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In this paper, we investigated of a new self-scaling by use quasi-Newton method and conjugate gradient method. The new algorithm satisfies a quasi-newton condition and mutually conjugate, and practically proved its efficiency when compared with the well-known algorithms in this domain, by depending on efficiency measure, number of function, number of iteration, and number of constrained, NOF, NOI and NOC.

In this paper, we used the homotopy analysis method to ordinary differential equations of type boundary value problems with a parameter representing turning points."To show the high accuracy of the solution results, we compare the numerical results applying the standard homotopy analysis method with the integral equation and the numerical solution of the Simpson and Trapezoidal rules."Also, we give the estimated order of convergence (local) and the global estimated order of convergence along the interval.

In this paper, we present the Generalized Gamma-Exponentiated Weibull distribution as a special case of new generated Generalized Gamma - G family of probability distribution. The cumulative distribution, probability density, reliability and hazard rate functions are introduced. Furthermore, the most vital statistical properties, for instance, the r-th moment, characteristic function, quantile function, simulated data, Shannon and relative entropies besides the stress-strength model are obtained.

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

In this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using Mathcad 15.and graphic in Matlab R2015a.

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model. Mathematical Subject Classification (2010): 45P05, 45G10, 47H99

This paper is concerned with, the proof of the existence and the uniqueness theorem for the solution of the state vector of a couple of nonlinear elliptic partial differential equations using the Minty-Browder theorem, where the continuous classical boundary control vector is given. Also the existence theorem of a continuous classical boundary optimal control vector governing by the couple of nonlinear elliptic partial differential equation with equality and inequality constraints is proved. The existence of the uniqueness solution of the couple of adjoint equations associated with the considered couple of the state equations with equality and inequality constraints is studied. The necessary conditions theorem and the sufficient conditions theorem for optimality of the couple of nonlinear elliptic equations with equality and inequality constraints are proved using the Kuhn-Tucker-Lagrange multipliers theorems

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a wide time frame. Two examples are provided for showing the ability and advantages of the proposed method to approximate the solution of the power law nonlinearity of NLSEs. For pictorial representation, graphical inputs are included to represent the solution and show the precision as well as the validity of the MMRDTM.

In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

This paper deals with using one method for transforming two parameters given distribution to another form with three parameters distribution, through using idea of reparameterization with powering the given cumulative distribution function by new parameter, where this work gives a new family through using new parameter which is necessary for generating values of the r.v from given CDF through smoothing the values of the given random variable to obtain new values of r.v using three set of parameters rather than two. The new model Frechet p.d.f is obtained and also its Cumulative distribution function is found then we apply three methods of estimation (which are Maximum likelihood , moments estimator , and the third method is depend on using least square regression approach). Different set of initial values of parameters ( , , ) and different samples size (n=25,50,75,100). The simulation procedure is done using matlab-R2014b, and results are compared using integrated Mean square error.

The nonlinear conjugate gradient method is widely used to solve unconstrained optimization problems. In this paper the development of different versions of nonlinear conjugate gradient methods with global convergence properties proved. Numerical results indicated that the proposed method is very efficient.

This paper aims to evaluate the reliability analysis for steel beam which represented by the probability of Failure and reliability index. Monte Carlo Simulation Method (MCSM) and First Order Reliability Method (FORM) will be used to achieve this issue. These methods need two samples for each behavior that want to study; the first sample for resistance (carrying capacity R), and second for load effect (Q) which are parameters for a limit state function. Monte Carlo method has been adopted to generate these samples dependent on the randomness and uncertainties in variables. The variables that consider are beam cross-section dimensions, material property, beam length, yield stress, and applied loads. Matlab software has been adopted to generate these pseudo-random variables dependent on its statistical characteristics such as coefficient of variance and probability density function that gathered from a review of literatures.

In this paper, we are concerned with the conjugate gradient method for solving unconstrained optimization problems due to its simplicity and don’t store any matrices. We proposed two spectral modifications to the conjugate descent (CD). These two proposed methods produces sufficient descent directions for the objective function at every iteration with strong Wolfe line searches and with inexact line search, and also they are globally convergent for general non-convex functions can be guaranteed. Numerical results show the efficiency of these two proposed methods.

In this paper, we shall study the existence of a new class called fractional Caputo type of order sobolev type fractional order differential Equations motion in separable Banach spaces. The class of impulsive nonlinear fractional order bilinear control differential Equations with Riemann Leovel differential initial value studied and discussed also given the important results for the almost periodic mild solution to be sTable by using Menards function and granwal fractional inequality.

In this paper, we focus on designing feed forward neural network (FFNN) for solving Mixed Volterra – Fredholm Integral Equations (MVFIEs) of second kind in 2–dimensions. in our method, we present a multi – layers model consisting of a hidden layer which has five hidden units (neurons) and one linear output unit. Transfer function (Log – sigmoid) and training algorithm (Levenberg – Marquardt) are used as a sigmoid activation of each unit. A comparison between the results of numerical experiment and the analytic solution of some examples has been carried out in order to justify the efficiency and the accuracy of our method.

This paper focuses on the methodology and howthe concept of qarīna (circumstantial evidence) were used by the Muslimscholars in order to interpret hadith in the mushkil al-hadith and annotationsto hadith works. In particular, the subjects of what the apparent meaning (ẓāhir) of the hadith text(naṣṣ)or statement gives, the composition of the text (siyāq al-naṣṣ), the contextualindications of the text (time frame and other contextual indications), and thecondition of the text are taken into consideration. This method also includesqualifying the meaning of the statement, and if it is necessary, to refer toal-wujūh wa al-naẓāir, and to digress from the apparentindications of the statement. Qarīna is used as a means when the literalmeaning of the statement contradicts with the Sharī’a, or if the statementindicates multiple meanings and thus a particular meaning cannot beascertain. After explaining theseinterpretation methods, the pitfalls of interpreting (ta’wīl) the statementwithout taken into consideration the above mentioned indications are alsoseparately stated. They are: the misapplication of the text resulting frommisunderstanding the intention of the Sharī’a and employing the statementbeyond its meaning, or extending the influence area of a text which is specific(khāṣ),or vice versa limiting the meaning of the text, or prioritising only onemeaning over other meanings when the statement indicates multiple meanings., Buçalışma hadis ulemasının hadis şerhlerinde ve müşkilü’l-hadis literatüründehadisleri tevil ederken kullandıkları yöntemi ve delilleri incelemektedir.Özellikle, nassın zahirî anlamı, nassın siyâkı, nass sahibinin içinde bulunduğudurum, nassın zaman ve bağlamla bağlantılı değişkenleri dikkate alınmıştır. Buyöntem aynı zamanda hadisin manasının belirlenmesini, ihtiyaç halinde vücûh venezâir literatürüne başvurulmasını ve gerektiğinde nassın zahirî manasını terketmeyi içerir. Hadisin zahirî anlamı şeriatın kabul etmeyeceği hususlarıiçerdiğinde ya da hadisin birden fazla manaya işaret etmesi sebebiyle kesin birmana seçilemediğinde sözü edilen yönteme başvurulmaktadır. Çalışma aynı zamandahadisleri tevil etme yönteminden bahsettikten sonra, bu yöntem dikkatealınmadan hadislerin tevil edilmesinden kaynaklanan tehlikelere de ayrıcadeğinmiştir. Bu tehlikeler; şeriatın muradını tespit edememek, hadisi işaretettiği mananın dışında kullanmak, hadisin işaret ettiği hâs yani özel olan birhükmün genelleştirilmesi (âmm) ya da tam tersi âmm olan hükmü hâs olarakdeğerlendirmek ve birden fazla manaya işaret eden veya çok yönlü olan hadisitek bir mana üzerinden yorumlamaktır., هذا البحث تم فيه عَرضُ أهمِّ القرائن الـمُهِمّة التي تم استقراؤها من كتبالشُّروح وكتب مُشكل الحديث، مما استعمله العلماء في تأويل الأحاديث، وأبرزها مايتعلق بظاهر النص؛ كسياق النص، وزمانه ومتغيّراته، ومراعاة حالة صاحب النص. ومنهاما يتعلق بجانب فقه النص؛ كاشتماله في ظاهره على ما تأباه الشريعة الغَرّاء، مما يَتطلّبالخروجَ عن معناهُ الظاهري، إلى معنًى آخرَ مجازي لا تَدفَعُه الأُصول، وكتَعدُّدالوجُوه الـمُحتمَلة في النص مما يَحُولُ دون الجزم بأحد تلك الوجُوه، وكالنصوصالتي يَتطلّب تأويلُها النظرَ في الأشباه والنظائر التي تُرشِد إلى فَهمِها، ثمتلا ذلك بيانُ أخطر الآثار المترتبة على التأويل بمعزل عن القرائن، مما يتعلقبجانبَي الفهم والتطبيق؛ كإساءة فهم صاحب الشريعة، وما ينبني عليه من إساءةالتطبيق، باستعمال النص في غير محلِّه، وتَعديةِ ما حَقُّه القَصرُ، وقَصرِ ما حَقُّهالتَّعديةُ، وإلزامُ الناس بأحد الوجوه الـمُحتمَلة، مع تخطئة المخالِف.

In this paper we presented a new way based on neural network has been developed for solutione of two dimension partial differential equations . A modified neural network use to over passing the Disadvantages of LM algorithm, in the beginning we suggest signaler value decompositions of Jacobin matrix (J) and inverse of Jacobin matrix( J-1), if a matrix rectangular or singular Secondly, we suggest new calculation of μk , that ismk=|| E (w)||2 look the nonlinear execution equations E(w) = 0 has not empty solution W* and we refer to the second norm in all cases ,whereE(w): is continuously differentiable and E(x) is Lipeschitz continuous, that is=|| E(w 2)- E(w 1)||£ L|| w 2- w 1|| ,where L is Lipeschitz constant.