In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

Internal control system is a safety valve that preserves economic units assets and ensure the accuracy of financial data, as well as to obligation in the laws, regulations, administrative policies ,and improve the efficiency, effectiveness and economic of operation, so it has become imperative for these units attention to internal and developed control system The research problem in exposure the economic units when the exercise of their business to many of the risks to growth or hinder the achievement of its objectives and the risks (financial, operational, strategy, risk) and not it rely on risk Assessment according to modern scientific methods, as in Brown's risk Classification, Which led to the weakness of the internal control identif

Moisture induced damage in asphaltic pavement might be considered as a serious defect that contributed to growth other distresses such as permanent deformation and fatigue cracking. This paper work aimed through an experimental effort to assess the behaviour of asphaltic mixtures that fabricated by incorporating several dosages of carbon fiber in regard to the resistance potential of harmful effect of moisture in pavement. Laboratory tests were performed on specimens containing fiber with different lengths and contents. These tests are: Marshall Test, the indirect tensile test and the index of retained strength. The optimum asphalt contents were determined based on the Marshall method. The preparation of asphaltic mixtures involved

Building Information Modeling (BIM) and Lean Construction (LC) are two quickly growing applied research areas in construction management. This study focuses on identifying the most essential benefits and analyzing the most affecting constraints on the construction sector that construction players face as they attempt to combine BIM-LC in Iraqi construction. Experts assessed 30 benefits and 28 constraints from examining the previous literature, and a two-round Delphi survey formed the responses. Expert consensus analysis was utilized to elaborate and validate responses after descriptive statistical checks had been used for data processing.

According to the study's findings, the benefits include ensuring the most ef

Abstract

Characterized by the Ordinary Least Squares (OLS) on Maximum Likelihood for the greatest possible way that the exact moments are known , which means that it can be found, while the other method they are unknown, but approximations to their biases correct to 0(n^-1) can be obtained by standard methods. In our research expressions for approximations to the biases of the ML estimators (the regression coefficients and scale parameter) for linear (type 1) Extreme Value Regression Model for Largest Values are presented by using the advanced approach depends on finding the first derivative, second and third.

This paper presents the Extended State Observer (ESO) based repetitive control (RC) for piezoelectric actuator (PEA) based nano-positioning systems. The system stability is proved using Linear Matrix Inequalities (LMIs), which guarantees the asymptotic stability of the system. The ESObased RC used in this paper has the ability to eliminate periodic disturbances, aperiodic disturbances and model uncertainties. Moreover, ESO can be tuned using only two parameters and the model free approach of ESO-based RC, makes it an ideal solution to overcome the challenges of nano-positioning system control. Different types of periodic and aperiodic disturbances are used in simulation to demonstrate the effectiveness of the algorithm. The comparison studi