Successive Linearization Methods for Nonlinear Semidefinite Programs

We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Numerical results on some nonlinear semidefinite programs including optimization problems with bilinear matrix inequalities are reported to illustrate the behaviour of the proposed method.The research of the fourth author was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science. The research of the second author was supported by the DFG (Deutsche Forschungsgemeinschaft).     

Raman scattering in low wavenumber region as a new probe to structural properties of microcrystalline silicon

The structural properties of microcrystalline silicon (μc-Si) are studied by Raman scattering. It is found that the intensity of each Raman band closely correlates with the absorption coefficient in the interband region and that the Raman band at ca. 150 cm^?1 is a sensitive probe to randomness of Si-Si bonding structure in μc-Si.     

Selective determination of pentoses,hexoses and 6-deoxyhexoses by dual-wavelength spectrophotometry with the cysteine—phenol—sulfuric acid system

A convenient method is described for the selective determination of pentoses, hexoses and 6-deoxyhexoses by dual-wavelength spectrophotometry with the l-cysteine—phenol—sulfuric acid system. Excellent linearity was observed for 25–250 nmol of pentoses, and for 25–500 nmol of hexoses and 6-deoxyhexoses. These aldoses in those sample ranges could be determined selectively with high accuracy and precision by the k -factor mode. The appropriate, wavelength of λ₂ was 462, 499 and 398 nm for pentoses, hexoses and 6-deoxyhexoses, respectively, whereas that of λ₁ was commonly 424 nm.     

Cation-controlled assembly of Na+-linked lacunary alpha-Keggin tungstosilicates

Two novel salts of lacunary tungstosilicates with guanidinium and alkali metal cations, (CH6N3)7Na[SiW11O39].(CH3)2CO.8H2O (1) and (CH6N3)K6Na[SiW11O39].11.5H2O (2), have been synthesized and their crystal structures have been determined by synchrotron X-ray diffraction. In both crystals, the Na+ cations link the lacunary Keggin-type tungstosilicate anions into linear structures. The neighboring [SiW11O39]8- anions are related by two-fold screw and translational operations in compounds 1 and 2, respectively. Second harmonic generation was observed for compound 1.     

Spatial arrangement of metal nanoparticles supported by porous polymer substrates studied by transmission electron microtomography

Fine metal particles (nanoparticles) stabilized on porous (polymeric) substrates can be considered as a model system of a high-performance catalyst. In the present study, the substrate was made using the periodic microphase-separated structure of a block copolymer as the template, and the Pd nanoparticles were formed inside the porous material by reduction of the Pd2+ ions with 1-propanol as the reductant. The three-dimensional morphology of such a polymer-Pd hybrid material was studied by transmission electron microtomography. The characteristic structural parameters of the hybrid, e.g., the penetration of the Pd nanoparticles into the polymer substrate, number density of the Pd nanoparticles, and size distribution of the Pd nanoparticles, were measured for the first time.     

Possibility of a non-amino acid pathway in the biosynthesis of marine-derived oxazoles

A novel avenue for oxazoles via Beckmann rearrangement of alpha-formyl ketoxime dimethyl acetals is described that indicates the possibility of a non-amino acid biosynthetic pathway in marine natural products.     

Existence and uniqueness of stabilized propagating wave segments in wave front interaction model

Recent experimental studies of photosensitive Belousov–Zhabotinskii reaction have revealed the existence of propagating wave segments. The propagating wave segments are unstable, but can be stabilized by using a feedback control to continually adjust the excitability of the medium. Experimental studies also indicate that the locus of the size of a stabilized wave segment as a function of the excitability of the medium gives the excitability boundary for the existence of 2D wave patterns with free ends in excitable media. To study the properties of this boundary curve, we use the wave front interaction model proposed by Zykov and Showalter. This is equivalent to study a first order system of three ordinary differential equations which includes a singular nonlinearity. Using two different reduced first order systems of two ordinary differential equations, we first show the existence of wave segments for any given propagating velocity. Then the wave profiles can be classified into two types, namely, convex and non-convex types. More precisely, when the normalized propagating velocity is small, we show that the wave profile is of convex type, while the wave profile is of non-convex type when the normalized velocity is close to 1.     

Global solvability for abstract semilinear evolution equations

The Cauchy problem for the abstract semilinear evolution equation u^′(t) = Au (t) + B (u (t)) + C (u (t)) is discussed in a general Banach space X. Here A is the so‐called Hille‐Yosida operator in X, B is a differentiable operator from D (A) into X, and C is a locally Lipschitz continuous operator from D (A) into itself. A vectorvalued functional defined only on X is used and appropriate conditions on the nonlinear operators B and C are imposed so that a vector‐valued functional defined on the domain of the operator A may be constructed in order to specify the growth of a global solution. The advantage of our formulation lies in the fact that it is possible to obtain a global solution by checking some energy inequalities concerning only low order derivatives (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Entire Solutions with Merging Fronts to Reaction–Diffusion Equations

We deal with a reaction–diffusion equation u _t = u _xx + f(u) which has two stable constant equilibria, u = 0, 1 and a monotone increasing traveling front solution u = φ(x + ct) (c > 0) connecting those equilibria. Suppose that u = a (0 < a < 1) is an unstable equilibrium and that the equation allows monotone increasing traveling front solutions u = ψ₁(x + c ₁ t) (c ₁ < 0) and ψ₂(x + c ₂ t) (c ₂ > 0) connecting u = 0 with u = a and u = a with u = 1, respectively. We call by an entire solution a classical solution which is defined for all . We prove that there exists an entire solution such that for t≈ − ∞ it behaves as two fronts ψ₁(x + c ₁ t) and ψ₂(x + c ₂ t) on the left and right x-axes, respectively, while it converges to φ(x + ct) as t→∞. In addition, if c > − c ₁, we show the existence of an entire solution which behaves as ψ₁( − x + c ₁ t) in and φ(x + ct) in for t≈ − ∞.