Applied Mathematics-A Journal of Chinese Universities Series B最新文献

In this article, we are exploring the hemodynamics of nanofluid, flowing through a bifurcated artery with atherosclerosis in the presence of a catheter. For treating obstruction in the artery, one can use the catheter whose outer surface is carrying the drug coated with nano-particles. The resultant solvent is considered as blood nano-fluid. Blood being a complex fluid, is modeled by couple stress fluid. In the presence of nano-particles, the temperature and the concentration distribution are understood in a bifurcated stenotic artery. The concluded mathematical model is governed by coupled non-linear equations, and are solved by using the homotopy perturbation method. Consequently, we have explored is the effects of fluid and the embedded geometric parameters on the hemodynamics characteristics. It is also realized that high wall shear stress exists for couple stress nano-fluid when compared to Newtonian nanofluid. which is computed at a location corresponding to maximum constriction (z = 12.5) of the artery.

In this paper, we investigate the CUSUM statistic of change point under the negatively associated (NA) sequences. By establishing the consistency estimators for mean and covariance functions respectively, the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge, which extends the results obtained under the case of an independent normal sample and the moving average processes. Finally, the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.

In this paper, we consider the following generalized nonlinear k-Hessian system

where ({cal G}) is a nonlinear operator and S_k (λ(D²z)) stands for the k-Hessian operator. We first are interested in the classification of positive entire k-convex radial solutions for the k-Hessian system if φ(∣x∣, z₁, z₂) = b(∣x∣)φ(z₁, z₂) and ψ(∣x∣, z₁, z₂) = h(∣x∣)ψ(z₁). Moreover, with the help of the monotone iterative method, some new existence results on the positive entire k-convex radial solutions of the k-Hessian system with the special non-linearities ψ,φ are given, which improve and extend many previous works.

Particle Swarm Optimization, a potential swarm intelligence heuristic, has been recognized as a global optimizer for solving various continuous as well as discrete optimization problems. Encourged by the performance of Gompertz PSO on a set of continuous problems, this works extends the application of Gompertz PSO for solving binary optimization problems. Moreover, a new chaotic variant of Gompertz PSO namely Chaotic Gompertz Binary Particle Swarm Optimization (CGBPSO) has also been proposed. The new variant is further analysed for solving binary optimization problems. The new chaotic variant embeds the notion of chaos into GBPSO in later stages of searching process to avoid stagnation phenomena. The efficiency of both the Binary PSO variants has been tested on different sets of Knapsack Problems (KPs): 0–1 Knapsack Problem (0-1 KP) and Multidimensional Knapsack Problems (MKP). The concluding remarks have made on the basis of detailed analysis of results, which comprises the comparison of results for Knapsack and Multidimensional Knapsack problems obtained using BPSO, GBPSO and CGBPSO.

Although there are many papers on variable selection methods based on mean model in the finite mixture of regression models, little work has been done on how to select significant explanatory variables in the modeling of the variance parameter. In this paper, we propose and study a novel class of models: a skew-normal mixture of joint location and scale models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The problem of variable selection for the proposed models is considered. In particular, a modified Expectation-Maximization(EM) algorithm for estimating the model parameters is developed. The consistency and the oracle property of the penalized estimators is established. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. An example is illustrated by the proposed methodologies.

In this paper, first, Bernstein multi-scaling polynomials (BMSPs) and their properties are introduced. These polynomials are obtained by compressing Bernstein polynomials (BPs) under sub-intervals. Then, by using these polynomials, stochastic operational matrices of integration are generated. Moreover, by transforming the stochastic integral equation to a system of algebraic equations and solving this system using Newton’s method, the approximate solution of the stochastic Itô-Volterra integral equation is obtained. To illustrate the efficiency and accuracy of the proposed method, some examples are presented and the results are compared with other methods.

As is well known, the definitions of fractional sum and fractional difference of f (z) on non-uniform lattices x(z) = c₁z² + c₂z + c₃ or x(z) = c₁q^z + c₂q^−z + c₃ are more difficult and complicated. In this article, for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways. The analogue of Euler’s Beta formula, Cauchy’ Beta formula on non-uniform lattices are established, and some fundamental theorems of fractional calculas, the solution of the generalized Abel equation on non-uniform lattices are obtained etc.

Based on the quantile regression, we extend Koenker and Xiao (2004) and Ling and McAleer (2004)’s works from finite-variance innovations to infinite-variance innovations. A robust t-ratio statistic to test for unit-root and a re-sampling method to approximate the critical values of the t-ratio statistic are proposed in this paper. It is shown that the limit distribution of the statistic is a functional of stable processes and a Brownian bridge. The finite sample studies show that the proposed t-ratio test always performs significantly better than the conventional unit-root tests based on least squares procedure, such as the Augmented Dick Fuller (ADF) and Philliphs-Perron (PP) test, in the sense of power and size when infinite-variance disturbances exist. Also, quantile Kolmogorov-Smirnov (QKS) statistic and quantile Cramer-von Mises (QCM) statistic are considered, but the finite sample studies show that they perform poor in power and size, respectively. An application to the Consumer Price Index for nine countries is also presented.

In this paper, we formulate and analyze a new fractional-order Logistic model with feedback control, which is different from a recognized mathematical model proposed in our very recent work. Asymptotic stability of the proposed model and its numerical solutions are studied rigorously. By using the Lyapunov direct method for fractional dynamical systems and a suitable Lyapunov function, we show that a unique positive equilibrium point of the new model is asymptotically stable. As an important consequence of this, we obtain a new mathematical model in which the feedback control variables only change the position of the unique positive equilibrium point of the original model but retain its asymptotic stability. Furthermore, we construct unconditionally positive nonstandard finite difference (NSFD) schemes for the proposed model using the Mickens’ methodology. It is worth noting that the constructed NSFD schemes not only preserve the positivity but also provide reliable numerical solutions that correctly reflect the dynamics of the new fractional-order model. Finally, we report some numerical examples to support and illustrate the theoretical results. The results indicate that there is a good agreement between the theoretical results and numerical ones.

In this paper, weak optimal inverse problems of interval linear programming (IvLP) are studied based on KKT conditions. Firstly, the problem is precisely defined. Specifically, by adjusting the minimum change of the current cost coefficient, a given weak solution can become optimal. Then, an equivalent characterization of weak optimal inverse IvLP problems is obtained. Finally, the problem is simplified without adjusting the cost coefficient of null variable.