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71.
Jeff Kahn 《Proceedings of the American Mathematical Society》2002,130(2):371-378
For -regular, -vertex bipartite graphs with bipartition , a precise bound is given for the sum over independent sets of the quantity . (In other language, this is bounding the partition function for certain instances of the hard-core model.) This result is then extended to graded partially ordered sets, which in particular provides a simple proof of a well-known bound for Dedekind's Problem given by Kleitman and Markowsky in 1975.
72.
Lutz Mattner 《Probability Theory and Related Fields》2004,130(2):151-166
This is a contribution to the theory of sums of independent random variables at an algebraico-analytical level: Let Prob denote the convolution semigroup of all probability measures on with all moments finite, topologized by polynomially weighted total variation. We prove that the cumulant sequence regarded as a function from Prob into the additive topological group ofall real sequences, is universal among continuous homomorphisms from Prob into Hausdorff topological groups, in the usual sense that every other such homomorphism factorizes uniquely through . An analogous result, referring to just the first cumulants,holds for the semigroup of all probability measures with existing rth moments. In particular, there is no nontrivial continuous homomorphism from the convolution semigroup of all probability measures, topologized by the total variation metric, into any Hausdorff topological group.Mathematics Subject Classification (2000): 60B15, 60E10, 60G50 相似文献
73.
We address the problem of finding the worst possible traffic a
user of a telecommunications network can send.
We take worst to mean having the highest effective
bandwidth, a concept that arises in the Large Deviation theory of
queueing networks.
The traffic is assumed to be stationary and to satisfy leaky bucket
constraints, which represent the a priori knowledge the network
operator has concerning the traffic.
Firstly, we show that this optimization problem may be reduced to an
optimization over periodic traffic sources.
Then, using convexity methods, we show that the realizations of a
worst case source must have the following properties:
at each instant the transmission rate must be either zero,
the peak rate, or the leaky bucket rate; it may only be the latter when
the leaky bucket is empty or full;
each burst of activity must either start with the leaky
bucket empty or end with it full. 相似文献
74.
Hongbin Zhang 《International Journal of Infrared and Millimeter Waves》2007,28(9):713-723
A spatially independent model of vertical-cavity surface-emitting lasers (VCSELs) is derived by integrating the spatially
dependent rate equations over the cross section of the cavity of a VCSEL. The angular and radial non-uniformities of the injection
current are taken into account. The well-known LP modes of a weakly-guiding cylindrical waveguide are employed to describe
the transverse modal structure in the VCSEL cavity. This model is solved in a self-consistent way by using the 4th order Runge-Kutta
method. The dependence of transverse mode competition on the current intensity, the angular and radial non-uniformities of
the injection current, and the geometrical parameters of the electrical contact are thoroughly investigated and analyzed.
The results are useful to the optimum design of the optical transverse modal structure of VCSELs. 相似文献
75.
Michał Dobrski 《Central European Journal of Physics》2007,5(3):313-323
In this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by
canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time
independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian
for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.
相似文献
76.
为解决独立学院数学教学中能力强的学生"吃不饱",能力欠佳的学生"吃不消"的问题,提出了"基础+提高"统筹优化的数学课程体系."基础"模块的教学坚持为后续专业课服务,并穿插教书中"育人"理念;"提高"模块作为公共选修范畴,具有自主性、多元化特点,并突出人才培养的阶梯式发展.通过近5年的教学改革与实践,新课程体系有效地提高了学生学习数学的兴趣,降低了期末考试的不通过率,并造就一批有创新意识的人才. 相似文献
77.
The transport coefficients for the nine point groups
—which represent the symmetry groups of the quasicrystals in two and three dimensions—have been evaluated and tabulated in
this work, employing group-theoretical methods. 相似文献
78.
G.A. Gerolymos E. Sauret I. Vallet 《Theoretical and Computational Fluid Dynamics》2004,17(5-6):407-431
This paper is concerned with recent advances in the development of near wall-normal-free Reynolds-stress models, whose single point closure formulation, based on the inhomogeneity direction concept, is completely independent of the distance from the wall, and of the normal to the wall direction. In the present approach the direction of the inhomogeneity unit vector is decoupled from the coefficient functions of the inhomogeneous terms. A study of the relative influence of the particular closures used for the rapid redistribution terms and for the turbulent diffusion is undertaken, through comparison with measurements, and with a baseline Reynolds-stress model (RSM) using geometric wall normals. It is shown that wall-normal-free rsms can be reformulated as a projection on a tensorial basis that includes the inhomogeneity direction unit vector, suggesting that the theory of the redistribution tensor closure should be revised by taking into account inhomogeneity effects in the tensorial integrity basis used for its representation. PACS 47.32.Fg; 47.85.Gj; 47.27.Eq 相似文献
79.
For weighted sums Σj = 1najVj of independent random elements {Vn, n ≥ 1} in real separable, Rademacher type p (1 ≤ p ≤ 2) Banach spaces, a general weak law of large numbers of the form (Σj = 1najVj − vn)/bn →p 0 is established, where {vn, n ≥ 1} and bn → ∞ are suitable sequences. It is assumed that {Vn, n ≥ 1} is stochastically dominated by a random element V, and the hypotheses involve both the behavior of the tail of the distribution of |V| and the growth behaviors of the constants {an, n ≥ 1} and {bn, n ≥ 1}. No assumption is made concerning the existence of expected values or absolute moments of the {Vn, n >- 1}. 相似文献
80.
Quay van der Hoff Ansie Harding 《International Journal of Mathematical Education in Science & Technology》2017,48(1):16-30
This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause–effect analysis, often used for business improvement. The cause–effect analysis indicates that there are many factors that impact on secondary school teaching of mathematics, factors that the tertiary sector has no control over. The analysis also indicates the undesirable issues that are at the root of impeding success in the calculus module. Most important is that students are not encouraged to become independent thinkers from an early age. This triggers problems in follow-up courses where students are expected to have learned to deal with the work load and understanding of certain concepts. A new model was designed to lessen the impact of these undesirable issues. 相似文献