the conditional probability of finding a particle at position x after time t with the particle located for t ϭ 0 at x ϭ 0. In Fig. 3A, we show the result of p(x, t) for ⌫ ϭ 4 at four different times, which are all greater than t c. Self-diffusion of particles causes p(x, t) to broaden with time. Despite the simplicity of the physical situation describing SF… (More)
One-way wave operators are powerful tools for forward modeling and inversion. Their implementation, however, involves introduction of the square-root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel-times of the full wave equation, but do not… (More)
We state a general principle for seismic migration/inversion (M/I) processes: think image point coordinates; compute in surface coordinates. This principle allows the natural separation of multiple travel paths of energy from a source to a reflector to a receiver. Further, the Beylkin determinant (Jacobian of transformation between processing parameters and… (More)
In the title compound, C(9)H(11)NO(3), the oxime grouping is twisted by 12.68 (6)° with respect to the dimethoxyl-benzene ring. In the crystal, mol-ecules are linked into an infinite  chain via O-H⋯N hydrogen bonds, instead of the more common oxime packing motif of dimers with an R(2) (2)(6) graph-set motif.
In the title compound, C(13)H(17)NO, the cyclo-hexane ring adopts a chair conformation and the amide C(=O)-N moiety is almost coplanar with the phenyl ring [C-N-C-O = 4.1 (2)°]. In the crystal, mol-ecules are linked to form a C(4) infinite  chain via N-H⋯O hydrogen bonds, unlike the cyclic motif seen in related structures.
The title compound, [Sb(C(5)H(10)NS(2))(3)], was synthesized from Sb(2)O(3), diethyl-amine, carbon dis-ulfide, hydro-chloric acid and sodium hydroxide. The structure has been published previously but H atoms were not included in the model [Raston & White (1976 ▶). Chem. Soc. Dalton Trans. p. 791]. The current determination has significantly higher precision… (More)
Currently used one-way wave equations in depth fail at horizontal propagation. One-way wave equations in time do not have that shortcoming; they are omni-directional in space. In these equations, spatial derivatives appear in a pseudo-differential operator—the square root of the Laplacian. With an appropriate definition of this operator, we have proved via… (More)