Sharif Digital Repository

In this research, we consider the question of finding approximate bounds on some of computational geometry problems with uncertain data. We use color spanning set to model the uncertainty. Given a set of n points colored with m colors in d-dimension. The problem of minimum diameter in color spanning set model is finding a set of m points with distinct colors so as to minimize diameter of the points. We give an algorithm with an approximation factor (1 + ϵ) with running time O(21ϵd .ϵ−2d.n3) which improves the previous results. Next,we consider a new problem of finding bounds on unit covering in color-spanning set model:Minimum color spanning-set ball covering problem is to select m points of... 

In 1975 a Chemist Milan Randić proposed a concept named Randić index which is defined as follows: This index is generalized by replacing any real number α with which is called the general Randić index. Let G be a graph of order n. Erdős and Bollobás showed the lower bound for Randić index, Also, an upper bound for Randić index is n/2. In 2018 Suil O and Yongtang Shi proved a lower bound with minimum and maximum degree of a graph. They have shown for graph G we have, R(G) Also, a relation between Randić index and the energy of the graph has found. Indeed, it was proved that E(G) ⩾ 2R(G), where E(G) is the energy of graph. Many important bounds related to graph parameters for Randić index... 

In the oil industry, a better understanding of the well condition leads to improve the management and increase the oil production. Production logging tools is a set of tools for measuring different parameters such as density, diameter and flow in oil and gas wells. These tools are considered among high-tech tools in the oil industry. The reason is that they should work in harsh conditions, i.e. high temperature about 170 ° C and pressure around 15000 psi, and at the same time give an accurate measurement of the quantity. Current production-logging tools measure the fluid velocity and the diameter of an oil well by individual mechanical tools, and the density by a radioactive densitometer. ...