Kirchhoo migration operator is a highly oscillatory integral operator. In our primary work 1] (Wu and Yang, 1997), it has been shown that the matrix representation of Kirchhoo migration operator for homogeneous background in space-frequency domain is a dense matrix, while the compressed operator in beamlet-frequency domain, which is the wavelet decomposition of the Kirchhoo migration operator, ...

Wave-equation migration velocity analysis is based on the linear relation that can be established between a perturbation in the migrated image and the corresponding perturbation in the slowness function. Our method formulates an objective function in the image space, in contrast with other wave-equation tomography techniques which formulate objective functions in the data space. We iteratively ...

we discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of kirchhoff type [ u_{tt}-phi (x)||nabla u(t)||^{2}delta u+delta u_{t}=|u|^{a}u,, x in mathbb{r}^{n} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $n geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $l^{n/2}(mathb...

where the limit is taken in the strong operator topology (see e.g. Goldstein [G, Theorem 8.12.] or ChernofF [C] for a comprehensive treatment of product formulas). Now let P G £ (E) be a contractive projection. Then we may consider P as a constant degenerate semigroup on E. It is interesting to know under which circumstances the limit in (1) exists if we replace e by P. More precisely, we ask f...

Consider additive functionals of a Markov chain Wk , with stationary (marginal) distribution and transition function denoted by π and Q, say Sn = g(W1) + · · · + g(Wn), where g is square integrable and has mean 0 with respect to π . If Sn has the form Sn =Mn + Rn, where Mn is a square integrable martingale with stationary increments and E(R2 n) = o(n), then g is said to admit a martingale appro...

In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems with Neumann Boundary conditions, which involves general variable exponent elliptic operator critical growth. Under some suitable conditions on the nonlinearities, establish existence and multiplicity solutions for problem by using concentration-compactness principle Lions exponents mountain pass theor...

Abstract Consider additive functionals of a Markov chain Wk, with stationary (marginal) distribution and transition function denoted by π and Q, say Sn = g(W1) + · · ·+ g(Wn), where g is square integrable and has mean 0 with respect to π. If Sn has the form Sn = Mn + Rn, where Mn is a square integrable martingale with stationary increments and E(R 2 n) = o(n), then g is said to admit a martinga...