Almost Split Sequences in Dimension One

Let R be a complete discrete valuation ring with quotient field K, and let Λ be an R-order in a semisimple K-algebra. For an indecomposable Λ-lattice E, a sublattice Bi E satisfying Rad E ? Bi E is defined, and it is shown that the middle term H of an almost split sequence τE ? H ? E can be obtained by an amalgamation of E/Bi E with E′/τE for a suitable overlattice E′ of τE. The method is bound to dim R = 1.     

A Non-Existence Theorem for Almost Split Sequences

Let k be a field, Q a quiver with countably many vertices and I an ideal of kQ such that kQ/I is a spectroid. In this note, we prove that there is no almost split sequence ending at an indecomposable not finitely presented representation of the bound quiver (Q, I). We then get that an indecomposable representation M of (Q, I) is the ending term of an almost split sequence if and only if it is finitely presented and not projective. The dual results are also true.     

Viscosity Approximation Methods for Generalized Multi-Valued Nonexpansive Mappings with Applications

Abstract

In this article, we study viscosity approximation methods for generalized multi-valued nonexpansive mappings and we present some new results related to strong convergence, variational inequality, convex optimization, split and common split feasibility problems (SFPs). Some numerical computations are also presented to illustrate our results.     

On the role of pressure in elasto-inertial turbulence

The dynamics of elasto-inertial turbulence is investigated numerically from the perspective of the coupling between polymer dynamics and flow structures. In particular, direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 are used to study the formation and dynamics of elastic instabilities and their effects on the flow. Based on the splitting of the pressure into inertial and polymeric contributions, it is shown that the polymeric pressure is a non-negligible component of the total pressure fluctuations, although the rapid inertial part dominates. Unlike Newtonian flows, the slow inertial part is almost negligible in elasto-inertial turbulence. Statistics on the different terms of the Reynolds stress transport equation also illustrate the energy transfers between polymers and turbulence and the redistributive role of pressure. Finally, the trains of cylindrical structures around sheets of high polymer extension that are characteristics of elasto-inertial turbulence are shown to be correlated with the polymeric pressure fluctuations.     

Theoretical Contribution towards Understanding Specific Behaviour of “Simple” Protein‐film Reactions in Square‐wave Voltammetry

Surface reactions of uniformly adsorbed redox molecules at working electrode surface are seen as adequate models to studying chemical reactivity of many lipophilic enzymes. When considered under pulse voltammetric techniques, these systems show several uncommon features, whose origin is still not completely clear. The phenomena of “quasireverible maximum”, “splitting” of the net peak in square‐wave voltammetry, and the very steep descent of Faradaic currents of simple surface redox reactions exhibiting fast electron transfer are just some of the features that make these systems quite interesting for further elaborations. In this work, we present a set of theoretical calculations under conditions of square‐wave voltammetry in order try to explain some of aforementioned phenomena. The major goal of our work is to get insight to some voltammetric and chrono‐amperometric features of two considered surface reactions, i. e. (1) the “simple” surface redox reaction, and (2) surface redox reaction coupled to follow‐up irreversible chemical reaction of electrochemically generated redox species (or surface ECirr). We focus on the role of created Red(ads) (here in the reduction pulses only) to the current components of calculated square‐wave voltammograms exhibiting fast electrode reaction. We show that the irreversible chemical removal of electrochemically generated Red(ads) species, created in the potential pulses where half‐reaction of reduction Ox(ads)+ne‐?→Red(ads) is “defined” to take place, causes significant increase of all square‐wave current components. The results presented in this work show how complex the chrono‐amperometric features of surface redox reactions under pulse voltammetric conditions might be. In addition, we point out that both half reactions of a given simple surface redox process can occur, at both, “only reduction” and “only oxidation” potential pulses in square‐wave voltammetry. This, in turn, contributes to the occurrence of many phenomena observed in simple protein‐film voltammetry reactions. The effects of chemical reaction rate to the features of calculated square‐wave voltammograms of surface ECirr systems with fast electrode reaction are reported for the first time in this work.     

多重边融合复杂动态网络的自适应同步

基于网络拆分的思想对多重边融合复杂动态网络局部和全局的自适应同步进行了研究.通过给出严格的数学定义及假设,运用Lyapunov稳定理论得出了网络局部和全局的同步准则,给出了更为简单的网络同步的控制器.最后以Lorenz 系统为例进行数值仿真,验证了结论的正确性和有效性. 关键词： 多重边融合复杂动态网络 自适应同步 网络拆分 时滞     

均匀光纤Bragg光栅局部横向受力特性研究

对均匀光纤Bragg光栅(FBG)局部横向受力特性进行了理论和实验研究.采用传输矩阵法分析了FBG其中一段横向受力时的反射光谱变化,并且建立了相应的数学模型.研究表明,当FBG局部横向受力时,受压长度对反射光谱无影响,反射光谱分裂点的波长与横向作用力呈线性正比关系并具有周期性,分裂点反射率与受力位置的关系为近似双曲正切关系. 关键词： 光纤Bragg光栅 传输矩阵法 局部横向受力 分裂点     

Similarity of hybrid numbers

The set of hybrid numbers $𝕂$ is a noncommutative number system that unified and generalized the complex, dual, and double (hyperbolic) numbers with the relation ih =− hi =ε+ i. Two hybrid numbers p and q are said to be similar if there exist a nonlightlike hybrid number x satisfying the equality x ⁻¹ qx = p . And, it is denoted by p ∼ q . In this paper, we study the concept of similarity for hybrid numbers by solving the linear equations px = xq and qx − xp = c for $\text{◂,▸}\mathbf{p},\mathbf{q},\mathbf{c}\in 𝕂\mathbf{.}$     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

考虑完全拆分的拣选分批与拣选路径集成优化模型

在电商海量订单背景下,在线订单拣选作业难度加大,因此设计了基于订单完全拆分的拣选分批与拣选路径综合优化模型解决此问题.模型共分两阶段.第一阶段,基于种子算法,设计考虑订单完成度、等待时间与拣选路径的拣选分批模型;第二阶段以拣选单流为单队列,设计多拣选员并行服务的拣选系统.行走策略为基于返回型和遍历型的综合策略,拣选路径优化模型采用模拟退火算法求解.算例分析表明,与传统的不拆分拣选分批模型相比,构建的综合优化模型能够显著提高拣选系统效率.拣选员为4人时,模型能够使总服务时间减少58.79%,订单完成率提高10.09%.