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11.
We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and variance of the exponentials of graph eigenvalues cluster around a line segment that we call a filar. Zooming-in reveals that this cluster splits into smaller segments (filars) labeled by the number of triangles in graphs. Further zooming-in shows that the smaller filars split into subfilars labeled by the number of quadrangles in graphs, etc. We call this fractal structure, discovered in a numerical experiment, a multifilar structure. We also provide a mathematical explanation of this phenomenon based on the Ihara-Selberg trace formula, and compute the coordinates and slopes of all filars in terms of Bessel functions of the first kind. 相似文献
12.
P.A. Kuzmin 《Journal of Mathematical Analysis and Applications》2007,330(1):744-750
This note is devoted to construction of the domain of the regular representation of Diff+(S1). We consider a subgroup of diffeomorphism group such that the Malliavin-Shavgulidze measure is quasi-invariant with respect to the left action of the subgroup. The measure appears to be quasi-invariant with respect to the left action of diffeomorphisms with discontinuous second derivative. We derive an expression for quasi-invariance density and obtain an additional PSL(2,R) symmetry breaking term. 相似文献
13.
This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution
has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail,
and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the
tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result
in (de Meyer and Teugels, J. Appl. Probab. 17: 802–813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions.
I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008. 相似文献
14.
S. De Winter 《Advances in Mathematics》2007,214(1):146-156
We solve a long-standing open problem by proving that the automorphism group of any thick Payne derived generalized quadrangle with ambient quadrangle S a thick generalized quadrangle of order s, s?5 and odd, with a center of symmetry, is induced by the automorphism group of S. 相似文献
15.
S. Juneja 《Queueing Systems》2007,57(2-3):115-127
Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems
in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient
algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such
tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable
bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric
sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key
idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation
then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance
sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates
it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for
the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.
相似文献
16.
JINJIANG YUAN 《运筹学学报》1998,(3)
1.IntroductionGraphsconsideredinthispaperarefiniteandsimple.FOragraphG,V(G)andE(G)denoteitssetofvenicesandedges,respectively.AbijectionwillbecalledalabellingofG.Letpbeapositiverealnumber.ForagivenlabellingTofagraphG,definethegndiscrepencya.(G,ac)ofTasTheobjectiveoftheminimum-p--sumproblemistofindalabelling7ofagraphGsuchthatac(G,T)isassmallaspossible.ThelabellingTminimizinga.(G,7)iscalledanoptimalHsumlabellingofG.Theminimumvalueiscalledtheminimum-psumofG.ItisshowninI31thattheminimum-… 相似文献
17.
The micellization behavior of an anionic gemini surfactant, GA with nonionic surfactants C12E8 and C12E5 in presence of 0.1 M NaCl at 298 K temperature, has been studied tensiometrically in pure and mixed states, and the related
physicochemical parameters (cmc, γ
cmc, pC
20, Γ
max, and A
min) have been evaluated. Tensiometric profile (γ vs log [surfactant]), for conventional surfactants, generally consists of a single point of intersection; a gradually decreasing
line (normally linear, or with slight curvature) ultimately saturates in γ at a particular [surfactant], corresponding to complete monolayer saturation. The gemini, in this report, led to two unequivocal
breaks in the tensiometric isotherm. An attempt to the interpretation of the two breaks from molecular point of view is provided,
depending solely on the chemical structure of the surfactant. The gemini, even in mixed state with the conventional nonionic
surfactants C12E5 and C12E8, manifested the dual breaks; of course, the dominance of the feature decreases with increasing mole fraction of the nonionics
in the mixture. Theories of Clint, Rosen, Rubingh, Motomura, Georgiev, Maeda, and Nagarajan have been used to determine the
interaction between surfactants at the interface and micellar state of aggregation, the composition of the aggregates, the
theoretical cmc in pure and mixed states, and the structural parameters according to Tanford and Israelachvili. Several thermodynamic
parameters have also been predicted from those theories. 相似文献
18.
用二维色谱技术测定聚合反应气体组成 总被引:1,自引:1,他引:1
介绍一种无阀切换的二维气相色谱分析方法。采用两根不同性质的色谱柱并联连接,样品分别经两根色谱柱分离后汇合在一起进入同一检测器。一次进样可同时测定H2、O2、N2及C1~C3的组分。 相似文献
19.
矩阵平方根在数学的许多应用中起着重要的作用.本文研究M-矩阵平方根的计算问题,提出一种计算正则M-矩阵平方根的迭代方法.首先将这个问题转化为M-矩阵代数Riccati方程,进而提出一种有效的方法来求解这个特殊的MARE.理论分析表明,该方法在一定条件下是收敛的.数值实验表明该方法是可行的,且优于二项式迭代法. 相似文献
20.
Shinsaku Fujita 《Theoretical chemistry accounts》1990,78(1):45-63
Summary A coset representation (G(/G
i
)), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG
i
, is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G
i
) orbit belongs to theG
i
site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions. 相似文献