School of Math and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China (Received March 21 2019, accepted September 20 2019) The existence of positive periodic solutions is studied for the Rayleigh equation with a singularity of attractive type

*Department of Mathematics, Karnatak University, Dharwad, India. **Department of Mathematics, MES Degree College, Bangalore, India. (Received March 05 2019, accepted September 28 2019) Laguerre wavelet based numerical method is developed for the solution of Abel’s integral equations. This method is based on Laguerre wavelets basis. Laguerre wavelet method is then utilized to reduce the Abel’s Integral Equations into the solution of algebraic equations. Illustrative examples are shows that the validity, efficiency and applicability of the proposed technique. This algorithm provides high accuracy and compared with other existing methods.

2Faculty of Science, Jiangsu University, Zhenjiang Jiangsu 212013, China, (Received September 03 2019, accepted October 27 2019) The main aim of this manuscript is to investigate the control issue for a Lorenz system with time delay applying a hybrid control method based on state feedback and parameter perturbation. By choosing the time delay as the bifurcation parameter and utilizing stability theory for delay differential equation, the local stability in two different cases with time delay equal to 0 and not equal to 0 is discussed. With the help of Hopf bifurcation theorem, the beingness of Hopf bifurcation is established by combining the distribution results of the characteristic roots. And the hybrid control method can availably postpone the Hopf bifurcation by numerical simulations.

1 Textile Material and Processes Research Unit, University of Monastir, Tunisia (Received October 11 2019, accepted November 28 2019) Decisions trees are one of the most commonly used data mining techniques to practically solve classification and prediction problems. They have tree shaped structures in which construction of trees is simple and unlike the logistic regression models, decision tree results can be easily understood by the users. In this study, a decision tree induction algorithm known as CART (Classification and Regression Trees) has been employed in order to better understand the influence of plasma parameters adjustment on polypropylene (PP) film’s hydrophilic surface properties. The cross-validation method was used for pruning the decision tree. The root mean square errors (RMSE) and correlation coefficients (R) for training and test subsets were used in order to get the best fitting model. The obtained decision tree regression model showed excellent learning performance and achieved good predictive accuracy.

1 School of Information Engineering, Yancheng Teachers University, Yancheng 224002, China 2 Department of Medical Instrumen,Yancheng Third People’s Hospital, Yancheng 224001, China (Received August 01 2019, accepted September 26 2019) In this paper, structure entropy which is based on classes dependency graph of a software system is proposed to measure the complexity of the system. In order to research the structure entropy metrics of classes dependency graph in some large software systems, this paper takes the first step to mathematically prove that structure entropy does not have the property of cohesion. Thus, a structure entropy can be used as a single metric of complexity. And then, a program is written based on relevant matrix algorithm with the construction of classes dependency graph. The corresponding metrics of structure entropy of three pieces of open source software are calculated and figured out based on classes dependency graph. The calculation shows that most classes in the three pieces of the open source software are of randomness. Meanwhile, values of structure entropy features complex network Scale-free. Therefore, the different values of the structure entropy of open source software classes dependency graph influences the evaluation of software quality. Furthermore, some complex network statistical characteristics are found out in this paper, which will facilitate the further research on structure entropy as a metric of software complexity for sophisticated networks.

1 Department of Computer Engineering, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran 2 Department of Computer Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran (Received October 15 2019, accepted December 26 2019) Nowadays, according to the increasingly increasing information, the importance of its presentation is also increasing. The internet has become one of the main sources of information for users and their favorite topics. It also provides access to more information. Understanding this information is very important for providing the best set of information resources for users. Content providers now need a precise and efficient way to retrieve news with the least human help. Data mining has led to the emergence of new methods for detecting related and unrelated documents. Although the conceptual relationship between documents may be negligible, it is important to provide useful information and relevant content to users. In this paper, a new approach based on the Combination of Features (CoF) for information retrieval operations is introduced. Along with introducing this new approach, we proposed a dataset by identifying the most commonly used keywords in documents and using the most appropriate documents to help them with the abundance of vocabulary. Then, using the proposed approach, techniques of text categorization, evaluation criteria and ranking algorithms, the data were analyzed and examined. The evaluation results show that using the combination of features approach improves the quality and effects on efficient ranking.

1 College of Information and Science Technology, Jinan University, Guangzhou, 51000, China (Received November 02 2019, accepted December 28 2019) The combination of advanced computer vision technology and insect image recognition technology can be effectively applied to environmental monitoring, pest diagnosis, epidemiology and other fields. However, accurate location and classification of relatively small insects in complex scenes has always been a difficult problem for this technology. Although YOLOv3 combines deep features with shallow features to facilitate the detection of small objects, experiments have found that YOLOv3 has more undetected cases for small target insects in complex backgrounds. In order to solve this problem, this paper optimizes YOLOv3 algorithm. Firstly, the SE blocks are embedded into YOLOv3 network to learn global features and enhance the expression ability of feature maps, so that the network can detect more objects. Because YOLOv3 itself has a complex network structure and the amount of parameters and calculations are increased after embedding the SE block, so this paper also uses depthwise separable convolutions, which greatly reduces the amount of parameters and computation under the condition of little loss of accuracy, thus improving the detection speed. Training and testing on the insect dataset made in this paper, the original YOLOv3 runs at 33 f / s, and the mean Average Precision (mAP) is only 86.8%, While the improved YOLOv3 runs at 38 f / s, the mAP reaches 90.6%. The improved algorithm can detect more targets, reduce the omission factor and improve the detection speed.

1 Department of Mathematics, Jinan University, Guangzhou, 510632, China (Received November 06 2019, accepted December 28 2019) The multiple sequence alignment (MSA) is a usual tool in DNA sequence comparison. However, this method meets a hard challenge for a large number of long DNA sequences. To remedy this problem, we propose a new way for DNA sequence comparison based on a novel DNA map. The method is that, by assigning a dinucleotide to a number, we construct a new graphical representation of DNA sequences based on horizontal lines. We further utilize the maximal eigenvalue of a related matrix to derive a mathematical descriptor for a DNA sequence. We also perform the similarity/dissimilarity analysis among the coding sequences of ribulose bisphosphate carboxylase small chain gene and large chain gene of flowering plants. The results indicate that this method can be reliable in the comparison of the flowering plant DNA sequences.

In this paper, we introduce a piecewise modified matrix Padé-type approximation of hybrid order in the interval [0, 1]. It yields highly accurate results and exact values at some given points. The accuracy of this approximation increases as the order or the node increases. This method can be applied to approximate the exponential function. The explicit formula for computing the matrix exponential is presented. A numerical example is given to illustrate the effectiveness of this method.