Interval estimation of the critical value in a general linear model

Summary This paper concerns interval estimation of the critical value θ which satisfies under the general linear model,Y _i =μ(x _i )+ε _i (i=1,2,···), where for and the functional forms off _j ^′ s are known. From an asymptotic expansion it is shown that, under reasonable conditions, the limiting distribution of is normal. Thus in the large-sample case a confidence interval for θ can be obtained. Such a result is useful when one is interested in carrying out a retrospective analysis rather than designing the experiment (as in the Kiefer-Wolfowitz procedure). In Section 3 a sequential procedure is considered for confidence intervals with fixed width 2d. It is shown that, for a given stopping variableN, is also asymptotically normal asd→0. Thus the coverage probability converges to 1−α (preassigned) asd→0. An example of application in estimating the phase parameter in circadian rhythms is given for the purpose of illustration. Research partially supported by the NSF Grant DMS-8502346.     

Existence and uniqueness for nonlinear boundary value problems in kinetic theory

A boundary value problem for the stationary nonlinear Boltzmann equation in a slab has been examined in a weightedL space. It has been proved that the problem possesses a unique solution for boundary data small enough. The proof is based on the implicit function theorem. It has also been shown that for the linearized problem the Fredholm alternative applies.     

Nitrite formation in aerated aqueous azide solutions: A radiation chemical study

Gamma radiolysis of oxygenated 1–10 mM azide solutions was carried out at various pH values. In oxygenated 10 mM azide solutions, H₂O₂ and NO ₂ ⁻ were observed as radiolytic products while NH3 was not. The concentration of H₂O₂ reached its maximum level at a dose of 1 kGy, whereas NO ₂ ⁻ yield increased non-linearly beyond 2 kGy in this system. Both in aerated and oxygenated systems, G(NO ₂ ⁻ ) and G(H₂O₂) were found to vary with N ₃ ⁻ concentration. The yield of NO ₂ ⁻ was found to be dependent on both dose rate and pH. On pulse radiolysis, NO ₂ ⁻ was found as a radiolytic product in aerated 1 mM azide solution at pH 6.8. In this system the intermediate generated exhibits absorbance around 250 nm. The overall results obtained during the present study reveal that in presence of both reducing radical (mainly e _aq ⁻ ) and oxygen, N ₃ ⁻ produced an intermediate possibly NH₂O ₂ ^• radical, which is the prime source for NO ₂ ⁻ generation.     

Retention modeling and simultaneous optimization of pH value and gradient steepness in RP‐HPLC using feed‐forward neural networks

A novel approach is proposed for the simultaneous optimization of mobile phase pH and gradient steepness in RP‐HPLC using artificial neural networks. By presetting the initial and final concentration of the organic solvent, a limited number of experiments with different gradient time and pH value of mobile phase are arranged in the two‐dimensional space of mobile phase parameters. The retention behavior of each solute is modeled using an individual artificial neural network. An “early stopping” strategy is adopted to ensure the predicting capability of neural networks. The trained neural networks can be used to predict the retention time of solutes under arbitrary mobile phase conditions in the optimization region. Finally, the optimal separation conditions can be found according to a global resolution function. The effectiveness of this method is validated by optimization of separation conditions for amino acids derivatised by a new fluorescent reagent.     

Molecular conformation search by distance matrix perturbations

Three-dimensional molecular structure is fundamental in chemical function identification and computer-aided drug design. The enumeration of a small number of feasible conformations provides a rigorous way to determine the optimal or a few acceptable conformations. Our contribution concerns a heuristic enhancement of a method based on distance geometry, typically in relation with experiments of the NMR type. Distance geometry has been approached by different viewpoints; ours is expected to help in several subtasks arising in the process that determines 3D structure from distance information. More precisely, the input to our algorithm consists of a set of approximate distances of varying precision; some are specified by the covalent structure and others by Nuclear Magnetic Resonance (NMR) experiments (or X-ray crystallography which, however, requires crystallization). The output is a valid tertiary structure in a specified neighborhood of the input. Our approach should help in detecting outliers of the NMR experiments, and handles inputs with partial information. Moreover, our technique is able to bound the number of degrees of freedom of the conformation manifold. We have used numerical linear algebra algorithms for reasons of speed, and because they are well-implemented, fully documented and widely available. Our main tools include, besides distance matrices, structure-preserving matrix perturbations for minimizing singular values. Our MATLAB (or SCILAB) implementation is described and illustrated.AMS subject Classification: 92E10 Molecular structure, 92C40 Biochemistry, molecular biology, 65F15 Eigenvalues, eigenvectors, 15A18 Eigenvalues, singular values, and eigenvectors     

Dynamics of excited m-dichlorobenzene

Dichlorobenzene is a precursor molecule of di-oxins, which are some of the most toxic chemicals and are suspected of being mutagenic with the structure of benzene rings containing different numbers of chlorine atoms. They are seriously harmful to the health of human. Therefore, it is necessary to study these aryl chemicals especially dichlorobenzene molecules in great detail. In recent years, a number of groups have investi-gated the molecules of aryl halide. The near ultraviolet absorption sp…     

Lifetimes and Quenching of the Ā 2A′(υ3′ = 0 – 2) → X̄ 2A″ Fluorescence of HSO

Fluorescence lifetimes of vibrational levels of the first electronically excited state (ā ² A′) of HSO, determined by the technique of discharge flow and laser-induced fluorescence, are 81 ± 10, 74 ± 8, and 76 ± 14 μs for υ₃′ = 0, 1 and 2, respectively. The rate coefficients of quenching of each level by He, N₂, O₂ and O₃ were measured; the coefficients for HSO (ā, υ₃′ = 0 – 2) quenched by O₃ arc 35–50 times as great as those of HSO by He.     

阳极氧化膜WO3（Ⅱ）：电显色的介质效应

用循环计时电量法、循环伏安法、电化学现场(in-situ)紫外可见反射光谱技术和光电流谱技术研究了溶剂和阳离子(H~+,Li~+)对阳极氧化膜WO_3电显色稳定性和过程的影响。从循环计时电量图可以测定表征膜稳定性的氢或锂的累积量和暂态周期数。实验发现W/WO_3/LiCLO_4乙腈溶液体系具有高的电显色稳定性。引起WO_3膜可逆电显色的H~+和Li~+离子的嵌-脱过程的界面电化学机理不同。着色态WO_3膜的色心是自由电子,其密度超过10~(21)/cm~3,生色机理是等离子体振荡。     

对MDTA中测样品热容量的准恒温法的评述

对用调制差热分析（ＭＤＴＡ）准恒温法测样品热容量的情形进行了讨论。通过结合最基本的热传导定律和ＭＤＴＡ模型，指出了目前国际上测量样品热容量的准恒温法只能得到在所测温度范围内的物质热容量平均值，调制温度的幅度越大或调制频率越高，所得到的热容量数据越平滑。在所测温度范围内样品热容量基本不变时，用ＭＤＴＡ准恒温法较好；但当样品热容量在所测温度范围内有明显变化时，用传统差热分析法（ＤＴＡ）更好一些。     

丙酮中除虫脲溶液标准物质研制

采用重量-容量法制备丙酮中除虫脲溶液标准物质。准确称量国家二级标准物质除虫脲溶解到色谱纯丙酮中,通过A级容量瓶定容至500 mL,摇匀后分装到2 mL安瓿瓶内共460瓶,每瓶为1 mL,保持低温迅速封口,配制过程中室温保持在(20±2)℃。采用液相色谱法进行均匀性、稳定性检验和定值结果验证。从样品中随机抽取16瓶进行均匀性检验,经F检验表明,在95%的置信区间范围内该标准物质均匀性良好;采用t检验对标准物质稳定性进行检验,标准物质在12月内稳定性良好。对该标准物质的不确定度进行了评定,研制的丙酮中除虫脲溶液标准物质定值结果为100μg/mL,相对扩展不确定度为2%(k=2)。结果表明,该标准物质均匀性与稳定性良好,量值准确,可用于日常分析检测中的方法评价和仪器校准。