Hybrid optical resonator type laser proposed for direct coupling into optical fiber

Combining one stable resonator with a concave mirror and a coupling-hole plane mirror, and another unstable resonator having a concave mirror and a convex mirror, a new hybrid optical resonator type laser has been proposed by overlapping the concave mirror as a common one and fitting the convex mirror exactly to the coupling-hole. Using theABCD law, the so-called g-parameters are first found for beam confinement. Then, based on the eigen-equation, the field distribution on the plano-convex mirror is obtained with the g-parameters above. Knowing this field distribution results in an effective transmittanceG _{e e}. Finally, the ratio of the inner convex to outer plane mirror radii can be determined for an optimum coupling in both the limiting cases of homogeneously and inhomogeneously broadened gain media. Some numerical examples will also be given for a CO₂ laser having the proposed hybrid resonator.     

Surface morphology of siloxane block copolymer crystals: (Tetramethyl-p-silphenylenejsiloxane—dimethylsiloxane

The metal decoration technique was applied to solution grown crystals and cast thin films of (tetramethyl-p-silphenylene) siloxane and dimethylsiloxane (DMS) block copolymers in order to elucidate their surface textures as a function of copolymer composition. Electron diffraction and microscopy studies were used. Metal-free zones are observed at surface steps of single crystals, and decorating particles occasionally form spiral growths in the inner regions of crystals. However, the decorating particles form regular patterns, particularly on the copolymer crystal surfaces. In the case of solution-cast thin films, deposition of metallic particles occurs along lamellar crystal edges or where a fibrillar morphology occurs. The nucleation density of metallic particles depends on the copolymer composition and increases with increasing crystallinity of the samples. Probable models are suggested to account for this surface texture. The propensity for screw-dislocations crystal growths on the crystal surfaces decreases as the noncrystallizable DMS component increases.     

Parallel Implementation of Successive Convex Relaxation Methods for Quadratic Optimization Problems

As computing resources continue to improve, global solutions for larger size quadrically constrained optimization problems become more achievable. In this paper, we focus on larger size problems and get accurate bounds for optimal values of such problems with the successive use of SDP relaxations on a parallel computing system called Ninf (Network-based Information Library for high performance computing).     

Maximization of the total population in a reaction–diffusion model with logistic growth

This paper is concerned with a nonlinear optimization problem that naturally arises in population biology. We consider the effect of spatial heterogeneity on the total population of a biological species at a steady state, using a reaction–diffusion logistic model. Our objective is to maximize the total population when resources are distributed in the habitat to control the intrinsic growth rate, but the total amount of resources is limited. It is shown that under some conditions, any local maximizer must be of “bang–bang” type, which gives a partial answer to the conjecture addressed by Ding et al. (Nonlinear Anal Real World Appl 11(2):688–704, 2010). To this purpose, we compute the first and second variations of the total population. When the growth rate is not of bang–bang type, it is shown in some cases that the first variation becomes nonzero and hence the resource distribution is not a local maximizer. When the first variation becomes zero, we prove that the second variation is positive. These results implies that the bang–bang property is essential for the maximization of total population.     

Equivalences and differences in conic relaxations of combinatorial quadratic optimization problems

Various conic relaxations of quadratic optimization problems in nonnegative variables for combinatorial optimization problems, such as the binary integer quadratic problem, quadratic assignment problem (QAP), and maximum stable set problem have been proposed over the years. The binary and complementarity conditions of the combinatorial optimization problems can be expressed in several ways, each of which results in different conic relaxations. For the completely positive, doubly nonnegative and semidefinite relaxations of the combinatorial optimization problems, we discuss the equivalences and differences among the relaxations by investigating the feasible regions obtained from different representations of the combinatorial condition which we propose as a generalization of the binary and complementarity condition. We also study theoretically the issue of the primal and dual nondegeneracy, the existence of an interior solution and the size of the relaxations, as a result of different representations of the combinatorial condition. These characteristics of the conic relaxations affect the numerical efficiency and stability of the solver used to solve them. We illustrate the theoretical results with numerical experiments on QAP instances solved by SDPT3, SDPNAL+ and the bisection and projection method.     

Beijing Lectures on the Grade Restriction Rule

The authors describe the relationships between categories of B-branes in different phases of the non-Abelian gauged linear sigma model.The relationship is described explicitly for the model proposed by Hori and Tong with non-Abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rφdland.A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.     

Synthesis and characterization of bromonium ylides and their unusual ligand transfer reactions with N-heterocycles

Stable aliphatic bromonium ylides (RfSO2)2C--Br+C6H4-p-CF3 (Rf = CF3, CF3(CF2)3) have been synthesized and structurally characterized for the first time. X-ray crystallographic analyses indicated a ylide structure with an sp2 hybridization of the ylide carbanions and with little double-bond character for the ylidic bond. The bromonium ylides selectively undergo transfer of the aryl group to nitrogen heterocycles, such as pyridines, yielding N-arylpyridinium salts. This is in a marked contrast to the reaction of the iodonium ylides, which produces pyridinium ylides through transylidations.     

Comparison of the characteristics of cellulose microfibril aggregates of wood, rice straw and potato tuber

The focus of this study has been to isolate cellulose microfibril aggregates by the one-time grinding treatment from wood, rice straw and potato tuber, and to compare their morphological and mechanical properties. Field emission scanning electron microscopy images showed that the diameter range of isolated microfibril aggregates from wood, 12–20 nm, was smaller than those from rice straw and potato tuber, 12–35 nm and 12–55 nm, respectively. These differences were observed even in the purified rice straws and potato tuber before the grinder treatment, but were hardly observed in the purified wood. The results of X-ray analysis and tensile tests indicated that there were no significant differences among the sources in the cellulose crystallinity and Young’s modulus of the isolated microfibril aggregates in the dry state. These results suggest that the inherent characteristics of cellulose microfibril aggregates in the dry state are very similar regardless of plant sources and tissue functions.     

A variety of spin-crossover behaviors depending on the counter anion: two-dimensional complexes constructed by NH...Cl- hydrogen bonds, [FeIIH3LMe]Cl.X (X = PF6 -, AsF6 -, SbF6 -, CF3SO3 -; H3L(Me) = Tris[2-{[(2-methylimidazol-4-yl)methylidene]amino}ethyl]amine)

A family of spin-crossover (SC) complexes, [Fe(II)H(3)L(Me)]Cl.X (X(-) = PF(6) (-), AsF(6) (-), SbF(6) (-), CF(3)SO(3) (-)), 1-4, has been synthesized, in which H(3)L(Me) denotes the hexadentate N(6) tripod-like ligand tris[2-{[(2-methylimidazol-4-yl)methylidene]amino}ethyl]amine, containing three imidazole groups, with a view to establishing the effect of the counter anion on the SC behavior. These complexes have been found to crystallize in the same monoclinic crystal system with similar cell dimensions. The general crystal structure consists of a two-dimensional (2D) extended network constructed by NH...Cl- hydrogen bonds between Cl- and the imidazole NH groups of three neighboring [Fe(II)H(3)L(Me)]2+ ions, while the anion X exists as an isolated counter anion and occupies the space between the 2D sheets. Magnetic susceptibilities and M?ssbauer spectra have revealed a variety of SC behaviors depending on the counter anion, including a one-step HS<==>(HS + LS)/2 (1, X = PF(6) (-)), a two-step HS<==>(HS + LS)/2<==>LS with a slow thermal relaxation (2, X = AsF(6) (-)), a gradual one-step HS<==>LS (3, X = SbF(6) (-)), and a steep one-step HS<==>LS with hysteresis (4, X = CF(3)SO(3) (-)). The complexes assume the space group P2(1)/n in the HS state, P2(1) in the HS + LS state, and P2(1)/n in the LS state. The Fe-N bond lengths and the N-Fe-N bond angles are indicative of the HS, HS + LS, and LS states. The molecular volumes, V, of the counter anions have been evaluated by quantum-chemical calculations as follows: 53.4 A(3) (BF(4) (-)), 54.4 A(3) (ClO(4) (-)), 73.0 A(3) (PF(6) (-)), 78.5 A(3) (AsF(6) (-)), 88.7 A(3) (SbF(6) (-)), and 86.9 A(3) (CF(3)SO(3) (-)). The size and shape of the counter anion affects the flexible 2D network structure constructed by the hydrogen bonds, leading to modifications of the SC behavior. These estimated relative sizes of the counter anions correlate well with the observed SC behaviors.