Due to the complex environment which neurons are located in, Hindmarsh-Rose neuron model is modified by introducing a new variable and linear coupling. Via numerical simulations, multiple modes of electric activities of the addressed neuron model can be observed by changing external forcing current. To explore the energy transition between different electric activity modes, Hamilton energy is calculated when the proposed neuron is disturbed by periodic signal. It is found that the energy is closely dependent on the electric activity mode caused by external forcing current. An interesting phenomenon is also obtained that the Hamilton energy is delayed by external forcing current, which means that the neuron plays an important role in energy coding.

This paper explores the advantage of Pythagorean fuzzy sets in personnel appointments by employing normalized Euclidean similarity to find the similarity between applicants to each positions. The choice of Euclidean similarity for Pythagorean fuzzy sets by incorporating the three traditional parameters, is because it gives a reliable similarity with respect to other similarity measures for Pythagorean fuzzy sets that incorporate the three traditional parameters as studied in literature. By finding the similarity of the applicants and positions (both in Pythagorean fuzzy pairs/values), in the light of the qualifications require by the organisation, we determine the suitable applicants for the available positions. Also, we propose the notions of level sets of Pythagorean fuzzy sets and Pythagorean fuzzy pairs.

In this paper we consider Bagley-Torvik fractional differential equations, which are arising in the modeling of motion of rigid plate immersed in a Newtonian fluid. The main attribution of our content is that it transforms the fractional differential equations to a system of algebraic equations without any restrictions and assumptions. Theoretical results are authenticated by five numerical examples of both linear and nonlinear. To demonstrate the accuracy and efficiency of the Haar wavelet collocation method and results are compared with the existing methods.

Excessively optimistic and negative investor sentiment will affect the stability of stock market. In this paper, we investigate investor sentiment diffusion considering hesitating and forgetting mechanism on homogeneous network. Different from previous studies, we introduce the exponent form forgetting rate into SEIR model and figure out the basic reproduction number and existence of equilibrium point. Meantime, the locally asymptotic stability and global stability of internal equilibrium point are established. Finally, we illustrate the impact of forgetting rate on the investor sentiment diffusion through carrying out numerical simulations.

Based on Hindmarsh-Rose neuron model, a 4D neuron model is addressed. Dynamical behaviors of the proposed neuron model are investigated under external periodic disturbance. The diversity of dynamics of the neuron is revealed via altering the parameters in the external periodic disturbance. The research results may be beneficial for further exploring the dynamic behaviors relative to the mode transition of neuron network.

This research paper is deals with the behavior of gyrotactic in peristaltic transport of nano Eyring-Powell fluid in non-uniform channel. The advantages of adding motile micro-organism to the nanofluid suspension enhanced the heat transfer, mass transfer and improve the nanofluids stability. The governing equations have been fabricated for long wavelength and low Reynolds number assumptions. The solutions have been described for pressure gradient, temperature, nanoparticle concentration and density of motile microorganism equations and solved by using powerful technique known as Homotopy Analysis Method (HAM). Results are reported for different values of the some significant parameters on peristaltic transport through a non-uniform channel and obtained results are displayed in graphs.

Wavelet based methods are the new development in the area of applied mathematics. Wavelets are mathematical tools that cut functions or operators into different frequency components, and then study each component with a resolution matching to its scale. In this paper, we proposed Biorthogonal wavelet based full-approximation scheme for the numerical solution of Burgers’ equation arising in fluid dynamics using biorthogonal wavelet filter coefficients as prolongation and restriction operators. The proposed method gives higher accuracy in terms of better convergence with low computational time, which has been demonstrated through the illustrative problem.

In the development of medical image segmentation, the application of convolutional neural networks has begun a profound revolution. The deep learning model is famous for excellent flexibility, efficiency and accuracy. The U-Net model is the beginning of task in the segmentation of medical images, which includes the basic operations of convolution, maxpooling, deconvolution, and concatenation. However, the U-Net model is disable to perform well on many types of data sets, because the model can’t solve the exact segmentation of the details. We proposed Residual and Dense Fully Convolutional Network (RDFCN) that consist of Residual Connection Block and Dense Connection Block, which makes up for the shortcomings of U-Net. The dataset we used for training and testing comes from iSeg-2017 challenge (http://iseg2017.web.unc.edu). This dataset is comprised of infant(between 6 and 9 months of age) brain MR images. After the testing, our model outperforms the U-Net and some of its improved models in evaluation of WM, GM and CSF.