The local resolving neighborhood  of a pair of vertices  for  and  is if there is a vertex  in a connected graph  where the distance from  to  is not equal to the distance from  to , or defined by . A local resolving function  of  is a real valued function   such that  for  and . The local fractional metric dimension of graph  denoted by , defined by  In this research, the author discusses about the local fractional metric dimension of comb product are two graphs, namely graph  and graph , where graph  is a connected graphs and graph  is a complate graph &

Based on analyzing the properties of Bernstein polynomials, the extended orthonormal Bernstein polynomials, defined on the interval [0, 1] for n=7 is achieved. Another method for computing operational matrices of derivative and integration D_b and R_(n+1)^B respectively is presented. Also the result of the proposed method is compared with true answers to show the convergence and advantages of the new method.

Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes app

In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

The rotor dynamics generally deals with vibration of rotating structures. For designing rotors of a high speeds, basically its important to take into account the rotor dynamics characteristics. The modeling features for rotor and bearings support flexibility are described in this paper, by taking these characteristics of rotor dynamics features into standard Finite Element Approach (FEA) model. Transient and harmonic analysis procedures have been found by ANSYS, the idea has been presented to deal with critical speed calculation. This papers shows how elements BEAM188 and COMBI214 are used to represent the shaft and bearings, the dynamic stiffness and damping coefficients of journal bearings as a matrices have been found

Piled raft is commonly used as foundation for high rise buildings. The design concept of piled raft foundation is to minimize the number of piles, and to utilize the entire bearing capacity. High axial stresses are therefore, concentrated at the region of connection between the piles and raft. Recently, an alternative technique is proposed to disconnect the piles from the raft in a so called unconnected piled raft (UCPR) foundation, in which a compacted soil layer (cushion) beneath the raft, is usually introduced.  The piles of the new system are considered as reinforcement members for the subsoil rather than as structural members. In the current study, the behavior of unconnected piled rafts systems has been studie

The aerodynamic and elastic forces may cause an oscillation of the structure such as the high frequency of the airfoil surfaces and the dynamic instability occurring in an aircraft in flight and failure may occur at a speed called flutter speed. In this work, analytical and numerical investigations of flutter limits of thin plates have been carried out. The flutter speed of rectangular plates were obtained and compared with some published results. Different design parameters were investigated such as aspect ratio, thickness and their effects on flutter velocity. It was found that the structural mode shape plays an important role in the determination of the flutter speed and the coupling between the bending and torsional mode is the main

Corrosion behavior of aluminum alloy 7025 was investigated in hydrochloric acid (pH=1) containing 0.6 mol.dm-3 NaCl in the existence and absence of diverse concentrations of sulphamethoxazole as environmentally friendly corrosion inhibitor over the temperature range (298-313)K. Electrochemical polarization method using potentiostatic technique was employed. The inhibition efficiency has been raised with increased sulphamethoxazole concentration but lessened at temperature increases. The highest efficiency value was 96.5 at 298 K and 2 x10-4 mol.dm-3 concentration of sulphamethoxazole. The sulphamethoxazole adsorption was agreed with Langmuir adsorption isotherm. Some thermodynamic parameter (△Gads) and activation energy (Ea) were determin