This paper studies a novel technique based on the use of two effective methods like modified Laplace- variational method (MLVIM) and a new Variational method (MVIM)to solve PDEs with variable coefficients. The current modification for the (MLVIM) is based on coupling of the Variational method (VIM) and Laplace- method (LT). In our proposal there is no need to calculate Lagrange multiplier. We applied Laplace method to the problem .Furthermore, the nonlinear terms for this problem is solved using homotopy method (HPM). Some examples are taken to compare results between two methods and to verify the reliability of our present methods.

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

The present study aimed to identify teaching problems which facing the teachers for first three grades classes, and if these problems different according to some variables teacher qualification, experience period, class grade). The study sample consist of (137 )

 female teachers who teach the first three grades in Braimy city in Oman, teachers spread in five government schools. Both researchers developed questionnaire to measure problems faced by the mentioned teachers, consist of 50 questions distributed into 4 dimensions (teacher, students, the curriculum, the evaluations), Also researchers checked questionnaire validity and stability. The results indicate to: The most common probl

The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

In this paper, we discuss physical layer security techniques in downlink networks, including eavesdroppers. The main objective of using physical layer security is delivering a perfectly secure message from a transmitter to an intended receiver in the presence of passive or active eavesdroppers who are trying to wiretap the information or disturb the network stability. In downlink networks, based on the random feature of channels to terminals, opportunistic user scheduling can be exploited as an additional tool for enhancing physical layer security. We introduce user scheduling strategies and discuss the corresponding performances according to different levels of channel state information (CSI) at the base station (BS). We show that the avai

The development of wireless sensor networks (WSNs) in the underwater environment leads to underwater WSN (UWSN). It has severe impact over the research field due to its extensive and real-time applications. However effective execution of underwater WSNs undergoes several problems. The main concern in the UWSN is sensor nodes’ energy depletion issue. Energy saving and maintaining quality of service (QoS) becomes highly essential for UWASN because of necessity of QoS application and confined sensor nodes (SNs). To overcome this problem, numerous prevailing methods like adaptive data forwarding techniques, QoS-based congestion control approaches, and various methods have been devised with maximum throughput and minimum network lifesp

In this paper, we characterize the percolation condition for a continuum secondary cognitive radio network under the SINR model. We show that the well-established condition for continuum percolation does not hold true in the SINR regime. Thus, we find the condition under which a cognitive radio network percolates. We argue that due to the SINR requirements of the secondaries along with the interference tolerance of the primaries, not all the deployed secondary nodes necessarily contribute towards the percolation process- even though they might participate in the communication process. We model the invisibility of such nodes using the concept of Poisson thinning, both in the presence and absence of primaries. Invisibility occurs due to nodes

The development of wireless sensor networks (WSNs) in the underwater environment leads to underwater WSN (UWSN). It has severe impact over the research field due to its extensive and real-time applications. However effective execution of underwater WSNs undergoes several problems. The main concern in the UWSN is sensor nodes’ energy depletion issue. Energy saving and maintaining quality of service (QoS) becomes highly essential for UWASN because of necessity of QoS application and confined sensor nodes (SNs). To overcome this problem, numerous prevailing methods like adaptive data forwarding techniques, QoS-based congestion control approaches, and various methods have been devised with maximum throughput and minimum network lifesp