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).     

Complexation and fluorescence behavior of diazacrown ether carrying two anthryl pendants

Photoinduced electron transfer (PET) fluoroionophores (1b, 2b) that consist of diazacrown and two 9-anthryl pendants show fluorescent enhancement with various guest salts. The diaza-12-crown-4 derivative (2b) exhibited Zn(2+) selectivity and in the presence of this cation the host fluorescence intensity was increased by a factor of 182. The guest cation-induced fluorescence enhancement of 2b was larger than the diaza-18-crown-6 derivative (1b).     

Regiospecific cycloaddition reactions using functionalized isoprenylsilane and related compounds

1-Alkoxy-3-trimethylsilylmethyl- and 1-alkoxy-3-trimethylsilyl-l,3-butadienes ($\text{1}$) were newly prepared. The cycloaddition reactions of $\text{1}$ with various dienophiles including heterodienophiles were found to proceed very smoothly in a perfectly regiospecific mode.     

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.     

Asymmetric synthesis of 2-substituted-3-aminocarbonyl propionic acid

An asymmetric synthetic route to 2-substituted-3-aminocarbonyl propionic acid, which is the significant component of low-molecular-weight renin inhibitors, is described. The key step of this synthesis is diastereoselective alkylation by using chiral oxazolidinone and benzyl bromoacetate.     

10B quantitative determination in ppb range by particle tracks reading for boron neutron capture therapy

Quantitative determination of ppb-order ¹⁰B was carried out in a small number of cultured tumor cells by particle tracks by the ₁₀B(n,)⁷Li reactions using solid state nuclear track detector (SSNTD) for boron neutron capture therapy research. The detection limit of ¹⁰B concentration in tumor cells is less than 1·10^-3 ppm under our experimental conditions which permits the quantitative determination of ¹⁰B in a small number of boronated tumor cells (10⁵/ml = ca. 0.1 mg). Boron quantities in tumor cells determined were well compatible with the tumor cell killing effects of boron neutron capture therapy.     

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).