Invariant elliptic estimates

In this paper, we revisit elliptic estimates invariant under domain expansion. We improve the invariant elliptic estimates in the previous paper [Y. Cho, T. Ozawa, Y. Shim, Calc. Var. PDE 34 (2009) 321-339] via gradient estimate and discuss an application to the Lamé system.     

Design of chiral bis-phosphoric acid catalyst derived from (R)-3,3'-di(2-hydroxy-3-arylphenyl)binaphthol: catalytic enantioselective Diels-Alder reaction of α,β-unsaturated aldehydes with amidodienes

Chiral bis-phosphoric acid 1 was designed to identify a new class of structural features in chiral Br?nsted acid catalysts. X-ray diffraction analysis revealed the single atropisomer 1, bearing S axial chirality at 3,3'-biaryl substituents on (R)-binaphthyl and intramolecular hydrogen bonding between the two phosphoric acid moieties. The newly designed bis-phosphoric acid 1 was evaluated in the Diels-Alder reaction of α,β-unsaturated aldehydes 4 with 1-N-acylamino-1,3-butadienes 3. After systematic variation of the catalyst substituents, as well as the N-acyl substituents of 1,3-butadiene, the use of an N-Cbz amidodiene 3a in the presence of bis-phosphoric acid 1e with a 2,4,6-tri-isopropylphenyl group was found to be optimal to yield the 1S,6R enantiomeric product 5aa in a Diels-Alder reaction of acrolein (4a). Application of this method to substituted substrates was found to be an efficient approach to the enantioselective synthesis of 3- and 3,6-substituted cyclic formylcarbamates 5. The specific character as well as the utility of 1e was further established by comparing its enantioselectivity, absolute stereochemistry, and catalytic efficiency with those of mono-phosphoric acid 2.     

Dioxygenases, key enzymes to determine the aglycon structures of fusicoccin and brassicicene, diterpene compounds produced by fungi

Fusicoccin A and cotylenin A are structurally related diterpene glucosides and show a phytohormone-like activity. However, only cotylenin A induces the differentiation of human myeloid leukemia cells. Since the cotylenin A producer lost its ability to proliferate during preservation, a study on the relationship between structure and activity was carried out and a modified fusicoccin A with hydroxyl group at the 3-position showed a similar biological activity with that of cotylenin A. We then searched for an enzyme source that catalyzes the introduction of a hydroxyl group into the 3-position and found that brassicicene C, which is structurally related to fusicoccin A with hydroxyl group at the 3-position, was produced by Alternaria brassicicola ATCC96836. We recently cloned a brassicicene C biosynthetic gene cluster including the genes encoding fusicocca-2,10(14)-diene synthase and two cytochrome P450s, which were responsible for the formation of fusicocca-2,10(14)-diene-8β,16-diol. In this study, we report that a α-ketoglutarate dependent dioxygenase, the gene coding for which was located in the cluster, catalyzed a hydroxylation at the 3-position of fusicocca-2,10(14)-diene-8β,16-diol. On the other hand, a α-ketoglutarate-dependent dioxygenase, which had been identified in a fusicoccin A biosynthetic gene cluster, catalyzed the 16-oxidation of fusicocca-2,10(14)-diene-8β,16-diol to yield an aldehyde (8β-hydroxyfusicocca-1,10(14)-dien-16-al), although both dioxygenases had 51% amino acid sequence identity. These findings suggested that the dioxygenases played critical roles for the formation of the fusicoccin A-type and cotylenin A-/brassicicene C-type aglycons. Moreover, we showed that short-chain dehydrogenase/reductase located in the fusicoccin A biosynthetic gene cluster catalyzed the reduction of the aldehyde to yield fusicocca-1,10(14)-diene-8β,16-diol.     

DIBAL-mediated reductive transformation of trans-dimethyl tartrate acetonide into ε-hydroxy α,β-unsaturated ester and its derivatives

Stepwise, selective DIBAL reduction of the acetonide diester derived from tartaric acid followed by the Horner-Emmons reaction effectively provided desymmetrized hydroxy mono-olefination products in a one-pot operation.     

Capillary electrophoretic discrimination of single nucleotide polymorphisms using an oligodeoxyribonucleotidepolyacrylamide conjugate as a pseudo-immobilized affinity ligand: optimum ligand length predicted by the melting temperature values.

We developed a weak-affinity separation system for single-nucleotide polymorphisms (SNPs) based on capillary electrophoresis. In this approach, single-stranded DNA (ssDNA)-polyacrylamide (polyAAm) conjugate was used as a pseudo-immobilized affinity ligand to separate the target DNA, cytochrome P450 2C9 (CYP2C9), and its point mutant. The ligand DNA was designed to be complementary to the normal DNA, and the target DNA was electrophoretically separated by the difference in the affinity with the pseudo-immobilized ligand in the capillary. We showed that the separation efficiency was closely associated with the Tm value of double-stranded DNA (dsDNA) consisting of the target and ligand DNA, which depends on the measurement conditions, such as the base number of the ligand DNA and the concentration of Mg2+ in the buffer solution.     

Prediction of carcinogenicity of polynuclear aromatic hydrocarbons on the basis of their chemical structures

The carcinogenicities of polynuclear aromatic hydrocarbons in particulates extracted from diesel engine exhaust are predicted on the basis of the combined bay-L region theory proposed earlier, in conjunction with pattern recognition techniques. The predicted carcinogenicities agree well with experimental data, thus showing the validity of the proposed model equations.     

Spectral Gap and Exponential Decay of Correlations

We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two observables anticommute with each other at large distance, then the nonvanishing spectral gap implies exponential decay of the corresponding correlation. When two observables commute with each other at large distance, the connected correlation function decays exponentially under the gap assumption. If the observables behave as a vector under the U(1) rotation of a global symmetry of the system, we use previous results on the large distance decay of the correlation function to show the stronger statement that the correlation function itself, rather than just the connected correlation function, decays exponentially under the gap assumption on a lattice with a certain self-similarity in (fractal) dimensions D < 2. In particular, if the system is translationally invariant in one of the spatial directions, then this self-similarity condition is automatically satisfied. We also treat systems with long-range, power-law decaying interactions.     

Measurement of Principal-Stress Directions from Photoelastic Experiment Using Generalized Phase-Shift Method

A generalized phase-shift method is developed for automatic measurement of principal-stress directions in the whole field of a model from photoelastic experiments. This method uses a set of light intensities obtained from the rotation of polaroids in dark-field plane polariscopes at each point. To investigate the accuracy of the measurement, time-series light intensity curves with different noise and different numbers of data which constitute the curves are used in computer simulation. The error of the measurement of the principal-stress directions obtained by the method is not greatly affected by noise when the number of data exceeds 50. This method is applied to a circular disk subjected to a concentrated load. The principal-stress directions obtained by the method are found to be in good agreement with the theory.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27–29, Saitama, Japan.     

Exponential decay of solutions to nonlinear elliptic equations with potentials

Exponential decay estimates are obtained for complex-valued solutions to nonlinear elliptic equations in \mathbbRⁿ ,\mathbb{R}^{n} , where the linear term is given by Schr?dinger operators H =  − Δ  +  V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We describe specific rates of decay in terms of V, some of which are shown to be optimal. Moreover, our estimates provide a unified understanding of two distinct cases in the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V(x) = |x|².