Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3

The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with $p^4$ elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined.     

Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogenous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school. Supplementary material for this article is available online.     

Variational Bayes With Intractable Likelihood

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes their use in many interesting situations such as in state--space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This article extends the scope of application of VB to cases where the likelihood is intractable, but can be estimated unbiasedly. The proposed VB method therefore makes it possible to carry out Bayesian inference in many statistical applications, including state--space models and ABC. The method is generic in the sense that it can be applied to almost all statistical models without requiring too much model-based derivation, which is a drawback of many existing VB algorithms. We also show how the proposed method can be used to obtain highly accurate VB approximations of marginal posterior distributions. Supplementary material for this article is available online.     

Resilient dissipative dynamic output feedback control for uncertain Markov jump Lur’e systems with time-varying delays

The resilient dissipative dynamic output feedback control problem for a class of uncertain Markov jump Lur’e systems with piecewise homogeneous transition probabilities and time-varying delays in the discrete-time domain are examined in this study. The designed controller can tolerate additive uncertainties in the controller gain matrix, which result from controller implementations. The time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. By constructing a Lyapunov–Krasovskii functional candidate, the sufficient conditions regarding the existence of desired resilient dissipative controllers are obtained in terms of linear matrix inequalities, thereby ensuring that the resulting closed-loop system is stochastically stable and strictly dissipative. Two numerical examples were established to illustrate the effectiveness of the proposed theoretical results.     

The Highly Controlled and Efficient Polymerization of Ethylene

The highly controlled and efficient polymerization of ethylene is a very attractive but challenging target. Herein we report on a Coordinative Chain Transfer Polymerization catalyst, which combines a high degree of control and very high activity in ethylene oligo- or polymerization with extremely high chain transfer agent (triethylaluminum) to catalyst ratios (catalyst economy). Our Zr catalyst is long living and temperature stable. The chain length of the polyethylene products increases over time under constant ethylene feed or until a certain volume of ethylene is completely consumed to reach the expected molecular weight. Very high activities are observed if the catalyst elongates 60 000 or more alkyl chains and the polydispersity of the strictly linear polyethylene materials obtained are very low. The key for the combination of high control and efficiency seems to be a catalyst stabilized by only one strongly bound monoanionic N-ligand.     

ABC三嵌段共聚物胶束从多间隔结构到多核结构转变的Monte Carlo模拟

采用Monte Carlo模拟方法研究了疏水-亲水-疏水(H-P-H)型ABC三嵌段共聚物在B嵌段的选择性溶剂中的自组装行为. 模拟结果表明, 通过调节A嵌段和C嵌段的疏水性和二者之间的不相容性, 体系中可以形成多种形貌各异的胶束. 根据胶束中疏水核结构的特点, 这些胶束大体上可以被分为多核型胶束和多间隔型胶束两种类型. 通过增强疏水嵌段的疏水性或降低A嵌段和C嵌段间的不相容性, H-P-H型ABC三嵌段共聚物胶束能够发生从多核型胶束向多间隔型胶束的转变. 进一步分析胶束中聚合物的链构象等微观结构信息发现, A嵌段和C嵌段间的排斥作用和疏水作用之间存在竞争关系, 而这种竞争关系是影响体系中形成多核型胶束还是多间隔型胶束的决定性因素.     

Computer Simulation Study on Adsorption and Conformation of Polymer Chains Driven by External Force

In this work, Monte Carlo simulations are used to study the critical adsorption behaviors of flexible polymer chains under the action of an external driving force F parallel to an attractive flat surface. The critical adsorption temperature T_c decreases linearly with increasing F,indicating that the driving force suppresses the adsorption of polymer. The conformation of polymer is also affected by the driving force.However, the effect of F is dependent on the competition between the driving force and temperature. Under strong force or at low temperature,the polymer is stretched along the direction of the force, while under weak force or at high temperature, the polymer is not stretched. When the force is comparable to the temperature, the polymer may be stretched perpendicular to the driving force, and below T_c, we observe conformational transitions from parallel to perpendicular and again to parallel by decreasing the temperature. We found that the perpendicular stretched conformation leads the polymer chain to synchronously move along the direction of the driving force. Moreover, the conformational transitions are attributed to the competition and cooperation between the driving force and the temperature.     

Synthesis and Assessment of Two Malonyl Dihydrazide Derivatives as Corrosion Inhibitors for Carbon Steel in Acidic Media: Experimental and Theoretical Studies

Despite the extensive use of carbon steel in all industrial sectors, particularly in the petroleum industry, its low corrosion resistance is an ongoing problem for these industries. In the current work, two malonyl dihydrazide derivatives, namely 2,2’-malonylbis (N-phenylhydrazine-1-carbothiamide (MBC) and N’1, N’3-bis(-2-hydroxybenzylidene) malonohydrazide (HBM), were examined as inhibitors for the carbon steel corrosion in 1.0 M HCl. Both MBC and HBM were characterised using thin-layer chromatography, elemental analysis, infrared spectroscopy, and nuclear magnetic resonance techniques. The corrosion tests were performed using mass loss measurements, polarisation curves, and electrochemical impedance spectroscopy. It is obtained from the mass loss studies that the optimal concentration for both inhibitors is 2.0 × 10⁻⁵ mol/L, and the inhibition efficiencies reached up to 90.7% and 84.5% for MBC and HBM, respectively. Electrochemical impedance spectroscopy (EIS) and potentiodynamic polarisation (PDP) indicate an increased impedance in the presence of both MBC and HBM and mixed-type inhibitors, respectively. Both inhibitors can mitigate corrosion in the range of 298–328 K. Values of free energy changes obtained from the Langmuir model suggest that the inhibitors suppress the corrosion process principally by chemisorption. The computational investigations were conducted to identify the factors connected with the anti-corrosive properties of the examined inhibitors.