Odd-even staggering for production cross sections ofnuclei near the neutron drip-line

In our previous studies [Phys. Rev. C 97, 044619 (2018); Phys. Rev. C 103, 044610 (2021)], a universal odd-even staggering (OES) has been observed in extensive cross sections of isotopes not far from stability, measured for different fragmentation and spallation reactions. Four OES relations have been proposed on the basis of this OES universality. However, it is still unclear whether this OES universality and OES relations are applicable to many isotopes near the drip-lines. Here, the OES in recent experimental cross sections of very neutron-rich nuclei approaching the drip-line (from \begin{document}$^{76}$\end{document}Ge,\begin{document}$^{82}$\end{document}Se+\begin{document}$^{9}$\end{document}Be) is quantitatively investigated, to further validate the OES universality and OES relations. The OES magnitudes in these experimental data approaching the neutron drip-line generally agree with those evaluated previously, mainly from experimental data near stability. New OES evaluations derived from these experimental data are also recommended for more exotic nuclei near the neutron drip-line, which extends the conclusions of our previous OES studies. In addition, the OES relation calculations are consistent with these experimental data of very neutron-rich nuclides according to their comparisons in this work. Finally, comparisons with additional experimental data (from \begin{document}$^{238}$\end{document}U+\begin{document}$^{9}$\end{document}Be) also support that new OES evaluations and OES relation calculations can be applied for exotic nuclei near the neutron drip-line.     

Prioritizing replenishments of the piece picking area

Having sufficient inventories in the forward or piece picking area of a warehouse is an essential condition for warehouse operations. As pickers consume the inventory in the piece racks, there is a risk of stockout. This can be reduced by the timely replenishment of products from the bulk reserve area to the forward area. We develop and compare three policies for prioritizing replenishments for the case where order picking and replenishments occur concurrently because of time restrictions. The first policy, based on the ratio of available inventory to wave demand, reduces the number of stockouts considerably. The other two more sophisticated policies reduce the number of stockouts even more but require much more computation time, and are more costly in terms of implementation, maintenance and software updates. We present the results of implementing one of these policies in the warehouse of a large cosmetics firm.     

An inventory system with two suppliers and default risk

This paper considers the problem of joint replenishment and pricing for a single product with two suppliers and supply disruption. Our objective is to maximize the total profit by choosing an appropriate replenishment and pricing policy. We not only obtain that the form of the optimal policy has a (s,S,p,σ,Σ)-type, but also analyze how supply disruption affects the profit function and the optimal policy.     

Thermal–Statistical Odd–Even Fermions’ Staggering Effect and the Order–Disorder Disjunction

We review thermal–statistical considerations on the odd–even staggering effect (OES) in fermions. There is a well known OES in nuclear binding energies at zero temperature. We discuss here a thermal OES (finite temperatures) that establishes links with the order–disorder disjunction. The present thermal considerations cannot be found in the nuclear literature.     

三体势对含f玻色子的IBM1的O(6)极限能谱修正

在s–dIBM1的O(6)极限下,引入d玻色子之间相互作用的等效三体势,考虑f玻色子产生的八极态,导出了正负宇称态能谱解析表达式,并对过渡区偶偶核¹¹⁸Xe、¹²⁰Xe进行了能谱计算,得到了与实验能谱符合更好的结果,然后用Staggering指数定量分析了正负宇称态能谱中的Staggering现象.     

Evolution of nuclear charge radii in copper and indium isotopes

Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton (np) correlations, is here applied for the first time to the study of odd-Z copper and indium isotopes. Theoretical results obtained by the relativistic mean field (RMF) model with NL3, PK1 and NL3^* parameter sets are compared with experimental data. Our results show that both OES and the abrupt changes across \begin{document}$ N = 50 $\end{document} and 82 shell closures are clearly reproduced in nuclear charge radii. The inverted parabolic-like behaviors of rms charge radii can also be described remarkably well between two neutron magic numbers, namely \begin{document}$ N = 28 $\end{document} to 50 for copper isotopes and \begin{document}$ N = 50 $\end{document} to 82 for indium isotopes. This implies that the np-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-Z isotopic chains. Also, our conclusions have almost no dependence on the effective forces.     

The capacitated arc routing problem with refill points

This article introduces the capacitated arc routing problem with refill points (CARP-RP). The vehicle servicing arcs must be refilled on the spot by using a second vehicle. The problem consists on simultaneously determining the vehicles routes that minimize the total cost. An integer linear programming model is proposed and tested.     

Offsetting inventory replenishment cycles to minimize storage space

In a recent paper, [Murthy, N.N., Benton, W.C., Rubin, P.A., 2003. Offsetting inventory cycles of items sharing storage. European Journal of Operational Research 150, 304–319] discussed the problem of offsetting inventory replenishment cycles of several items in order to minimize the maximum required storage space. They analyzed the case where replenishment cycles are given integer multiples of a basic period and proposed a heuristic to solve the problem. While they provided a good analysis of the considered problem, the proposed heuristic produces less interesting results. In the following, a simpler, more efficient and easier to implement heuristic is proposed. Numerical results are provided to prove its superiority.     

Replenishment routing problems between a single supplier and multiple retailers with direct delivery

We consider the replenishment routing problems of one supplier who can replenish only one of multiple retailers per period, while different retailers need different periodical replenishment. For simple cases satisfying certain conditions, we obtain the simple routing by which the supplier can replenish each retailer periodically so that shortage will not occur. For complicated cases, using number theory, especially the Chinese remainder theorem, we present an algorithm to calculate a feasible routing so that the supplier can replenish the selected retailers on the selected periods without shortages.     

The multi-depot vehicle routing problem with inter-depot routes

This article addresses an extension of the multi-depot vehicle routing problem in which vehicles may be replenished at intermediate depots along their route. It proposes a heuristic combining the adaptative memory principle, a tabu search method for the solution of subproblems, and integer programming. Tests are conducted on randomly generated instances.