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Published in Nirdosh Bhatnagar, Introduction to Wavelet Transforms, 2020
The ultimate performance of the learning algorithm depends upon the following: The points in the training data set D are not too noisy.The size of the data set |D| is sufficiently large.The selected wavelet ψ (·) and its modifications are good enough to model the function f (·).
DC Transport Critical Currents
Published in David A. Cardwell, David C. Larbalestier, Aleksander I. Braginski, Handbook of Superconductivity, 2022
In most metallic superconductors, the coherence length ξ is sufficiently large for the superconducting wave function to extend right through ‘intrinsic’ imperfections such as metallurgical grain boundaries or small amounts of secondary phases, and this type of dissipation is absent. In oxide superconductors, on the other hand, the coherence length is much smaller and the wave function is strongly depressed at imperfections. This causes these materials to be much more susceptible to junction-related dissipation, especially at grain boundaries. Figure G2.3.14(b) shows the transition of a bulk untextured YBa2Cu3O7 sample (Wördenweber et al., 1988). At higher current levels the sample retains ∼40% of its normal-state resistance even at the lowest temperatures. Figure G2.3.14(c) shows the field-induced transition of a similar sample measured at several temperatures in a pulsed magnetic field (Boon et al., 1989). A temperature-independent resistance of ∼10% of the normal-state value develops well before the main transition. In subsection G2.3.6 we will see how such residual resistance can be described with a simple model.
Review of The Theory of Stochastic Modelling of Subsurface Porous Flow and Transport
Published in Amro M.M. Elfeki, Gerard J.M. Uffink, Frans B.J. Barends, Groundwater Contaminant Transport, 2017
Amro M.M. Elfeki, Gerard J.M. Uffink, Frans B.J. Barends
Ergodicity is a statistical property which implies that the statistics of a single realization in space (spatial statistics) are equivalent to the ensemble of all possible realizations (ensemble statistics). In other words, by observing the variability in space of a property from one realization in enough detail, it is possible to determine the probability distribution function of the random process for all possible realizations. This equivalence is achieved when the size of the space domain is sufficiently large or tends to infinity.
Confidence regions of stochastic variational inequalities: error bound approach
Published in Optimization, 2022
Let be a sequence of solutions to SAA-SVIP (8) and S be the set of solutions to SVIP (3). Suppose that the error bound condition (11) holds with residual function . Suppose further that the corresponding residual function 7 for SAA-SVIP (8) converges to uniformly on with probability one (w.p.1). Then the limit point of sequence is a solution to SVIP (3) w.p.1;there exists a sufficiently large such that, for any , w.p.1.
New algorithms for the split variational inclusion problems and application to split feasibility problems
Published in Optimization, 2019
Luong Van Long, Duong Viet Thong, Vu Tien Dung
Let be a sequence of nonnegative real numbers such that there exists a subsequence of such that Then there exists a non-decreasing sequence of such that and the following properties are satisfied by all (sufficiently large) number In fact, is the largest number n in the set such that
Split common fixed point problem for demimetric mappings and Bregman relatively nonexpansive mappings
Published in Optimization, 2022
Let be a sequence of real numbers such that there exists a subsequence of such that for all Then there exists a subsequence such that and the following properties are satisfied by all (sufficiently large) numbers In fact,