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*North-Holland*

"... We study the reaction front for the diffusion-reaction system A + B + C with initially separated reactants. We present analytical results for the form of the front and the exponents that characterize its width and height asymptotically, which appear to hold in d Z = 2. We also present analytical and ..."

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We study the reaction front for the diffusion-reaction system A + B + C with initially separated reactants. We present analytical results for the form of the front and the exponents that characterize its width and height asymptotically, which appear to hold in d Z = 2. We also present analytical and numerical results for the form of the reaction front for the 1D case in which one of the reactants is static, and find the width exponent (Y = l/4, which is larger than the mean field exponent (CI = 116) but smaller than the value for the case in which both species diffuse (a = 0.3). Recently there has been considerable interest in the study of the irreversible reaction A + B+ C (inert) in which the reactants are transported by diffusion and are initially separated in space [l-9]. Under these conditions the system is characterized by a “reaction front ” that develops at the interface between the two reactants, and that is marked by the presence of the inert C particles. The time evolution of the reaction front is usually characterized by two exponents, (Y and p, that describe how its width (w- t”) and height (h- t-P) vary asymptotically with time. Galfi and Racz [l], using “mean field ” argu-ments, found scaling relations for these two exponents for the case in which both reactants move, which give the values (Y = 116 and /? = 2/3. These exponents have been confirmed experimentally [8] and numerically [2,4, 81. More recently, the explicit form of the front was obtained analytically [7] as the solution of the mean field reaction-diffusion equations believed to describe the system. It was found that the reaction front R(x, t) had the form (see fig. 1) R(x, t)- t-2i3($)3’4exp[-; (&!?!)3’2] ; (1) in the region t”‘lh < (x1-c t”2/a, where A and a are constants that depend on the details of the system. This form, which is consistent with the mean field

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*North-Holland*

, 1985

"... Intrinsic character&tics as the interface CAD and machine v&ion systems between ..."

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Intrinsic character&tics as the interface CAD and machine v&ion systems between

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*North-Holland*

, 1990

"... Over-rejections in rational expectations models A non-parametric approach to the Ma&w-Shapiro problem * ..."

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Over-rejections in rational expectations models A non-parametric approach to the Ma&w-Shapiro problem *

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*North-Holland*

, 1988

"... Strongly regular pk-circulants, where p is a prime number, are characterised and a representation of Paley graphs of order p * as metacirculants is given. 1, Induction All the graphs and digraphs considered in this paper are finite. By p we shall always denote a prime number. If S is a subset of Z,, ..."

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Strongly regular pk-circulants, where p is a prime number, are characterised and a representation of Paley graphs of order p * as metacirculants is given. 1, Induction All the graphs and digraphs considered in this paper are finite. By p we shall always denote a prime number. If S is a subset of Z,,, the ring of residue classes modulo n, and j E Z,, we let jS={js:sES} and S+j={s+j:seS}. If S=-S we say that S issymmet& and if S n-S = # we say that S is antisymmetic. Let S c 2, \ (0). The n-dicirculant G(n, S) with a symbol S is the digraph with vertex-set {u,, ul,..., u,,-1) and Ui+Uj if and only if j-i ES where all arithmetic is done modulo n. (Note that n-dicirculants are precisely the Cayley digraphs of a cyclic group of order n.) If S is symmetric, then G(n, S) is a graph. We call it an n-circulant graph or simply an n-circulant. (Also, Ui- Uj if and only ifj-itzS.) If G is a graph and Y E V(G), then N(V) = {u E V(G) : u- v} denotes the set of neighbors of V. If 1 V(G) 1 = n, then G is an n-graph. A (k, A, &-strongly regular graph in a k-regular graph G such that: (i) the number il of 3-cliques K3 in G containing a given edge is independent of the choice of edge and (ii) the number p of 2-claws & in G containing a given nonedge is independent of the choice of nonedge. The numbers il and y are called the intersection numbers of G. A strongly regular graphs is trivial if either G or G ” is disconnected and is nontrivial otherwise. Clearly, a strongly regular graph is disconnected if and only if p = 0 in which case G is a disjoint union of isomorphic complete graphs. Moreover, the complement of a strongly regular graph is strongly rp?ular too. Proposition 1.1 [3, p. 1451. Let G be a (k, A, p)-strongly regular n-graph. Then G ” is (k’, A’, u’)-strongly regular where 0 k-k-l, A’=n-2k-2+p, p’=n-2k+A, (ii) k;k=-“n- 1) = pk ’ and (iii) G is nontrivial if and only if p # 0, k.

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*North-Holland*

, 1988

"... Rate distortion lower bound for a of nonlinear estimation problems special class ..."

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Rate distortion lower bound for a of nonlinear estimation problems special class

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*North-Holland*

, 1983

"... Abstract: A hierarchical three-stage syntactic recognition algorithm using context-free grammars is described for automatic identification of skeletal maturity from X-rays of hand and wrist. The primitives considered are dot, straight line and arcs of three different curvatures (including both sense ..."

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Abstract: A hierarchical three-stage syntactic recognition algorithm using context-free grammars is described for automatic identification of skeletal maturity from X-rays of hand and wrist. The primitives considered are dot, straight line and arcs of three different curvatures (including both senses) in order to describe and interpret the structural development of epiphysis and metaphysis with growth of a child. Key words: Syntactic pattern recognition, X-ray iJT1age. 1. Introduction The

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*North-Holland*

"... By mapping nucleotide sequences onto a “DNA walk”, we uncovered remarkably longrange power law correlations [Nature 356 (1992) 1681 that imply a new scale invariant property of DNA. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences, but ..."

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By mapping nucleotide sequences onto a “DNA walk”, we uncovered remarkably longrange power law correlations [Nature 356 (1992) 1681 that imply a new scale invariant property of DNA. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences, but not in cDNA sequences or intron-less genes. In this paper, we present more explicit evidences to support our findings. The DNA walk (see ref. [la]) # ’ is defined by the rule that the walker steps up (u(i) = + 1) if a pyrimidine occurs at position a linear distance i along the DNA chain, while the walker steps down (u(i) =-1) if a purine occurs at position i. The trajectories of the DNA walk, defined as y(l) = Cf,l u(i), produce a contour reminiscent of the irregular fructul landscapes (see fig. la) that have been widely studied in physical systems [2]. A quantitative characterization of such a “landscape ” is the mean fluctuation function F(Z), defined as F2(Z) = [Ay(l)- Ay(1)] * = [Ay(Z)12-B, (1) of a quantity Ay(Z) defined by A.y(l) = ~(4, + 0- ~(4,). (2) Here the bars indicate an average over all positions I, in the gene. If the nucleotides are uncorrelated or only short-range correlated (i.e., with a characteristic correlation length), then F(Z)- Z1 ” (as expected for a normal * ’ Long-range correlations in non-coding regions of DNA were reported independently by Li

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*North-Holland*

"... It is generally considered that for a so-called normal system dissipation decreases tunneling rates. Here we show that at least oneexample of anormal heatbath, the blackbody radiation field, leads toan increase in tunneling. Thereason forthis exception to the general rule is thepresence of mass reno ..."

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It is generally considered that for a so-called normal system dissipation decreases tunneling rates. Here we show that at least oneexample of anormal heatbath, the blackbody radiation field, leads toan increase in tunneling. Thereason forthis exception to the general rule is thepresence of mass renormalization. The pioneering work of Caldeira and Leggett [1] gevin equation. This is the Heisenberg equation of on the effect ofdissipation on quantum tunneling has motion for a dynamical variable x(t) and takes the generated an extensive literature. It is generally form [5] thought that tunneling rates decreasein the presence of so-called normal coupling to the environment. Al-though it is possible to construct models for which tnic+ J dt ’ Au(t—t’)~(l’)+V’(x) the tunneling rates increase [3,4], such models are generally unphysical, and Leggett has used the term =F(t) +f ( t), (1) “anomalous dissipation ” to characterize them [4]. Our purpose here is to show that the blackbody ra- where the dot indicates the time derivative and diation field is an example of a normal dissipative V ’ = 8 V/8x. On the right-hand side F ( t) is a random system for which the coupling increases the tunnel- operator force with vanishingmean, <F(t)> = 0, and

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*North-Holland*

, 1990

"... A simple proof of Liang’s lower bound for on-line bin packing and the extension to the parametric case ..."

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A simple proof of Liang’s lower bound for on-line bin packing and the extension to the parametric case