Production and shipment lot sizing in a vendor–buyer supply chain with transportation cost

Previous research on the joint vendor–buyer problem focused on the production shipment schedule in terms of the number and size of batches transferred between the two parties. It is a fact that transportation cost is a major part of the total operational cost. However, in most joint vendor–buyer models, the transportation cost is only considered implicitly as a part of fixed setup or ordering cost and thus is assumed to be independent of the size of the shipment. As such, the effect of the transportation cost is not adequately reflected in final planning decisions. There is a need for models involving transportation cost explicitly for better decision-making. In this study we analyze the vendor–buyer lot-sizing problem under equal-size shipment policy. We introduce the complete solution of the problem in an explicit and extended manner that has not existed in the literature. We incorporate transportation cost explicitly into the model and develop optimal solution procedures for solving the integrated models. All-unit-discount transportation cost structures with and without over declaration have been considered. Numerical examples are presented for illustrative purpose.     

Crystallization of mechanically alloyed amorphous W-Mg alloy under high pressure

Pure metal powder mixtures of W and Mg at the desired composition were milled in conventional high-energy ball mill, and amorphous alloy W₅₀Mg₅₀ was obtained after milling for 20 h. The structure evolution of elemental powder mixtures was studied following milling and subsequent high pressure and high temperature treatment. The amorphous alloy transform into a nanocrystalline material below 1050 °C at 4.0 GPa. On increasing the temperature, it transforms into a mixture of several new crystal phases under high-pressure condition. It also found that both mechanical alloying and high pressure treatment are the two necessary processes to form the nanocrystalline and the new phases.     

Subdivisions of large complete bipartite graphs and long induced paths in k‐connected graphs

It is proved that for every positive integers k, r and s there exists an integer n = n(k,r,s) such that every k‐connected graph of order at least n contains either an induced path of length s or a subdivision of the complete bipartite graph K_k,r. © 2004 Wiley Periodicals, Inc. J Graph Theory 45: 270–274, 2004     

Increase in Tc and spin glass transition in La0.9Ca0.1Mn1−yCryO3 (y=0, 0.1 and 0.2)

We report on the structural, frequency dependent ac susceptibility, dc magnetization and magnetoresistance (MR) measurements on polycrystalline samples of La_0.9Ca_0.1Mn_1−yCr_yO₃ (y=0, 0.1 and 0.2) prepared by sol-gel technique. For y=0, a paramagnetic to ferromagnetic transition is observed at T_c=136 K. Both for y=0.1 and 0.2, T_c increases from 136 to 180 K. For y=0, the imaginary part of the ac susceptibility shows a broad transition at T_f<T_c which does not depend very much on the frequency. However, for y=0.1 and 0.2, the frequency dependence resembles that of a spin glass. Though all the three samples show a semi-conducting behavior between 300 and 5 K, a negative MR is observed corresponding to T_c and T_f. The value of MR decreases for the Cr substituted samples.     

Growth mechanism and characterization of zinc oxide microcages

We report the growth mechanism and structural properties of micrometer sized ZnO cages which were synthesized directly from Zn vapor deposition and oxidation. The ZnO microcages exhibit a hexagonal or spherical shape with partly or completely open surfaces and hollow interiors. The growth process of the microcages includes the deposition of Zn polyhedral particles, top face breaking of the Zn particles and Zn sublimation, and subsequent reaction to ZnO. By controlling the various growth stages, we obtained information on the growth mechanism of the ZnO cages, which appears to be different from a mechanism reported previously. The chemical composition and crystalline structure were studied using energy dispersive X-ray spectroscopy and transmission electron microscopy, respectively. The room-temperature photoluminescence spectrum indicates a large quantity of oxygen-vacancy related defects within the wall of the ZnO cages.     

Evidence for a gravitational Myers effect

An indication for the existence of a collective Myers solution in the non-abelian D0-brane Born-Infeld action is the presence of a tachyonic mode in fluctuations around the standard diagonal background. We show that this computation for non-abelian D0-branes in curved space has the geometric interpretation of computing the eigenvalues of the geodesic deviation operator for U(N)-valued coordinates. On general grounds one therefore expects a geometric Myers effect in regions of sufficiently negative curvature. We confirm this by explicit computations for non-abelian D0-branes on a sphere and a hyperboloid. For the former the diagonal solution is stable, but not so for the latter. We conclude by showing that near a Schwarzschild black hole one also finds a tachyonic mode in the fluctuation spectrum, signaling the possibility of a near-black-hole gravitationally induced Myers effect.     

由轮图导出的某些平面图类的星色数

图的星色数是通常色数概念的推广.本文求出了几类由轮图导出的平面图的星色数.前两类是由3-或5-轮图经细分等构造出的,其星色数分别为2+2/(2n+1),2+3/(3n+1)和2+3/(3n-1).第三类平面图是由n-轮图经过Hajos构造得到的,其星色数为3+1/n.本类图的星色数结果推广了已有结论.     

Computational modelling of nonlinear calcium waves

The calcium transport in biological systems is modelled as a reaction–diffusion process. Nonlinear calcium waves are then simulated using a stochastic cellular automaton whose rules are derived from the corresponding coupled partial differential equations. Numerical simulations show self-organized criticality in the complex calcium waves and patterns. Both the stochastic cellular automaton approach and the equation-based simulations can predict the characteristics of calcium waves and complex pattern formation. The implication of locality of calcium distribution with positional information in biological systems is also discussed.