In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

Granular  Pile  Anchor  (GPA)  is  one  of  the  innovative  foundation  techniques,  devised  for mitigating heave of footing resulting from the expansive soils. This research attempts to study the heave behavior of (GPA-Foundation System) in expansive soil. Laboratory tests have been conducted on an experimental model in addition to a series of numerical modeling and analysis using the finite element package PLAXIS software. The effects of different parameters, such as (GPA) length (L) and diameter (D), footing diameter (B), expansive clay layer thickness (H) and presence of non-expansive clay are studied. The results proved the efficiency of (GPA) in reducing the heave of exp

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

Rutting in asphalt mixtures is a very common type of distress. It occurs due to the heavy load applied and slow movement of traffic. Rutting needs to be predicted to avoid major deformation to the pavement. A simple linear viscous method is used in this paper to predict the rutting in asphalt mixtures by using a multi-layer linear computer programme (BISAR). The material properties were derived from the Repeated Load Axial Test (RLAT) and represented by a strain-dependent axial viscosity. The axial viscosity was used in an incremental multi-layer linear viscous analysis to calculate the deformation rate during each increment, and therefore the overall development of rutting. The method has been applied for six mixtures and at different tem

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

Signal denoising is directly related to sample estimation of received signals, either by estimating the equation parameters for the target reflections or the surrounding noise and clutter accompanying the data of interest. Radar signals recorded using analogue or digital devices are not immune to noise. Random or white noise with no coherency is mainly produced in the form of random electrons, and caused by heat, environment, and stray circuitry loses. These factors influence the output signal voltage, thus creating detectable noise. Differential Evolution (DE) is an effectual, competent, and robust optimisation method used to solve different problems in the engineering and scientific domains, such as in signal processing. This paper looks

Static loads exposing to mechanical components can cause cracks, which are lead to form stress concentration regions causing the failure of structure. Generally, from 80% to 90% of structure failure is due to initiation of the cracks. Therefore, it is necessary to repair the crack and reduce its effect on the structure where the effect of the crack is modelled as an additional flexibility to the structure. In the last few years, piezoelectric materials have been considered as one of the most favourable repairing techniques. The piezoelectric material converts the applied voltage on it to a bending moment to counter the bending moment caused by the external load on the beam at the crack location. In this study, the design of the piez

In this paper we estimate the coefficients and scale parameter in linear regression model depending on the residuals are of type 1 of extreme  value distribution for the largest values . This can be regard as an improvement for the studies with the smallest values . We study two estimation methods ( OLS  & MLE ) where we resort to Newton – Raphson (NR) and Fisher Scoring methods to get MLE estimate because the difficulty of using the usual approach with MLE . The relative efficiency criterion is considered beside to the statistical inference procedures for the extreme value regression model of type 1 for largest values . Confidence interval , hypothesis testing for both scale parameter and regression coefficients

This paper studies the effect of contact areas on the transient response of mechanical structures. Precisely, it investigates replacing the ordinary beam of a structure by two beams of half the thickness, which are joined by bolts. The response of these beams is controlled by adjusting the tightening of the connecting bolts and hence changing the magnitude of the induced frictional force between the two beams which affect the beams damping capacity. A cantilever of two beams joined together by bolts has been investigated numerically and experimentally. The numerical analysis was performed using ANSYS-Workbench version 17.2. A good agreement between the numerical and experimental results has been obtained. In general, results s