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...

Aim : To assess the importance of continuity of care among diabetic patients attending a primary care clinic and to correlate degree of continuity of care with diabetic control. Methods : A cross sectional survey was carried out among diabetic patients ( n = 166) attending followup consultations in a family practice clinic of a teaching hospital. Face-to-face interviews were carried out on pati...

In this paper we show that the best constrained degree reduction of a given Bézier curve f of degree from n to m with Cα−1-continuity at the boundary in L2-norm is equivalent to the best weighted Euclidean approximation of the vector of Bernstein–Bézier (BB) coefficients of f from the vector of degree raised BB coefficients of polynomials of degree m with Cα−1-continuity at the boundary.  2003...

In this paper, I discuss a method for increasing the continuity between two polynomial patches by adjusting their control points. The method described in this paper leaves the control points unchanged if the patches already meet with the desired level of continuity. Next I give two C degree n polynomial interpolation schemes that reproduce degree n polynomials, and show how to apply my continui...

In this paper, we consider multi-degree reduction of Bézier curves with constraints of endpoints continuity with respect to L2 norm. The control points of the degree reduced Bézier curve can be obtained as a product of the degree reduction matrix and the vector of original control points. We find an explicit form of the multi-degree reduction matrix for Bézier curve with constraints of endpoint...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

BackgroundThe purpose of this study was to quantitate the degree of left-to-right shunt in patients with secundum atrial septal defect (2o ASD) with the PISA method and compare the results with the usual continuity equation. Although the PISA method has been used extensively for the quantitative measurement of regurgitant severity and valve area in patients with valvular regurgitation and steno...

In this paper we present a novel approach to consider the multi-degree reduction of Bézier curves with G2-continuity in L2norm. The optimal approximation is obtained by minimizing the objective function based on the L2-error between the two curves. In contrast to traditional methods, which typically consider the components of the curve separately, we use geometric information on the curve to ge...