In the last years, the self-balancing platform has become one of the most common candidates to use in many applications such as flight, biomedical fields, industry. This paper introduced the simulated model of a proposed self-balancing platform that described the self–balancing attitude in (X-axis, Y-axis, or both axis) under the influence of road disturbance. To simulate the self-balanced platform's performance during the tilt, an integration between Solidworks, Simscape, and Simulink toolboxes in MATLAB was used. The platform's dynamic model was drawn in SolidWorks and exported as a STEP file used in the Simscape Multibody environment. The system is controlled using the proportional-integral-derivative (PID) co

     . Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper,we introduce the generalized Cayley graph denoted by  which is a graph with a vertex set consisting of all column matrices  in which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of the similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and  and m . We aim to provide some basic properties of the new graph and determine the structure of  when  is a complete graph  for every , and n, m  .

The fouling depositions of crude oil stream were studied theoretically in a shell and tube heat exchanger to investigate the effect of depositions on the heat transfer process. The employed heat exchanger was with steam flowing in the inner tubes and crude oil in the shell at different velocities and bulk temperatures. It is assumed that fouling occurs only on the heated stream side (crude oil). The analysis was carried out for turbulent flow heat transfer conditions with wide range of Reynolds number, bulk temperature and time. Many previously proposed models for fouling resistance were employed to estimate a new model for fouling rate. It is found that the fouling rate and consequently the heat transfer coefficient were affected by Rey

The main goal of this paper is to study applications of the fractional calculus techniques for a certain subclass of multivalent analytic functions on Hilbert Space. Also, we obtain the coefficient estimates, extreme points, convex combination and hadamard product.