Dagestan state university of national economy, Makhachkala, Russia E-mail: arslan_mustafaev@mail.ru (Received May 10 2018, accepted August 21 2018) Abstract One of the problems with the use of renewable energy sources is the determination of the optimal location of a wind or solar power station on the earth's surface. The paper suggests a model for predicting the solar energy level in the region, which allows choosing the most effective location for the location of a solar power plant. The forecast of the solar energy level is made by means of an artificial neural network, trained at the data of meteorological stations, using the backpropagation algorithm. Comparison of results of the solar energy level forecast made by the artificial neural network with the actual values shows a good correlation. This confirms the possibility of using artificial neural networks for modeling and forecasting in regions where there is no data on the level of solar energy, but there are other data from meteorological stations.

1 Prema Ramasamy, Assistant Professor, New Horizon College of Engineering, Bangalore E-mail:premabit@gmail.com 2 Professor, Department of Computer Science and Engineering, Bannari Amman Institute of Techlology, Sathyamangalam. (Received May 11 2018, accepted July 16 2018) Contemporary biological technologies like gene expression microarrays produce extremely high- dimensional datasets with limited samples. Analysis of gene expression data is essential in microarray gene expression studies in order to retrieve the required information. Gene expression data generally contain a large number of genes but a small number of samples. The complicated relations among the different genes make analysis more difficult, and removing irrelevant genes improves the quality of results. In this regard, a new feature selection algorithm called 2-level MRMS is presented based on rough set theory. It selects a set of genes from microarray data by maximizing the relevance and significance of the selected genes. The paper also presents a novel discretization method, Gaussian Fuzzy Discretization based on fuzzy logic to discretize the continuous gene expression values. The performance of the proposed algorithm, along with a comparison with other related feature selection methods, is studied using the classification accuracy of k-Nearest Neighbor (kNN) and Support Vector Machine (SVM) on four microarray data sets. The experimental results show that the genes selected using 2-level MRMS feature selection give high classification accuracy than other methods.

(Received May 06 2018, accepted August 10 2018) Based on Laguerre wavelets, an efficient numerical method is proposed for the numerical solution of initial and boundary value Bratu-type problems arising in fuel ignition of the combustion theory and heat transfer. Convergence of the method for these kinds of problems is addressed in the form of theorems with proof. To illustrate the ability of the method is validated on test problems, numerical results are compared with exact and those from existing methods in the literature. The results demonstrate the accuracy and the efficiency of the Laguerre wavelet based numerical method.

1School of Binjiang, Nanjing University of Information Science & Technology, Nanjing 210044, China 2School of Applied Meteorology, Nanjing University of Information Science & Technology, Nanjing 210044, China 3Department of Mathematics, Southeast University, Nanjing 210000, China (Received March 12 2018, accepted August 28 2018) Abstract We present a relaxation algorithm for solving linear programming (LP) problems under the framework of the primal-dual simplex algorithm. Each iteration, based on a heuristic representation of the optimal basis (the principle of the most obtuse Angle), the algorithm constructs and solves a sub-problem, whose objective function is the same as the original problem, but only contains partial constraints.The primal- dual simplex algorithm is used to solve the sub-problem. If the sub-problem has an optimal solution or the sub-problem has no feasible solution, the constraint is added according to the principle of the obtuse Angle and then the final solution of the old sub-problem is taken as the starting point. Our preliminary numerical experiments show that the proposed algorithm can effectively reduce the number of iterations compared with the traditional two-stage simplex algorithm. Iterations for sub-problems take up a significant proportion, which greatly reduces the CPU time required for each iteration. The new algorithm has potential advantages in solving large-scale problems. It's a very promising new algorithm.

1School of Binjiang, Nanjing University of Information Science & Technology, Nanjing 210044, China 2Department of Mathematics, Southeast University, Nanjing 210000, China (Received March 03 2018, accepted August 19 2018) When the linear programming (LP) problem satisfies neither the primal feasibility nor the dual feasibility, the primal-dual simplex method can be used to solve the problem in order to avoid the defect of the increase of decision variables caused by the addition of artificial variables in the two-stage algorithm. In this paper, we use PPSM (primitive - primitive simplex method) and DDSM(dual - dual simplex method) to solve these problems. Compared with the simplex method of two-stages, a better result is obtained.

Shuxian Huang, Wenbing Chen Nanjing University of Information Science and Technology, Nanjing 210044, China (Received January 17 2018, accepted July 05 2018) In this paper, a salient object-based image retrieval method (SOBIR) is presented, which linearly combines the shape and colour features of the salient objects contained in target and candidate images respectively to carry out content-based image retrieval (CBIR). The framework of the proposed method is carried out as follows: first, the mean shift and region growing algorithms are used to segment an input image into many regions; secondly, based on these regional contrasts the saliency map, the binary image, and the salient object image are extracted respectively; thirdly, the shape representation of the salient object is extracted from the binary image using an improved polar Fourier Descriptor method, meanwhile the salient object contained in the input image is converted into a representation of its histogram in the L∗a∗b∗ colour space; Finally, the similarity between the two salient objects contained in the target and candidate images is defined by linearly combining both the shape and colour representations. Experimental results show that, compared to the latest two CBIR methods, the proposed SOBIR method exhibits an excellent performance in precision, recall, flexibility and efficiency.

School of Information Engineering, Yancheng Teachers University, 224002 Yancheng, China (Received June 07 2018, accepted August 22 2018) In this paper, the problem of asymptotic stability for Takagi-Sugeno (T-S) fuzzy Hopfield neural networks with time-varying delays is studied. Based on the Lyapunov functional method, considering the system with uncertainties or without uncertainties, new delay-dependent stability criteria are derived in terms of Linear Matrix Inequalities (LMIs) that can be calculated easily by the LMI Toolbox in MATLAB. The proposed approach does not involve free weighting matrices and can provide less conservative results than some existing ones. Besides, numerical examples are given to show the effectiveness of the proposed approach.

Abstract In this paper, the problem of periodic solutions is studied for singular Liénard equations

Tang Jie, Liu Xiaoli Nanjing University of Information Science and Technology, Key Laboratory of aerosol and cloud precipitation in China Meteorological Administration, Nanjing, Jiangsu 210044 (Received January 07 2018, accepted May 25 2018) Abstract Three boundary layer parameterization schemes (MRF,UW,YSU) in mesoscale numerical model (WRF) are used to simulate a severe convective weather in Zhejiang on November 9, 2009 without considering the rainwater evaporation term and considering the rainwater evaporation term. The numerical simulation results of macroscopic and microscopic physical mechanisms of strong convection were compared. The results show that without considering the evaporation of rainwater, the rainbands simulated by the three boundary layer schemes are narrower, hourly precipitation is smaller, convective monomer moves slower, and the precipitation overlap area is more. The simulated radar reflectivity intensity is significantly reduced and the echo band is narrower. Whether rain evaporation is considered or not, the YSU scheme simulates the strongest precipitation and radar reflectivity, MRF scheme is close to it and the UW scheme is the weakest. By analyzing the macro conditions of convection development, it can be seen that under the condition of considering the rainwater evaporation, high and low altitude divergence configuration simulated by the three boundary layer schemes is better, the water vapor transport is more abundant, updraft and downdraft are stronger, providing more favorable conditions for the occurrence and development of strong convection. Whether rain evaporation is considered or not, the water vapor conditions and high and low altitude divergence configuration simulated by the YSU scheme are better, results simulated by MRF scheme is similar to YSU scheme. The convection generation condition simulated by the UW scheme is the weakest of the three schemes. Under the condition of considering the rainwater evaporation, more hydrogel particles simulated by three boundary layer schemes, and stronger updraft, which is more conducive to development of convection. Whether rain evaporation is considered or not, the MRF and YSU schemes can simulate more rain, mainly because the vertical movement of the airflow is stronger, and more cloud water becomes cold cloud water under the strong ascending airflow, and more cold water frozen with graupel to form graupel, graupel melts to produce more rain. The UW scheme have poor macroscopic conditions, and the updraft is weaker. Cold cloud water is less, and cold cloud water and graupel are less frozen, resulting in less rainwater content