Three formulae connecting the spectral elements to the potential are derived for the tridimensional Schrdinger equation with spherical symmetry. They make apparent the natural character of the Marchenko inversio
The results are used in Section 6 to treat a host of optimal stopping problems with explicit solutions, and in Section 7 to discuss further consequences of the new characterization for the value functions. We address especially the smoothness of the value function and take a new look at the ...
A problem of many statistical learning approaches including boosting with early stopping is that despite regularization one often ends up with relatively rich models [17,40]. A lot of noise variables might be erroneously selected. To improve the selection process and to obtain an error control for...
whereVis the kernel of the Bessel potential\(\langle \nabla \rangle ^{-\beta }\)of order\(\beta > 0\).Footnote5In [48], the authors proved local well-posedness for\(\beta > 1\)by viewing the nonlinearity as the nested bilinear interactions and utilizing the paracontrolled operators int...
Cartilage repair in osteoarthritic patients remains a challenge. Identifying resident or donor stem/progenitor cell populations is crucial for augmenting the low intrinsic repair potential of hyaline cartilage. Furthermore, mediating the interaction betw
The different formulae for the selector statistic depending on the difference of the two group medians (positive or negative, within or without the tolerance region) ensure an appropriate sorting of the variables giving the procedure a high power. In the following sections, the Bonferroni-Holm ...
projected onto 12 bins [91]. The method takes into account the fact that pitch consists of two components: tone height and chroma [92,93]. The features represent the distribution of signal energy over chroma and time. The relationship between components can be defined by the following formula...
1.2. Recurrence of Simple RandomWalk. The formula for the ruin probability (Proposition 1) has an interesting qualititative consequence. Suppose we start a simple random walk at some integer x. By Proposition 1, the probability that we reach 0 before hitting A is 1−x/A, and so the pro...
Under the time theme of the energy crisis and environmental pollution, a great deal of attention has been devoted to the field of supercapacitors (SCs) for relieving this situation. Two-dimensional (2D) materials show great potential in various energy storage fields due to their unique and attrac...
For purposes of the present disclosure, the term “membrane” refers to layer acting as a selective barrier that may allow some elements to pass through but stopping others such as molecules, ions, or other small particles. For purposes of the present disclosure, the term “non-transient storag...