under suitable assumptions on their covariance structure (see Louhichi [7] and Oliveira and Suquet =-=[11, 12]-=- for the best known results on the covariance decrease rates for the convergence in D[0, 1], L2[0, 1] or Lp[0, 1], respectively), Zn converges weakly to a centered ...
Let {mN,t}N∈N be the 1-particle Husimi measure; then, there exists a subsequence {mNj,t}j∈N that converges weakly in L1(R3 × R3) to a function (2π)3mt; i.e., for all Φ∈ L∞(R3 × R3), it holds that 1 (2π)3 dqdp mNj,t(q, p)Φ(q, p) → dqdp mt(q, ...
We say that a family of functions {f h ∈ L2(Ω(h)) : h > 0} converges strongly in L2(Ω(h)) to a function f 0 ∈ L2(ω), as h → 0, if f h converges to f 0 weakly in L2(Ω(h)), and lim h→0 1 h fh; L2(Ω(h)) 2 = S0 f0; L2(ω) 2. Theorem 3. 1...
weakly-quasi-first-countablesigma-compact frontierWe consider the numerical solution of the first-order-system version of the Tricomi problem. A new Galerkin method, using differing spaces of test and trial functions, is presented. We show that the error in the L2 norm is O(hk) if finite ...
Quasicontinuum modelling of short-wave instabilities in crystal lattices We propose a hybrid quasicontinuum model which captures both long and short-wave instabilities of crystal lattices and combines the advantages of weakly no... L Truskinovsky,A Vainchtein - 《Philosophical Magazine》 被引量: 31...
This implies that {xn} converges weakly to q. The proof of Theorem 1 is completed. 2 Proof of Theorem 2. Taking γn = 0, ∀n 1, and βn = 1 − αn, ∀n 1, in Theorem 1, then the conclusion of Theorem 2 can be obtained from Theorem 1 immediately. 2 Proof of Theorem ...
Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fr... The use of these transformations resulted in increasing the order of convergence of the trapezoidal and the midpoint quadrature rule. In this ...
Very recently, Assani claimed the convergence for weakly mixing transformations [2]. The study of the limiting behavior of the averages along cubes was initiated by Bergelson in [5], where convergence in L2(µ) was shown in dimension 2. Bergel- son's result was later extended by Host ...
Observations over the last few decades from a number of orogenic systems have highlighted the possible importance of tectonic exhumation, i.e., ductile thinning and normal faulting, in exhuming rocks once buried in high-pressure conditions. Taiwan is one of the few active orogens in the world ...
Choosing yn so that |yn| →∞ it is not difficult to realize that the sequences {φn±}∞n=1 con- verge weakly towards 0 in L2(R3): This follows from the fact that they are translations of a fixed L2-function. With such sequence of yn's we get thus (φ, ψ), vn = φ, ...