We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The are given in terms convolution, our proposed numerical approach is not only super-algebraically convergent, but it also satisfies an important property convolution—namely, preservation bandwidth. Furthermore, accuracy depends how well source field approx...

Introduction: Hadamard-encoded (H-encoded) fMRI [1] is a method that acquires a slab of multiple subslices with each RF excitation [2]. The subslices can then be extracted using temporal filtering, analogous to UNFOLD [3]. By setting the subslice width equal to that of a conventional fMRI scan, SNR is increased because of the larger slab thickness. However, since H-encoding uses complex data fo...

A general theory is given for discretized versions of the Galerkin method for solving Fredholm integral equations of the second kind. The discretized Galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the Galerkin method. The theoretical framework that is given parallels that of the regular Galerkin method, including the error analysis of the sup...

A lower bound on the sinc function is given. Application for the sequence {b(n)}(n=1)(∞) which related to Carleman inequality is given as well.

Prolate spheroidal wave functions have recently attracted much attention in applied harmonic analysis, signal processing, and mathematical physics. They are eigenvectors of the sinc-kernel operator Qc: time- band-limiting operator. The corresponding eigenvalues play a key role, aim this paper is to obtain precise non-asymptotic estimates with explicit constants related spectrum Qc. This issue r...

The sinc method is known as an ecient numerical method for solving ordinary or par-tial dierential equations but the system of dierential equations has not been solved by this method which is the focus of this paper. We have shown that the proposed version of sinc is able to solve sti system while Runge-kutta method can not able to solve. Moreover, Due to the great attention to mathematical mod...

a new approach for analyzing cracked problems in 2d orthotropic materials using the well-known element free galerkin method and orthotropic enrichment functions is proposed. the element free galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. in this study, element free galerkin is extrinsically enriched by the recently developed crack-tip orthot...