact Ricci flat manifolds from certain standard constructions. Research supported in part by NSF grant #DMS84-09447 and ONR contract #N-00014-85-K-0367.     

Geometric singularities and spectra of Landau-Ginzburg models

Some mathematical and physical aspects of superconformal string compactification in weighted projective space are discussed. In particular, we recast the path integral argument establishing the connection between Landau-Ginzburg conformal theories and Calabi-Yau string compactification in a geometric framework. We then prove that the naive expression for the vanishing of the first Chern class for a complete intersection (adopted from the smooth case) is sufficient to ensure that the resulting variety, which is generically singular, can be resolved to a smooth Calabi-Yau space. This justifies much analysis which has recently been expended on the study of Landau-Ginzburg models. Furthermore, we derive some simple formulae for the determination of the Witten index in these theories which are complimentary to those derived using semiclassical reasoning by Vafa. Finally, we also comment on the possible geometrical significance ofunorbifolded Landau-Ginzburg theories.     

Principal component analysis for emergent acoustic signal detection with supporting simulation results

A method is introduced that uses principal component analysis (PCA) to detect emergent acoustic signals. Emergent signal detection is frequently used in radar applications to detect signals of interest in background clutter and in cognitive radio to detect the primary user in a frequency band. The method presented differs from other standard techniques in that the detection of the signal of interest is accomplished by detecting a change in the covariance between two channels of data instead of detecting the change in statistics of a single channel of data. For this paper, PCA is able to detect emergent acoustic signals by detecting when there is a change in the eigenvalue subspace of the covariance matrix caused by the addition of the signal of interest. The algorithm's performance is compared to an energy detector and the Neyman-Pearson theorem. Acoustic simulations were used to verify the performance of the algorithm. Simulations were also used to examine the effectiveness of the algorithm under various signal-to-interferer and signal-to-noise ratios, and using various test signals.     

Excitation spectrum and phase structure of the chiral Potts model

The spectrum of low lying excitations of the integrable chiral Potts model is computed. It is shown that there is a region in the parameter space where the excitation energies become negative thus indicating that a level crossing transition to a new incommensurate ground state has occurred.