Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries

We consider nonnegative solutions of a parabolic equation in a cylinder D×(0,T), where D is a noncompact domain of a Riemannian manifold. Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(M_∂D×[0,T)), where M_∂D is the Martin boundary of D for the associated elliptic operator. We apply it in a unified way to several concrete examples to explicitly represent nonnegative solutions. We also show that [IU] implies the condition [SP] (i.e., the constant function 1 is a small perturbation of the elliptic operator on D).     

Synthetic studies toward maytansinoids (2) a new strategy based on asymmetric induction by heteroconjugate addition of methyllithium onto pyranosyl hetero-olefins

The functionalized pyranosyl hetero-olefins $\text{4a}$, $\text{13}$ and $\text{15}$ received a remarkable diastereoselective addition of methyllithium to form $\text{threo}$ adducts, one of which was introduced into a possible synthetic intermediate as $\text{3}$ for maytansine ($\text{1}$) along Scheme I.     

Fock representations of the affine Lie algebraA 1 (1)

The aim of this note is to show that the affine Lie algebraA ₁ ⁽¹⁾ has a natural family _, ,v of Fock representations on the spaceC[x _i,y _j;i andj ], parametrized by (,v) C ². By corresponding the highest weight _, of _, to each (,), the parameter spaceC ₂ forms a double cover of the weight spaceC₀C –₁ with singularities at linear forms of level –2; this number is (–1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA ₁ ⁽¹⁾ -modules for generic (,v).     

Photo-initiated base-formation in a polymer matrix

It was found that amines were formed efficiently by the photolysis of O-acyloximes followed by hydrolysis in polystyrene films and the relationship between structures of O-acyloximes and yields of amines were investigated. O-phenylacetyl acetophenone oxime (PaApO), O-pivaloyl acetophenone oxime (PApO), and O-benzoyl acetophenone oxime (BApO) as monofunctional O-acyloximes and O,O′-succinyl diacetophenone oxime (SDApO) and O,O′-glutaryl diacetophenone oxime (GDApO) as bifunctional O-acyloximes were examined. The yields of amines for PaApO and SDApO under N₂ were ca. 70%, which was the highest among O-acyloximes examined in this experiment. On the other hand, the yields for PApO, BApO, and GDApO were less than 15% and it was verified that the hydrogen abstraction by imino radicals via 6-membered cyclic intermediates resulted in the lowering of yields. Although the effect of oxygen under photolysis on the yields of amine for PaApO was negligible under 50% conversion of PaApO, the yield decreased with further increase in the conversion and was 50% at 90% conversion. © 1994 John Wiley & Sons, Inc.     

Chlorodimethylaluminum-promoted nucleophilic addition of lithium pentamethylcyclopentadienide to aliphatic aldehydes and DDQ-mediated carbon-carbon bond cleavage of the adducts providing the parent aldehydes

Treatment of aliphatic aldehyde with lithium pentamethylcyclopentadienide in the presence of chlorodimethylaluminum provided the corresponding carbinol in excellent yield. The carbinol returns to the parent aldehyde and pentamethylcyclopentadiene by the action of a catalytic amount of 2,3-dichloro-5,6-dicyanobenzoquinone (DDQ).     

Vinyl polymerization. CCCXXXIX. Effect of chain length of nylon 3 on the polymerization of methyl methacrylate initiated with the system of nylon 3, copper(II) ion,and water

It was found recently that the system of nylon 3, copper(II) ion, and water could initiate a radical polymerization of methyl methacrylate(MMA). In the present paper, the effect of average chain length of the molecules of nylon 3 on the rate of polymerization of MMA was studied. The rate increased with the chain length of nylon 3. This result was explained well by the fact that the shorter nylon 3 forms a complex with copper (II) ion more easily than longer nylon 3. It was assumed that the shorter nylon 3 fills three or four coordination sites of copper(II) ion and loses the ability to initiate the polymerization. The efficiency of grafting of MMA and the degree of polymerization of MMA homopolymer were independent of the chain length of nylon 3.     

Synthesis and polymerization of N-[N′-(α-methylbenzyl)aminocarbonyl-n-alkyl]maleimide

Two types of optically active N-[N′-(α-methylbenzyl)amino/carbonyl-n-alkyl]maleimides (MBAC) were synthesized from maleic anhydride, 6-amino-n-caproic acid (or 12-amino-n-dodecanoic acid), and (R)-(+)-α-methylbenzylamine. Radical homopolymerizations of MBAC were performed in several solvents at 60 and 110°C for 24 h to give optically active polymers. Radical copolymerizations of MBAC were performed with styrene (ST) and methyl methacrylate (MMA) in dioxane at 60°C. The monomer reactivity ratios and the Alfrey-Price Q-e values were determined. Chiroptical properties of the polymers and copolymers were investigated. © 1995 John Wiley & Sons, Inc.     

Cellulose Synthesized by Acetobacter Xylinum in the Presence of Acetyl Glucomannan

Acetobacter xylinum was cultured in Hestrin-Schramm medium (control medium) and Hestrin-Schramm medium containing acetyl glucomannan (mannan medium). Loose bundles of the cellulose microfibrils are formed in the mannan medium in contrast to the normal ribbons being produced in the control medium. Rapid-freeze and substitution method followed by metal-shadowing revealed the droplet-like structures around the microfibril synthesized in the mannan medium. The cellulose synthesized in the mannan medium was stained heavily by the periodic acid-thiocarbohydrazide-silver proteinate (PATAg) method, while the cellulose synthesized in the control medium was not stained. X-ray diffractometry and FT-IR spectroscopy indicated that the addition of mannan induced a change in the crystal structure from the algal-bacterial type to the cotton-ramie type. Thus the presence of acetyl glucomannan in the medium prevents the assembly of cellulose microfibrils and changes the crystal structure of cellulose.     

Two-dimensional self-organization of phthalocyanine and porphyrin: dependence on the crystallographic orientation of Au

By immersing Au substrate into a benzene solution containing both cobalt(II) phthalocyanine (CoPc) and copper(II) tetraphenyl-21H,23H-porphine (CuTPP), a two-dimensional alternate bimolecular structure was formed on the reconstructed Au(100)-(hex) surface.     

Detection of bilayer packing stress and its release in lamellar-cubic phase transition by time-resolved fluorescence anisotropy

An introduction of nonlamellar-forming lipids into planar bilayers generates packing stress, which is important for the biological functions of plasma membranes and is a driving force for the lamellar-nonlamellar phase transition. We have investigated the phase behavior of a binary system consisting of egg yolk phosphatidylcholine and monoolein (MO) and the changes in the local orientation order of lipids in a lamellar-bicontinuous cubic phase transition. Small-angle X-ray scattering has revealed that the lamellar-bicontinuous cubic phase transition occurs at an MO molar fraction (X(MO)) between 0.6 and 0.7. These phases were dispersed to form liposomes and cubosomes to monitor the anisotropy of the incorporated fluorescence probe, in which Pluronic F127, used as a dispersion stabilizer of the cubic phase, has been proven not to alter the cubic structure and the location of the probes. Time-resolved fluorescence anisotropy measurements on these dispersions have revealed that the order parameter of the probe in the lamellar phase increases with increasing X(MO), and that it decreases during the transition to the cubic phase. This observation suggests that packing stress generated by the addition of the nonlamellar-forming lipid is released by the phase transition.