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who introduced me to time series analysis and much more besides Abstract This thesis is about sampling theory and methods for analysing signals that have been sampled at irregularly spaced points. Irregular sampling may arise naturally (examples of its occurrence may be found in geophysics, tomography, astronomy, and laser anemometry). In many cases it(More)
The area swept out under a one-dimensional Brownian motion till its first-passage time is analysed using a Fokker-Planck technique. We obtain an exact expression for the area distribution for the zero drift case, and provide various asymptotic results for the non-zero drift case, emphasising the critical nature of the behaviour in the limit of vanishing(More)
Let s(N) denote the edge length of the smallest square in which one can pack N unit squares. A duality method is introduced to prove that s(6) = s(7) = 3. Let n r be the smallest integer n such that s(n 2 + 1) ≤ n + 1/r. We use an explicit construction to show that n r ≤ 27r 3 /2 + O(r 2), and also that n 2 ≤ 43. 1. Introduction. Erd˝ os and Graham [1](More)
We derive , the joint probability density of the maximum) , (m t M P M and the time at which this maximum is achieved, for a class of constrained Brownian motions. In particular, we provide explicit results for excursions, meanders and reflected bridges associated with Brownian motion. By subsequently integrating over m t M , the marginal density is(More)
We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function U (a, b, z). By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the nth coefficient is expressed as the (n(More)
— A new quasi-two-dimensional (Q2D) model is described for microwave laterally diffused MOS (LDMOS) power transistors. A set of one-dimensional energy transport equations are solved across a two-dimensional cross-section in a "current-driven" form. This process-oriented nonlinear model accounts for thermal effects, avalanche breakdown and gate conduction.(More)
We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework.(More)
A detailed study is undertaken of the v{max}=1 limit of the cellular automaton traffic model proposed by Nagel and Paczuski [Phys. Rev. E 51, 2909 (1995)]. The model allows one to analyze the behavior of a traffic jam initiated in an otherwise freely flowing stream of traffic. By mapping onto a discrete-time queueing system, itself related to various(More)
Normalized functionals of first passage Brownian motion and a curious connection with the maximal relative height of fluctuating interfaces Abstract Direct variational methods are used to find simple approximate solutions of the Thomas–Fermi equations describing the properties of self-gravitating radially symmetric stellar objects both in the(More)
A theoretical study is undertaken of the dynamics of a ball which is bouncing inelastically on a randomly vibrating platform. Of interest are the distributions of the number of flights nf and the total time tauc until the ball has effectively "collapsed," i.e., coalesced with the platform. In the strictly elastic case both distributions have power law tails(More)