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.     

Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Synthesis of Diethyl Oxalate by a Coupling-Regeneration Reaction of Carbon Monoxide

This article describes a process for the synthesis of diethyl oxalate by a coupling reaction of carbon monoxide, catalyzed by palladium in the presence of ethyl nitrite. The kinetics and mechanism of the coupling and regeneration reaction are also discussed. This paper presents the results of a scale-up test of the catalyst and the process based on an a priori computer simulation.     

Spectrophotometric flow-injection determination of zinc in plant digests based on a spot test

A spot test was implemented in a flow-injection system for the spectrophotometric determination of zinc in digests of plant materials. It is based on the influence of Zn²⁺ on the oxidation rate of 1-naphthylethylenediamine (NED) by hexacyanoferrate(III) under acidic conditions. In order to control the precipitate formation and to maintain the resulting suspension, a micellar medium was established by adding Triton X-100. The proposed system handles about 65 samples per hour, meaning 72 μg NED and 9.0 mg K₃[Fe(CN)₆] per determination. Baseline drift is usually <0.01 absorbance per hour and the analytical signals for 0.5-2.5 mg l⁻¹ Zn range within ca. 0.07-0.45 absorbance. Linearity of the analytical curve is fair (r>0.999, n=6) and detection limit was estimated as 0.2 mg l⁻¹ Zn. Results are precise (R.S.D.<1%, n=10) and in agreement with flame atomic absorption spectrometry and with certified values of standard reference materials.     

片螺素中间体——2,4,5-三甲氧基-α-卤代苯乙酮的合成研究

片螺素[1](Lamel larin)及其类似生物碱是近年来自海洋生物中分离得到的一种海洋活性物质,迄今为止发现有39种[1][2]。所有的片螺素都具有一定的生物活性[3]。但由于海洋生物中片螺素具有含量低,分离困难等特点,因而其合成研究是十分有意义的。本课题组在国家自然基金资助下,设     

SHAPE MEMORY EFFECT OF PU IONOMERS WITH IONIC GROUPS ON HARD-SEGMENTS

SMPU （shape memory polyurethane） non-ionomers and ionomers, synthesized with poly（c-caprolactone） （PCL）, 4, 4＇-diphenylmethane diisocyanate （MDI）, 1,4-butanediol （BDO）, dimethylolpropionic acid （DMPA） were measured with cyclic tensile test and strain recovery test. The relations between the structure and shape memory effect of these two series were studied with respect to the ionic group content and the effect of neutralization. The resulting data indicate that, with the introduction of asymmetrical extender, the stress at 100% elongation is decreased for PU non-ionomer and ionomer series, especially lowered sharply for non-ionomer series; the fixation ratio of ionomer series is not affected obviously by the ionic group content; the total recovery ratio of ionomer series is decreased greatly. After sufficient relaxation time for samples stretched beforehand, the switching temperature is raised slightly, whereas the recovery ratio measured with strain recovery test method is lowered with increased DMPA content. The characterization with FT-IR, DSC, DMA elucidated that, the ordered hard domain of the two series is disrupted with the introduction of DMPA which causes more hard segments to dissolve in soft phase; ionic groups on hard segment enhance the cohesion between hard segments especially at high ionic group content and significantly facilitate the phase separation compared with the corresponding non-ionomer at moderate ionic group content.     

Characterization of the Effects of Vanadium Traps in Cracking Catalysts by Imaging Secondary Ion Mass Spectrometry and Microactivity Test

The vanadium trapping effect of Mg and La containing additives in cracking catalyst contaminated with 2300 ppm Ni and 4700 ppm V has been analyzed by microactivity test (MAT) and imaging secondary ion mass spectrometry (SIMS). The results of SIMS imaging are consistent with cracking activity data and show that the La/spinel is a superior vanadium trap for the fluid catalytic cracking of hydrocarbons (FCC) operation. La/spinel serves as a dual function additive for both vanadium trap and SO_x removal. The optimum amount of La/spinel added to the cracking catalyst is about 15% by weight. This results in an increased catalytic activity, an increase in gasoline yield, and a decrease in coke and gas factors. The MgAl₂O₄ phase of Mg/Al₂O₃ additive is found capable of trapping vanadium while its MgO of Mg/Al₂O₃ phase can migrate to zeolite particles (the active component of the FCC catalyst) that, in turn, causes a decline in the activity of that catalyst.