Chemistry of the neopolyoxins,pyrimidine and imidazoline nucleoside peptide antibiotics

New chitin synthetase inhibitors, neopolyoxins A, B, and C were isolated from the culture filtrate of Streptomyces cacaoi subsp. asoensis. Their absolute structures have been established on the basis of chemical and spectroscopic evidence. They are structural analogs of the polyoxins. As a nucleobase, neopolyoxin C possesses uracil, while neopolyoxins A and B contain the imidazoline moiety. A ring contraction reaction of pyrimidine nucleoside into imidazoline nucleoside played a key role in the structure determination of the nucleoside moiety. A similar transformation was suggested for the biosynthesis of neopolyoxins A and B.     

Enantioselective conjugate additions of organolithiums to BHA enoates mediated by A chiral ligand

The conjugate addition reactions of BHA alkenoates with organolithiums in toluene or toluene-hexane at −78 °C were mediated by the chiral ligands 1 and 2 to give the corresponding 3-substituted alkanoates in high ees and high yields. The two ligands are complementary each other, 1 is effective for phenyl- and vinyllithiums to give the adducts in 64–93% ee, while 2 is effective for butyl- and ethyllithiums to give the adducts in 91–99% ee.     

Vertices of Degree 5 in a Contraction Critically 5-connected Graph

An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is said to be contraction critically k-connected. We prove that a contraction critically 5-connected graph on n vertices has at least n/5 vertices of degree 5. We also show that, for a graph G and an integer k greater than 4, there exists a contraction critically k-connected graph which has G as its induced subgraph.     

Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Even subgraphs of bridgeless graphs and 2-factors of line graphs

By Petersen's theorem, a bridgeless cubic multigraph has a 2-factor. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing that every such multigraph has a spanning even subgraph. Our main result is that every bridgeless simple graph with minimum degree at least three has a spanning even subgraph in which every component has at least four vertices. We deduce that if G is a simple bridgeless graph with n vertices and minimum degree at least three, then its line graph has a 2-factor with at most max{1,(3n-4)/10} components. This upper bound is best possible.     

Total energy decay for the wave equation in exterior domains with a dissipation near infinity

We show that the energy of solutions to the initial boundary value problem for the wave equation in exterior domains with a dissipation which is localized only near infinity tends to zero as the time goes to infinity. We do not make any geometrical condition like star-shapedness on the boundary.     

Thermodynamic performance of a hybrid air cycle refrigeration system using a desiccant rotor

Due to the concern on global warming, the demand for a system using natural refrigerant is increasing and many researches have been devoted to develop systems with natural refrigerants. Among natural refrigerant systems, an air cycle system has emerged as one of alternatives of Freon gas system due to environmentally friendly feature in spite of the inherent low efficiency. To overcome the technical barrier, this study proposed combination of multiple systems as a hybrid cycle to achieve higher efficiency of an air cycle system. The hybrid air cycle adopts a humidity control units such as an adsorber and a desorber to obtain the cooling effect from latent heat as well as sensible heat. To investigate the efficacy of the hybrid air cycle, the cooling performance of a hybrid air cycle is investigated analytically and experimentally. From the simulation result, it is found that COP of the hybrid air cycle is two times higher than that of the conventional air cycle. The experiments are conducted on the performance of the desiccant system according to the rotation speed in the system and displayed the feasibility of the key element in the hybrid air cycle system. From the results, it is shown that the system efficiency can be enhanced by utilization of the exhausted heat through the ambient heat exchanger with advantage of controlling the humidity by the desiccant rotor.     

Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces

Let H be a real Hilbert space and let T: H→2^H be a maximal monotone operator. In this paper, we first introduce two algorithms of approximating solutions of maximal monotone operators. One of them is to generate a strongly convergent sequence with limit vT⁻¹0. The other is to discuss the weak convergence of the proximal point algorithm. Next, using these results, we consider the problem of finding a minimizer of a convex function. Our methods are motivated by Halpern's iteration and Mann's iteration.     

Cyclic posets and triangulation clusters

Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures.We give an overview, and then analyze "triangulation clusters" which are those corresponding to topological triangulations of the 2-disk. Locally finite nontriangulation clusters give topological triangulations of the "cactus space" associated to the "cactus cyclic poset".