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).     

Sensitive determination of anandamide in rat brain utilizing a coupled-column HPLC with fluorimetric detection

A fluorimetric determination method for N-arachidonoylethanolamine (anandamide) was developed using a precolumn fluorescence derivatization followed by coupled-column high-performance liquid chromatography (HPLC). Anandamide extracted from the rat brain tissue was derivatized with 4-N-chloroformylmethyl-N-methylamino-7-N, N-dimethylaminosulfonyl-2,1,3-benzoxadiazole (DBD-COCl), purified by a solid-phase extraction (Emporetrade mark), and assayed by the coupled-column HPLC. The HPLC consisted of phenyl (100 x 4.6 mm i.d. ) and octadecylsilica columns (250 x 4.6 mm i.d.), both connected by a six-port valve. The concentration of anandamide in rat brain was 3. 37 +/- 0.73 pmol/g with 6.47 and 3.57% of intra- and inter-day precisions, respectively. Using this method, we investigated the alteration of anandamide concentration in rat brain 30 min after administration of anandamide (2 mg/kg, i.p.) to rats pretreated with or without phenylmethylsulfonyl fluoride (PMSF; 30 mg/kg, i.p.), an inhibitor of amidohydrolase. In rats pretreated with PMSF, the brain concentration of anandamide was approx. 16-fold higher than that of rats without PMSF (p < 0.01).     

Rapid determination method of radiocesium in sea water by cesium-selective resin

A rapid and precise method of determining radiocesium corresponding to 5 mrem/y, the Japan AEC's guideline, was proposed. The development and practical performance of cesium-selective resin and the determination method was described in this paper. The resin was prepared by the formation of ammonium molybdophosphate in the structure of Amberlite XAD-7 resin. It took only 3 hours to carry out all the procedures the authors proposed. This value represents 1/10∼1/2 of the time of conventional method. The concentration of¹³⁷Cs and¹³⁴Cs in sea water was determined to be 0.13∼0.16 pCi/1 and less than 7.1·10⁻² pCi/1, respectively.     

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.     

Adsorption Isotherm of Water Vapor and Its Large Hysteresis on Highly Ordered Mesoporous Silica

The first and second adsorption–desorption isotherms of water vapor on a new mesoporous material derived from kanemite have been measured. The isotherms show unusual type V isotherms and large hysteresis. The type V isotherms, which have never been observed for the other adsorbates, suggest that the mesoporous material has a hydrophobic surface, although the hydrophobicity decreased after treatment with water vapor because of rehydration of the surface. The significantly large hysteresis could be explained by the difference in contact angle between adsorption and desorption.     

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.