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91.
92.
Summary This paper contains three applications of the technique of limit series (our [1986]) to the theory of ramification of linear series on smooth curves, and curves of compact type, overC.Let {L
t
t|<}, be a family of linear series on a smooth family of smooth curves {C
t
}, and letp
1(t),p
2(t)C
t
be sections of the family which coincide (only) att=0. Setp=p
1())=p
2(0)C
0.We first give a condition related to the Schubert calculus which must be satisfied by the ramification series
and the
. We then take up the converse problem: In what ways can a given ramification point arise as a limit? We show that if the ramification point isdimensionally proper in the sense of our [1986], then families of every kind allowed by the Schubert calculus condition can actually be constructed. Finally, we prove that dimensional propriety is in a strong sense an open condition, so that ramification points constructed as above are again dimensionally proper.In the body of the paper we work not with pairs of points, as above, but with arbitrary finite collections of points approaching (possibly) several points of the limit curve. Further, by their nature, the results are valid for families of curves of compact type. 相似文献
93.
94.
J. R. Norris L. C. G. Rogers David Williams 《Probability Theory and Related Fields》1987,74(2):271-287
Summary A natural model for a self-avoiding Brownian motion inR
d, when specialised and simplified tod=1, becomes the stochastic differential equation
, where {L(t, x):t0,xR} is the local time process ofX. ThoughX is not Markovian, an analogue of the Ray-Knight theorem holds for {L(,x):xR}, which allows one to prove in many cases of interest that
exists almost surely, and to identify the limit. 相似文献
95.
The equality of two critical points — the percolation thresholdp
H
and the pointp
T
where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP
— at the bond densityp=1–e
–
in the single parameter case. These are: (1)MhM/h+M
2+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a 3 structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents
and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that
. An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation
and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department 相似文献
96.
David A. McCron 《The Journal of the Operational Research Society》1987,38(11):1067-1072
In modern processor-controlled systems, it is common to find a central processor polling a number of message queues, where at most one message is processed from each queue during one polling cycle. This paper shows how one important parameter can be estimated quickly, namely the cycle-time distribution. This is the distribution of times taken for the cyclic server to perform one complete cycle in its continuous scan of a number of queues. The method of solution is to identify various constraints which will determine the cycle-time distribution, formulate them as linear inequality and equality constraints and, by determining an appropriate objective function, apply the simplex method to find upper and lower bounds on the values taken by the cycle-time distribution itself. A great strength of this technique is its overall simplicity, which enables it to be used to obtain important results very quickly and cheaply. 相似文献
97.
David Akers 《International Journal of Theoretical Physics》1987,26(12):1169-1173
Recently evidence was presented for the existence of magnetic charge from Zeeman splitting in meson states. The model by Akers predicted the existence of a new meson at 1814 MeV withI
G(J
PC
)=0+(0–+). Experimental evidence for this new meson is cited and discussed. 相似文献
98.
99.
100.
David Whitley 《Acta Appl Math》1986,5(3):279-311
We study the dynamics of a two-parameter family of noninvertible maps of the plane, derived from a model in population dynamics. We prove that, as one parameter varies with the other held fixed, the nonwandering set changes from the empty set to an unstable Cantor set on which the map is topologically equivalent to the shift endomorphism on two symbols. With the help of some numerical work, we trace the genealogies of the periodic points of the family of period 5, and describe their stability types and bifurcations. Among our results we find that the family has a fixed point which undergoes fold, flip and Hopf bifurcations, and that certain families of period five points are interconnected through a codimension-two cusp bifurcation. 相似文献