Euler函数的一个组合-数论推广（英）

Recently, L.C.Hsu and Wang Jun generated new combinatorial number theoreticfunctions serving as generalizations of Euler′s totient. In this paper we form an extensive class of generalized Euler totients by translating the most general counting functions of Hsu and Wang on integers to the setting of Narkiewicz′s regular convolution. This class casts in the same framework various famous generalizations of Euler′s totient, such as Cohen′s totient, Jordan′s totient, Klee′s totient, Schemmel′s totient,Stevens′s to tient, the unitary analogue of Euler′s to tient and Euler′s to tient with respect to Narkiew icz′s regular convo lution.     

Application of a model‐free isoconversional method to the cure of phenolic systems

The curing process of a phenolic resole was monitored with differential scanning calorimetry under nonisothermal and isothermal conditions, the curing kinetics were analyzed with a model‐fitting approach and a model‐free isoconversional method, and the activation energy of this phenolic system was found to be close to 46 ± 4 kJ mol^?1. For complicated cures, the model‐free isoconversional method was found to be a simpler and more reliable approach. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1525–1528, 2001     

Effects of discontinuous magnetic permeability on magnetodynamic problems

A novel approximation technique using Lagrange finite elements is proposed to solve magneto-dynamics problems involving discontinuous magnetic permeability and non-smooth interfaces. The algorithm is validated on benchmark problems and is used for kinematic studies of the Cadarache von Kármán Sodium 2 (VKS2) experimental fluid dynamo.     

A generalization of Descartes’ rule of signs and fundamental theorem of algebra

Descartes’ rule of signs yields an upper bound for the number of positive and negative real roots of a given polynomial. The fundamental theorem of algebra implies a similar property; every real polynomial of degree n ? 1 has at most n real zeroes. In this paper, we describe axiomatically function families possessing one or another of these properties. The resulting families include, at least, all polynomial functions and sums of exponential functions. As an application of our approach, we consider, among other things, a method for identifying certain type of bases for the Euclidean space.     

Electrochemical Cells Employing (Ch)x -Cathodes In A Nonaqueous Electrolyte

Polyacetylene films have been used as cathodes in electrochemical cells of the type A1/Li/LiC10₄(l…2M) - PC/ (CH)_X/Pt. Their performance characteristics have been measured. The results show that these cells can be cycled 10 to 15 times at deep discharges, over 300 times at shallow discharges and over 1000 times at very light discharges. Due to the instability of the oxidized (CH)_X the charge retention of the cells is poor.     

Impact of impellers on the axisymmetric magnetic mode in the VKS2 dynamo experiment

In the von Kármán Sodium 2 (VKS2) successful dynamo experiment of September 2006, the observed magnetic field showed a strong axisymmetric component, implying that nonaxisymmetric components of the flow field were acting. By modeling the induction effect of the spiraling flow between the blades of the impellers in a kinematic dynamo code, we find that the axisymmetric magnetic mode is excited. The control parameters are the magnetic Reynolds number of the mean flow, the coefficient measuring the induction effect alpha, and the type of boundary conditions. We show that using realistic values of alpha, the observed critical magnetic Reynolds number, Rm;{c} approximately 32, can be reached easily with ferromagnetic boundary conditions. We conjecture that the dynamo action achieved in this experiment may not be related to the turbulence in the bulk of the flow, but rather to the alpha effect induced by the impellers.     

X-ray measurement of cellulose crystallite orientation in cotton fibers

The orientation of crystallites in a bundle of parallel cotton fibers was studied by x-ray diffraction. The intensity distributions of the 101 and 002 diffraction rings showed the distributions of (101) and (002) planes to be identical within the limits of accuracy. Therefore, the crystallites in the cotton fibers very likely had random orientation about their long axes. The orientation distribution of these axes was calculated by using the intensity distribution of the 002 diffraction ring. The cylindrically symmetrical density distribution J(β) thus obtained was multiplied by sin β to obtain the distribution of relative numbers of crystallites at given angles β to the long axis of the fiber. The average 〈β〉 was found to be in agreement with the value of 〈sin²β〉 measured from the 002 diffraction ring. The intensity distributions on the 101 and 002 diffraction rings showed small fluctuations. These fluctuations appeared much stronger in the J(β) and sin β J(β) distributions, indicating clear discontinuities in the pitch angle distribution.     

Effects of conductivity jumps in the envelope of a kinematic dynamo flowInfluence des discontinuités de conductivité dans l'enveloppe de l'écoulement d'une dynamo cinématique

This Note reports on numerical simulations of the kinematic dynamo action in a test flow modeling the Von Kármán Sodium (VKS) experiment performed at CEA-Cadarache. We show that the conductivity of the vessel greatly influences the critical magnetic Reynolds number. These effects are dramatically amplified as the ratio of the conductivity of the vessel to that of the sodium increases from 1 to 5. To cite this article: R. Laguerre et al., C. R. Mecanique 334 (2006).     

Various aspects of fluid vortices

A general review of the current research in vortex dynamics is presented, based on contributions given during a workshop held in May 2003 at Porquerolles, France. This article aims at providing a picture of the work performed on this subject in the French community. Various cases are covered, from 2D vortex patches to 3D vortex tubes; from isolated vortices to shear flows. Different contexts are considered: pure Euler and Navier–Stokes flows as well as stratified, rotating and magnetic flows. To cite this article: I. Delbende et al., C. R. Mecanique 332 (2004).     

Effect of missing values in estimation of mean of auto-correlated measurement series

Sampling and uncertainty of sampling are important tasks, when industrial processes are monitored. Missing values and unequal sources can cause problems in almost all industrial fields. One major problem is that during weekends samples may not be collected. On the other hand a composite sample may be collected during weekend. These systematically occurring missing values (gaps) will have an effect on the uncertainties of the measurements. Another type of missing values is random missing values. These random gaps are caused, for example, by instrument failures. Pierre Gy's sampling theory includes tools to evaluate all error components that are involved in sampling of heterogeneous materials. Variograms, introduced by Gy's sampling theory, have been developed to estimate the uncertainty of auto-correlated process measurements. Variographic experiments are utilized for estimating the variance for different sample selection strategies. The different sample selection strategies are random sampling, stratified random sampling and systematic sampling. In this paper both systematic and random gaps were estimated by using simulations and real process data. These process data were taken from bark boilers of pulp and paper mills (combustion processes). When systematic gaps were examined a linear interpolation was utilized. Also cases introducing composite sampling were studied. Aims of this paper are: (1) how reliable the variogram is to estimate the process variogram calculated from data with systematic gaps, (2) how the uncertainty of missing gap can be estimated in reporting time-averages of auto-correlated time series measurements. The results show that when systematic gaps were filled by linear interpolation only minor changes in the values of variogram were observed. The differences between the variograms were constantly smallest with composite samples. While estimating the effect of random gaps, the results show that for the non-periodic processes the stratified random sampling strategy gives more reliable results than systematic sampling strategy. Therefore stratified random sampling should be used while estimating the uncertainty of random gaps in reporting time-averages of auto-correlated time series measurements.