Quantized Hamilton Dynamics

The paper describes the quantized Hamilton dynamics (QHD) approach that extends classical Hamiltonian dynamics and captures quantum effects, such as zero point energy, tunneling, decoherence, branching, and state-specific dynamics. The approximations are made by closures of the hierarchy of Heisenberg equations for quantum observables with the higher order observables decomposed into products of the lower order ones. The technique is applied to the vibrational energy exchange in a water molecule, the tunneling escape from a metastable state, the double-slit interference, the population transfer, dephasing and vibrational coherence transfer in a two-level system coupled to a phonon, and the scattering of a light particle off a surface phonon, where QHD is coupled to quantum mechanics in the Schrödinger representation. Generation of thermal ensembles in the extended space of QHD variables is discussed. QHD reduces to classical mechanics at the first order, closely resembles classical mechanics at the higher orders, and requires little computational effort, providing an efficient tool for treatment of the quantum effects in large systems.     

Simultaneous determination of traces of heavy metals by solid-phase spectrophotometry

A coupling sensitive solid phase spectrophotometric (SPS) procedure for determination of traces of heavy metals (Me-SPS) and multicomponent analysis by multiple linear regressions (MA), a simple methodology for simultaneous determination of metals in mixtures was inaugurated. The Me-SPS procedure is based on sorption of heavy metals on PAN-resin and direct absorbance measurements of colour product Me-PAN sorbed on a solid carrier in a 1-mm cell. This methodology (Me-SPS-MA) was checked by simultaneous determination of metals in synthetic mixtures with different compositions and contents of metals important in pharmaceutical practice: Zn, Pb, Cd, Cu, Co, and Ni. Good agreement between experimental and theoretical amounts of heavy metals is obtained from the recovery test (78.3–110.0%). The proposed method enables determination of particular metal ion at the ng mL⁻¹ level and it was successfully applied to the determination impurities from heavy metal traces in pharmaceutical substances (Cu in ascorbic acid, Pb in glucose, and Zn in insulin). The proposed procedure could be possible contribution to the development of pharmacopoeial methodology for a heavy metals test.     

微量元素锌在治疗Bell麻痹中的作用

为探讨急性早期应用补锌和综合疗法治疗Bell麻痹 ,将 1 5 8例Bell麻痹患者 ,随机分成两组 :(1 )补锌组 (补锌 +综合疗法 ) ;(2 )对照组 (单纯综合疗法 )。对其进行了观察对比治疗 ,同时检测了所有患者治疗前后自身对照发锌值 ,还对所有患者进行了定位诊断、面神经电反应测试、并对面肌功能进行评分。结果表明 ,对定位诊断其病变在D段、面肌功能评分在 1 1分以下、面神经无电反应患者 ,即使给予早期综合治疗 ,效果仍较差 ,而早期给予补锌加综合治疗效果优于对照组 ,其它段内患者治疗次数和治愈天数也均优于对照组。可见微量元素锌在发挥免疫应答、免疫调控中的重要作用     

含聚醚间隔链的扩链脲改性环氧树脂/双氰双胺固化体系性能研究

合成了一系列含不同分子量聚环氧丙烷 (PPG)柔性间隔链的扩链脲 ,系统考察了扩链脲改性环氧树脂E 5 1/双氰双胺 (dicy)固化体系的固化反应活性、动态力学行为、冲击性能和断裂面形态结构 ,并对体系的冲击性能、形态结构与动态力学行为之间的关系进行了探讨 .结果表明 ,改性体系固化反应活性明显提高 ,固化反应表观活化能降低 ,固化反应峰顶温度从 190℃降低至 14 0℃ ,固化反应的表观活化能由 14 5 5kJ/mol降至 70～ 80kJ mol;改性体系冲击强度明显提高 ,其中所含PPG柔性链分子量为 10 0 0的扩链脲改性的E 5 1/dicy体系冲击强度较未改性的E 5 1/dicy体系提高了 8倍 ,其冲击试样断裂面的形态具有明显的韧性断裂特征 ,微观两相网络结构的存在导致了改性体系冲击强度显著提高     

Bayesian sequential reliability for Weibull and related distributions

Assume that the probability density function for the lifetime of a newly designed product has the form: [H(t)/Q()] exp{–H(t)/Q()}. The Exponential(), Rayleigh, WeibullW(, ) and Pareto pdf's are special cases.Q() will be assumed to have an inverse Gamma prior. Assume thatm independent products are to be tested with replacement. A Bayesian Sequential Reliability Demonstration Testing plan is used to eigher accept the product and start formal production, or reject the product for reengineering. The test criterion is the intersection of two goals, a minimal goal to begin production and a mature product goal. The exact values of various risks and the distribution of total number of failures are evaluated. Based on a result about a Poisson process, the expected stopping time for the exponential failure time is also found. Included in these risks and expected stopping times are frequentist versions, thereof, so that the results also provide frequentist answers for a class of interesting stopping rules.This research was supported by NSF grants DMS-8703620 and DMS-8923071, and forms part of the Ph.D. Thesis of the first author, the development of which was supported in part by a David Ross grant at Purdue University. The authors thank the editors and a referee for insightful comments and suggestions.     

Bahadur efficiency and robustness of studentized score tests

We derive the exact Bahadur slopes of studentized score tests for a simple null hypothesis in a one-parameter family of distributions. The Student's t-test is included as a special case for which a recent result of Rukhin (1993, Sankhy Ser. A, 55, 159–163) was improved upon. It is shown that locally optimal Bahadur efficiency for one-sample location models with a known or estimated scale parameter is attained within the class of studentized score tests. The studentized test has an asymptotic null distribution free of the scale parameter, and the optimality of likelihood scores does not depend on the existence of a moment generating function. We also consider the influence function and breakdown point of such tests as part of our robustness investigation. The influence of any studentized score test is bounded from above, indicating certain degree of robustness of validity, but a bounded score function is needed to cap the influence from below and to ensure a high power breakdown point. We find that the standard Huber-type score tests are not only locally minimax in Bahadur efficiency, but also very competitive in global efficiency at a variety of location models.     

Whitehead test modules

A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.

A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.

     

Wiener's test for space-time random walks and its applications

This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.

     

A predictive model for impact response of viscoelastic polymers in drop tests

We show for the first time that a classical Hookean viscoelastic constitutive law for rubbery materials can predict the impact forces and deflections measured with a commercial drop tester when a mass, or tup with a flat impacting surface is dropped onto a flat pad of commercial impact-absorbing rubber. The viscoelastic properties of the rubber, namely the relaxation times and strengths, are obtained by a standard rheological linear-oscillatory test, and the equation of momentum transfer is then solved, using these measured parameters, assuming a uniaxial deflection of the pad during the impact. Good agreement between measured and predicted forces and deflections is obtained for a series of various drop heights, tup masses, impact areas, and pad thicknesses, as long as the deflection of the pad relative to its thickness is small or modest (<50% or so), and as long as the area of the pad is less than or equal to that of the tup. When the pad area is greater than the tup, forces are higher than predicted, unless an empirical factor is introduced to account for the nonuniaxial stretching of the ring of material that extends outside of the impact area. These results imply that the impact-absorbing properties of a rubbery polymeric material can be assessed by simply examining the material's linear viscoelastic spectrum.