A retractable structure based on Bricard linkages and rotating rings of tetrahedra

Retractable structures which alter their geometries according to practical requirements are widely used in roof structures of stadiums for their versatility. A retractable structure based on threefold-symmetric Bricard linkages and rotating rings of tetrahedra is proposed and developed in this paper. By replacing each link of a threefold-symmetric Bricard linkage with a tetrahedron, a retractable structure is obtained which can repeatedly open and close by rotating the tetrahedra. The geometric relationship between the retractable structure and the threefold-symmetric Bricard linkage is derived and ranges of main geometric parameters are determined to ensure a continuous and smooth movement in the deployment of the structure. Then the relative displacement of the support and the open rate of the structure, two main parameters concerned in practical applications, are investigated. Preferred ranges of main geometric parameters are proposed and a physical model is manufactured to verify them. A discussion on some possible improvements and modifications of the structure is also presented.     

On reinsurance and investment for large insurance portfolios

We consider a problem of optimal reinsurance and investment for an insurance company whose surplus is governed by a linear diffusion. The company’s risk (and simultaneously its potential profit) is reduced through reinsurance, while in addition the company invests its surplus in a financial market. Our main goal is to find an optimal reinsurance-investment policy which minimizes the probability of ruin. More specifically, in this paper we consider the case of proportional reinsurance, and investment in a Black-Scholes market with one risk-free asset (bond, or bank account) and one risky asset (stock). We apply stochastic control theory to solve this problem. It transpires that the qualitative nature of the solution depends significantly on the interplay between the exogenous parameters and the constraints that we impose on the investment, such as the presence or absence of shortselling and/or borrowing. In each case we solve the corresponding Hamilton-Jacobi-Bellman equation and find a closed-form expression for the minimal ruin probability as well as the optimal reinsurance-investment policy.     

Preparation and optical properties of silver chromate self-assembly necklace structures

The silver chromate self-assembly necklace structures were synthesized using high-active acrylicamide template. The whole length of the necklace structure was between 1.2 and 1.5 μm. The product was composed of single crystalline nanorods with diameters of about 40 nm and lengths of 300 nm. The synthetic mechanism and product’s optical properties were also studied.     

Numerical study of optical properties of single silver nanobowtie with anisotropic topology

Optical properties of silver nanobowtie with anisotropic topology, which is separated with nanogap that is horizontal (Y direction) and vertical (Z direction) to the line between the two constituent triangles (i.e., the bowtie axis), are studied. A discrete dipole approximation (DDA) method is used to determine the extinction efficiency and the electric field (E-field) distribution, then the corresponding enhancement factor (EF) and the full width half maximum (FWHM) of the E-field are obtained and analyzed. Our results show that the wavelength of localized surface plasmon resonance (LSPR)-induced blue-shifts and the maximum EF decrease were observed with increasing gap size for the parallel polarized (Z-polarized) excitation. It is also found that the light spot at the “hot spot” in the gap becomes larger and deviates from the rectangular pattern with the increase of the gap in the Z direction (Z-gap), and the FWHM in the Z direction of the localized E-field in the gap broadens with either an increase in the gap in the Y direction (Y-gap) or the Z-gap. These behaviors are due to the decrease of the coupling efficiency of near-field plasmon coupling. In contrast, the wavelength of the LSPR and the maximum EF excited by the perpendicularly polarized (Y-polarized) light show less dependence on the gap size than that of the Y-polarized light. PACS  73.20.Mf; 78.67.-n     

Dynamics of a small vibro-impact pile driver

A mathematical model is developed to study periodic-impact motions and bifurcations in dynamics of a small vibro-impact pile driver. Dynamics of the small vibro-impact pile driver can be analyzed by means of a three-dimensional map, which describes free flight and sticking solutions of the vibro-impact system, between impacts, supplemented by transition conditions at the instants of impacts. Piecewise property and singularity are found to exist in the Poincaré map. The piecewise property is caused by the transitions of free flight and sticking motions of the driver and the pile immediately after the impact, and the singularity of map is generated via the grazing contact of the driver and the pile immediately before the impact. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. The influence of piecewise property, grazing singularities and parameter variation on the performance of the vibro-impact pile driver is analyzed. The global bifurcation diagrams for the impact velocity of the driver versus the forcing frequency are plotted to predict much of the qualitative behavior of the actual physical system, which enable the practicing engineer to select excitation frequency ranges in which stable period one single-impact response can be expected to occur, and to predict the larger impact velocity and shorter impact period of such response.     

Improvement of Steroid Biotransformation with Hydroxypropyl-β-Cyclodextrin Induced Complexation

The inclusion complexes induced by cyclodextrins and its derivates have been shown previously to enhance the biotransformation of hydrophobic compounds. Using hydroxypropyl-β-cyclodextrin (HP-β-CD; 20% w/v), the water solubility of cortisone acetate increased from 0.039 to 7.382 g L⁻¹ at 32 °C. The solubilization effect of HP-β-CD was far superior to dimethylformamide (DMF) and ethanol. The dissolution rate also significantly increased in the presence of HP-β-CD. The enzymatic stability of Δ¹-dehydrogenase from Arthrobacter simplex TCCC 11037 was not influenced by the increasing concentrations of HP-β-CD contrary to the organic cosolvents which negatively influenced in the order DMF > ethanol. The activity inhibition effect caused by HP-β-CD was not so conspicuous as ethanol and DMF. Inactivation constants of ethanol, DMF, and HP-β-CD were 5.832, 4.541, and 1.216, respectively. The inactivation energy (E _a) was in the order of HP-β-CD (55.1 kJ mol⁻¹) > ethanol (39.9 kJ mol⁻¹) > DMF (37.1 kJ mol⁻¹).     

One-step synthesis and characterization of dendrimer-protected gold nanoparticles

We proposed an economic, convenient, and mild synthesis of dendrimer-protected gold nanoparticles by exposing a third-generation poly(propyleneimine) dendrimer-HAuCl₄ aqueous solution to sunlight without the additional step of introducing other reducing agents and protective agents. Most importantly, it is found that the size of the gold nanoparticles thus formed can be controlled by the molar ratio of the dendrimer to gold. The text was submitted by the author in English.     

Optimal control for a population dynamics with age-dependent and diffusion in a periodic environment

Here we consider the optimal harvesting problem for a periodic age-dependent population dynamics with diffusion. Namely, we investigate the model with periodic vital rates and a periodic forcing term that sustains oscillations. By using Mazur’s theorem, we demonstrate existence of solutions of the optimal control problem and by the conception of normal cone, we also obtain the first order necessary conditions of optimality for the problem. Our results extend some known criteria.