It is correct that one can estimate the elevation angles by using [1, Eq. (25)], because the direction cosine relative to the z-axis v̂k only contains the information of the elevation angle ̂k . However, the elevation angle estimate ̂k and (̂2;x)kk in [1, Eq. (32)] are not one-to-one related to the direction cosines v̂k and ŵk (k = 1; 2; . . . ; K), respectively. Thus, the expression of [1, Eq. (...

A binary split tree is a search structure combining features of heaps and binary search trees. Building an optimal binary split tree was originally conjectured to be intractable due to di culties in applying dynamic programming techniques to the problem. However, two algorithms have recently been published which generate optimal trees in O(n5) time, for records with distinct access probabilitie...

We confirm the planetary nature of two gas giants discovered by TESS to transit M dwarfs with stellar companions at wide separations. TOI-3984 A ($J=11.93$) is an M4 dwarf hosting a short-period ($4.353326 \pm 0.000005$ days) giant ($M_p=0.14\pm0.03~\mathrm{M_{J}}$ and $R_p=0.71\pm0.02~\mathrm{R_{J}}$) separation white companion. TOI-5293 ($J=12.47$) M3 ($2.930289 0.000004$ ($M_p=0.54\pm0.07~\m...

Derivation of the self-consistent multimode laser equations. The Green function which forms the kernel of the fundamental self-consistent equation Eq. 1 has a non-hermitian spectral representation of the form (S1) G(x, x ′ ; k) = ∞ m=1 ϕ m (x, k) ¯ ϕ * m (x ′ , k) 2 k a (k − k m (k)). (S1) where the CF states ϕ m (x, k) satisfy the equation − 1 ǫ(x) ∇ 2 ϕ m (x, k) = k 2 m (k) ϕ m (x, k) (S2) wi...

where up in Eq. (2) corresponds to u(jôx, not) in Eq. (1), and where a = cSt/Sx. Here öt and Sx are the time and space intervals, respectively. We consider the case — co < x < », í > 0. It was shown by Courant, Friedrichs, and Lewy in a wellknown paper [1] that if up and u,x are prescribed for ally, then the computational process represented by Eq. (2) will yield values for w/ which converge to...

By single crystal NMR the nuclear quadrupole coupling constants eQ,.h~ (H), the asymmetry parameters >/(H) and the dircetion cosines of the principal axes of the electric field gradient tensors of the H atoms of the two kinds of D 2 0 molecules have been determined at 295 K in RbAl(S04)2 • 1 2 D 2 0 . The results show that the D 2 0 molecules surrounding the ion Al + are "static" within the ...