Some necessary and sufficient conditions are given for the existence of a G-positive (G-repositive) solution to adjointable operator equations $AX=C,AXA^{left( astright) }=C$ and $AXB=C$ over Hilbert $C^{ast}$-modules, respectively. Moreover, the expressions of these general G-positive (G-repositive) solutions are also derived. Some of the findings of this paper extend some known results in the...

One-pass three-dimensional (3-D) depth migration potentially offers more accurate imaging results than does conventional two-pass 3-D migration for variable velocity media. Conventional one-pass 3-D migration, using the method of finite-difference inline and crossline splitting, however, creates large errors in the image of complex structures. These errors are due to paraxial wave-equation appr...

We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups...

The numerical solution of the one-dimensional nonlinear Klein-Gordon equation on an unbounded domain is studied in this paper. Split local absorbing boundary (SLAB) conditions are obtained by the operator splitting method, then the original problem is reduced to an initial boundary value problem on a bounded computational domain, which can be solved by the finite difference method. Several nume...

In this article we present a fuzzy logic based method for the construction of thoughts of artificial animals (animats). Due to the substantial increase of the processing power of personal computers in the last decade there was a notable progress in the field of animat construction and simulation. Regardless of the achieved results, the coding of the animat’s behaviour is very inaccurate and can...

We present an explicit second-order-accurate Godunov finite difference method for the solution of the equations of solid mechanics in one, two, and three spatial dimensions. The solid mechanics equations are solved in nonconservation form, with the novel application of a diffusion-like correction to enforce the gauge condition that the deformation tensor be the gradient of a vector. Physically ...