The minimal entropy conjecture for nonuniform rank one lattices

The Besson–Courtois–Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices. This research was partially supported by an NSF Postdoctoral Fellowship. Received: June 2004; Revision: January 2006; Accepted: March 2006     

Carbohydrate carbocyclization by a zinc-mediated tandem reaction and ring-closing enyne metathesis

Methyl 5-deoxy-5-iodo-pentofuranosides are reductively ring-opened and propargylated in a tandem fashion in the presence of zinc. The 1,7-enynes thus obtained are subjected to ring-closing enyne metathesis with catalyst B to produce functionalized 1-vinyl cyclohexenes. By adding BnNH(2) to the tandem reaction, an amino group can be introduced in the 1,7-enyne products. Addition of 2-TMS-ethynylcerium(III) chloride after the reductive ring-opening produces the corresponding 1,6-enynes. Further annulation of the product 1,3-dienes can be achieved through a Diels-Alder reaction with good control of stereochemistry. These procedures constitute efficient methods for rapid carbocyclization and annulation of carbohydrates to produce a variety of functionalized five- and six-membered ring systems.     

Online measurement of thermal diffusivity during cure of an epoxy composite

Thermal diffusivity was measured online during cure of an epoxy composite using a method somewhat similar to the Ångström Method. It is shown that a simple experimental setup can be used, thus avoiding expensive instrumentation. The experimental instrumentation is explained in detail. The measurements show an increase of thermal diffusivity during the cure of composite material. Using modulated differential scanning calorimetry (MDSC), heat capacity was measured online during the cure of an epoxy composite. Combining thermal diffusivity measurements with MDSC measurements, the thermal conductivity was found to change during the cure process, similar to the measurements of heat capacity. These changes are referred to vitrification at the end of the cure process.     

An explicit height bound for the classical modular polynomial

For a prime l, let Φ _l be the classical modular polynomial, and let h(Φ _l ) denote its logarithmic height. By specializing a theorem of Cohen, we prove that \(h(\Phi_{l})\le 6l\log l+16l+14\sqrt{l}\log l\). As a corollary, we find that h(Φ _l )≤6llog?l+18l also holds. A table of h(Φ _l ) values is provided for l≤3600.     

Intrinsic route to melt fracture in polymer extrusion: a weakly nonlinear subcritical instability of viscoelastic poiseuille flow

As is well known, the extrusion rate of polymers from a cylindrical tube or slit (a "die") is in practice limited by the appearance of "melt fracture" instabilities which give rise to unwanted distortions or even fracture of the extrudate. We present the results of a weakly nonlinear analysis which gives evidence for an intrinsic generic route to melt fracture via a weakly nonlinear subcritical instability of viscoelastic Poiseuille flow. This instability and the onset of associated melt fracture phenomena appear at a well-defined ratio of the elastic stresses to viscous stresses of the polymer solution.     

Alkylpyrazines from hymenoptera: Isolation,identification and synthesis of 5-methyl-3- n-propyl-2-(1-butenyl)pyrazine from Aphaenogaster ants (formicidae)

Mandibular glands of Aphaenogaster rudis workers contain 5 - methyl - 3-n - propyl - 2 -(1 -butenyl)pyrazine, a new natural product. This pyrazine and several of its isomers have been synthesized from the corresponding 2,3-, 2,5- or 2,6-dimethylpyrazines. Marked differences in the mass spectra of these multialkylated pyrazines are discussed. In addition, dimethylalkylpyrazines are reported from a variety of aculeate wasps.     

Migration Study of Polypropylene (PP) Oil Blends in Food Simulants

Migration study in aqueous and olive oil food simulants was carried out on PP and its blend with oil mixture. It was found that after 10 days at 44 °C PP with oil content up to 0.83% had overall migration into olive oil less than 10 mg/dm². However, under high temperature migration test (at 110–138 C for 4 hours), the overall migration into olive oil was large for both the virgin PP and all its blends. The overall migration in water, 10% ethanol, and 3% acetic acid was smaller than those in olive oil under both migration test conditions. DSC and density measurement showed that addition of oil in PP led to smaller spherulite size and increased degree of crystallinity in the pure PP part. Small decrease in tensile strength in the oil blends was also observed but there was no significant change in tensile strength after migration test.