This paper considers an inverse problem for a logistic model with free boundary. This inverse problem aims to identify the growth coefficient only depending on time from a fixed point measurement data. Based on a fixed point argument, we prove the local in time existence and uniqueness of our inverse problem.

1 Department of Mathematics, Karnatak University Dharwad-580003, India 2 Department of Mathematics, Govt. First Grade College, Chikodi – 591201, India (Received September 03 2018, accepted November 21 2018) Abstract Wavelet analysis is a recently developed mathematical tool in applied mathematics. In this paper, we proposed the wavelet based Galerkin method for the numerical solution of one dimensional elliptic problems using Hermite wavelets. Here, Galerkin bases are constructed Hermite functions which are orthonormal bases and these are assumed bases elements which allow us to obtain the numerical solutions of the elliptic problems. The obtained numerical solutions are compared with the existing numerical methods and exact solution. Some of the test problems are considered to demonstrate the applicability and validity of the purposed method.

In this paper, we investigate the local stability and Hopf bifurcation analysis in a predator-prey model with square root response function and two time delays. By choosing the two delays as the bifurcation parameter and by analyzing the corresponding characteristic equations, the conditions for the stability and existence of Hopf bifurcation for the system are obtained. Finally, the corresponding numerical simulations are carried out to support the theoretical analysis.

For a m-equation seemingly unrelated regression(SUR) model, this paper derives two basic confidence ellipsoids(CEs) respectively based on the two-stage estimation and maximum likelihood estimation(MLE), and corrects the two CEs using the Bartlett correction method, resulting in four new CEs. In the meantime via using the partition matrix, we derive a new matrix-derivative-based formulation of Fisher's information matrix for calculating the maximum likelihood estimator of the m-equation SUR model. By Monte Carlo simulation, the coverage probabilities and average volumetric characteristics of CEs are compared under different sample values and different correlation coefficients. Moreover, it is proved that the CE based on the second bartlett correction method performs better even in the case of small samples. Finally, we apply these CEs to the actual data for analysis. The CEs of the SUR model with multiple equations are found to be more accurate than the case with only two equations.

1College of Electronic and information Engineering, Southwest University, China 2School of Computer and Information Science, Southwest University, Chongqing, China (Received September 09 2018, accepted November 22 2018) Abstract Sleep deprivation adversely affects the brain and cognitive function. Few studies have analyzed effect of the sleep deprivation and partial sleep restriction on rest-state brain functional network. In this study, we investigated the changes of rest-state functional magnetic resonance imaging (fMRI) in topological architectures of brain functional networks in sleep deprivation among 36 samples in sleep deprivation and 40 normal sleep controls. Our analysis revealed that the brain functional network of the clustering coefficient, characteristic path length and local efficiency are significantly increased but the global efficiency decreased significantly in sleep deprivation. Additionally, significant alterations in nodal efficiency were also found in sleep deprivation, involving anterior cingulate, inferior parietal, supramarginal gyrus, caudate nucleus, thalamus are significant decreased, and themiddle temporal gyrus are significant increased.Our results suggested that the groups of sleep deprivation were associated with disruptions in the topological structure of brain functional networks.

In this paper, we study the generalized iteration of entire functions and investigate the growth of iterated entire functions of finite iterated order. Here we prove some results on the growth of iterated entire functions of finite iterated order. The results improve and generalize some earlier results.

Abstract In this paper, a two person zero- sum matrix game with fuzzy numbers payoff is introduced. Using the fuzzy number comparison introduced by Rouben's method, 1996, the fuzzy payoff is converted into the corresponding crisp payoff. Then, For each player, a linear programming problem is formulated. Also, a solution procedure for solving each problem is proposed. Finally, a numerical example is given for illustration.

In this paper, a novel high accurate and efficient finite difference scheme is proposed for solving the Schrödinger-Poisson System. Applying a local extrapolation technique in time to the nonlinear part makes the proposed scheme linearized in the implementation. In fact, at each time step, only two tri-diagonal linear systems of algebraic equations are solved by using Thomas method. Another feature of the proposed method is the high spatial accuracy on account of adopting the compact finite difference approximation to discrete the system in space. Moreover, the proposed scheme preserves the total mass in discrete sense. Under certain regularity assumptions of the exact solution, the local truncation error of the proposed scheme is analyzed in detail by using Taylor’s expansion, and consequently the optimal error estimates of the numerical solutions are established by using the standard energy method and a mathematical induction argument. The convergence order is of O(τ 2 + h4) in the discrete L2-norm and L∞-norm, respectively. Numerical results are reported to measure the theoretical analysis, which shows that the new scheme is accurate and efficient and it preserves well the total mass and energy.