In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i

In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

In this research, the size strain plot method was used to estimate the particle size and lattice strain of CaTiO3 nanoparticles. The SSP method was developed to calculate new variables, namely stress, and strain energy, and the results were crystallite size (44.7181794 nm) lattice strain (0.001211), This method has been modified to calculate new variables such as stress and its value (184.3046308X10-3Mpa) and strain energy and its value (1.115833287X10-6 KJm-3).

This paper presents a numerical simulation of the flow around elliptic groynes by using CFD ‎software. The flow was simulated in a flume with 4m long, 0.4m wide, ‎and 0.175m ‎high ‎‎with a constant bed slope. Moreover, the first Groyne placed at 1m from the flow ‎‎inlet with a ‎constant the Groyne height of 10cm and a 1cm thickness, and the ‎width of Groynes equals ‎7cm‎. A submergence ratio of the elliptic Groynes of 75% was assumed, corresponding to a discharge of ‎0.0057‎m³/sec. The CFD ‎model showed a good ability to simulate the flow ‎around ‎Groynes with ‎ good accuracy. The results of ‎CFD software showed that when using double elliptic Groy

Providing useful information in estimating the amount and timing and the degree of uncertainty concerning the future cash flows is one of the three main objectives of the financial reporting system, which is done through the main financial statements. The interest on standard-setting bodies in the forecasting of future cash flows, especially Financial Accounting Standards Board (FASB) explain under Accounting Standard (1) of the year 1978 "Objectives of Financial Reporting by Business Enterprises", paragraph (37) thereof that accounting profits better than cash flows when forecasting future cash flows, In contrast, IAS (7) as amended in 1992 aims to compel economic units to prepare statement of c

      Assume that G is a finite group and X is a subset of G. The commuting graph is denoted by С(G,X) and has a set of vertices X with two distinct vertices x, y Î X, being connected together on the condition of xy = yx. In this paper, we investigate the structure of Ϲ(G,X) when G is a particular type of Leech lattice groups, namely Higman–Sims group HS and Janko group J₂, along with  X as a G-conjugacy class of elements of order 3. We will pay particular attention to analyze the discs’ structure and determinate the diameters, girths, and clique number for these graphs.

An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

Trimmed Linear moments (TL-moments) are natural generalization of L-moments that do not require the mean of the underlying distribution to exist. It is known that the sample TL-moments is unbiased estimators to corresponding population TL-moment. Since different choices for the amount of trimming give different values of the estimators it is important to choose the estimator that has minimum mean squares error than others. Therefore, we derive an optimal choice for the amount of trimming from known distributions based on the minimum errors between the estimators. Moreover, we study simulation-based approach to choose an optimal amount of trimming and maximum like hood method by computing the estimators and mean squares error for range of