Fuzzy logic is a new scientific field which is employed in mathematics, computer science and Engineering. Fuzzy logic calculates the extent to which a proposition is correct and allows computer to manipulate the information. The aim of this paper is to prove some common fixed point theorems using the property E.A. in the setting of G-metric and Fuzzy metric space by taking a set of three conditions for self mappings. Here the notion of semi compatibility and occasionally compatibility is used to replace the assumption of continuity and completeness of space. Our result generalizes the result of Tanmony Som [1] and Mujahid Abbas [2].

Min Sun1, Jing Liu2 1.School of Mathematics and Statistics, Zaozhuang University , Zaozhuang, 277160, China. 2.School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, 310018, China. (Received November 08, 2014, accepted March 07, 2015) This paper proposes a parallel descent-like prediction-correction method(PDPCM) for structured variational inequalities with three blocks. In the prediction step, the intermediate point is produced by solving three low-dimensional variational inequalities in parallel. In the correction step, a descent direction is first constructed using the iterate and the intermediate point, and then the new iterate is obtained along this descent direction. Global convergence of the proposed method is proved under mild assumptions, and we also establish its worse-case

In this paper, we consider a new suitable lacunary fractional interpolation with the idea of the spline function of polynomial form, and the method applied to solve linear fractional differential equations. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented by several examples, results also show that the technique introduced here is robust and easy to apply.

In order to keep stable in reinforcement learning process, a novel robust reinforcement learning decoupling control (RRLDC) based on integral quadratic constraints（IQC）is presented in this paper. It composes of a linear model to approximate the nonlinear plant, a state feedback K controller to generate the basic control law, and an adaptive critic unit to evaluate decoupling performance, which tunes an actor unit to compensate decoupling action and model uncertainty as well as system nonlinearity. By replacing nonlinear and time-varying aspects of a neural network and model uncertainty with IQC, the stability of the control loop is analyzed. As a result, the range of the adjusted parameters is found within which the stability is guaranteed, the control system performance is improved through learning and the algorithm convergence speed is accelerated. The proposed RRLDC is applied to gas collector pressure control of coke ovens. The simulation results show the proposed control strategy can not only obtain the good performance, but also avoid unstable behavior in learning process. It is an effective multivariable decoupling control method for a class of strong coupling systems such as the gas collector pressure control of coke ovens.the effectiveness of proposed control strategy for the collector gas pressure of coke ovens

In this work, the homotopy perturbation method, a powerful technique, is applied to obtain an unknown time-dependent function in a semi-linear parabolic equation with given initial and boundary conditions. This kind of problem plays a very important role in many branches of science and engineering. Using the homotopy perturbation method a rapid convergent sequence can be constructed which tends to the exact solution of the problem. Some examples are presented to illustrate the strength of the method.

In recent years, the rise of GPGPU as a viable solution for high performance computing has been accompanied by fresh challenges for developers. Chief among these challenges is efficiently harnessing the formidable power of the GPU and finding performance bottlenecks. Many factors play a role in a GPU application’s performance. This creates the need for studies performance comparisons, and ways to analyze programs from a fundamental level. With that in mind, our goal is to present an in-depth performance comparison of the CUDA and OpenCL platforms, and study how PTX code can affect performance. In order to achieve this goal, we explore the subject from three different angles: kernel execution times, data transfers that occur between the host and device, and the PTX code that is generated by each platform’s compiler. We carry out our experiments using ten real-world GPU kernels from the digital image processing domain, a selection of variable input data sizes, and a pair of GPUs based on the Nvidia Fermi and Kepler architectures. We show how PTX statistics and analysis can be used to provide further insight on performance discrepancies and bottlenecks. Our results indicate that, in an unbiased comparison such as this one, the OpenCL and CUDA platforms are essentially similar in terms of performance.

In this paper, the homotopy perturbation method is proposed to solve an inverse problem of finding an unknown function in parabolic equation with overspecified data. Comparison is made between Adomian decomposition method and the proposed method. It is shown; Adomian decomposition method is equivalent to the homotopy perturbation method in the model problem. To show the efficiency of these methods, several test problems are presented for one-, two- and three-dimensional cases. Comparison of the applied methods with exact solutions reveals that both methods are tremendously effective.

The problem of controlling chaotic system is studied by using back stepping design method. This technique is applied to achieve chaos control for each state of the nonlinear dynamical system. Based on Lyapunov stability theory, control laws are derived. The same technique is used to enable the stabilization of the chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the theoretical results..

As an important new laser processing technique, the high-power disk laser welding has been increasingly widely used in the manufacturing area. Aiming at the strong coupling multi-variable and real- time feedback requirements of the welding process, a new method using support vector machine is proposed to predict the width of the molten pools. The performance of this model is validated by the test data. Meanwhile, analysis and comparison between the support vector machines and the BP neural network are conducted. Experiment results show that the support vector machine and the BP neural network both have a good predictive ability. However, in comparison with the BP neural network, the support vector machine is more suitable for high-power disk laser welding process.