Single machine group scheduling with ordered criteria

The single machine group scheduling problem is considered. Jobs are classified into several groups on the basis of group technology, i.e. jobs of the same group have to be processed jointly. A machine set-up time independent of the group sequence is needed between each two consecutive groups. A schedule specifies the sequence of groups and the sequence of jobs in each group. The quality of a schedule is measured by the criteriaF ₁, ...,F _m ordered by their relative importance. The objective is to minimize the least important criterionF _m subject to the schedule being optimal with respect to the more important criterionF _m–1 which is minimized on the set of schedules minimizing criterionF _m–2 and so on. The most important criterion isF ₁, which is minimized on the set of all feasible schedules. An approach to solve this multicriterion problem in polynomial time is presented if functionsF ₁, ...,F _m have special properties. The total weighted completion time and the total weighted exponential time are the examples of functionsF ₁, ...,F _m–1 and the maximum cost is an example of functionF _m for which our approach can be applied.The research of the authors was partially supported by a KBN Grant No. 3 P 406 003 05, the Fundamental Research Fund of Belarus, Project N 60-242, and the Deutsche Forschungsgemeinschaft, Project Schema, respectively. The paper was completed while the first author was visiting the University of Melbourne.     

Estimation of a quantile in some nonstandard cases

A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon.     

Sequential estimation of a parameter of an exponential distribution

We consider the problem of minimum risk point estimation for the parameter =a+b of the exponential distribution with unknown location parameter and scale parameter when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268).     

The BKK root count in

The root count developed by Bernshtein, Kushnirenko and Khovanskii only counts the number of isolated zeros of a polynomial system in the algebraic torus . In this paper, we modify this bound slightly so that it counts the number of isolated zeros in . Our bound is, apparently, significantly sharper than the recent root counts found by Rojas and in many cases easier to compute. As a consequence of our result, the Huber-Sturmfels homotopy for finding all the isolated zeros of a polynomial system in can be slightly modified to obtain all the isolated zeros in .

     

A note on the weighted norm inequality for the one-sided maximal operator

Let be the one-sided maximal function. In this note we obtain some necessary and sufficient conditions in order that the weighted weak type inequality holds for . Meanwhile, some necessary or sufficient conditions for the weighted inequality for are given.

     

Synthesis and performance of HPTLC plates modified with cyanopropyl- and octadecyl-trichlorosilane

Chemical modification of commercial high performance thin-layer chromatography plates with various mixtures of cyano-propyltrichlorosilane and octadecyltrichlorosilane is described. Surface coverage by different treatments is demonstrated as well as the variations in chromatographic performance. With regard to the development in aqueous media the utility of CN/ ODS plates compared to ODS plates is also shown.     

Characterization of OV-1/FFAP-mixture coated glass capillary columns used for the separation of free fatty acids

As an alternative to acid pretreated UCON and FFAP capillaries for the analysis of wide-boiling free fatty acid mixtures, OV-1 : FFAP phase mixtures were used on high-temperature silylated inert glass capillary columns. The HETP-carrier gas velocity curves, peak asymmetry factors, coating efficiency, gas phase and stationary phase contributions to the mass transfer resistance were determined for various OV-1 : FFAP ratios. Mixed-phase capillaries showed optimum performance at a 2 : 1 OV-1 : FFAP ratio. The thermal and long-term stability of OV-1-stabilized FFAP columns surpassed those of the UCON and pure FFAP reference column used.     

Ionization constants for deuterium oxide in deuterium oxide-organic mixtures

A potentiometric method using a glass electrode has been applied to determination of ionization constants for deuterium oxide (D₂O) in binary mixtures of D₂O with dioxane, tetrahydrofuran, acetone, dimethylsulfoxide, CH₃CH₂OD, and CH₃OD at 25°C. The results are compared with values of ionization constants for H₂O obtained previously in the corresponding H₂O-organic mixtures, and the isotope effect is shown to be small. Further calculations with the D₂O results show that the first five solvents mentioned above are neither appreciably acidic nor basic in D₂O solution, but that CH₃OD shows slightly acidic behavior (pK_a=16.0±0.3).     

Calcined Ni—Al layered double hydroxide as a catalyst for total oxidation of volatile organic compounds: Effect of precursor crystallinity

The effect of hydrothermal treatment on properties (crystallinity, porous structure, reducibility, acidity, basicity, and catalytic activity and selectivity in toluene and ethanol total oxidation) of Ni—Al layered double hydroxide precursors and related mixed oxides was examined. The hydrothermal treatment increased considerably both the content of crystalline phase and LDH crystallite size. On the other hand, only a slight effect of the precursor hydrothermal treatment on crystallinity of the related Ni—Al mixed oxides obtained by calcination at 450°C was observed. The reducibility of NiO particles appeared to be hindered considerably compared to the reducibility of pure NiO. Catalytic activity of the Ni—Al mixed oxides prepared from the precursors hydrothermally treated for a short time (4 h) was the highest. The highest amount of acetaldehyde formed during the total oxidation of ethanol, i.e. the worst selectivity was found for the calcined Ni—Al LDH without hydrothermal treatment. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

药用缓释辅料——羟丙基甲基纤维素的合成及其缓释性能的研究

本文研究了药物缓释材料HPMC的合成方法,探讨了碱纤维素制备,醚化剂浓度,混合醚化剂配经以及产品后处理对高粘度HPMC的影响。本文还初步对KCl,氨茶碱,硝酸异山梨醇酯等药物采用合成的HPMC作辅料,进行了缓释制剂的研究,结果表明合成的HPMC具有满意的缓释性能。