Variational sets: Calculus and applications to nonsmooth vector optimization

We develop elements of calculus of variational sets for set-valued mappings, which were recently introduced in Khanh and Tuan (2008) [1] and [2] to replace generalized derivatives in establishing optimality conditions in nonsmooth optimization. Most of the usual calculus rules, from chain and sum rules to rules for unions, intersections, products and other operations on mappings, are established. Direct applications in stability and optimality conditions for various vector optimization problems are provided.     

Oleanolic triterpene saponins from the roots of Panax bipinnatifidus

Ten oleanane-type saponins (1-10), including three new compounds, namely bifinosides A-C (1-3), were isolated from the roots of Panax bipinnatifidus SEEM. Their structures were elucidated on the basis of chemical and spectroscopic methods.     

Synthesis, structures and membrane properties of siloxane-imide co-polymers produced by aqueous polymerization

We report for the first time, the synthesis of siloxane-imide co-polymers by the reaction of mixtures of 1,4-bis(aminobutyl)tetramethyldisiloxane (ABTMDS) and 1,3-bis(4-aminophenoxy)benzene (TPE-R) with bisphenol A diphthalic anhydride (BPADA) using water as the polymerization solvent. A series of co-polymers were prepared incorporating 10, 20, 40 and 100 mol% of ABTMDS with the aromatic diamine TPE-R as the co-monomer. The synthesized co-polymers showed number average molecular weights in the range of 25,000–60,000. As expected the glass transition temperatures (T_gs) and moduli of the polymers were found to decrease with increasing amounts of the siloxane monomer and the homo-polymer containing only the siloxane diamine showing the lowest T_g (60 °C). The resulting polymers could be solution cast into strong and flexible membranes which showed significant decreases in water absorption and moisture permeability compared to the control polymer without siloxane groups. The polymers were characterized by FTIR, ¹³C and ¹H NMR, GPC, DSC and mechanical properties and structural comparisons were made with similar polymers made by standard solvent synthesis methods. Also cross-linked polymers were prepared by the reaction of ABTMDS with the aromatic homo-polymer control and their membrane properties were compared to those of the water synthesized siloxane co-polymers with a similar siloxane content.     

Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects

This paper presents an analytical approach to investigate the non-linear axisymmetric response of functionally graded shallow spherical shells subjected to uniform external pressure incorporating the effects of temperature. Material properties are assumed to be temperature-independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for shallow spherical shells are derived by using the classical shell theory and specialized for axisymmetric deformation with both geometrical non-linearity and initial geometrical imperfection are taken into consideration. One-term deflection mode is assumed and explicit expressions of buckling loads and load-deflection curves are determined due to Galerkin method. Stability analysis for a clamped spherical shell shows the effects of material and geometric parameters, edge restraint and temperature conditions, and imperfection on the behavior of the shells.     

Size-dependent heterogeneity benefits the mechanical performance of bone

Heterogeneity of biological materials, such as bone, tooth, and mollusc shells, plays a key role in determining their mechanical performance (e.g. the strength, damage tolerance, etc.). Here, we quantify heterogeneities in elasticity and inelasticity of bovine cortical bone between 100 nm and a few microns and identify a characteristic length scale (λ_c) of approximately 200 nm. Below λ_c the mechanical heterogeneity of bone is pronounced and exhibits a strong nonlinear size-dependence, while above λ_c the heterogeneity is much less. Such size-dependent heterogeneity benefits the mechanical performance of bone since it not only promotes the energy dissipation at nanoscale, but also suppresses heterogeneity-induced stress concentration and strain localization at larger length scales. This is one of the possible mechanisms functioning at multiple length scales that make bone a well-designed tough natural material. Utilizing experimentally measured data, systematic computational simulations were carried out, showing that the heterogeneity in inelasticity, rather than elasticity, plays a dominant role in promoting energy dissipation during deformation. Possible parameters that determine the inelasticity heterogeneity (e.g. mean value and standard deviation of heterogeneous yield stress) and therefore affect energy dissipation are investigated under typical deformation modes of bone. The analysis presented suggests that there exists an optimum ratio of macroscopic strength to elastic modulus for improving energy dissipation under tension. All these findings are of great value to the design and synthesis of improved bio-inspired composites.     

A stochastic model of the influence of buffer gas collisions on Mollow spectra

In this paper, using the idea introduced in (K. Wódkiewicz, Noise in strong laser-atom interaction, Proceedings of the VI International School of Coherent Optics, Ustron, Poland, September (1985) 19–26) and developed in (Cao Long Van, Stochastic Models of Isolated Collisions: Applications to Optical Phenomena, paper presented in LAMP Conference’89, Trieste, Italy (1989) II) we consider the influence of collisional fluctuations on the Mollow spectra of resonance fluorescence (RF). The fluctuations are taken into account by a simple shift of the constant detuning, involved in a set of optical Bloch equations by collision frequency noise which is modelled by a two-step random telegraph signal (RTS). We consider in detail the Mollow spectra for RF in the case of an arbitrary detuning of the laser frequency, where the emitter is a member of a statistical ensemble in thermodynamic equilibrium with the buffer gas at temperature T which is treated as a colored environment, and velocity v is distributed with the Maxwell-Boltzmann density.     

Pulse propagation in an autoionization medium with double Fano profile

We discuss the propagation of a short laser pulse in an auto- ionizing (AI) medium with degenerate double Fano model. By solving numerically the coupled equations for atoms and fields we show that by the proper choice of Fano parameters involved in the problem (contrary to the case considered in (E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A60 (1999)) we have now two Fano asymmetry parameters) one can eliminate almost completely the absorption in the pulse propagation. It means that we have the transparency in the medium. From the connection between population trapping in short pulsed laser field and transparency in the propagation of the laser pulse which has been fixed by Paspalakis et al., Phys. Rev. A60 (1999) we conclude that this proper choice leads to the presence of the population trapping (or the existence of the “dark” states) in the atomic system. Moreover, instead of one value of the laser detuning for which the dark states exist in the case of one AI level, we find numerically two such values in the case of two AI levels.     

Improvement of Biological Effects of Root-Filling Materials for Primary Teeth by Incorporating Sodium Iodide

Therapeutic iodoform (CHI₃) is commonly used as a root-filling material for primary teeth; however, the side effects of iodoform-containing materials, including early root resorption, have been reported. To overcome this problem, a water-soluble iodide (NaI)-incorporated root-filling material was developed. Calcium hydroxide, silicone oil, and NaI were incorporated in different weight proportions (30:30:X), and the resulting material was denoted DX (D5~D30), indicating the NaI content. As a control, iodoform instead of NaI was incorporated at a ratio of 30:30:30, and the material was denoted I30. The physicochemical (flow, film thickness, radiopacity, viscosity, water absorption, solubility, and ion releases) and biological (cytotoxicity, TRAP, ARS, and analysis of osteoclastic markers) properties were determined. The amount of iodine, sodium, and calcium ion releases and the pH were higher in D30 than I30, and the highest level of unknown extracted molecules was detected in I30. In the cell viability test, all groups except 100% D30 showed no cytotoxicity. In the 50% nontoxic extract, D30 showed decreased osteoclast formation compared with I30. In summary, NaI-incorporated materials showed adequate physicochemical properties and low osteoclast formation compared to their iodoform-counterpart. Thus, NaI-incorporated materials may be used as a substitute for iodoform-counterparts in root-filling materials after further (pre)clinical investigation.     

广山药中16种元素的分析比较

用原子吸收法和分光光度法测定了5个产地的广山药及怀山药中16种元素的含量，并进行了比较。发现广山药及怀山药中均含有Mn,Fe,Zn,Ca,Cu,Mg,P,Se等元素，5个产地的广山药中的Cu/Zn值均低于正常人血清的Cu/Zn，这些元素可能是怀山药，广山药具有补脾养胃，生津益肺，补肾涩精，治疗糖尿病等功效的物质基础之一；广山药长期作为山药的一个品种同等入药，食用是有科学根据的；广山药，怀山药中含有一定量的As,Hg。     

A Construction of Multiresolution Analysis on Interval

We present a concrete method of constructing multiresolution analysis on interval. The method generalizes the corresponding results of Cohen, Daubechies and Vial [Appl. Comput. Harmonic Anal., 1（1993）, 54-81]. By the use of the subdivision operator, the expressions of the constructed functions are more compact. Furthermore, the method reveals more clearly some properties of multiresolution analysis with certain approximation order.