This course will consist of two parts with the common theme of analyzing a geometric object via geometric sub-objects which are ‘small’ in an appropriate sense. This is an expanded course outline which includes some background references as well as some exercises relevant to this background. For an explanation of terminology used in the next three paragraphs, see the following sections. In the ...

The use of graph theory can be visualized in nanochemistry, computer networks, Google maps, and molecular which are common areas to elaborate application this subject. In a numeric number (topological index) is used estimate the biological, physical, structural properties chemical compounds that associated with graph. paper, we compute first second multiplicative Zagreb indices ( <math xmlns="h...

physical properties are often required for designing post harvest handling and processing equipment for agricultural products. persimmon (khormandy cultivar) is rich in vitamin a, calcium, potassium, tannic acid and antioxidant phenolic compounds. in this study changes in the physical properties of persimmon fruit during storage were studied. properties such as fruit dimensions, mass, geometric...

We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also critical for most applications, hence the need for delaying the exact computations at run time until they are actually needed. Our approach is generic and extensible in the sen...

Copulas represent the dependence structure of multivariate distributions in a natural way. In order to generate new copulas from given ones, several proposals found its way into statistical literature. One simple approach is to consider convex-combinations (i.e. weighted arithmetic means) of two or more copulas. Similarly, one might consider weighted geometric means. Consider, for instance, the...

In this note, we show that the set of n such that the arithmetic mean of the first n primes is an integer is of asymptotic density zero. We use the same method to show that the set of n such the sum of the first n primes is a square is also of asymptotic density zero. We also prove that both the arithmetic mean of the first n primes as well as the square root of the sum of the first n primes ar...

Practical solid modeling systems are plagued by numerical problems that arise from using oating-point arithmetic. For example, polyhedral solids are often represented by a combination of geometric and combinatorial information. The geometric information might consist of explicit plane equations, with oating-point coeecients; the combinatorial information might consist of face, edge, and vertex ...

A random A yields A+A of size closer to the high end of |A|2. Furthermore, any set A whose members are sufficiently separated has |A+A| close to this high end, and the high end is actually tight for sets A that are geometric progressions, e.g. the first n powers of two. What about the low end of |A|: what is the structure of sets A where |A+A| is close to |A|? We can see that this low-end estim...