An abstract proximal point algorithm

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions. The algorithm works by applying successively so-called “resolvent” mappings associated to the original object that one aims to optimize. In this paper we abstract from the corresponding resolvents employed in these problems the natural notion of jointly firmly nonexpansive families of mappings. This leads to a streamlined method of proving weak convergence of this class of algorithms in the context of complete CAT(0) spaces (and hence also in Hilbert spaces). In addition, we consider the notion of uniform firm nonexpansivity in order to similarly provide a unified presentation of a case where the algorithm converges strongly. Methods which stem from proof mining, an applied subfield of logic, yield in this situation computable and low-complexity rates of convergence.     

Interaction Between Pr3☎ Pairs and Excitons in CsCdBr3

CsCdBr₃ consists of linear chains of [CdBr₆]^4- octahedra separated by Cs^? ions. The excited states of the covalently bound [CdBr₆]^4- octahedra form the lowest excitonic states of the crystal lattice. The trivalent Pr ions substitute for the divalent Cd ions. For reasons of charge compensation in the linear Cd^2? chains, pair centers of the form Pr^3?-(Cd vacancy)-Pr^3? are predominantly formed. In CsCdBr₃ the optical band gap is wider than the electronic one. This allows to study the interaction between Pr^3? ions and excitons by means of optical spectroscopy. The interaction leads to quantum up- and down-conversion generating one photon from two lower ones in energy and vice versa. Related experiments are discussed.     

Theoretical studies of carbocations in ion pairs. 8. Search for anchimeric assistance in the ionization of 2-butyl cation precursors

The structures of carbocations formed in the ionization of 2-butyl precursors were investigated by high level ab initio MO calculations on the reaction of 2-butyl fluoride (1) with borane, which gives a C4H9+ cation paired with trihydrofluoroborate (FBH3-, A). Two conformations of the "open," secondary cation (2) in the ion pair resulted from two conformations of 1, with F gauche and trans to C4 (2-g and 2-t, respectively). No anchimeric assistance by hydrogen (in 1-g) or methyl (in 1-t) was evidenced. In fact, attempts at optimizing the geometry of the H-bridged (3) and methyl-bridged (6) cations at short interionic distances (d) led to the corresponding conformations of 2. Upon ion separation, proton transfer from 2 to the anion occurred at intermediate interionic distances, consonant with experimental observations in trifluoroacetic acid. Elimination was prevented by addition of a lithium cation to the ion pair, i.e., running computations on triple ions (2.A.Li+). Cation 6 became an energy minimum beyond d = 2.5 A and 3 beyond 2.8 A. Cation 2-g was still the most stable isomer at d = 3.2 A, which was greater than the interionic distance in the crystals of the isomeric tert-butyl cation salts (3-3.1 A). Thus, spectral determinations of 2-butyl cations in the solid state should be interpreted with 2-g as the main component of the ion mixture. When the ions became separated (d >/= 4 A), only the bridged ions were energy minima. In this process, bridging did not occur opposite to the leaving group to assist the ionization, but on the same side with it, being controlled by the electrostatic interaction with the anion, as it departed from the vicinity of the cation. Such behavior was also noted in the ionization of the 3-methyl-2-butyl homolog.     

Stiffness,resilience, compressibility

The flexibility of a protein is an important component of its functionality. We use nuclear resonance vibrational spectroscopy (NRVS) to quantify the flexibility of the heme iron environment in the electron-carrying protein cytochrome c by measuring the stiffness and the resilience. These quantities are sensitive to structural differences between the active sites of different proteins, as illustrated by a comparative analysis with myoglobin. The elasticity of the entire protein, on the other hand, can be probed quantitatively from NRVS and high energy-resolution inelastic X-ray scattering (IXS) measurements, an approach that we used to extract the bulk modulus of cytochrome c.     

On the Design of Double‐Ellipsoid Mirror Furnace and its Thermal Characteristics for Floating‐Zone Growth of SrxBa1‐xTiO3 Single Crystals

We have designed a double ellipsoid mirror furnace for floating‐zone crystal growth using lamps with rectangular filaments. Its thermal characteristics were studied using an alumina tube for several system configurations. A simple comparison with a commercial furnace that used cylinder lamps for the heating profile was also conducted. By adjusting lamp orientation and positions, one could modify heating profiles easily. In general, the thermal characteristics of the furnace were consistent with the model's prediction [J. Crystal Growth 173 (1997) 561]. The effects of growth chamber and heat pipe were further illustrated. Furthermore, a suitable system configuration leading to better heating uniformity and lower thermal gradients near the growth interface was found for the floating‐zone growth of Sr_xBa_1‐xTiO₃ single crystals.     

Analytical and numerical investigation for true and spurious eigensolutions of an elliptical membrane using the real-part dual BIEM/BEM

The paper performs analytical and numerical investigation of the true and spurious eigensolutions of an elliptical membrane using the real-part boundary integral equation method (BIEM) following the successful work on a circular case by using the dual boundary element method (BEM) (Kuo et al. in Int. J. Numer. Methods Eng. 48:1401–1422, 2000). We extend to the elliptical case in this paper. To analytically study the eigenproblems of an elliptical membrane, the elliptical coordinates and Mathieu functions are adopted. The fundamental solution is expanded into the degenerate kernel by using the elliptical coordinates and the boundary densities are expanded by using the eigenfunction expansion. The Jacobian terms may exist in the degenerate kernel, boundary density and boundary contour integration but they can cancel each other out. Therefore, the orthogonal relations are reserved in the boundary contour integral. It is interesting to find that the BIEM using the real or the imaginary-part kernel to deal with an elliptical membrane yields spurious eigensolutions. This finding agrees with those corresponding to the circular case. The spurious eigenvalues in the real-part BIEM are found to be the zeros of the mth-order (even or odd) modified Mathieu functions of the second kind or their derivatives. To verify this finding, the BEM is implemented. Furthermore, the commercial finite-element code ABAQUS is also utilized to provide eigensolutions for comparisons. It is found that good agreement is obtained.     

Push-pull macrocycles: donor-acceptor compounds with paired linearly conjugated or cross-conjugated pathways

Two-dimensional π-systems are of current interest in the design of functional organic molecules, exhibiting unique behavior for applications in organic electronics, single-molecule devices, and sensing. Here we describe the synthesis and characterization of "push-pull macrocycles": electron-rich and electron-poor moieties linked by a pair of (matched) conjugated bridges. We have developed a two-component macrocyclization strategy that allows these structures to be synthesized with efficiencies comparable to acyclic donor-bridge-acceptor systems. Compounds with both cross-conjugated (m-phenylene) and linearly conjugated (2,5-thiophene) bridges have been prepared. As expected, the compounds undergo excitation to locally excited states followed by fluorescence from charge-transfer states. The m-phenylene-based systems exhibit slower charge-recombination rates presumably due to reduced electronic coupling through the cross-conjugated bridges. Interestingly, pairing the linearly conjugated 2,5-thiophene bridges also slows charge recombination. DFT calculations of frontier molecular orbitals show that the direct HOMO-LUMO transition is polarized orthogonal to the axis of charge transfer for these symmetrical macrocyclic architectures, reducing the electronic coupling. We believe the push-pull macrocycle design may be useful in engineering functional frontier molecular orbital symmetries.     

An efficient synthesis of a potent anti-inflammatory agent, viscolin, and its inducible nitric oxide synthase inhibitory activity

A new and efficient synthetic pathway employed the aldol condensation between the acetophenone (3) and vanillin derivative (4) resulted in the precursor chalcone intermediate (14). The target compound viscolin (1) could be afforded through the hydrogenation of the chalcone and followed by deprotection. The present strategy described the development of a more efficient procedure that allowed large-scale production of viscolin for the further research of biological activity both in vitro and in vivo.     

Ion-implanted treatment of (Ba,Sr)TiO3 films for DRAM applications

The effects of ion implantation on the properties of spin-on sol–gel Ba_0.7Sr_0.3TiO₃ (BST) thin films were studied by implanted Ar⁺, N⁺, and F⁺ doses. The F⁺-implanted BST samples present leakage current density <10⁻⁶ A/cm² at 2.5 V and dielectric constant 450. The leakage current of F⁺-implanted BST samples was reduced about one order of magnitude as compared with that of samples with implanted Ar⁺, N⁺ or without implantation. The thickness shrinkage from 135 to 115 nm was observed in F⁺-implanted BST films (before annealing treatment) and a respective increase in the refractive index from 1.84 to 2.05 was measured. After annealing the implanted samples, the changes of thickness and refractive index depend on the concentration of implanted dose. Based on an infrared transmission study of the samples we suggest that the ion-implanted samples with smaller dose (5×10¹⁴ cm⁻²) have fewer −OH contaminants than the non-implanted or implanted samples with the larger doses (1×10¹⁵ cm⁻²). Based on the results presented, we conclude that suitable ion implantation densifies the spin-on sol–gel BST films and reduces the −OH contaminants in the films.     

Pb1－xMnxSe薄膜的光学特性

采用分子束外延的方法在BaF₂(111)衬底上制备出了高质量的Pb_1-xMn_xSe(0≤x≤0.0681)薄膜.X射线衍射结果表明，Pb₁-xMn_xSe薄膜为立方相NaCl型结构，没有观察到MnSe相分离现象，薄膜的取向为平行于衬底(111)晶面.晶格常数随着Mn含量的增加逐渐减小，Mn含量由Vegard公式得到.通 关键词： 1-xMn_xSe外延薄膜')" href="#">Pb_1-xMn_xSe外延薄膜 透射光谱 带隙 折射率