Travel time estimation and order batching in a 2-block warehouse

Order batching problem (OBP) is the problem of determining the number of orders to be picked together in one picking tour. Although various objectives may arise in practice, minimizing the average throughput time of a random order is a common concern. In this paper, we consider the OBP for a 2-block rectangular warehouse with the assumptions that orders arrive according to a Poisson process and the method used for routing the order-pickers is the well-known S-shape heuristic. We first elaborate on the first and second moment of the order-picker’s travel time. Then we use these moments to estimate the average throughput time of a random order. This enables us to estimate the optimal picking batch size. Results from simulation show that the method provides a high accuracy level. Furthermore, the method is rather simple and can be easily applied in practice.     

On the Range of Certain ASH Algebras of Real Rank Zero*

In this paper, the authors consider the range of a certain class of ASH algebras in [An, Q., Elliott, G. A., Li, Z. and Liu, Z., The classification of certain ASH C*-algebras of real rank zero, J. Topol. Anal., 14(1), 2022, 183–202], which is under the scheme of the Elliott program in the setting of real rank zero C*-algebras. As a reduction theorem, they prove that all these ASH algebras are still the AD algebras studied in [Dadarlat, M. and Loring, T. A., Classifying C*-algebras via ordered, m...     

Local fracture resistance based on microstructural efficiency concept and simulation of injection molding

Local fracture resistance (FR) of short (SGF) and discontinuous long glass fibre (LGF) reinforced polypropylene (PP) was predicted using the ‘microstructural efficiency concept’ together with a simulation program for fibre orientation in injection molding. The ‘microstructural efficiency concept’ describes the relation between microstructural parameters such as the fibre content, the fibre aspect ratio and the processing (injection molding) induced layer structure taking also into account the local fibre orientation. The local fibre orientation in injection molding was predicted with the MOLDFLOW^®-software. The predicted local FR was compared with the measured one, which was determined by using compact tension samples and linear elastic fracture mechanics (LEFM). The comparison showed, that for SGF-PP good consistence between the predicted and measured FR existed, for LGF-PP the discrepancy was higher. Yet for both materials, the ‘microstructural efficiency concept’ together with the results obtained from the simulation of the fibre orientation can be used for FR prediction of an injection molded workpiece.     

On the basic laws of anisotropic viscoelasticity

The main aim of this work is to develop a consistent formulation of the rheological behavior for different anisotropic polymer systems. The unified theory of anisotropic viscoelasticity is developed based on the symmetry principles. The Maxwell rheological equation is extended to nonsymmetric anisotropic liquids. Transitions from the most general anisotropy to particular cases of anisotropy are established. It appears that the coupled relaxation of symmetric and antisymmetric stresses is a natural phenomenon in nonsymmetric viscoelasticity. Within the concept of an internal state variable, a stress–order relation is derived for a fully nonlinear case. The order tensor dynamics is also considered. A simple method of deriving the equation of the internal rotational motion is developed for the general macroscopic anisotropy. This paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece     

Characterization of short duration stress pulses generated by impacting laminated carbon-fiber/epoxy composites with magnetic flyer plates

Short duration stress pulses are of particular interest in determining the interfacial crack tip instability criteria for the dynamic fracture behavior of laminated carbon-fiber/epoxy composites. However, the heterogeneous architectures of laminated composites can alter the characteristics of a stress pulse as it propagates toward a crack tip. This makes it difficult to use standard dynamic testing techniques for characterizing these materials, since these techniques assume the characteristics of the stress pulse do not change as a result of propagation and can therefore be unambiguously determined from impact conditions. This paper presents a novel experimental technique that has been developed for characterizing short duration stress pulse propagation in laminated composite materials. In this technique, a dynamic moiré interferometer is used to capture fringe patterns corresponding to displacement fields associated with short duration stress pulses that were generated by impacting 0° and 90°/0°/90° carbon-fiber/epoxy composites with a magnetic flyer plate. Appropriate dynamic testing conditions for capturing high fidelity fringe patterns were determined using the recently developed dynamic moiré fringe contrast factor. The effects of the composite architecture on the propagation of short duration stress pulses observed with the dynamic moiré interferometer were confirmed by transient dynamic finite element analysis. From comparisons of experimental and numerical data, it was determined that the impact conditions for the magnetic flyer plate and laminated composite will not necessarily be planar, which has a significant effect on the intensity and duration of the propagating stress pulse.     

补偿效应研究的一个新视角

补偿效应与Arrhenius方程关系密切。本文为补偿效应研究提供了新视野。用几何图象分析了Arrhenius方程,指出过去认为此方程只表示速率与温度关系是不全面的,忽视了速率常数与活化能关系的研究。从图形看出,指前因子与活化能本身就具有互补关系,虽仅限于每两个不同活化能的情况。反应是一自组织过程。补偿效应的成立有必要条件和充分条件。欲实现补偿效应,从协同学角度考虑,E/T作为参变量必需小于一阈值,以使反应起活。并有一自变量做系列改变,以使A、E随其相似地连续变化,从而连通所有A、E的内在联系,1/T-lnk图中诸直线交于一点。指数分布是非均匀体系最具有普遍意义的分布函数。概率分析指出,补偿效应是A、E在固体表面和内部均呈相似指数分布的产物。对催化反应与非催化反应有普适性。在速率常数中体现为结构分布概率因子及能量分布概率因子。     

Growth of meromorphic solutions of linear difference equations

In this paper, the authors continue to study the growth of meromorphic solutions of homogeneous or non-homogeneous linear difference equations with entire coefficients, and obtain some results which are improvement and extension of previous results in Chiang and Feng (2008) [7] and Laine and Yang (2007) [19]. Examples are also given to illustrate the sharpness of our results.     

Numerical solution of multiple nonlinear Volterra integral equations

We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution.     

kth Order convergence for a semilinear elliptic boundary value problem in the divergence form

The convergence problem of approximate solutions for a semilinear elliptic boundary value problem in the divergence form is studied. By employing the method of quasilinearization, a sequence of approximate solutions converging with the kth (k ? 2) order convergence to a weak solution for a semilinear elliptic problem is obtained via the variational approach.     

New third and fourth order nonlinear solvers for computing multiple roots

We present a new third order method for finding multiple roots of nonlinear equations based on the scheme for simple roots developed by Kou et al. [J. Kou, Y. Li, X. Wang, A family of fourth-order methods for solving non-linear equations, Appl. Math. Comput. 188 (2007) 1031-1036]. Further investigation gives rise to new third and fourth order families of methods which do not require second derivative. The fourth order family has optimal order, since it requires three evaluations per step, namely one evaluation of function and two evaluations of first derivative. The efficacy is tested on a number of relevant numerical problems. Computational results ascertain that the present methods are competitive with other similar robust methods.