منابع مشابه
Monodromy problem for the degenerate critical points
For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...
متن کاملMultiple points of the Brownian sheet in critical dimensions
It is well-known that an N -parameter d-dimensional Brownian sheet has no k-multiple points when (k − 1)d > 2kN , and does have such points when (k− 1)d < 2kN . We complete the study of the existence of k-multiple points by showing that in the critical cases where (k − 1)d = 2kN , there are a.s. no k-multiple points. Abbreviated title: Multiple points of the Brownian sheet
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Abstact: Let B be a Brownian motion in R d , d = 2; 3. A time t 2 0; 1] is called a cut time for B0; 1] if B0; t) \ B(t; 1] = ;: We show that the Hausdorr dimension of the set of cut times equals 1 ? , where = d is the intersection exponent. The theorem, combined with known estimates on 3 , shows that the percolation dimension of Brownian motion (the minimal Hausdorr dimension of a subpath of a...
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Uncovering DNA sequence variations that correlate with phenotypic changes, e.g., diseases, is the aim of sequence variation studies. Common types sequence variations are Single nucleotide polymorphism (SNP, pronounced snip).SNPs are the third-generation molecular marker. SNP represents a DNA sequence variant of a single base pair with the minor allele occurring in more than 1% of a given popula...
متن کاملSlow kinetics of Brownian maxima.
We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t and find the algebraic decay P ∼ t(-β) with exponent β = 1/4. When the two particles have diffusion constants...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 1996
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s004400050039