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.     

STUDY ON THE DUCTILE DEFORMATION DOMAIN OF THE SIMPLE SHEAR IN ROCKS——TAKING BRITTLE FAULTS OF THE COVERING STRATA IN THE SOUTHERN JIANGSU AREA AS AN EXAMPLE

A study on the ductile deformation domain of the brittle fault in the shallow level ofthe crust is a new probe field for the modern structural geology. Taking the southern Jiang-su Province area as an example the orientation measurement of quartz crystals, the com-positional texture observation of three pressure sensitive minerals and the rheological param-eter determination of dislocation densities, etc. have been demonstrated and analysed basedon typical samples in the present paper. In addition, their generation mechanisms arealso discussed from the cataclastic rheology, the dynamic differentiation and the simpleshearing, specially, from the Ode strength theory. Finally, a generative relationship betweenthe ductile deformation domain of the brittle fault system, in the regional layer--slip andthe formation of the stratabound ore deposit is shown as well.     

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.     

橡胶中简单剪切与纯剪切的关系

研究了简单剪切与纯剪切的关系，得出了：（１）简单剪切可看成纯剪切加转动，转动角θ有；（２）若简单剪切椭圆的长轴与坐标轴Ｘ的夹角为φ，相应的纯剪椭圆长袖与坐标轴ｙ的夹角为β０，则φ＝β０；（３）橡胶在双向拉伸时剪应变γ的一般表达式为，对简单剪切而言即为     

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.     

Surface viscoelasticity of phospholipid monolayers at the air/water interface

The surface viscoelastic properties of monolayers of two phospholipids DPPC (L--dipalmitoylphosphatidylcholine) and DMPE (L--dimyristoylphosphatidyl-ethanolamin), at the air-water interface have been investigated. Two techniques were used for the investigation. One involved use of an interfacial shear rheometer (torsion pendulum apparatus ISR1), to provide measurements of the shear viscosity _s as a function of surface pressure, and the second, a modified LB trough with an oscillating barrier to generate periodie dilation and compression so as to measure the dilational elastic modulusE as a function of surface area.Results indicate a strong dependence of _s andE upon monolayer phases. This suggests that the viscoelastic relaxation of monolayers can be understood as molecular rearrangements, domain exchange and molecular reorientations between different monolayer states.