A dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.     

The spectral analysis and exponential stability of a bi‐directional coupled wave‐ODE system

In this paper, an unstable linear time invariant (LTI) ODE system is stabilized exponentially by the PDE compensato—a wave equation with Kelvin‐Voigt (K‐V) damping. Direct feedback connections between the ODE system and wave equation are established: The velocity of the wave equation enters the ODE through the variable v_t(1,t); meanwhile, the output of the ODE is fluxed into the wave equation. It is found that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point , and there are two branches of asymptotic eigenvalues: the first branch approaches to , and the other branch tends to ?∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum‐determined growth condition and exponential stability of the system are concluded.     

含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理，本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件，并通过数值算例验证了理论结果的有效性.     

Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.     

Inhibition effect of butan-1-ol on the corrosion behavior of austenitic stainless steel (Type 304) in dilute sulfuric acid

The electrochemical behavior of austenitic stainless steel (Type 304) in 3 M sulfuric acid with 3.5% recrystallized sodium chloride at specific concentrations of butan-1-ol was investigated with the aid of potentiodynamic polarization, open circuit measurement and weight loss technique. Butan-1-ol effectively inhibited the steel corrosion with a maximum inhibition efficiency of 78.7% from weight-loss analysis and 80.9% from potentiodynamic polarization test at highest concentration studied. Adsorption of the compound obeyed the Freundlich isotherm. Thermodynamic calculations reveal physiochemical interactions and spontaneous adsorption mechanism. Surface characterizations showed the absence of corrosion products and topographic modifications of the steel. Statistical analysis depicts the overwhelming influence and statistical significance of inhibitor concentration on the inhibition performance.     

Synthesis and Structures of Arene Ruthenium (II)–NHC Complexes: Efficient Catalytic α‐alkylation of ketones via Hydrogen Auto Transfer Reaction

A panel of six new arene Ru (II)‐NHC complexes 2a‐f , (NHC = 1,3‐diethyl‐(5,6‐dimethyl)benzimidazolin‐2‐ylidene 1a , 1,3‐dicyclohexylmethyl‐(5,6‐dimethyl)benzimidazolin‐2‐ylidene 1b and 1,3‐dibenzyl‐(5,6‐dimethyl)benzimidazolin‐2‐ylidene 1c ) were synthesized from the transmetallation reaction of Ag‐NHC with [(η⁶‐arene)RuCl₂]₂ and characterized. The ruthenium (II)‐NHC complexes 2a‐f were developed as effective catalysts for α‐alkylation of ketones and synthesis of bioactive quinoline using primary/amino alcohols as coupling partners respectively. The reactions were performed with 0.5 mol% catalyst load in 8 h under aerobic condition and the maximum yield was up to 96%. Besides, the different alkyl wingtips on NHC and arene moieties were studied to differentiate the catalytic robustness of the complexes in the transformations.     

A stable pillared metal–organic framework constructed by H4TCPP ligand as luminescent sensor for selective detection of TNP and Fe3+ ions

A novel luminescent metal–organic framework ( Zn‐TCPP/BPY ) with pillared structure based on 2,3,5,6‐tetrakis(4‐carboxyphenyl)pyrazine (H₄TCPP) and 4,4′‐bipyridine (BPY) has been designed and synthesized through a solvothermal reaction. The [Zn₂(COO)₄] paddlewheel units are linked by TCPP^4? ligands to form two‐dimensional layers and further connected by BPY ligands as pillars to construct the twofold interpenetrating three‐dimensional framework. Interestingly, Zn‐TCPP/BPY possesses outstanding stability in organic solvents and water as well as maintains its structural rigidity in aqueous solutions of different pH values (3–12). After activation, Zn‐TCPP/BPY possesses permanent porosity with Brunauer–Emmett–Teller surface area of 630 m² g^–1. Remarkably, Zn‐TCPP/BPY displays excellent fluorescent property in virtue of the aggregation‐induced emission effect of the H₄TCPP ligand, which can be highly active and quenched by small amounts of 2,4,6‐trinitrophenol (TNP) and Fe³⁺ ions. Furthermore, the detection effect of Zn‐TCPP/BPY remains basically the same even after five cycles. The excellent stability, high sensitivity, and recyclability of Zn‐TCPP/BPY make it an outstanding chemical sensor for detecting TNP and Fe³⁺ ions.