In this paper, an extended spectral conjugate gradient method is proposed for solving unconstrained optimization problems, where the search direction is a linear combination of the gradient vector at current iteration and the search direction at the previous iteration. Instead of specifying a fixed expression to compute each combination coefficient in the existent methods, only suitable conditions are presented for the combination coefficients such that the values of coefficients are chosen freely in a range. Under some mild assumptions, with step lengths satisfying the Armijo condition, global convergence is established for the developed algorithm. It is shown that some existent methods are the special cases of the presented method in this paper.

Commercial Off-The-Shelf (COTS) technology is widely used in many industries and also in scientific computing. This paper will first explore the term itself and then tries to find how it typically manifests itself in the softwares used in physical sciences. Some details regarding one of the popular software used for crystal structure elucidation in Crystallography, viz., SHELX are furnished. Since this is a freely available program and a non-commercial one, it is better to consider this as an example of Scientific Off-The-Shelf (SOTS) components, a newly coined acronym.

Aims: We give some families which are meromorhic outside a compact countable set B of essential singularities. Our aim is to give some examples of the stable set (called the Fatou set) and the unstable set (called the Julia set) since there is not study of examples of any parametric family of this class of functions (called in the introduction functions of class K) in complex dynamics. Study design: We study components of the Fatou set and some theorems related with the iteration of functions in class K and design a computational program to give examples of the Julia and Fatou sets. Place and Duration of Study: F.C. F´isico-Matem´ ticas, Benem´ erita Universidad Aut ´onoma de Puebla, M´exico between June 2011 and July 2012. Methodology: We use some theorems of complex dynamics in order to study components of the Fatou set. We program some algorithms in C and get the picture of this set. Results: Given a family in class K we get some mathematical results of the Fatou and Julia sets and its pictures for some parameters given. Conclusion: Taking some families in class K ∩ S_{k} we give examples of the Fatou set which can be either simply-connected or multiply-connected in the last case the Julia set is a totally disconnected set.

In this article, we consider a stochastic inventory system with two different items in stock, one is major item (I- commodity) and other is gift item (II- commodity). The maximum storage capacity for the th commodity is The demand time points for each commodity are assumed to form a independent Poisson processes. The second commodity is supplied as a gift whenever the demand occurs for the first commodity, but no major item is provided as a gift for demanding a second commodity. type control policy for the first commodity, with random lead time but instantaneous replenishment for the second commodity are considered. If the inventory position of first commodity (major item) is zero then any arriving primary demand for the first commodity enters into an orbit of finite size . These orbiting customers compete for service by sending out signals that are exponentially distributed. The joint probability distribution for both commodities and the number of demands in the orbit, is obtained in the steady state case. Various system performance measures in the steady state are derived. The results are illustrated with numerical examples.In this article, we consider a stochastic inventory system with two different items in stock, one is major item (I- commodity) and other is gift item (II- commodity). The maximum storage capacity for the th commodity is The demand time points for each commodity are assumed to form a independent Poisson processes. The second commodity is supplied as a gift whenever the demand occurs for the first commodity, but no major item is provided as a gift for demanding a second commodity. type control policy for the first commodity, with random lead time but instantaneous replenishment for the second commodity are considered. If the inventory position of first commodity (major item) is zero then any arriving primary demand for the first commodity enters into an orbit of finite size . These orbiting customers compete for service by sending out signals that are exponentially distributed. The joint probability distribution for both commodities and the number of demands in the orbit, is obtained in the steady state case. Various system performance measures in the steady state are derived. The results are illustrated with numerical examples.

Aims: Using Simple Artificial Neural Networks, and away from strict Boolean logic, this paper proposes a new design of memory array that has the ability to recognize erroneous and deformed data and specify the rate of error. Methodology: To achieve this work, artificial neural network was exploited to be the actor responsible of representing the crude of the building. It’s worth mentioning that simple neurons with binary step function and identity function were used, which will facilitate the way of implementation. The connection of few neurons in a simple network issues an exclusive X gate, which accepts only one value X (where X âˆŠ â„+) with an acceptable error rate α. This gate will be the main core of designing a memory cell that can learn a value X and recognized this value when requested. Results: After several stages of development, the final version of this memory cell will serve as a node unit of a large memory array which can recognize a data word or even a whole image with the ability to accept and recognize distorted data. Specific software that simulates the designed networks was developed in order to declare the efficiency of this memory. The obtained result will judge the Network.

In the present paper, we construct the analytical solutions of some nonlinear evolution equations involving Jumarie’s modified Riemann–Liouville derivative in mathematical physics; namely the space–time fractional modified Benjamin-Bona-Mahony(mBBM) equation and the space–time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony(ZKBBM) equation by using a simple method which is called the fractional sub-equation method. As a result, three types of exact analytical solutions are obtained. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear fractional PDEs arising in mathematical physics.

Aims: In this paper an approximate method for the solution of third-order differential equation with two and three point boundary condition is developed using iterative reproducing kernel method. Methods: The third order boundary value problem is converted into integro-differential equation of second order two point boundary value problem. The reproducing kernel method which takes the form of a convergent series with easily computable components is used for the solution of second order two point boundary value problem. Results: Six numerical examples are given to demonstrate the efficiency of the present method. The results obtained are better than the existing methods developed in [19,20,21,22,23]. Conclusions: In this paper, the solution of linear and nonlinear third order (two and three point) boundary value problem is determined. For the solution of third order three point boundary value problem reproducing kernel method is proposed and obtained a good accuracy in absolute errors. As the reproducing kernel method cannot solve the third order three-point boundary value problems directly, so the third order boundary value problem is converted to second order two point boundary value problem after absorbing the nonlocal condition at . The method developed is compared with those developed by Li et al. [19], El-Salam et al. [20], Khan and Aziz [21], Li and Wu [22] and Wu and Li [23]. As observed in Example 3, 4, 5 and 6 that the method obtained in this paper is better than [19]-[23]. Results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for third-order linear as well as nonlinear boundary value problem.

After a brief exploration of certain topological features of the unit octonions, we identify the Nash equilibria in a quantized version of three-player dilemma game using an octonionic representation of the payoff function. This representation is an important tool for the relative ease in working with octonionic arithmetic as opposed to multi-variant tensors and provides a fresh computational framework that can be utilized for the classification of Nash equilibria in generic three-player two-strategy games. While the full classification of equilibria remains a goal of future research, our representation has already established certain family of equilibria in a quantized version of three-player dilemma game.

In this paper, autoregressive integrated moving average (ARIMA) model is used to predict the prevalence and incidence of measles in the Ashanti Region of Ghana. The Mean Absolute Error (MAE) and the Mean Squared Error (MSE) are used to compare the in-sample forecasting performance of four selected competing models. The working data from the Ashanti Health Services spans from 2001 to 2011. It is evident from the analysis that measles data in the Ashanti Region of Ghana could best be modeled with ARIMA (2, 1, 1) and that measles prevalence in the Ashanti Region is expected to increase if no preventative measures are taken. The forecasting accuracy using MAE for ARIMA (2, 1, 1) is calculated as 28.1141 and the forecasting accuracy using MSE for ARIMA (2, 1, 1) is calculated as 2947.15.