Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided differences at the knots. Direct algorithms and recurrence relations are proposed for constructing discrete generalized B-splines (discrete GB-splines for short). Properties of discrete GB-splines and their series are studied. It is shown that discrete G...

The McCarran-Ferguson Act provides a limited exemption to the insurance industry from the federal antitrust laws. The act provides that the Sherman Act, the Clayton Act, and the Federal Trade Commission Act apply to the business of insurance "to the extent that such business is not regulated by state law." That limited exemption from federal antitrust law does not extend to "any agreement to bo...

The Bomhuetter/Fergnason loss reserving method consists of selecting a development pattern and, for each accident year, an initial ultimate loss ratio. From these, the reserve estimate is derived. In this paper, the usual way to obtain the development pattern from the cl~in ladder link ratios is criticized because it assumes a multiplicat~ve connection between past and future loss amounts where...

The US Supreme Court case Ferguson v. City of Charleston (2001) established that public hospitals couldn't legally drug test pregnant women without their consent when those women sought prenatal care at those hospitals. The court held that such searches violated the pregnant women's protections under the Fourth Amendment to the US Constitution. The decisions also indicated those circumstances t...

This paper re-conceptualizes the relationship between Ferguson's life and work by locating him in his biographical and geographical context for the purposes of better understanding his proto-sociological writings. Ferguson's work is relatively unknown outside limited sets of literature and current representations of the link between his life and work risk misplacing him as both Scotsman and soc...

In science and engineering there often is a need for the approximation of scattered multi-dimensional data. A class of powerful scattered data approximators are the multivariate simplex B-splines. Multivariate simplex B-splines consist of Bernstein basis polynomials that are defined on a geometrical structure called a triangulation. Multivariate simplex B-splines have a number of advantages ove...

In this paper, we forecast ground level ozone concentrations over the USA, using past spatially distributed measurements and the functional linear regression model. We employ bivariate splines defined over triangulations of the relevant region of the USA to implement this functional data approach in which random surfaces represent ozone concentrations. We compare the least squares method with p...

This paper compares two techniques for the approximation of the offsets to a given planar curve. The two methods are based on approximate conversion of the planar curve into circular splines and Pythagorean hodograph (PH) splines, respectively. The circular splines are obtained using a novel variant of biarc interpolation, while the PH splines are constructed via Hermite interpolation of C boun...

Employing discrete B-splines instead of the Gaussian distribution, we construct an algorithm for the analysis of ionmobility spectrometry profiles. The algorithm is suitable for hardware implementation because the discrete B-splines are supported by a simple digital filter to compute their weighted sum and their correlations with a given signal. Minutely shifted discrete B-splines are deployed ...