Dispersion and localisation in structured Rayleigh beams

This paper brings a comparative analysis between dynamic models of couple-stress elastic materials and structured Rayleigh beams on a Winkler foundation. Although physical phenomena have different physical origins, the underlying equations appear to be similar, and hence mathematical models have a lot in common. In the present work, our main focus is on the analysis of dispersive waves, band-gaps and localised waveforms in structured Rayleigh beams. The Rayleigh beam theory includes the effects of rotational inertia which are neglected in the Euler–Bernoulli beam theory. This makes the approach applicable to higher frequency regimes. Special attention is given to waves in pre-stressed Rayleigh beams on elastic foundations.     

Path-following barrier and penalty methods for linearly constrained problems

In the present paper some barrier and penalty methods (e.g. logarithmic barriers, SUMT, exponential penalties), which define a continuously differentiable primal and dual path, applied to linearly constrained convex problems are studied, in particular, the radius of convergence of Newton’s method depending on the barrier and penalty para-meter is estimated, Unlike using self-concordance properties the convergence bounds are derived by direct estimations of the solutions of the Newton equations. The obtained results establish parameter selection rules which guarantee the overall convergence of the considered barrier and penalty techniques with only a finite number of Newton steps at each parameter level. Moreover, the obtained estimates support scaling method which uses approximate dual multipliers as available in barrier and penalty methods     

On Landis’ Conjecture in the Plane

In this paper we prove a quantitative form of Landis’ conjecture in the plane. Precisely, let W(z) be a measurable real vector-valued function and V(z) ≥0 be a real measurable scalar function, satisfying ‖W‖ _{L ^∞(R ²)} ≤ 1 and ‖V‖ _{L ^∞(R ²)} ≤ 1. Let u be a real solution of Δu ? ?(Wu) ? Vu = 0 in R ². Assume that u(0) = 1 and |u(z)| ≤exp (C ₀|z|). Then u satisfies inf _{|z 0| =R}  sup _{|z?z 0| <1}|u(z)| ≥exp (?CRlog R), where C depends on C ₀. In addition to the case of the whole plane, we also establish a quantitative form of Landis’ conjecture defined in an exterior domain.     

生态平衡制约下离散尺度结构种群的最优收获

研究基于扩展Leslie投影矩阵的离散尺度结构种群模型的最优收获问题,约束条件包括生态平衡和开发成本等.运用凸优化理论证明了最优收获策略的存在性,导出了最优收获模式,应用模型参数给出了收获比率.结论显示:最优策略具有两阶段结构.     

On the inverse spectral theory in a non-homogeneous interior transmission problem

We study the inverse spectral problem in an interior transmission eigenvalue problem. The Cartwright’s theory in value distribution theory gives a connection between the distributional structure of the eigenvalues and the asymptotic behaviours of its defining functional determinants. Given a sufficient quantity of transmission eigenvalues, we prove a uniqueness of the refraction index in inhomogeneous medium as an uniqueness problem in entire function theory. The asymptotically periodical structure of the zero set of the solutions helps to locate infinitely many eigenvalues of infinite degree of freedom.     

Flow Through Diffusion Cell Method: A Better Approach to Study Drug Release Behavior as Compared to Traditional Dissolution Test Method

Co‐polymeric hydrogels consisting of N‐vinyl‐2‐pyrrolidone (NVP) and acrylic acid (AAc) were synthesized and evaluated for release of a model drug, i.e., vitamin B₁₂. Release studies in simulated gastric fluid (pH 1.2) and intestinal fluid (pH 7.4), at 37°C, showed the hydrogels to be pH sensitive. An in vitro release study by ‘traditional dissolution test’ (TDT) showed that percent drug released from the hydrogel was nearly 8.6±2.1 and 83.2±4.8 in the media of pH 1.2 and 6.8, respectively. However, in order to incorporate in vivo GI conditions such as acidic pH and high water content in the stomach, low water content and the presence of a semi–solid mass in the large intestine, a new test model, called flow through diffusion cell (FTDC) was also used. The two approaches yielded almost different release profiles. The gels were characterized by thermogravimetric analysis and FTIR spectroscopy.     

Dynamic Release of Propranolol HCl from Cationic Ion–Exchanger–Loaded Calcium Alginate Beads

The dynamic release of drug propranolol HCl from the propranolol HCl–resin complex (PRC) loaded calcium alginate beads has been studied in the buffer media of pH 1.2 at the physiological temperature 37°C. The PRC encapsulated beads demonstrated nearly 58.04% release while naked PRC particles released 98.00% drug in 24 h in the gastric fluid. The amount of drug released was found to increase with and decrease in the amount of sodium alginate in the beads. Similarly, with the increase in the amount of entrapped PRC particles within the beads, the quantity of drug released was also observed to increase. The degree of crosslinking of beads also affected the release kinetics. Interestingly, the release from naked PRC particles followed ‘first‐order’ kinetics while PRC particles, entrapped in calcium–alginate beads, exhibited ‘diffusion controlled’ release behavior as indicated by liner nature of fractional release vs. √t plot.     

Finite Element Based Micro-mechanical Modeling of Interphase in Filler Reinforced Elastomers

Characteristic properties of elastomers can be tailored by embedding them with filler particles. Along with enhancing the overall properties of the composite, filler particles also induce some inelastic effects. In this paper, a finite element computational model is used to study the effect of microstructure morphology in filled elastomers, on its macroscopic large deformation behavior. A multiphase material model that accounts for the hypothesis of shift in glass transition temperature in the vicinity of the filler particle is developed to simulate the interphase between the fillers and the matrix. It also accounts for the breakdown and re-aggregation of filler networks under cyclic loading. Examples at the microstructural level, demonstrating the dynamics of the interphase using the developed multiphase model have been successfully simulated. The obtained results are in good qualitative agreement with the Mullins effect. Therefore, computational experiments using this methodology enable the prediction of the experimentally observed softening behavior in filled elastomers based on its microstructure evolution.     

Water-dispersible non-aqueous emulsions stabilized by a poly(butadiene)-b-poly(2-vinylpyridine) block copolymer

Submicron non-aqueous emulsions, of interest for biomedical and cosmetic formulations, were developed for the system comprising poly(ethylene glycol) (PEG) 400 and Miglyol 812, an enzymatic degradable liquid glycerine ester. These emulsions, with PEG 400 as continuous phase and Miglyol 812 droplets, in the size range of 200 nm, were stabilized by a poly(butadiene)-b-poly(2-vinylpyridine) (PBut-b-P2VP) block copolymer with a composition close to 50/50 wt%. The droplet size, stability and the rheological characteristics were examined as a function of the copolymer concentration. An original aspect of these anhydrous emulsions, with a water miscible continuous phase, is their water dispersibility without additional surfactant. In fact, the initial anhydrous emulsion is sterically stabilized and after water addition at low pH, the protonated P2VP sequence of the copolymer provides the electro-steric stabilization. This oil-in-water emulsion is characterized by sub micron sized Miglyol 812 droplets in an aqueous phase of PEG 400 and water at pH 1.