We consider region of interest (ROI) tomography of piecewise constant functions. We prove that continuous ROI data determine piecewise constant functions. Additionally, an algorithm is developed for ROI tomography of piecewise constant functions using a Haar wavelet basis. A weighted `p–penalty is used with weights that depend on the relative location of wavelets to the region of interest. We p...

We further consider the Galerkin method for advective-diiusive equations in two-dimensions. The nite dimensional space employed is of piecewise polynomials enriched with residual-free bubbles (RFB). We show that, in general, this method does not coincide with the SUPG method, unless the piecewise polynomials are spanned by linear functions. Furthermore a simple stability analysis argument displ...

Generalizations of the well-known simplex method for linear programming are available to solve the piecewise linear programming problem and the linear fractional programming problem. In this paper we consider a further generalization of the simplex method to solve piecewise linear fractional programming problems unifying the simplex method for linear programs, piecewise linear programs, and the...

A biochemical network can be simulated by a set of ordinary differential equations (ODE) under well stirred reactor conditions, for large numbers molecules, and frequent reactions. This is no longer robust representation when some molecular species are in small reactions changing them infrequent. In this case, discrete stochastic events trigger changes the smooth deterministic dynamics network....

We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and Gδ-piecewise continuity. Our aim is to understand how a priority argument in computability theory is connected to the notion of Gδ-piecewise continuity, and then we utilize this connection to obtain separation results on subclasses of Gδ-piecewise continuous reductions for unif...

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the...

In this paper, an approximate solution of sensitivity matrix of required velocity with final velocity constraint is derived using a piecewise linear gravity assumption. The total flight time is also fixed for the problem. Simulation results show the accuracy of the method. Increasing the midway points for linearization, increases the accuracy of the solution, which this, in turn, depends on the...

Most image smoothing filters in the literature assume a piecewise constant model of smoothed output images. However, the piecewise constant model assumption can cause artifacts such as gradient reversals in applications such as image detail enhancement, HDR tone mapping, etc. In these applications, a piecewise linear model assumption is more preferred. In this paper, we propose a simple yet ver...