A note on the inventory models for deteriorating items with ramp type demand rate

In this research we study the inventory models for deteriorating items with ramp type demand rate. We first clearly point out some questionable results that appeared in (Mandal, B., Pal, A.K., 1998. Order level inventory system with ramp type demand rate for deteriorating items. Journal of Interdisciplinary Mathematics 1, 49–66 and Wu, K.S., Ouyang, L.Y., 2000. A replenishment policy for deteriorating items with ramp type demand rate (Short Communication). Proceedings of National Science Council ROC (A) 24, 279–286). And then resolve the similar problem by offering a rigorous and efficient method to derive the optimal solution. In addition, we also propose an extended inventory model with ramp type demand rate and its optimal feasible solution to amend the incompleteness in the previous work. Moreover, we also proposed a very good inventory replenishment policy for this kind of inventory model. We believe that our work will provide a solid foundation for the further study of this sort of important inventory models with ramp type demand rate.     

交比和Poincaré度量在平面拟共形映射下的偏差

研究了交比和Poincaré度量在平面拟共形映射下的偏差估计,得到了如下两个结果(1)若f是■~2到■~2上的k-拟共形映射,则对任意x_1,x_2,x_3,x_4∈■~2有16~((1/k)-1)(|(x_1,x_2,x_3,x_4)| 1)~(1/k)■|(f(x_1),f(x_2),f(x_3),f(x_4))| 1 ■16~(k-1)(|(x_1,x_2,x_3,x_4)| 1)~k;(2)若f是R~2到R~2上的k-拟共形映射,D是R~2中的任一真子域,则对任意x_1,x_2∈D有(1/k)λ_D(x_1,x_2) 4((1/k)-1)log 2■λ_(f(D))(f(x_1),f(x_2)) ■kλ_D(x_1,x_2) 4(k-1)log 2.     

限量分配问题的一个注记

§1 引言 限量分配问题是古典概率论,组合论的重要内容。本文将文献[1]、[2]中的一类广泛的限量分配问题给以统一的处理并加以推广,归结为如下问题: 问题Ⅰ 内无序分配问题。给定m类盒和n类球,假定第i类球和第j类盒的个数分别为r_i、s_j(1≤i≤n,1≤j≤m),即所谓球的规格为(?)=(r_1,r_2,…,r_n)和盒的规格为(?)=(s_1,s_2,…,s_m)。已知第i类盒对于球的限量集为A_i(这里A_i∈N_0~t,其中每个元素表示该类盒所能容纳之球的规格,1≤i≤m),记A=(A_1,A_2,…,A_m)。则分配规格为(?)的球至规     

Synthesis and electroluminescent properties of fluorene‐based copolymers containing electron‐withdrawing thiazole derivatives

We synthesized two fluorene‐based copolymers poly[(2,5‐bis(4‐hexylthiophen‐2‐yl)thiazolo[5,4‐day]thiazole‐5,5′‐diyl)‐alt‐(9,9′‐dioctylfluorene‐2,7‐diyl)] ( PF‐TTZT), and poly[(5,5′‐bis(4‐hexylthiophen‐2‐yl)‐2,2′‐bithiazole‐5,5′‐diyl)‐alt‐(9,9′‐dioctylfluorene‐2,7‐diyl)] (PF‐TBTT), which contain the electron‐withdrawing moieties, thiazolothiazole, and bithiazole, respectively. Through electrochemical studies, we found that these two polymers exhibit stable reversible oxidation and reduction behaviors. Moreover, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of PF‐TBTT are lower than those of PF‐TTZT, and the bandgap of PF‐TBTT is smaller than that of PF‐TTZT. Thus the bithiazole moiety in PF‐TBTT is more electron‐withdrawing than the thiazolothiazole moiety in PF‐TTZT. Light‐emitting devices with indium tin oxide (ITO)/poly(3,4‐ethylene dioxythiophene):poly(styrenesulfonate)(PEDOT)/polymer/bis(2‐methyl‐8‐quinolinato)‐4‐phenylphenolate aluminum (BAlq)/LiF/Al configurations were fabricated. The performance of the PF‐TBTT device was found to be almost three times better than that of the PF‐TTZT device, which is because electron injection from the cathode to PF‐TBTT is much easier than for PF‐TTZT. We also investigated the planarity and frontier orbitals of the electron donor‐acceptor (D‐A) moieties with computational calculations using ab initio Hartree–Fock with the split‐valence 6‐31G* basis set. These calculations show that TBTT has a more nonplanar structure than TTZT and that the bithiazole moiety is more electron‐withdrawing than thiazolothiazole. These calculations are in good agreement with the experimental results. © Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7148–7161, 2008     

Plasma assisted preparation of cobalt catalysts by sol–gel method for methane combustion

Novel cobalt catalysts were prepared by sol–gel method, and enhanced by plasma treatment, for methane catalytic combustion. These samples were characterized using X-ray diffraction, X-ray photoelactron spectroscopy, UV-vis spectroscopy, Fourier transform infrared spectroscopy, thermal gravimetrical analysis, N₂ Adsorption–desorption, temperature-programmed reduction and hydrogen–oxygen titration technologies. The XPS characterizations suggested that plasma treatment was favorable for the enrichment of surface cobalt, with a value of surface cobalt from 2.2% to 8.5% in mole. The specific surface area of the glow plasma assised sample (Co-Plas-Solgel-2) increased to 320 m²/g comparing with 305 m²/g of the conventional sample (Co-Solgel-1). The ignition temperature (T_10%) of Co-Plas-Solgel-2 catalyst was about 50 °C lower than that of Co-Solgel-1, and its CH₄ conversion was two times higher than that of Co-Solgel-1 during the whole range of catalytic combustion activity test (340–520 °C). With a better dispersion and more active sites, the plasma assisted sample exhibited significant enhancement in catalytic performances.