A surface-shrinking algorithm is demonstrated for automated source position localization one scattering depth into discretized simulation domains, in near-infrared imaging. The algorithm allows users to accurately place source fiber locations with minimal guidance. OCIS codes: (100.0100) Image Processing; (100.3010) Image Reconstruction Techniques

Put options are commonly used in the stock market to protect against the decline of the price of a stock below a specified price. On the other hand, finite difference approach is a well-known and well-resulted numerical scheme for financial differential equations. As such in this work, a new spatial discretization based on finite difference semi-discretization procedure with high order of accur...

Let $$X_N$$ be an N-dimensional subspace of $$L_2$$ functions on a probability space $$(\Omega , \mu )$$ spanned by uniformly bounded Riesz basis $$\Phi _N$$ . Given integer $$1\le v\le N$$ and exponent p\le 2$$ we obtain universal discretization for the integral norms $$L_p(\Omega ,\mu from collection all subspaces v elements with number m required points satisfying $$m\ll v(\log N)^2(\log v)^...