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1. Introduction In this paper we study non-negative smooth solutions of the conformally invariant equation in a punctured ball, B,(O) \ (0) c R " , n 2 3, with an isolated singularity at the origin. The model equation (1.1) arises in many physical contexts but its greatest interest in recent years lies in its relation to the Yamabe problem. From this(More)
31 as a sum of scaled versions of the measure dx=x 2 on intervals 0; a], and this proves the theorem. QED Recall that the Cauchy distribution is innnitely divisible with Levy measure dx=jxj 2. This is why we call the random variables deened by C1 jxj 2 dx 0;a] `Cauchy-like'. In fact, it is easy to see that these have C 1 distribution functions. This follows(More)
The question of symmetry in nonlinear partial differential equations has been the subject of intensive investigations over the past 25 years. The general theme is the following. Suppose the domain ft, as well as the boundary condition on dft, has some symmetry, for example radial symmetry, axial symmetry or symmetry with respect to some hyperplane. Do(More)
This thesis introduces a syntactic and probabilistic approach to pattern recognition based on the use Compositional Grammars and Compositional Distributions. Such grammars are related in spirit to the constraint-based grammar formalisms now popular in linguistics. Analytic deenitions and some basic properties of several classes of compositional grammars and(More)
We present a new algorithmic procedure for the classiication and clustering of the En-glish six stop consonants /p, t, k, b, d, g/ on the basis of CV (Consonant-Vowel) or VC syllables. The central diiculties of the stop consonant problem lie in the nonstationary and nonlinear statistical structures of the acoustic signal in the burst and transition regions.(More)
In this thesis we restrict ourselves to stationary and discrete valued stochastic processes. A pair of stochastic processes (X, Y) is a Hidden Markov Model (HMM) if X (the state process) is a Markov process and Y (the observable process) is an incomplete observation of X. The observation can be deterministic or noisy and the observable can be a state or a(More)