To blend be~ween simple implicit surfaces, such as the sphere, the cone, the cylinder and the torus, we propose La locally employ the zero set of a serendipitous trivariate box spline. This box spline is defined by seven directions that form a regular partition of space into tetrahedra. The resulting blend surface is curvature continuous. An approxlmateparametrization of the piecewise implicit ...

The present time, denoted at n = 0 and the expiration time, denoted at n = N . The lower case letter n, k (and occasionally i, j,m) will be used to denote the time variable. The notation Sk (or Sn, Si, Sj · · · ) denotes the value of the stock (the underlying) at time k (or time n, i, j · · · ). An important convention we’ll use is that S0 will always be a constant, that is the present value of...

Derivatives pricing and investment management seem to have little in common. Even at the organizational level, they belong to two quite separate parts of financial markets. The so-called sell side, represented mainly by the investment banks, among other things offers derivatives products to their customers. Some of them are wealth managers, belonging to the so-called buy side of financial marke...

This paper proposes a solid model based on four-dimensional trivariate B-spline for strain and stress analysis of ventricular myocardium. With a series of processing steps in the four-dimensional medical images, the feature points of ventricular inner and outer wall are obtained. A B-spline surface is then used to build the dynamic deformation model of the myocardial walls. With such a surface ...

In this paper, we formulate a novel trivariate biharmonic B-spline defined over bounded volumetric domain. The properties of bi-Laplacian have been well investigated, but the straightforward generalization from bivariate case to trivariate one gives rise to unsatisfactory discretization, due to the dramatically uneven distribution of neighbouring knots in 3D. To ameliorate, our original idea is...

When faced with proportion data that exhibit extra-binomial variation, data analysts often consider the beta-binomial distribution as an alternative model to the more common binomial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observations on fetuses within a litter are often correlated with each other. In such instances, it may be o...