Induced product representations of extended Cuntz algebras

Let _H be the extended Cuntz algebra over the Hilbert space H. Since its zero grade part _H⁰ is the C^*-inductive limit of B(H^r), we look for some family of representations on an inductive limit of H^r as r. When such construction is shaped according to the structure of _H⁰, von Neumanns notion of a reference sequence of unit vectors for Hilbert infinite tensor products emerges; after a further Rieffel induction step, a class IPR[H] of representations of _H arises. For any two such representations, we describe explicitly their associated intertwiners. Any two representations in IPR[H] are either disjoint or unitarily equivalent. Actions of the group by translation on sequences of unit vectors are involved, as well as the ideals of .     

Radiative Properties of an SHF Discharge Formed by a Ring‐Type Waveguide‐Slot Radiator

The actual spatial distribution of the intensity of SHF discharge glow in oxygen at different distances from the zone of input of SHF power has been investigated by the method of optical emission spectroscopy with subsequent abelization of the experimentally obtained integral characteristics of the intensity of radiation emitted by the OI ( = 777.7 nm) line. The investigations were carried out in a plasmatron on the basis of a ringtype waveguideslot radiator. The experimental results obtained indicate that the best uniformity of optical radiation over the discharge length is attained in the mode of pressureoptimum gas breakdown. Radial distributions of the radiation intensity are complicated in nature, which can be attributed to the differently pronounced skin effect exerted by a plasma on an electromagnetic wave under different discharge conditions. The results of the present work make it possible to interpret the previously obtained data of technological experiments and can be employed in developing technological processes of SHF plasma processing of materials and in designing SHF plasmatrons.     

Factorization in generalized power series

The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group is a classical tool in the study of real closed fields. We prove the existence of irreducible elements in the ring consisting of the generalized power series with non-positive exponents. The following candidate for such an irreducible series was given by Conway (1976): . Gonshor (1986) studied the question of the existence of irreducible elements and obtained necessary conditions for a series to be irreducible. We show that Conway's series is indeed irreducible. Our results are based on a new kind of valuation taking ordinal numbers as values. If we can give the following test for irreducibility based only on the order type of the support of the series: if the order type is either or of the form and the series is not divisible by any monomial, then it is irreducible. To handle the general case we use a suggestion of
M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case . In the final part of the paper we study the irreducibility of series with finite support.

     

Dual-jet plasmatron for medical applications

We present a design for a dual-jet arc plasmatron operating at a frequency of 66 kHz in an argon flow at atmospheric pressure. We present the results of determination of the temperature, electron concentration, and electrode erosion obtained by atomic emission spectral analysis. The proposed convenient design for a dualjet plasmatron and the low erosion of the copper electrodes in the plasma make it possible to use it for medical purposes. Report given at the Fifth International Conference on Plasma Physics and Plasma Technologies (PPPT-5), 18–22 September 2006, Minsk, Belarus. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 1, pp. 139–140, January–February, 2007.     

Digital computation of transient characteristics of an induction motor on switched supply

A novel method of computing the nonlinear differential equations relating to the transient behaviour of an induction motor using a polynomial series, is presented. The stator and rotor currents and the angle of rotation are expressed as polynomial series dependent on time. These are then substituted into the differential equations of the induction motor to compute the polynomial coefficients and, consequently, the transient quantities. Since the equations are nonlinear, the computations are carried out using the step-by-step method. The stator and rotor currents, speed and torque are calculated for acceleration and braking conditions. The results are compared both analytically and experimentally.     

Velocity-dependent inertial induction and secular retardation of the earth’s rotation

According to the model of inertial induction proposed earlier, the inertia force consists of an acceleration-dependent term which comes out as identically equal to -ma. Besides, there is a velocity-dependent term which is exceedingly small to be easily detected. However, it has been shown that this results in a cosmological red shift of light coming from distant stars and galaxies; the magnitude of the red shift agrees very well with the observed values. Though this model yields correct results when applied to photons it needs modification before applying to other bodies. A modified form of the inertial induction model is now proposed where the proposed velocity-dependent inertia forces, when applied to the solar system, yields correct order of magnitude for the secular retardation of the earth’s rotation. Moreover, a combined model using the velocity term and the tidal friction also does not suggest any close proximity of the moon to the earth in the past. When the model is applied to the case of Phobos, a secular acceleration of the order of magnitude of 10⁻³ deg yr⁻² is obtained.     

关于Alzer不等式的一个简单证明

利用数学归纳法和函数的单调性，本给出了Alzer不等式的一个简单证明．     

数学归纳法与匹亚诺公理

数学归纳法推理是典型的三段论，而不是完全归纳法，其基础是自然数列的性质，而不是逻辑公理，皮亚诺公理中的归纳法公理并不是一种证明方法，而是自然数集的一条不可缺少的根据性质。     

网站用户登录信息挖掘特征规则

本文首先研究了基本的面向属性归纳，提出了从网站用户登录信息中挖掘用户特征规则的思路。问题从解决多属性归纳着手，特点是首先建立概念树，然后用条件属性组合与约束的方法进行挖掘。实验表明，本文设计的模型能客观地描述客户行为，为从Web信息挖掘客户特征规则提出了一条有效的途径。     

不对称Baylis-Hillman反应研究进展

综述了光学活性的活化烯、亲电试剂、催化剂和溶剂对Baylis_Hillman反应的不对称诱导效果