A unified analysis for the single-machine scheduling problem with controllable and non-controllable variable job processing times

We present a unified analysis for single-machine scheduling problems in which the actual job processing times are controlled by either a linear or a convex resource allocation function and also vary concurrently depending on either the job’s position in the sequence and/or on the total processing time of the already processed jobs. We show that the problem is solvable in O(nlogn)$O(n\log n)$ time by using a weight-matching approach when a convex resource allocation function is in effect. In the case of a linear resource allocation function, we show that the problem can be solved in O(n³)$O(n^3)$ time by using an assignment formulation. Our approach generalizes the solution approach for the corresponding problems with controllable job processing times to incorporate the variability of the job processing times stemming from either the job’s position in the sequence and/or the total processing time of the already processed jobs.     

Hybrid variable neighbourhood approaches to university exam timetabling

In this paper, we investigate variable neighbourhood search (VNS) approaches for the university examination timetabling problem. In addition to a basic VNS method, we introduce variants of the technique with different initialisation methods including a biased VNS and its hybridisation with a Genetic Algorithm. A number of different neighbourhood structures are analysed. It is demonstrated that the proposed technique is able to produce high quality solutions across a wide range of benchmark problem instances. In particular, we demonstrate that the Genetic Algorithm, which intelligently selects appropriate neighbourhoods to use within the biased VNS, produces the best known results in the literature, in terms of solution quality, on some of the benchmark instances. However, it requires relatively large amount of computational time. Possible extensions to this overall approach are also discussed.     

Hilbert空间中广义平衡问题和不动点问题的粘滞逼近法

在Hilbert空间,我们用粘滞逼近法建立了一迭代序列来逼近两个集合的公共点,这两个集合分别是广义平衡问题的解集和渐进非扩张映射的不动点集.我们表明这一迭代序列强收敛到这两个集合的公共点,而且这一公共点还是一变分不等式的解.用这一结果,还研究了三个强收敛问题和优化问题.     

偶数维空间耗散波动方程解的衰减估计

研究偶数维空间带粘性的波动方程柯西问题解的逐点估计.通过对格林函数的精细分析,得到解的大时间状态.解呈现出惠更斯现象.     

Marcinkiewicz 空间中带可变指数的熵解的先验估计

本文研究p(x)-Laplace方程的退化形式的带可变指数的Dirichlet问题,得到了Marcinkiewicz空间中带可变指数的熵解的先验估计.     

R~N上一类p(x)-Laplacian方程的无穷多解问题

该文主要讨论了如下p(x)-Laplacian算子方程的解.其中1P-≤p(x)≤P+N.得到了上述方程在变指数Sobolev空间W~(1,p(x))(R~N)中的一列能量值趋向正无穷的解.     

双亲催化剂作用超稠油水热裂解降黏机理研究

合成双亲催化剂,200℃与超稠油反应后,降黏率达96.26%。通过气相色谱仪、元素分析仪、分子量测定仪、红外光谱仪及核磁共振波谱仪对反应前后稠油的物化性质进行分析。结果表明,反应后稠油胶质与沥青质含量减小,稠油分子量下降,沥青质分子量降低幅度最大;稠油及其重质组分的氢碳原子比增加,硫的含量减小。稠油发生水热裂解反应的同时,存在沥青质的聚合反应,沥青质的裂解在降黏反应中起到了关键的作用;双亲催化剂促进了水热裂解反应,同时抑制了聚合反应;双亲型催化降黏剂携带的具有活性催化功能的离子协同高温水作用于分子中的C-S、C-N、C-O、C-C及C=S、C=O、C=N、C=S等键,使其发生系列链的断裂、加氢、开环、成环、脱硫等反应,促进了稠油黏度的降低,稠油及其重质组分的氢碳原子比增加,稠油的品质得到一定程度的改善。     

Improving the pressure accuracy in a projection scheme for incompressible fluids with variable viscosity

The incremental projection scheme and its enhanced version, the rotational projection scheme are powerful and commonly used approaches producing efficient numerical algorithms for solving the Navier–Stokes equations. However, the much improved rotational projection scheme cannot be used on models with non-homogeneous viscosity, imposing the use of the less accurate incremental projection. This paper presents a projection method for the Navier–Stokes equations for fluids having variable viscosity, giving a consistent pressure and increased accuracy in pressure when compared to the incremental projection. The accuracy of the method will be illustrated using a manufactured solution.     

Viscosity Results for a Class of Evolution Inclusions with Maximal Monotone Operators

In the finite dimensional setting, we investigate the existence of viscosity subsolutions of Hamilton–Jacobi–Bellman equations related to control problems subject to evolution inclusions governed by time-dependent maximal monotone operators with Young measures.