Contact between two plastically deformable crystals: a discrete dislocation dynamics study

It is customary to simplify the analysis of contact between two elastically deformable bodies by treating an equivalent problem where only one body is deformable and the other is rigid. This is possible provided that the gap geometry and the effective elastic modulus of the bodies in the simplified problem are the same as in the original problem. However, the question arises on whether – and to which extent – the simplification is still valid even when (size-dependent) plasticity occurs. Studies using discrete dislocation plasticity have also, so far, addressed simple contact problems where only one body can deform plastically. Here, we extend the analysis to two bodies in contact that can both deform by dislocation plasticity and investigate under which conditions the response agrees with that of an equivalent simplified problem. The bodies in contact are metal single crystals with sinusoidal and flat surface. It is found that the response of two plastically deformable bodies in contact can be simplified to an equivalent problem where one body is rigid and the other can deform plastically. Also, a plasticity size effect is observed, but the effect fades when the platen becomes more plastically deformable.     

0.6~T人体核磁共振成象及其图象的彩色化处理

在0.6~τ超导磁体人体核磁共振成象设备上获得了横断、矢状、冠状各种断层的成象。采用了直接两维傅里叶变换成象方法,应用了自旋回波脉冲序列。由于人体心脏跳动和呼吸运动会造成图象模糊而使用心电延迟触发及呼吸门控方法。作者用一种相位调制光密度分割的方法将原始黑白灰度表示的核磁共振成象进行彩色化处理。提高了原图象低密度梯度区的清晰度,为进行医学图象诊断及判读解译提供了方便度。山了光学系统图,解释了光学信息处理方法。由所处理的人体核磁共振成象图片可以看出,在低密度梯给区更易辨认。参考文献10种。     

Gas chromatographic study of the urinary codeine-to-morphine ratios in controlled codeine consumption and in mass screening for opiate drugs

The urinary codeine-to-morphine ratios in fifteen volunteers administered codeine tablets at intervals were studied by gas chromatography (GC) and compared with one month's GC results for enzyme multiplied immunoassay technique (EMIT)-screened urine specimens in a mass-screening programme for abuse of opiate drugs, particularly heroin. It appears that when M less than 2 and C/M greater than 0 or when M greater than 2 and C/M greater than 0.5, where C and M are codeine and morphine concentrations in micrograms per 10 ml of urine, codeine consumption has to be presumed.     

Spot focus size effect in spectroscopic ellipsometry of thin films

A focused as opposed to collimated light beam is typically used as probe in order to achieve a smaller as well as more intense light interrogation area in spectroscopic ellipsometry of thin films. In this work, we performed geometric ray analysis at the illumination and recording ends of such a system. The numerical results revealed substantial changes in (i) average optical path length and (ii) optical path length differences, which varied according to wavelength despite the film thickness remaining uniform. These results were able to consistently explain the anomalies found when different focus probe beam sizes were used in experimental spectroscopic ellipsometry measurements.     

Codiameters of 3-domination critical graphs with toughness more than one

A graph G is 3-domination-critical (3-critical, for short), if its domination number γ is 3 and the addition of any edge decreases γ by 1. In this paper, we show that every 3-critical graph with independence number 4 and minimum degree 3 is Hamilton-connected. Combining the result with those in [Y.J. Chen, F. Tian, B. Wei, Hamilton-connectivity of 3-domination critical graphs with α≤δ, Discrete Mathematics 271 (2003) 1-12; Y.J. Chen, F. Tian, Y.Q. Zhang, Hamilton-connectivity of 3-domination critical graphs with α=δ+2, European Journal of Combinatorics 23 (2002) 777-784; Y.J. Chen, T.C.E. Cheng, C.T. Ng, Hamilton-connectivity of 3-domination critical graphs with α=δ+1≥5, Discrete Mathematics 308 (2008) (in press)], we solve the following conjecture: a connected 3-critical graph G is Hamilton-connected if and only if τ(G)>1, where τ(G) is the toughness of G.     

Semitoric integrable systems on symplectic 4-manifolds

Let (M,ω) be a symplectic 4-manifold. A semitoric integrable system on (M,ω) is a pair of smooth functions J,H∈C ^∞(M,ℝ) for which J generates a Hamiltonian S ¹-action and the Poisson brackets {J,H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our goal is to prove that a semitoric system is completely determined by the invariants we introduce. A. Pelayo was partially supported by an NSF Postdoctoral Fellowship.     

Regional surveillance of disjoint rectangles: a travelling salesman formulation

Mission planning for surveillance coverage is of both practical and theoretical interest. In brief, regional surveillance involves planning the search of certain given regions in the minimum possible time. The surveillance problem can therefore be described as a variant of the classical travelling salesman problem. The uniqueness of the problem lies in the different allowed entry and exit points. Additionally, the mission schedule has to ensure the probability of target detection must not be compromised. From the practical perspective, any reduction in travelling time provides immediate cost savings to the defence department. A dynamic programming formulation is derived for the regional surveillance problem. An example is included to illustrate the methodology.     

The EOQ problem with decidable warehouse capacity: Analysis, solution approaches and applications

The Economic Order Quantity (EOQ) problem is a fundamental problem in supply and inventory management. In its classical setting, solutions are not affected by the warehouse capacity. We study a type of EOQ problem where the (maximum) warehouse capacity is a decision variable. Furthermore, we assume that the warehouse cost dominates all the other inventory holding costs. We call this the EOQ-Max problem and the D-EOQ-Max problem, if the product is continuously divisible and discrete, respectively. The EOQ-Max problem admits a closed form optimal solution, while the D-EOQ-Max problem does not because its objective function may have several local minima. We present an optimal polynomial time algorithm for the discrete problem. Construction of this algorithm is supported by the fact that continuous relaxation of the D-EOQ-Max problem provides a solution that can be up to 50% worse than the optimal solution, and this worst-case error bound is tight. Applications of the D-EOQ-Max problem include supply and inventory management, logistics and scheduling.     

Preemptive scheduling of jobs with agreeable due dates on a single machine to minimize total tardiness

We consider the problem of scheduling n preemptive jobs on a single machine to minimize total tardiness, subject to agreeable due dates, i.e., a later release date corresponds to a later due date. We prove that the problem is -hard in the ordinary sense by showing that it is -hard, and deriving a pseudo-polynomial algorithm for it.     

On a dual model with a dividend threshold

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual of the compound Poisson model under a threshold dividend strategy. We derive a set of two integro-differential equations satisfied by the expected total discounted dividends until ruin and show how the equations can be solved by using only one of the two integro-differential equations. The cases where profits follow an exponential or a mixture of exponential distributions are then solved and the discussion for the case of a general profit distribution follows by the use of Laplace transforms. We illustrate how the optimal threshold level that maximizes the expected total discounted dividends until ruin can be obtained, and finally we generalize the results to the case where the surplus process is a more general skip-free downwards Lévy process.