In this paper, effects of lacunary fractional derivatives and existence/ uniqueness on the fifth order spline function in fractional order have been studied. These results use in the convergence analysis of fractional spline polynomial method for such problems numerically. Theoretical results are illustrated with efficient of the absolute errors by some fractional differential examples.

In this paper we present the haar wavelet based numerical solution of the highly nonlinear with coupled differential equation, i. e., elasto-hydrodynamic lubrication with line contact problems. It is a new alternative approach and we explore its perspectives and effectiveness in the analysis of elasto-hydrodynamic lubrication problems. To confirm its versatile features solutions obtained, using haar wavelet based method, are compared with existing method.

The present article deals with the practical implementation of information technology for monitoring the gas consumption of the city (regional centers) on the basis of proposals additive model and taking meteorological factors. Justified and suggested automating the monitoring system of gas consumption. The functional diagram of the formation of a database of measurements and framework developed of a database to store statistical data measurement of gas consumption and meteorological factors for interval accumulation hour, day and week.

In this paper, we present the comparative study of Haar wavelet collocation method (HWCM) and Finite Element Method (FEM) for the numerical solution of parabolic type partial differential equations such as 1-D singularly perturbed convection-dominated diffusion equation and 2-D Transient heat conduction problems validated against exact solution. The distinguishing feature of HWCM is that it provides a fast converging series of easily computable components. Compared with FEM, this approach needs substantially shorter computational time, at the same time meeting accuracy requirements. It is found that higher accuracy can be attained by increasing the level of Haar wavelets. As Consequences, it avoids more computational costs, minimizes errors and speeds up the convergence, which has been justified in this paper through the error analysis.

Finding optimal k-anycast routing paths for sleep-wake scheduling wireless sensor networks(WSN) is a NP-complete problem. Most previous research work only attends to optimizing the time delay during a hop or a single path. But in terms of the performance of the end-to-end delay, this scheme is not optimal. In this paper, an optimal k-anycast routing algorithm for sleep-wake scheduling WSN is proposed to solve the problem. In the proposed algorithm, base stations apply AODV-based multipath routing protocol to acquire k-anycast routing information, then genetic algorithm is applied to search the optimal k routing paths between nodes and bases stations. Since the proposed algorithm has the feature of global optimization ability, in contrast to previous algorithms, experiment results show that the proposed algorithm can reduce end-to-end delay more efficiently．

Transmission control protocol (TCP) is a dominant transport layer protocol for reliable data delivery in the internet. When packet loss occurs, TCP makes an implicit assumption that all packet loss is due to congestion. This results in unnecessary degradation in the TCP performance while traversing over a wireless link. In this paper, to improve the performance of TCP, we use NTG loss-predictor to distinguish congestion loss from transmission loss. Based on the prediction of type of loss, an appropriate algorithm is invoked by using NTG loss-prediction parameter β. Frequency of congestion loss and wireless loss predictions are analysed. Performance of TCP is improved further by discussing stability analysis over the system. A time-delay control theory is used and by constructing Hermit matrix, analysis is made for asymptotic stability of the system. Explicit conditions are derived for Pmax (RED controller) and β (NTG loss controller) in terms of wireless network parameters. Using the characteristic equation of the matrix, convergence of the queue length at the bottleneck router is discussed. Analysis of convergence of queue length to a given target value is analysed. This establishes stability in the router performance. An approximate solution of queue length is derived. Our results provide better solutions for global stability and convergence conditions of the system.

In this paper, an image encryption is raised based on bursting synchronization of time-delay neuron system. The proposed method consists of two stages: permutation and diffusion. Security analysis illuminated the high security and the good resistance to statistical attacks.