A collocation procedure is developed for the initial value problem u′(t) = f(t, u(t)), u(0) = 0, using the globally defined sinc basis functions. It is shown that this sinc procedure converges to the solution at an exponential rate, i.e., O(M2 exp(−κ √ M)) where κ > 0 and 2M basis functions are used in the expansion. Problems on the domains R = (−∞,∞) and R+ = (0,∞) are used to illustrate the i...

In this article we illustrate some novel procedures of using Sinc methods to compute solutions to three types of medical problems. The rst of these is a novel way to solve optimal control problems. the second is a novel way to reconstruct images for X-ray tomography, and the third is a novel way to do ultrasonic tomography inversion. Each of these procedures uses Sinc convolution, which is a no...

This paper presents the design of a low power sinc3 filter implementing a decimation factor by 16 and suitable for a second order !" modulators running at 256 MHz. The circuit uses the cascade of two stages and consumes only 48.1 μW, with 1.2 V voltage supply. The ultra-low power features come from both an architectural optimization and the use of suitable transistor level schemes. The circuit,...

V. M. Sloutsky and A. V. Fisher reported 5 experiments documenting relations among categorization, induction, recognition, and similarity in children as well as adults and proposed a new model of induction, SINC (similarity, induction, categorization). Those authors concluded that induction depends on perceptual similarity rather than conceptual knowledge. Despite the useful contributions of th...

A quick and accurate way to rotate and shift nuclear magnetic resonance (NMR) images using the two-dimensional chirp-z transform is presented. When the desired image grid is rotated and shifted from the original grid due to patient motion, the chirp-z transform can reconstruct NMR images directly onto the ultimate grid instead of reconstructing onto the original grid and then applying interpola...

Suppose that red and blue points occur as independent Poisson processes of equal intensity in R, and that the red points are matched to the blue points via straight edges in a translation-invariant way. We address several closely related properties of such matchings. We prove that there exist matchings that locally minimize total edge length in d = 1 and d ≥ 3, but not in the strip R × [0, 1]. ...

Internal self-diagnosis and external evaluation of the obtained results are of major importance for the relevance of any automatic system for practical applications. Obviously, this statement is also true for automatic image analysis in photogrammetry and remote sensing. Recently, automatic systems for the extraction of road networks reached a state in which a systematic evaluation of the resul...

We develop the basic theory of hod mice below the Largest Suslin Axiom (LSA), which says that the largest Suslin cardinal is a member of the Solovay sequence. We also prove comparison theorem for such hod mice in the context of AD+. This is the first paper in planned sequence of three papers that eventually will establish that Mouse Set Conjecture holds provided there is no inner model satisfyi...

There are a lot of comparisons concerning the selection of the best approach for tumours of the cavernous sinus. Many experienced authors stated that the approach must be tailored to the nature and the exact location of the tumour in the cavernous sinus and neighbouring structures 2,4,5,6,11,12,13. Although chondromas are considering to be true tumours of the cavernous sinus, because of the rar...

For nonlinear difference equations of the form xn F n, xn−1, . . . , xn−m , it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the form xn anxn−1 bnf xn−k , where {an}, {bn} are periodic sequences and f is a nonlinear filtering function, and show how periodic solutions can be constructed. Several examples are also included to illust...