Copson, E. T., Metric Spaces, Cambridge University Press, Cambridge, 1968. Home/Search Document Not in Database Summary Related Articles Check |
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Global Attractors in Partial Differential Equations - Raugel (Correct)
....weakly damped dispersive equations, the prototype of which is the weakly damped Schr odinger equation. Many topics have been left on the side, including the non autonomous evolutionary equations leading to the notions of processes and skew product semi ows (see [Da75] Sell71] MiSe] Har91] [Vi92], ChVi1] etc : the generalization of the concept of attractor to multivalued mappings (see [Ba2] for instance) the notion of random attractors for dissipative stochastic dynamical systems (see [CFl] Deb] for basic properties) Only few applications to the class of retarded functional ....
....with much weaker concepts of comparison, like estimates of the Hausdor distance between the global attractors. We shall mainly give general comparison results and refer the reader to Section 4 and to [BV89b] Hal88] Hal98] HLR] HR89] HR90] HR92b] HR93b] Ko90] Ra95] ST] and [Vi92] for applications to (singularly) perturbed systems and discretised equations. In this paragraph, X; d) still denotes a metric space and we consider a family of semigroups S (t) t 2 G , depending on a parameter 2 , where = d ) is a metric space. For sake of clarity, we assume ....
M. I. Vishik: Asymptotic Behaviour of Solutions of Evolutionary Equations, Lezioni Lincee, Cambridge University Press (1992).
Some Approximate Methods For Computing Electromagnetic .. - Chiappetta.. (Correct)
....for (r) inside the scatterer, as follows. Expressing the integration variable r 00 in (37) in polar coordinates r 00 (r 00 ; 00 ; OE 00 ) set 00 = cos 00 . For the integration wrt , note that the integral is an oscillatory one. Using the integration by part lemma (see e.g. [55]) it is readily seen that up to terms of higher order in 1= kr 00 ) the integral is dominated by the contributions of integration bounds 00 = Sigma1. In addition, the bound 00 = Gamma1 gives rises to another oscillatory integral when integrating wrt r 00 . Therefore at first order, ....
E. Copson (1965): Asymptotic expansions, Cambridge University Press.
State-of-the-Art in Shape Matching - Veltkamp, Hagedoorn (1999) (27 citations) (Correct)
....transformation group that corresponds to the matching problem. Below, we discuss a number of properties of metrics, such as invariance for transformation groups. Let S be any set of objects. A metric on S is a function d : S S R satisfying the following three conditions for all x; y; z 2 S [Cop68] i) d(x; x) 0; ii) d(x; y) 0 implies x = y; iii) triangle inequality) d(x; y) d(x; z) d(y; z) If a function satis es only (i) and (iii) then it is called a semimetric. Symmetry follows from (i) and (iii) d(y; z) d(z; y) d(z; z) d(z; y) and d(z; y) d(y; z) d(y; y) ....
E. T. Copson. Metric spaces. Cambridge University Press, 1968.
The Change Set Problem. Part 1: Estimation of the.. - Khmaladze.. (Correct)
....the exponent attains its maximum at t = 1=2 and ( p t p 1 Gamma t) 00 t=1=2 = Gamma 1 p 2 . Therefore for L 1 the last integral is asymptotically equivalent to e 4 p 3 p L Z 1 0 e Gamma p L 3 (t Gamma 1 2 ) 2 dt 3 L 1=4 e 2 p 3 p L (see, e.g. Copson (1965), p.42) and, consequently L X L 0 =0 p(L 0 )p(L Gamma L 0 ) 3 1=4 L 3=4 e 2 p 3 p L (1 o(1) L 1 : Now taking a sum in L of the leading term on the right hand side of this inequality we obtain X Lt=ffi 2 3 1=4 L 3=4 e 2 p 3 p L 3 1=4 t 3=4 ffi ....
.... 2 3 1=4 L 3=4 e 2 p 3 p L 3 1=4 t 3=4 ffi 3=2 Z 1 0 z 3=4 e 2 p 3 t 1=2 ffi z 1=2 dz = 3 1=4 t 3=4 ffi 3=2 2 Z 1 0 s 5=2 e 2 p 3 t 1=2 ffi s ds 3 3=4 t 1=4 ffi 1=2 e 2 p 3 t 1=2 ffi (1 o(1) t=ffi 2 1 (see, e.g. Copson (1965), p.39) With similar though more elaborate technique we could obtain an upper bound for N ffi (t; f 2 ) which will reveal again quite different rate of N ffi (t; f 1 ) and N ffi (t; f 2 ) This will lead to different constants in the upper bound for n depending on f . Thus further work is ....
Copson, E. T., Asymptotic Expansions, Cambridge University Press, 1965.
Quantifying Olfactory Perception - Mamlouk (2002) (Correct)
No context found.
Copson, E. T., Metric Spaces, Cambridge University Press, Cambridge, 1968.
Measuring Resemblance of Complex Patterns - Hagedoorn, Veltkamp (1999) (Correct)
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E.T. Copson. Metric spaces. Cambridge University Press, 1968.
A Robust Ane Invariant Metric on Boundary Patterns - Hagedoorn, Veltkamp (1999) (Correct)
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E.T. Copson. Metric spaces. Cambridge University Press, 1968.
Metric Pattern Spaces - Hagedoorn, Veltkamp (1999) (Correct)
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E.T. Copson. Metric spaces. Cambridge University Press, 1968.
Pole Dynamics And Oscillations For Complex Burgers.. - Senouf, Caflisch.. (Correct)
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E.T. Copson, Asymptotic Expansions, Cambridge University Press, 1965. 22 D. SENOUF, R. CAFLISCH and N. ERCOLANI
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