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In this paper, we have investigated some of the most recent energy efficient routing protocols for wireless body area networks. This technology has seen advancements in recent times where wireless sensors are injected in the human body to sense and measure body parameters like temperature, heartbeat and glucose level. These tiny wireless sensors gather body data information and send it over a wireless network to the base station. The data measurements are examined by the doctor or physician and the suitable cure is suggested. The whole communication is done through routing protocols in a network environment. Routing protocol consumes energy while helping non-stop communication in a wireless environment. Because of the very tiny size, energy consumption matters a lot. We have focused on the protocols, which provide energy efficiency and improve network lifetime, through put and minimal path loss. We will be discussing some of the most recent energy efficient routing protocols in this paper; later their comparison with an appropriate table is presented. In addition, recent challenges, possible application and perspectives are discussed.

This paper is concerned with introducing an explicit expression for orthogonal Boubaker polynomial functions with some important properties. Taking advantage of the interesting properties of Boubaker polynomials, the definition of Boubaker wavelets on interval [0,1) is achieved. These basic functions are orthonormal and have compact support. Wavelets have many advantages and applications in the theoretical and applied fields, and they are applied with the orthogonal polynomials to propose a new method for treating several problems in sciences, and engineering that is wavelet method, which is computationally more attractive in the various fields. A novel property of Boubaker wavelet function derivative in terms of Boubaker wavelet themselves is also obtained. This Boubaker wavelet is utilized along with a collocation method to obtain an approximate numerical solution of singular linear type of Lane-Emden equations. Lane-Emden equations describe several important phenomena in mathematical science and astrophysics such as thermal explosions and stellar structure. It is one of the cases of singular initial value problem in the form of second order nonlinear ordinary differential equation. The suggested method converts Lane-Emden equation into a system of linear differential equations, which can be performed easily on computer. Consequently, the numerical solution concurs with the exact solution even with a small number of Boubaker wavelets used in estimation. An estimation of error bound for the present method is also proved in this work. Three examples of Lane-Emden type equations are included to demonstrate the applicability of the proposed method. The exact known solutions against the obtained approximate results are illustrated in figures for comparison

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.

MDS code is a linear code that achieves equality in the Singleton bound, and projective MDS (PG-MDS) is MDS code with independents property of any two columns of its generator matrix. In this paper, elementary methods for modifying a PG-MDS code of dimensions 2, 3, as extending and lengthening, in order to find new incomplete PG-MDS codes have been used over . Also, two complete PG-MDS codes over of length and 28 have been found.

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, new method have been investigated using evolving algorithms (EA's) to cryptanalysis one of the nonlinear stream cipher cryptosystems which depends on the Linear Feedback Shift Register (LFSR) unit by using cipher text-only attack. Genetic Algorithm (GA) and Ant Colony Optimization (ACO) which are used for attacking one of the nonlinear cryptosystems called "shrinking generator" using different lengths of cipher text and different lengths of combined LFSRs. GA and ACO proved their good performance in finding the initial values of the combined LFSRs. This work can be considered as a warning for a stream cipher designer to avoid the weak points, which may be found in the stream cipher, and may be explored by the cryptanalysts. This work can find the optimal solution for text with minimum lengths of 20 characters and 100 iteration were very enough to find the real initial values of key stream.

In this paper new methods were presented based on technique of differences which is the difference- based modified jackknifed generalized ridge regression estimator(DMJGR) and difference-based generalized jackknifed ridge regression estimator(DGJR), in estimating the parameters of linear part of the partially linear model. As for the nonlinear part represented by the nonparametric function, it was estimated using Nadaraya Watson smoother. The partially linear model was compared using these proposed methods with other estimators based on differencing technique through the MSE comparison criterion in simulation study.

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.

The wireless sensor network (WSN) consists mostly of a large number of nodes in a large area where not all nodes are directly connected. The applications of comprise a wide variety of scenarios.The mobile nodes are free to move because this network has selfــstructured topology. Routing protocols are responsible for detecting and maintaining paths in the network, and it classified into reactive (OnـــDemand), proactive (Table driven), and hybrid. In this paper represents a performance study of some WSN routing protocols: the Dynamic Source Routing (DSR), Ad hoc On-Demand Distance Vector (AODV), and Destination-Sequenced Distance-Vector (DSDV). The comparison made according to important metrics like packet delivery ratio (PDR), total packets dropped, Average end-to-end delay (Avg EED), and normalized routing load under the Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) traffic connection and with varying number of nodes, pause time; and varying speed. In this work used (NSــ2.35) that installed on (Ubuntu 14.04) operating system to implementing the scenario. Conclude that the DSR has better performance in TCP connection; while the DSDV has better performance in UDP protocol.