University, Diss., 1995--Kaiserslautern.

Generalising the divisibility relation of terms we introduce the lattice of so-called involutive divisions and define the admissibility of such an involutive division for a given set of terms. Based on this theory we present a new approach for building up a general theory of involutive bases of polynomial ideals. In particular, we give algorithms for checking the involutive basis property and for completing an arbitrary basis to an involutive one. It turns out that our theory is more constructive and more exible than the axiomatic approach to general involutive bases due to Gerdt and Blinkov. Finally, we show that an involutive basis contains more structural information about the ideal of leading terms than a Gröbner basis and that it is straight forward to compute the (affine) Hilbert function of an ideal I from an arbitrary involutive basis of I.

A method for compressing surfaces associated with C1 cubic splines defined on triangulated quadrangulations is described. The method makes use of hierarchical bases, and does not require the construction of wavelets.

Arkansas, Louisiana, Mississippi, and Tennessee all border the Mississippi River, a primary shipping channel in the United States. These Mid-South states serve as a southern agricultural hub in terms of corn and soybean production. The Mid-South is a prime location for merchandisers to take advantage of the Mississippi River in addition to a vast connection of railway systems and interstates for moving grain. The main objective of this study is to analyze local basis for selling locations in the Mid-South and connect basis movements with transportation flows to understand grain basis dynamics in the Mid-South better. An empirical analysis shows the nearby futures months have the greatest effect on both corn and soybean basis dynamics in the Mid-South. Farmers and merchandisers can take the results to better understand how changes in basis patterns can impact producer revenue and how to benefit from those changes.

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In approximation theory, three classical types of results are direct theorems, Bernstein inequalities, and inverse theorems. In this paper, we include results about radial basis function (RBF) approximation from all three classes. Bernstein inequalities are a recent development in the theory of RBF approximation, and on Rd, only L2 results are known for RBFs with algebraically decaying Fourier transforms (e.g. the Sobolev splines and thin-plate splines). We will therefore extend what is known by establishing Lp Bernstein inequalities for RBF networks on Rd. These inequalities involve bounding a Bessel-potential norm of an RBF network by its corresponding Lp norm in terms of the separation radius associated with the network. While Bernstein inequalities have a variety of applications in approximation theory, they are most commonly used to prove inverse theorems. Therefore, using the Lp Bernstein inequalities for RBF approximants, we will establish the corresponding inverse theorems. The direct theorems of this paper relate to approximation in Lp(Rd) by RBFs which are perturbations of Green's functions. Results of this type are known for certain compact domains, and results have recently been derived for approximation in Lp(Rd) by RBFs that are Green's functions. Therefore, we will prove that known results for approximation in Lp(Rd) hold for a larger class of RBFs. We will then show how this result can be used to derive rates for approximation by Wendland functions.

This paper reviews both the law and the theoretical accounts of the doctrine of consideration with a view to look for a normative, consistent and public basis of it. The thesis argues that such a basis can only be found by justifying it as what it is instead of considering it as a proxy for something else. The most promising justificatory account of the doctrine should look at its main features and try to make sense of them in consistency, instead of putting up assumption before analysis.

This paper reviews both the law and the theoretical accounts of the doctrine of consideration with a view to look for a normative, consistent and public basis of it. The thesis argues that such a basis can only be found by justifying it as what it is instead of considering it as a proxy for something else. The most promising justificatory account of the doctrine should look at its main features and try to make sense of them in consistency, instead of putting up assumption before analysis.

The developing of multimedia to make the video data to increase very quickly.So how to acquire the data that we want in a short time is a more important topic. Shot change detection is the first step for latter operation like classification and annotations. There are two type of shot change, one is abrupt shot change and the other one is gradual transition. Dissolve is the one of gradual transition that often seen but hard to detection, so in the paper would to propose a robust method to solve this problem. In this paper we use fractal orthonormal basis for our feature to compare frames in the video to the first frame of video, and use the quantification between those frames to draw a graph. By analyzing the graph and the characteristic of dissolve in the graph we can locate the approximately the start frame and the end frame of the dissolve. But by the action of video camera or motion of object in frame we may obtained the inaccurate start frame or end frame of the dissolve. So we need to refine the more accurate start and end frame of the dissolve, and we will explain about this in Chapter 3-4

Abstract The representation of 3D Computer Graphics has been studied for a long time. Most 3D object models are obtained by 3D scan systems. These kinds of data are not only very huge, but also have a lot of redundancy. It consumes a large mount of time and resources. For this reason, how to represent the object efficiently is always an important issue. The purpose of this study is to present the objects by implicit functions. Different with the presentation of polygon mesh, implicit function is very compact to present objects because that the mathematical form of object can be obtained in different data forms. The implicit function used is Radial Basis Function, and then the BSP tree is used to partition the object to reduce the amount of computing. We also use the compression of progressive mesh to decrease the storage and the computing time. In addition, the object can be rendered according to the sampling points on each implicit surface.