Synthesis of bicyclic bis(γ‐butyrolactone) derivatives bearing sulfide moieties and their alternating copolymers with epoxide

A series of bicyclic bis(γ‐butyrolactone)s (BBL) bearing sulfide moiety 2 were readily synthesized from a precursor BBL bearing isopropenyl group 1. This efficient and versatile synthesis of 2 was achieved by a highly reliable radical addition reaction of thiols to the C‐C double bond in the isopropenyl group 2 underwent anionic copolymerization with glycidyl phenyl ether in a 1:1 alternating manner to give a series of the corresponding polyester 3, of which side chains inherited the sulfide group from 2. The glass transition temperatures (T_g) of 3 showed clear dependence on the flexibility of the sulfide side chains. The scope of this copolymerization system was further expanded by synthesizing a bifunctional BBL 4 from 1 with using hexanedithiol and performing its copolymerization with bisphenol A diglycidyl ether 5. The copolymerization gave the corresponding networked polymer in high yield. During the copolymerization, the volume expanding nature of the double ring‐opening reaction of 4 contributed to the efficient compensation of the intrinsic volume shrinkage of the ring‐opening of epoxide to achieve a shrinkage‐free curing system. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Analogues of Jacobi’s derivative formula II

In this work, we use Jacobi’s derivative formula to obtain analogues to theta constants with rational characteristics. Furthermore, we show that the analogues yield many product-series identities by only using the elementary fact that a holomorphic elliptic function is a constant.     

Improved gradient method for monotone and lipschitz continuous mappings in banach spaces

Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {A_n}_(n∈N) be a family of monotone and Lipschitz continuos mappings of C into E~*. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [10] for solving the variational inequality problem for{A_n} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.     

Electronic stress tensor analysis of hydrogenated palladium clusters

We study the chemical bonds of small palladium clusters Pd _n (n?=?2?9) saturated by hydrogen atoms using electronic stress tensor. Our calculation includes bond orders which are recently proposed based on the stress tensor. It is shown that our bond orders can classify the different types of chemical bonds in those clusters. In particular, we discuss Pd?CH bonds associated with the H atoms with high coordination numbers and the difference of H?CH bonds in the different Pd clusters from viewpoint of the electronic stress tensor. The notion of ??pseudo-spindle structure?? is proposed as the region between two atoms where the largest eigenvalue of the electronic stress tensor is negative and corresponding eigenvectors forming a pattern which connects them.     

Characterization of heat-wave propagation through laser-driven Ti-doped underdense plasma

The propagation of a laser-driven heat-wave into a Ti-doped aerogel target was investigated. The temporal evolution of the electron temperature was derived by means of Ti K-shell X-ray spectroscopy, and compared with two-dimensional radiation hydrodynamic simulations. Reasonable agreement was obtained in the early stage of the heat-wave propagation. In the later phase, laser absorption, the propagation of the heat-wave, and hydrodynamic motion interact in a complex manner, and the plasma is mostly re-heated by collision and stagnation at the target central axis.     

Solvent-induced switching of the macromolecular helicity of poly[(4-carboxyphenyl)acetylene] induced by a single chiral amino alcohol

Cis–transoidal poly[(4-carboxyphenyl)acetylene] (poly- 1 ) complexed with optically active amines and amino alcohols showed an induced circular dichroism (ICD) in the ultraviolet–visible region because of a predominantly one-handed helix formation in water and in dimethyl sulfoxide (DMSO). The Cotton effect signs of the poly- 1 /chiral amino alcohol complexes were inverted in the presence of water, whereas the ICD pattern of the poly- 1 /chiral amine complexes showed no change, regardless of the water content. These results demonstrated that the helix sense of poly- 1 induced by optically active amino alcohols through noncovalent acid–base interactions could be switched by changes in the solvent ratio in the DMSO–water mixtures. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3625–3631, 2003     

Improvement in reliability of probabilistic test of significant differences in GeneChip experiments.

A probabilistic test (FUMI theory) for GeneChip experiments has been proposed for selecting the genes which show significant differences in the gene expression levels between a single pair of treatment and control. This paper describes that the reliability of the judgment by the FUMI theory can be enhanced, when the selected genes are referred to biomolecular-functional networks of a commercial database. The genes judged as being differently expressed are grouped into a cluster in the biomolecular networks. It is also demonstrated that false positive genes have a trend in the networks to be isolated from each other, and also away from the clustered genes, since the false positive genes are randomly selected.     

Exploiting sparsity in primal-dual interior-point methods for semidefinite programming

The Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-Hara/Monteiro and Nesterov-Todd search directions have been used in many primal-dual interior-point methods for semidefinite programs. This paper proposes an efficient method for computing the two directions when the semidefinite program to be solved is large scale and sparse.