a disk wang-bézier type generalized ball curve is a wang-bézier type generalized ball curve whose control points are disks in a plane. it can be viewed as a parametric curve with error tolerances. in this paper, we discuss the problem of degree reduction of disk wang-bézier type generalized ball curve, that is, bounding disk wang-bézier type generalized ball curves with lower degree disk wang-b...

A disk Wang-Bézier type generalized Ball curve is a Wang-Bézier type generalized Ball curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Wang-Bézier type generalized Ball curve, that is, bounding disk Wang-Bézier type generalized Ball curves with lower degree disk Wa...

The presence of clay-sized particles and clay minerals in modern sands and ancient sandstones has long presented an interesting problem, because primary depositional processes tend to lead to physical separation of fineand coarse-grained materials. Numerous processes have been invoked to explain the common presence of clay minerals in sandstones, including infiltration, the codeposition of floc...

Consider the Newtonian potential of a homogeneous bounded body D ⊂ R3 with known constant density and connected complement. If this potential equals to c/|x| in a neighborhood of infinity, where c > 0 is a constant, then the body is a ball. This known result is now proved by a different simple method. The method can be applied to other problems.

Clay-based nanostructured multilayers, such as clay-polymer multilayers and clay-oxide multilayers, have attracted growing attention owing to their remarkable mechanical properties and promising application in various fields. In this paper, synthesis of a new kind of nanostructured clay-oxide multilayers by layer-by-layer self-assembly was explored. Nano-mechanical characterization of 18 clay-b...

Composites based on high density polyethylene (HDPE), pine flour, and organic clay were made by melt compounding and then injection molding. The influence of clay on crystallization behavior, mechanical properties, water absorption, and thermal stability of HDPE/pine composites were investigated. The HDPE/pine composites containing exfoliated clay were made by a two-step melt compounding proced...

Example 3. How many ways are there to put m balls into n bins. Assume m ≤ n. 1. Balls are distinct and bins are distinct. Every ball has n choices. Hence n. Exercise 2. Why is the answer not m by looking at the opposite argument. 2. Balls are not distinct but bins are distinct. Take m identical balls and n− 1 identical sticks and permute them. Every permutation gives a different arrangement. So...

INTRODUCTION Clays, and more specifically 2 :1 phyllosilicates consisting of aluminoor magnesiosilicate negatively charged staked layers separated by van der Walls spacings where inorganic countercations (sodium, calcium,... cations) are located, can be associated with polymers to give interesting new materials called polymer/clay nanocomposites. Polymer/clay nanocomposites have been intensivel...

The present paper should be considered as a review of the application of Fourier Transform Infra-Red for surface clay characterization. The application of surface clay materials for water treatment, oil adsorption, excipients or as active in drugs has largely increased these recent years. The surface clay material presents hydroxyl groups, which can link very easily water molecules. These hydro...