P2-阶子群X-ss-半置换的有限群

设G是有限群,X是G的一个非空子集,子群H称为在G中X-ss-半置换,若H在G中有补充子群T,对于T的任意Sylowp-子群P,只要(p,|H|)=1,就存在x∈X使得HP^x=P^xH。通过对p²-阶子群的X-ss-半置换性研究,得到了p-幂零群的新判断。     

The empirical distribution function and strong laws for functions of order statistics of uniform spacings

Let N points be arbitrarily chosen on the circle with unit circumference, and order them clockwise. The uniform mth order spacings are then defined as the clockwise distances between any pair of points having m − 1 other points in between. A Glivenko-Cantelli theorem and nonlinear almost sure bounds for the empirical distribution function based on these uniform spacings are derived. The parameter m is allowed to increase with N to infinity. Applications to linear combinations of functions of mth order spacings are given.     

Ranking fuzzy numbers with maximizing set and minimizing set

Up to now, these are five methods of ranking n fuzzy numbers in order, but these methods contain some confusions and occasionally conflict with intuition. This paper introduces the concept of maximizing set and minimizing set to decide the ordering value of each fuzzy number and uses these values to determine the order of the n fuzzy numbers. In addition, we give a method for calculating the ordering value of each fuzzy number with triangular, trapezoidal, and two-sided drum-like shaped membership functions.     

An extremal property of rectangular distributions

It is proved that the correlation coefficient between the elements of the order statistics is maximal for a rectangularly (uniformly) distributed population.     

Maximum likelihood prediction

The principle of maximum likelihood is applied to the joint prediction and estimation of a future random variable and an unknown parameter. We assume dependence between present and future, and the approach is non-Bayesian. Our principal application is to the prediction of higher order statistics from lower ones in Type II censored random samples. Some simple criteria for existence and uniqueness of the predictor are given for this situation and the methods are illustrated with several examples.     

Effect of ordering transformation rate on the magnetic properties of Fe–Pt-based bulk alloys

We have investigated the ordering transformation and magnetic properties of Fe_59.75Pt_39.5Nb_0.75 bulk alloys in detail by using different high-temperature homogenization treatments, different cooling rates and different low-temperature annealing treatments to obtain samples with different microstructure and different atomically ordered states. The quenching rate after the high-temperature homogenization treatment was chosen much lower than in previous investigations. In this way, we were able to obtain nanostructured bulk alloys consisting exclusively of the hard-magnetic face-centered-tetragonal phase. A high remanence ratio was obtained by profiting from the nanocomposite exchange coupling between nearest-neighbor-ordered regions. The present results are compared with results of previous investigations in which much higher cooling rates were applied. We also discussed why the present alloy systems are less suitable for the attainment of exchange spring behavior.     

Phase transitions of a feedback amplifier

The phase transition behaviour of an amplifier with positive feedback is experimentally studied. The results are interpreted using catastrophe theory language. Zero (in Gilmore’s classification), first and second-order transitions are demonstrated by driving the system along appropriate trajectories in control parameter space and the cusp and the spinodal are mapped. The fluctuations of the order parameter are investigated and their relationship to system response time established. Quench experiments analogous to those familiar in condensed matter have also been performed and with similar results.     

Notes on a new chain condition for prime ideals

A chain condition intermediate to the catenary property and the chain condition for prime ideals (c.c.) is studied. Like the c.c., the condition is inherited from a semi-local domain R by integral extension domains, by local quotient domains, and by factor domains, and a semi-local ring that satisfies the condition is catenary. (Unlike the c.c., none of these statements is true when R is not semi-local.) A number of characterizations of a semi-local domain that satisfies the condition are given in terms of: integral (respectively, algebraic, transcendental) extension domains, Henselizations, completions, Rees rings, associated graded rings and certain discrete valuation over-rings. Then four of the catenary chain conjectures are characterized in terms of this condition.     

Molecular level study of the crystallization of a thermoplastic polyimide by infrared spectroscopy

The crystallization process of the thermoplastic polyimide derived from 3,3′,4,4′-benzophenonetetracarboxylic dianhydride (BTDA) and 2,2-dimethyl-1,3,-(4-aminophenoxy) propane (DMDA) is studied at the molecular level by utilizing infrared spectroscopy's sensitivity to local molecular environment. Assignments of the unique spectral features appearing upon crystallization are made with additional verification from crystalline model imide compounds. A direct comparison of an annealed polyimide film studied by both infrared spectroscopy and x-ray diffraction shows fairly close agreement in the amount of crystallinity obtained. The unique crystalline infrared spectral features provide insight into the molecular mechanism involved with the crystallization process. Spectral shifts occurring upon crystallization reflect intramolecular rotations toward increased coplanarity as well as intermolecular chain packing of certain molecular groups at specific sites of the chain backbone. The site specific information is then used to study the relative kinetic behavior of the intramolecular and intermolecular effects occurring during crystallization. © 1994 John Wiley & Sons, Inc.