Computational analysis of glycolytic reaction in open spatial reactor

We consider the computational analysis of processes within the spatially-distributed model simulating the glycolytic reaction taking place in the one-side fed open chemical reactor. The main point of the simulation is the decomposition of the reaction–diffusion system into unidirectional reaction in a bulk supplied by feedback terms stated as boundary conditions on the lower boundary of the reactor, i.e. the unique plane where an exchange with an outer medium is possible within the real experimental situation. Analysis of the curvature of the reagents distribution curves proves kinematic character of the observed lateral waves corresponding to the picture of experimentally observed glycolytic traveling waves. At the same time, their origin relates to diffusion of the reagents in a vertical cross-section of the reactor. Study of the solutions for the concerned reaction–diffusion model in the case of stochastically different diffusion coefficients reveals the Turing structures.     

Ligand Displacement Reaction Paths in a Diiron Hydrogenase Active Site Model Complex

The mechanism and energetics of CO, 1‐hexene, and 1‐hexyne substitution from the complexes (SBenz)₂[Fe₂(CO)₆] (SBenz=SCH₂Ph) ( 1 ‐CO), (SBenz)₂[Fe₂(CO)₅(η²‐1‐hexene)] ( 1 ‐(η²‐1‐hexene)), and (SBenz)₂[Fe₂(CO)₅(η²‐1‐hexyne)] ( 1 ‐(η²‐1‐hexyne)) were studied by using time‐resolved infrared spectroscopy. Exchange of both CO and 1‐hexyne by P(OEt)₃ and pyridine, respectively, proceeds by a bimolecular mechanism. As similar activation enthalpies are obtained for both reactions, the rate‐determining step in both cases is assumed to be the rotation of the Fe(CO)₂L (L=CO or 1‐hexyne) unit to accommodate the incoming ligand. The kinetic profile for the displacement of 1‐hexene is quite different than that for the alkyne and, in this case, both reaction channels, that is, dissociative (S_N1) and associative (S_N2), were found to be competitive. Because DFT calculations predict similar binding enthalpies of alkene and alkyne to the iron center, the results indicate that the bimolecular pathway in the case of the alkyne is lower in free energy than that of the alkene. In complexes of this type, subtle changes in the departing ligand characteristics and the nature of the mercapto bridge can influence the exchange mechanism, such that more than one reaction pathway is available for ligand substitution. The difference between this and the analogous study of (μ‐pdt)[Fe(CO)₃]₂ (pdt=S(CH₂)₃S) underscores the unique characteristics of a three‐atom S?S linker in the active site of diiron hydrogenases.     

Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.     

On the distribution of cumulative Parisian ruin

We introduce the concept of cumulative Parisian ruin, which is based on the time spent in the red by the underlying surplus process. Our main result is an explicit representation for the distribution of the occupation time, over a finite-time horizon, for a compound Poisson process with drift and exponential claims. The Brownian ruin model is also studied in details. Finally, we analyse for a general framework the relationships between cumulative Parisian ruin and classical ruin, as well as with Parisian ruin based on exponential implementation delays.     

On input-to-state stability for stochastic multi-group models with multi-dispersal

This paper focuses on the input-to-state stability for a general class of stochastic multi-group models with multi-dispersal. By incorporating graph theory with Lyapunov method as well as stochastic analysis techniques, novel sufficient criteria are derived, which are in the form of Lyapunov-type theorem and coefficient-type criterion, respectively. Moreover, to show the applicability of our findings, we employ coefficient-type criterion to analyze the input-to-state stability for stochastic coupled oscillators. Finally, a numerical example and its simulations are offered to demonstrate the validity and feasibility of the theoretic results.     

Numerical solution of a singular integral equation arising in a cruciform crack problem

A singular integral equation arising in a cruciform crack problem is investigated in the present paper. Based on the convex technique, the piecewise Taylor-series expansion method is extended by introducing a weight parameter. An approximate solution of the singular integral equation is constructed and its convergence and error estimate are made. The variations of the approximate solutions associating with stress intensity factors are analyzed by considering internal pressures of power and sine functions, respectively. By comparing with the known methods, the observations reveal that a good approximation can be achieved using less derivative times, less discretization points, and a suitable weight parameter. The obtained results show that the crack growth is dependent on applied mechanical loadings.     

An S‐Oxygenated [NiFe] Complex Modelling Sulfenate Intermediates of an O2‐Tolerant Hydrogenase

To understand the molecular details of O₂‐tolerant hydrogen cycling by a soluble NAD⁺‐reducing [NiFe] hydrogenase, we herein present the first bioinspired heterobimetallic S‐oxygenated [NiFe] complex as a structural and vibrational spectroscopic model for the oxygen‐inhibited [NiFe] active site. This compound and its non‐S‐oxygenated congener were fully characterized, and their electronic structures were elucidated in a combined experimental and theoretical study with emphasis on the bridging sulfenato moiety. Based on the vibrational spectroscopic properties of these complexes, we also propose novel strategies for exploring S‐oxygenated intermediates in hydrogenases and similar enzymes.     

相依误差广义线性模型的M估计的Bahadur表示

考虑如下广义线性模型y_i=h(x~T_i,β)+e_i=1,2,…,n,其中e_i=G(…,ε_(i-1),ε_i),h是一个连续可导函数,ε_i是独立同分布的随机变量,并且它的期望为0,方差σ~2有限.本文给出了参数β的M估计,并且得到了该估计的Bahadur表示,该结论推广了线性模型的相关结论.应用M估计的Bahadur表示,得到了相依误差的线性回归模型,poisson模型,logistic模型和独立误差的广义线性模型等模型的渐近性质.     

Approximate solutions and scalarization in set-valued optimization

Abstract

Certain notions of approximate weak efficient solutions are considered for a set-valued optimization problem based on vector and set criteria approaches. For approximate solutions based on the vector approach, a characterization is provided in terms of an extended Gerstewitz’s function. For the set approach case, two notions of approximate weak efficient solutions are introduced using a lower and an upper quasi order relations for sets and further compactness and stability aspects are discussed for these approximate solutions. Existence and scalarization using a generalized Gerstewitz’s function are also established for approximate solutions, based on the lower set order relation.     

Generalized immediate exchange models and their symmetries

We reconsider the discrete dual of the immediate exchange model and define a more general class of models where mass is split, exchanged and merged. We relate the splitting process to the symmetric inclusion process via thermalization and from that obtain symmetries and self-duality for it and its generalization. We show that analogous properties hold for models where the splitting is related to the symmetric exclusion process or to independent random walkers.