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In this paper, we consider a stochastic two-species competition system with impulsive effects. Some dynamical properties are investigated and sufficient conditions for the stochastic boundedness, stochastic permanence and global attractivity are established. Under some conditions, we conclude that the stochastic model is persistent in mean and extinction. An example is given to illustrate the main result.

Carbonate reservoir is one kinds of important reservoir in the world. Because of the characteristics of carbonate reservoir, horizontal well, and acid fracturing became a key technology for efficiently developing carbonate reservoir. Establishing corresponding mathematical models and analyzing transient pressure behaviors of this type of well-reservoir configuration can provide a better understanding of fluid flow patterns in formation as well as estimations of important parameters. A coupling mathematical model for a fractured horizontal well in triple media carbonate reservoir with three kinds of reservoir outer boundaries by conceptualizing vugs as spherical shapes is presented in this article, in which the infinite conductivity of the acid fractures is taken into account. A semi-analytical solution is obtained in the Laplace domain by using source function theory, Laplace transformation, discretization of fracture, and superposition principle. Analysis of transient pressure responses indicates that several characteristic flow periods of fractured horizontal wells in triple media carbonate reservoir can be identified. Parametric analysis shows that fracture half-length, fracture number, fracture spacing, conditions of reservoir outer boundary, and so on can significantly influence the transient pressure responses of fractured horizontal wells in triple media carbonate reservoir. The model presented in this article can be applied to obtain important parameters pertinent to reservoir or fracture by type curve matching, and it can also provide useful information for optimizing fracture parameters.

This paper describes a numerical model and its finite element implementation that used to compute the cavitation effects on nonlinear acoustic fluid and adjacent flexible structure interaction. The system is composed of two sub-systems, namely, the fluid and the flexible flat plate. A fully coupled approach using iterative implicit partitioned scheme was implemented in the present work which can account for the effects associated whit a mutual interaction. This approach included a compressible nonlinear acoustic fluid Eulerian solver and a Lagrangian solver for the flexible structure both in finite element formulation. A novel implementation of acoustic cavitation was made possible with the introduction of a simplified one-fluid cavitation model. The element-by-element PCG (Preconditioned Conjugate Gradient) solver together with diagonal preconditioning is used to solve the large equation system resulting from the finite element discretization of the governing equation of fluid domain. The capability of three different cavitation model, as the cut-off model, Modified Schmidt model and developed model are compared with each other in the evaluation of plate vibration response. Simulation results are presented on a large size shock tube, in which planar shock waves were impacting in “face on” configuration flat plates mounted at tube's end. Results are presented to demonstrate the capability of proposed solver in simulating cavitating nonlinear acoustic fluid. Obtained results show that impact forces caused impinging shock wave and reloading by cavitating region collapse have a considerable effect on the dynamic response of flexible plate.

The main aim of this paper is to present some basic as well as essential results involving the notion of p-Chebyshev sets in probabilistic normed spaces. In particular, we discuss the convexity of p-Chebyshev sets, decomposition of the space into its special subspaces, and we see a characterization of p-Chebyshev sets in quotient spaces.

This paper treats the existence of mild solutions for Sobolev-type Hilfer fractional nonautonomous evolution equations with delay in Banach spaces. We first characterize the definition of mild solutions for the studied problem which was given based on an operator family generated by the operator pair ( A , B ) and probability density function. And then via Hilfer fractional derivative and combining the techniques of fractional calculus, measure of noncompactness and Sadovskii fixed-point theorem, we obtain new existence result of mild solutions for Sobolev-type Hilfer fractional nonautonomous evolution equations. Particularly, the existence or compactness of an operator B−1$B^{-1} $ is not necessarily needed in our results. Furthermore, our results obtained improve and extend some related conclusions on this topic. At last, an example is given to illustrate our main results.

In this paper, we consider a non-linear sequential differential equation with Caputo fractional derivative of Blasius type and we reduce the problem to the equivalent non-linear integral equation. We prove the complete continuity of the non-linear integral operator. The theorem on the existence of a solution of the problem for the Blasius equation of fractional order is also proved.

Non-linear processes like conical tank control system is complex because of its non-linear characteristics, long-term interval and time difference between the system input and output. In this context, neural network based controller works since it is able to control and train the non-linear data set of liquid level in order to optimize the network performance. Hence, this article proposes a neural network control using gradient descent with adaptive learning rate that improves the performance and minimizes the errors, by using moving average filter and Hanning window to enhance the non-linear data. The article mainly deals with an application involving ARMA and artificial neural-based network (ANN) to model a conical tank system. To remove the recurrent components and to predict the future values of the process, the present paper employs an Autoregressive Moving Average Model (ARMA) by identifying its time varying parameters and combining with artificial neural network. MATLAB R2016b was applied for the entire simulation and training of non-linear data set. The simulation results indicate a minimization in the difference between the net input to the output and target value with that of error. The results indicated that the simulation took only 13 s to train the entire network for 6,135 iterations with the ARMA based model.

In this paper, we establish a new composition theorem for pseudo almost periodic functions under non-Lipschitz conditions. We apply this new composition theorem together with a fixed-point theorem for condensing maps to investigate the existence of p$p$-mean piecewise pseudo almost periodic mild solutions for a class of impulsive nonautonomous partial functional stochastic evolution equations in Hilbert spaces, and then, the exponential stability of p$p$-mean piecewise pseudo almost periodic mild solutions is studied. Finally, an example is given to illustrate our results.

This paper is devoted to investigate a question of the existence of solutions to boundary value problems for a class of nonlinear difference systems. The proof is based on the notable mountain pass lemma in combination with variational technique. By using the critical point theory, some new existence criteria are obtained.

In this paper, a higher order nonlinear difference equation is considered. By using the critical point theory, we obtain the existence and multiplicity for solutions of difference Dirichlet boundary value problems and give some new results. The proof is based on the variational methods and linking theorem.

In this study, we investigated the propagation of the compressive waves in twp-dimensional highly ordered particle assemblies with different material properties and confining stresses. We focused on the attenuation of velocity amplitude, wave speed and energy dispersion behaviors. The mechanisms of wave propagation through specimens containing inclusions that show different horizontal angles were simulated. The peak velocities change exponentially as a function of time along the wave propagation direction. Energy dispersion exhibits an increasing trend as the angle increases. Then the effects of material parameter on wave propagation speed and the confining stress with the dispersion relations are determined. Finally, the shape of wavefront is studied to show the propagation of stress wave. It is linked to the distribution of equivalent strain. The outer contours of wavefront and strain distribution have the same shape.

In this paper, Ulam’s-type stabilities are studied for a class of first-order impulsive differential equations with bounded variable delays on compact interval with finite number of impulses. Results of stability are proved via newly established integral inequality of Bellman–Grönwall–Bihari type with delay for discontinuous functions. Using this inequality for the first time and assumption of α$\alpha$-Ho¨$\ddot{o}$lder’s condition instead of common Lipschitz condition is novelty of this paper. Moreover, solution is obtained in quasi–Banach spaces which is best suited for obtaining results under the assumptions of α$\alpha$-Ho¨$\ddot{o}$lder’s condition.