Hopf-pitchfork bifurcation in van der Pol's oscillator with nonlinear delayed feedback

First, we identify the critical values for Hopf-pitchfork bifurcation. Second, we derive the normal forms up to third order and their unfolding with original parameters in the system near the bifurcation point, by the normal form method and center manifold theory. Then we give a complete bifurcation diagram for original parameters of the system and obtain complete classifications of dynamics for the system. Furthermore, we find some interesting phenomena, such as the coexistence of two asymptotically stable states, two stable periodic orbits, and two attractive quasi-periodic motions, which are verified both theoretically and numerically.     

Analysis of a delayed Monod type chemostat model with impulsive input the polluted nutrient

In this paper, a Monod type chemostat model with delayed response in growth and impulsive input the polluted nutrient is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution. Further, it is globally attractive. The permanent condition of the investigated system is also obtained by the theory of impulsive delay differential equation. Our results reveal that the delayed response in growth plays an important role on the outcome of the chemostat.     

Expected present value of total dividends in a delayed claims risk model under stochastic interest rates

In this paper, a compound binomial risk model with a constant dividend barrier under stochastic interest rates is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are K_n distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.     

Existence and asymptotic behavior of traveling wave solution for Korteweg-de Vries-Burgers equation with distributed delay

In this paper, we investigate the existence and asymptotic behavior of traveling wave solution for delayed Korteweg-de Vries-Burgers (KdV-Burgers) equation. Using geometric singular perturbation theory and Fredholm alternative, we establish the existence of traveling wave solution for this equation. Employing the standard asymptotic theory, we obtain asymptotic behavior of traveling wave solution of the equation.     

Surface modification of chromatography adsorbents by low temperature low pressure plasma

In this study we show how low temperature glow discharge plasma can be used to prepare bi-layered chromatography adsorbents with non-adsorptive exteriors. The commercial strong anion exchange expanded bed chromatography matrix, Q HyperZ, was treated with plasmas in one of two general ways. Using a purpose-designed rotating reactor, plasmas were employed to either: (i) remove anion exchange ligands at or close to the exterior surface of Q HyperZ, and replace them with polar oxygen containing functions (‘plasma etching and oxidation’); or (ii) bury the same surface exposed ligands beneath thin polymer coatings (‘plasma polymerization coating’) using appropriate monomers (vinyl acetate, vinyl pyrrolidone, safrole) and argon as the carrier gas. X-ray photoelectron spectroscopy analysis (first ∼10 nm depth) of Q HyperZ before and after the various plasma treatments confirmed that substantial changes to the elemental composition of Q HyperZ's exterior had been inflicted in all cases. The atomic percent changes in carbon, nitrogen, oxygen, yttrium and zirconium observed after being exposed to air plasma etching were entirely consistent with: the removal of pendant Q (trimethylammonium) functions; increased exposure of the underlying yttrium-stabilised zirconia shell; and introduction of hydroxyl and carbonyl functions. Following plasma polymerization treatments (with all three monomers tested), the increased atomic percent levels of carbon and parallel drops in nitrogen, yttrium and zirconium provided clear evidence that thin polymer coats had been created at the exteriors of Q HyperZ adsorbent particles. No changes in adsorbent size and surface morphology, nor any evidence of plasma-induced damage could be discerned from scanning electron micrographs, light micrographs and measurements of particle size distributions following 3 h exposure to air (220 V; 35.8 W L⁻¹) or ‘vinyl acetate/argon’ (170 V; 16.5 W L⁻¹) plasmas. Losses in bulk chloride exchange capacity before and after exposure to plasmas enabled effective modification depths within hydrated Q HyperZ adsorbent particles to be calculated as 0.2–1.2 μm, depending on the conditions applied. The depth of plasma induced alteration was strongly influenced by the power input and size of the treated batch, i.e. dropping the power or increasing the batch size resulted in reduced plasma penetration and therefore shallower modification. The selectivity of ‘surface vs. core’ modification imparted to Q HyperZ by the various plasma treatments was evaluated in static and dynamic binding studies employing appropriate probes, i.e. plasmid DNA, sonicated calf thymus DNA and bovine serum albumin. In static binding studies performed with adsorbents that had been exposed to plasmas at the 5 g scale (25 g L⁻¹ of plasma reactor), the highest ‘surface/core’ modification selectivity was observed for Q HyperZ that had been subjected to 3 h of air plasma etching at 220 V (35.8 W L⁻¹). This treatment removed ∼53% of ‘surface’ DNA binding at the expense of a 9.3% loss in ‘core’ protein binding. Even more impressive results were obtained in dynamic expanded bed adsorption studies conducted with Q HyperZ adsorbents that had been treated with air (220 V, 3 h) and ‘vinyl acetate/argon’ (170 V, 3 h) plasmas at 10.5 g scale (52.5 g L⁻¹ of plasma reactor). Following both plasma treatments: the 10% breakthrough capacities of the modified Q HyperZ adsorbents towards ‘surface’ binding DNA probes dropped very significantly (30–85%); the DNA induced inter-particle cross-linking and contraction of expanded beds observed during application of sonicated DNA on native Q HyperZ was completely eradicated; but the ‘core’ protein binding performance remained unchanged cf. that of the native Q HyperZ starting material.     

Speeding up MCMC by Delayed Acceptance and Data Subsampling

The complexity of the Metropolis–Hastings (MH) algorithm arises from the requirement of a likelihood evaluation for the full dataset in each iteration. One solution has been proposed to speed up the algorithm by a delayed acceptance approach where the acceptance decision proceeds in two stages. In the first stage, an estimate of the likelihood based on a random subsample determines if it is likely that the draw will be accepted and, if so, the second stage uses the full data likelihood to decide upon final acceptance. Evaluating the full data likelihood is thus avoided for draws that are unlikely to be accepted. We propose a more precise likelihood estimator that incorporates auxiliary information about the full data likelihood while only operating on a sparse set of the data. We prove that the resulting delayed acceptance MH is more efficient. The caveat of this approach is that the full dataset needs to be evaluated in the second stage. We therefore propose to substitute this evaluation by an estimate and construct a state-dependent approximation thereof to use in the first stage. This results in an algorithm that (i) can use a smaller subsample m by leveraging on recent advances in Pseudo-Marginal MH (PMMH) and (ii) is provably within O(m^{? 2}) of the true posterior.     

A queueing model of delayed product differentiation

We consider a production system in which a supplier produces semi-finished items on a make-to-stock basis for a manufacturer that will customize the items on a make-to-order basis. The proportion of total processing time undertaken by the supplier determines how suitable the semi-finished items will be to meet customer demand. The manufacturer wishes to determine the optimal point of differentiation (the proportion of processing completed by the supplier) and its optimal semi-finished goods buffer size. We use matrix geometric methods to evaluate various performance measures for this system, and then, with enumeration techniques, obtain optimal solutions. We find that delayed product differentiation is attractive when the manufacturer can balance the costs of customer order fulfillment delay with the costs associated with unsuitable items.     

Secondary‐Structure‐Driven Self‐Assembly of Reactive Polypept(o)ides: Controlling Size,Shape, and Function of Core Cross‐Linked Nanostructures

Achieving precise control over the morphology and function of polymeric nanostructures during self‐assembly remains a challenge in materials as well as biomedical science, especially when independent control over particle properties is desired. Herein, we report on nanostructures derived from amphiphilic block copolypept(o)ides by secondary‐structure‐directed self‐assembly, presenting a strategy to adjust core polarity and function separately from particle preparation in a bioreversible manner. The peptide‐inherent process of secondary‐structure formation allows for the synthesis of spherical and worm‐like core‐cross‐linked architectures from the same block copolymer, introducing a simple yet powerful approach to versatile peptide‐based core–shell nanostructures.     

New method for post-processing crosslinking reaction

A new processing method to process functionalized polymer materials that are able to crosslink has been developed. The crosslinking reaction occurs after the melt processing stage at moderate temperature and without the addition of external reagents. Maleic anhydride-ethylene copolymer was processed with 1,4-butanediol in the presence of para-toluene sulfonic acid as catalyst. To prevent the reaction in the melt, it was chosen to trap the 1,4-butanediol onto vector particles. The extent of the crosslinking reaction during the mixing at 110 °C has been studied for three different particles taken as vector particles. It was found that Orgasol^® polyamide particles are efficient to inhibit the crosslinking reaction in the mixer. The reaction then takes place at 40 °C and after 100 h the cured samples appeared to be highly and homogeneously crosslinked with a gel content above 90%.     

Ruin Probabilities for Large Claims in Delayed Renewal Risk Model

This paper investigates ruin probabilities (x) in the delayed renewal risk model, where x is the initial capital of an insurance company. Under the assumption that the claim size is heavy-tailed, we aim at a tail equivalence relationship of (x) as x . The result we obtain in this paper is surprisingly the same as the previous classical results.This work was supported by National Science Foundation of China (No. 10071081).