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61.
Cilanne E. Boulet 《The Ramanujan Journal》2006,12(3):315-320
We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrews in
which he considers the generating function for partitions with respect to size, number of odd parts, and number of odd parts
of the conjugate.
2000 Mathematics Subject Classification Primary—05A17; Secondary—11P81 相似文献
62.
We study a one-dimensional model for fracture, identifying fractured areas with intervals on which a stress field exceeds a threshold value. When is a diffusion process, the cumulative numberN(l) of fractured areas whose length is greater thanl obeys a power lawCl
–p
asl0 with probability one. The exponentp and the constantC are determined. The exponentp agrees with the Hausdorff dimension of the end points of fractured areas, i.e.,
–1(). Even if is self-similar with parameterH>0, i.e.,(cx)– is equivalent toc
H
{(x)–} for anyc>0, the exponentp does not depend solely onH;p=H, where(0, 1/H) is another parameter characterizing. Non-diffusion processes are given whereN(l) does not follow a power law. 相似文献
63.
We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) L
, is found to be =1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts 0.8. Our value for differs from earlier measurements of this quantity by other methods yielding =1.17±0.05 and 1.22±0.08 by Havlin et al.On leave from the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China. 相似文献
64.
Bruce J. West Raoul Kopelman Katja Lindenberg 《Journal of statistical physics》1989,54(5-6):1429-1439
The conditions for macroscopic segregation ofA andB in a steady-stateA+B 0 reaction are studied in infinite systems. Segregation occurs in one and two dimensions and is marginal ford=3. We note the dependence of these results on the precise experimental conditions assumed in the theory. We also note the difference between these results and our earlier ones for finite systems where the critical dimension isd=2. 相似文献
65.
66.
Using Monte Carlo molecular dynamics, a new, careful study is made of the approach of the trajectory of a typical particle in a hard sphere fluid to that of a Brownian particle, discussed before by Powles and Quirke and Rapaport. The apparent fractal dimension of the trajectory, as a function of reduced length scale,(), characterizes the transition from mechanical to Brownian motion and differs markedly from 2 in all present computer simulations. 相似文献
67.
We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT
c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y|
couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.). 相似文献
68.
Raoul Kopelman 《Journal of statistical physics》1986,42(1-2):185-200
Heterogeneous kinetics are shown to differ drastically from homogeneous kinetics. For the elementary reaction A + A products we show that the diffusion-limited reaction rate is proportional tot
– h[A]2 or to [A]x, whereh=1- d
s/2, X=1+2/d
s
=(h-2)(h-1), andd
s
is the effective spectral dimension. We note that ford = d
s
=1, h =1/2 andX = 3, for percolating clustersd
s = 4/3,h = 1/3 andX = 5/2, while for dust ds <1, 1 >h > 1/2 and >X > 3. Scaling arguments, supercomputer simulations and experiments give a consistent picture. The interplay of energetic and geometric heterogeneity results in fractal-like kinetics and is relevant to excitation fusion experiments in porous membranes, films, and polymeric glasses. However, in isotopic mixed crystals, the geometric fractal nature (percolation clusters) dominates. 相似文献
69.
Ole Toft Sørensen 《Journal of Thermal Analysis and Calorimetry》2005,80(3):793-794
Summary An enormous development has taken place within the last five years in synchronous teaching over the Internet, i.e. both the teacher and the students are simultaneously in direct communication with each other as in a normal class-room or auditorium. With this concept it is possible to communicate orally, to exchange Power Point Presentations, documents, programmes and live web-camera pictures. It is even possible to use an electronic black board on which both the teacher and the students can work simultaneously. The great advantage with this type of teaching is that it is not restricted to a single class-room/auditorium with limited access, but in a virtual room accessible to everybody in principle all over the world, and which certainly open up new possibilities in teaching. The purpose of this paper is to present and to discuss the concept of virtual class-room teaching, how the system operates in practice, its advantages and, finally, how its inherent limitations can be overcome. 相似文献
70.
原油三维荧光分析中猝灭现象辨析 总被引:5,自引:0,他引:5
研究了原油的三维荧光猝灭现象,指出浓度过高是原油产生荧光猝灭的主要原因,将会造成三维荧光等值线图畸变,致使定量分析数据失真,谱图特征变异,难以获取原油特征三维指纹图。提出了避免荧光猝灭的预试方法,并列出了不同类型原油的最佳测试浓度。 相似文献