Analytical models for supplier selection and order quantity allocation

In the literature, decision models and techniques for supplier selection do not often consider inventory management of the items being purchased as part of the analysis. In this article, two mixed integer nonlinear programming models are proposed to select the best set of suppliers and determine the proper allocation of order quantities while minimizing the annual ordering, inventory holding, and purchasing costs under suppliers’ capacity and quality constraints. The first model allows independent order quantities for each supplier while the second model restricts all order quantities to be of equal size, as it would be required in a multi-stage (supply chain) inventory model. Illustrative examples are used to highlight the advantages of the proposed models over a previous model introduced in the literature.     

Biaxial nematic phase of crank-like bis(β-diketonato)copper(II) complexes established by X-ray diffraction and Z-value calculations

We have synthesized a series of six novel bis(β-diketonate)copper (II) complexes, 1a, 1b, 2a, 2b, 3a, and 3b, substituted by two bulky substituents in the short molecular axis direction to investigate their mesomorphism. The m,p,m'-trimethoxylphenyl-substituted derivatives, 2a and 2b, and the m,p-dimethoxylphenyl-substituted derivatives, 3a and 3b, did not show mesomorphism, whereas each of the p-methoxyphenyl-substituted derivatives 1a and 1b only showed a nematic phase, which was revealed from polarizing microscopic observations. We established from X-ray diffraction and Z-value calculations that each of the crank-like derivatives 1a and 1b forms a rectangular parallelepiped dimer and shows a biaxial nematic phase.     

Order of Reactivity of OH/NH Groups of Glucosamine Hydrochloride and N-Acetyl Glucosamine Toward Benzylation Using NaH/BnBr in DMF

The order of reactivity of OH and NH groups of glucosamine hydrochloride (GlcNH₂^.HCl) and N-acetyl glucosamine (GlcNAc) toward benzylation with NaH/BnBr in DMF was investigated. For GlcNH₂^.HCl, benzyl groups were introduced in the order of N-Bn > N-Bn₂ > 1-O-Bn > 6-O-Bn > 4-O-Bn > 3-O-Bn; for GlcNAc, benzyl groups were introduced in the order of 1-O-Bn > 6-O-Bn > 4-O-Bn > 3-O-Bn > N-Bn. A range of partially benzylated 2-N,N′-dibenzyl glucopyranosides and GlcNAc derivatives were obtained in a single step.     

On the growth of meromorphic solutions of the Schwarzian differential equations

We study the properties of meromorphic solutions of the Schwarzian differential equations in the complex plane by using some techniques from the study of the class Wp. We find some upper bounds of the order of meromorphic solutions for some types of the Schwarzian differential equations. We also show that there are no wandering domains nor Baker domains for meromorphic solutions of certain Schwarzian differential equations.     

次序统计量线性函数的随机加权逼近速度

设ｘ１，ｘ２，…ｘｎ（连续未知），Ｆｎ为经验分布函数，Ｈｎ（ｘ）为随机加权经验分布函数，。ｘｎ１≤ｘｎ２≤…≤ｘｎｎ为次序统计量．记以Ｆｎ取代σ２（Ｊ，Ｆ）中的Ｆ即得σ２（Ｊ，Ｆｎ）．     

Regularized collocation method for Fredholm integral equations of the first kind

In this paper we consider a collocation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. An “unregularized” use of this method can give reliable results in the case when the rate at which smallest singular values of the collocation matrices decrease is known a priori. In this case the number of collocation points plays the role of a regularization parameter. If the a priori information mentioned above is not available, then a combination of collocation with Tikhonov regularization can be the method of choice. We analyze such regularized collocation in a rather general setting, when a solution smoothness is given as a source condition with an operator monotone index function. This setting covers all types of smoothness studied so far in the theory of Tikhonov regularization. One more issue discussed in this paper is an a posteriori choice of the regularization parameter, which allows us to reach an optimal order of accuracy for deterministic noise model without any knowledge of solution smoothness.     

关于弱Hilbert性质的一个问题

本文证明了这样一个主要结果：设（Ｋ，Ｓ）和（Ｋ，Ｓ）都是亚序域，且（Ｋ，Ｓ）是（Ｋ，Ｓ）的有限生成扩张，则当Ｋ在Ｋ上是超越时，（Ｋ，Ｓ）具有弱Ｈｉｌｂｅｒｔ性质．这一结果否定地回答了作者在文献［１］中所提的一个公开问题．此外，一些关于弱Ｈｉｌｂｅｒｔ性质的结果被建立．     

ON THE HYPER-ORDER OF MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS

In this paper the order and the hyper-order of the solutions of higher-order homoge-neous linear differential equations is investigated.