与时俱进，不断开创物理化学课程建设新局面

As a necessary basic theory course for undergraduates majoring in chemistry, materials, pharmacy, chemical engineering, and biology, physical chemistry plays an important role in cultivating talents to meet the needs of social and economic development. Over the years, the teaching team of physical chemistry of East China University of Science and Technology has carried out the curriculum reform and innovation persistently based on "Team building as the foundation, resource building as the root, mode innovation as the soul, ability training as the origin". This paper will summarize our thinking and experience in striving for the first-class course from the aspects of first-class team construction, first-class resource construction, teaching connotation innovation, teaching mode exploration, and extract the experience that can be used as reference by teaching peers.     

Multiplicity of Solutions of the Weighted p-Laplacian with Isolated Singularity and Diffusion Suppressed by Convection

In this paper, the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and di?usion suppressed by convection ?div(|x|^α|?u|^p?2?u) + λ 1/|x|^β |?u|^p?2?u · x = |x|^γg(|x|) in B \ {0} subject to nonlinear Robin boundary value condition |x|^α|?u|^p?2?u · ?n = A ? ρu on ?B,where λ > 0, B ? R^N(N ≥ 2) is the unit ball centered at the origin, α > 0, p > 1, β ∈ R, γ > ?N, g ∈ C([0,1]) with g(0) > 0, A ∈ R, ρ > 0 and ?n is the unit outward normal. The same problem with di?usion promoted by convection, namely λ ≤ 0, has already been discussed by the last two authors (Song-Yin (2012)), where the existence, nonexistence and classi?cation of singularities for solutions are presented. Completely di?erent from [Song, H. J. and Yin, J. X., Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection, Math. Meth. Appl. Sci., 35, 2012, 1089–1100], in the present case λ > 0, namely the di?usion is suppressed by the convection, non-singular solutions are not only existent but also may be in?nite which vary according only to the values of solutions at the isolated singular point. At the same time, the singular solutions may exist only if the di?usion dominates the convection.     

The potential-Ramsey number of Kn and K t −k

Czechoslovak Mathematical Journal - A nonincreasing sequence π = (d1,…, dn) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices. In this...     

Orientation control of perovskite thin films on glass substrates by the application of a seed layer prepared from oxide nanosheets

Orientation control of perovskite compounds was investigated by the application of a seed layer prepared from oxide nanosheets. An aqueous suspension of oxide nanosheets was prepared by the exfoliation of a layered compound of KCa₂Nb₃O₁₀ oxide grains. A seed layer composed of (TBA)Ca₂Nb₃O₁₀ nanosheets (TBA = tetrabutylammonium) was formed on a glass substrate by simply dip coating it in the suspension. Two kinds of perovskite compounds, LaNiO₃ (LNO) and Pb(Zr,Ti)O₃ (PZT) with a preferred orientation of (00l) were successfully grown on this seeded glass substrate. In this study, the relation between lattice mismatch and electrical properties is investigated. A large, oriented PZT film with a size of 5 ×4 cm shows an improved P-E hysteresis behavior by use of this orientation control.     

Safety Stock Determination with Serially Correlated Demand in a Periodic-Review Inventory System

We consider a periodic-review inventory replenishment model with an order-up-to-R operating doctrine for the case of deterministic lead times and a covariance-stationary stochastic demand process. A method is derived for setting the inventory safety stock to achieve an exact desired stockout probability when the autocovariance function for Gaussian demand is known. Because the method does not require that parametric time-series models be fit to the data, it is easily implemented in practice. Moreover, the method is shown to be asymptotically valid when the autocovariance function of demand is estimated from historical data. The effects on the stockout rate of various levels of autocorrelated demand are demonstrated for situations in which autocorrelation in demand goes undetected or is ignored by the inventory manager. Similarly, the changes to the required level of safety stock are demonstrated for varying levels of autocorrelation.     

Optimal Control of an <Emphasis Type="Italic">M/E</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript>/1 Queueing System with a Removable Service Station

This paper studies the optimal operation of an M/E _k /1 queueing system with a removable service station under steady-state conditions. Analytic closed-form solutions of the controllable M/E _k /1 queueing system are derived. This is a generalization of the controllable M/M/1, the ordinary M/E _k /1, and the ordinary M/M/1 queueing systems in the literature. We prove that the probability that the service station is busy in the steady-state is equal to the traffic intensity. Following the construction of the expected cost function per unit time, we determine the optimal operating policy at minimum cost.     

An Algorithm for the Economic Design of <Emphasis Type="Italic">np</Emphasis> Charts for a Multiplicity of Assignable Causes

Chiu, in 1976, studied the economic design of np charts for processes subject to a multiplicity of assignable causes. Chiu developed a two-step minimization procedure to obtain the three control variables, namely, the sampling interval, the sample size and the acceptance number. Although Chiu's two-step minimization procedure is simple, applicable and down to earth, it is rather inefficient and has some drawbacks. This paper presents an algorithm to overcome these drawbacks. The results and the execution times of all numerical examples show that the accuracy and the efficiency of the algorithm is reasonably good.     

A Heuristic Decomposition Algorithm for Scheduling Problems on Mixed Graphs

We consider a scheduling problem where a set of n jobs has to be processed on a set of m machines and arbitrary precedence constraints between operations are given. Moreover, for any two operations i and j values a _ij >0 and a _ji >0 may be given where a _ij is the minimal difference between the starting times of operations i and j when operation i is processed first. Often, the objective is to minimize the makespan but we consider also arbitrary regular criteria. Even the special cases of the classical job shop problem J//C_max belong to the set of NP-hard problems. Therefore, approximation or heuristic algorithms are necessary to handle large-dimension problems. Based on the mixed graph model we give a heuristic decomposition algorithm for such a problem, i.e. the initial problem is partitioned into subproblems that can be solved exactly or approximately with a small error bound. These subproblems are obtained by a relaxation of a subset of the set of undirected edges of the mixed graph. The subproblems are successively solved and a proportion of the results obtained for one subproblem is kept for further subproblem definitions. Numerical results of the algorithm presented here are given.     

Availability Analysis of Repairable <Emphasis Type="Italic">N</Emphasis>-Server <Emphasis Type="Italic">n</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>-Replicated Systems

We develop an exact closed-form expression for the steady-state availability of a repairable, N-server system in which the ith server contains n _i identical, reconfigurable, breakdown-prone units. Our approach, which follows from the Markov chain balance equations and the recursive properties of Hessenberg matrix determinants, is simpler than previously proposed matrix geometric approaches, and can readily be adapted to the availability analysis of more complicated structures. We illustrate this by computing the steady-state availability of a mixed parallel-serial gracefully degrading replicated system.