Abstract: The Broer-Kaup system with corrections is considered. Based on the inverse scattering transform, we extend the perturbation theory to discuss the adiabatic approximate solution and -order approximate solution of one soliton to the Broer-Kaup system with corrections. PubDate: Tue, 15 Sep 2020 14:05:02 +000

Abstract: Coating often plays a role in monitoring and protecting substrates in engineering applications. Interface cracks between the coating and the substrate can lead to crack growth under the action of external loading and will cause device failure. In this paper, the behavior of a fine-grained piezoelectric coating/substrate with a Griffith interface crack under steady-state thermal loading is studied. The temperature field, displacement field, and electric field of the coupling of thermal and electromechanical problems are constructed via integral transformation and the principle of superposition. Thus, problems are transformed into a system of singular integral equations, and the expressions of thermal intensity factor, thermal stress intensity factor, and electric displacement intensity factor are obtained. We used a numerical calculation and a system of singular equations to obtain the relationship of strength factor with material parameters, coating thickness, and crack size. PubDate: Tue, 15 Sep 2020 13:20:04 +000

Abstract: The purpose of this research is to inspect the mixed convection flow of Eyring-Powell nanofluid over a linearly stretching sheet through a porous medium with Cattaneo–Christov heat and mass flux model in the presence of Hall and ion slip, permeability, and Joule heating effects. Proper similarity transforms yield coupled nonlinear differential systems, which are solved using the spectral relaxation method (SRM). The story audits show that the present research problem has not been studied until this point. Efficiency of numerous parameters on velocity, temperature, and concentration curves is exposed graphically. Likewise, the numerical values of skin friction coefficients, local Nusselt, and Sherwood numbers are computed and tabulated for some physical parameters. It is manifested that fluid velocities, skin friction coefficients, local Nusselt, and Sherwood numbers promote with the larger values of Eyring-Powell fluid parameter . It is also noticed that primary velocity promotes with larger values of mixed convection parameter , Hall parameter and ion slip parameter while the opposite condition is observed for secondary velocity, temperature, and concentration. Furthermore, comparative surveys between the previously distributed writing and the current information are made for explicit cases, which are examined to be in a marvelous understanding. PubDate: Wed, 09 Sep 2020 15:20:00 +000

Abstract: A stochastic predator-prey model with disease in the prey and Holling type II functional response is proposed and its dynamics is analyzed. We discuss the boundedness of the dynamical system and find all feasible equilibrium solutions. For the stochastic systems, we obtain the conditions for the existence of the global unique solution, boundedness, and uniform continuity. We derive the conditions for extinction and permanence of species. Moreover, we construct appropriate Lyapunov functions and discuss the asymptotic stability of equilibria. To illustrate our theoretical findings, we have performed numerical simulations and presented the results. PubDate: Fri, 04 Sep 2020 18:05:00 +000

Abstract: For a system obtained by placing more than two elastic plates side by side, the transmission conditions are obtained at the common boundaries. Finite difference equations are developed for the problem of plates with internal hinges and applied for determination of the response of a system assembled from three different plates with different mechanical constraints between adjacent plates in this study. An algorithm is written to find out how long the size of the plates should be in order to obtain the desired amount of bending against the force affecting the system under different boundary conditions. The bisection and multigrid methods are used for this. These two methods are compared based on the obtained data. PubDate: Mon, 31 Aug 2020 06:20:06 +000

Abstract: Boron nitride (BN) nanomaterials such as boron nitride graphenes, boron nitride nanotubes, and boron nitride nanocones are attracting attention among the most promising nanomaterials due to their physical, chemical, and electronic properties when compared to other nanomaterials. BN nanomaterials suggest many exciting potential applications in various fields. Joining between BN nanostructures gives new enhanced structures with outstanding properties and potential applications for design of probes for scanning tunnelling microscopy and other nanoscale devices. This paper uses calculus of variations to model the joining between BN graphene with other BN nanostructures: BNNTs and BNNCs. Furthermore, during the joining between these BN nanostructures, this research examines two models which are depending on the curvature of the join profile. For the first case, Model I refers to when the join profile only includes positive curvature where for the second case, Model II is considered for both positive and negative curvatures. Thus, the purpose of this research is to formulate the basic underlying structure to present simple models based on joining BN graphene to other BN nanostructures. PubDate: Sun, 30 Aug 2020 15:35:06 +000

Abstract: Nonlinear hydroelastic interaction among a floating elastic plate, a train of deepwater waves, and a current which decays exponentially with depth is studied analytically. We introduce a stream function to obtain the governing equation with the dynamic boundary condition expressing a balance among the hydrodynamic, the shear currents, elastic, and inertial forces. We use the Dubreil-Jacotin transformation to reformulate the unknown free surface as a fixed location in the calculations. The convergent analytical series solutions for the floating plate deflection are obtained with the aid of the homotopy analysis method (HAM). The effects of the shear current are discussed in detail. It is found that the phase speed decreases with the increase of the vorticity parameter in the opposing current, while the phase speed increases with the increase of the vorticity parameter in the aiding current. Larger vorticity tends to increase the horizontal velocity. In the opposing current, the horizontal velocity under the wave crest delays more quickly as the depth increases than that of waves under the wave trough, while in the aiding current case, there is the opposite effect. Furthermore, the larger vorticity can sharpen the hydroelastic wave crest and smooth the trough on an opposing current, while it produces an opposite effect on an aiding current. PubDate: Wed, 26 Aug 2020 14:35:11 +000

Abstract: In this paper, we discuss the existence of solutions for nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. The Banach fixed point theorem and Krasnoselskii fixed point theorem are applied to establish the results. Some examples are provided for the illustration of the main work. PubDate: Wed, 19 Aug 2020 13:35:04 +000

Abstract: In this paper, we are concerned with the following coupled Schrödinger equations where ,,, and; is a parameter; and and . Under some suitable conditions that or and with , the above coupled Schrödinger system possesses nontrivial solutions if , where is related to , and . PubDate: Mon, 17 Aug 2020 10:05:05 +000

Abstract: In this research, under some appropriate conditions, we approximate stationary points of multivalued Suzuki mappings through the modified Agarwal-O’Regan-Sahu iteration process in the setting of 2-uniformly convex hyperbolic spaces. We also provide an illustrative numerical example. Our results improve and extend some recently announced results of the current literature. PubDate: Mon, 17 Aug 2020 10:05:05 +000

Abstract: The present research work is devoted to investigate fractional order Benjamin-Bona-Mahony (FBBM) as well as modified fractional order FBBM (FMBBM) equations under nonlocal and nonsingular derivative of Caputo-Fabrizio (CF). In this regards, some qualitative results including the existence of at least one solution are established via using some fixed point results of Krasnoselskii and Banach. Further on using an iterative method, some semianalytical results are also studied. The concerned tool is formed when the Adomian decomposition method is coupled with some integral transform like Laplace. Graphical presentations are given for various fractional orders. Also, the concerned method is also compared with some variational-type perturbation method to demonstrate the efficiency of the proposed method. PubDate: Thu, 13 Aug 2020 15:20:03 +000

Abstract: In this paper, a mathematical model for describing the solid-fluid transformation of ice water is put forward based on the special geometry cases. The correctness of the obtained model is verified through comparison with numerical analysis and experiments. The good agreement indicates that the obtained model is available for the study of the solid-fluid transformation of ice water. The theory derived in this paper lays a foundation for the research of solid-fluid transformation phenomena of other materials and may have important applications in engineering areas such as rheology, creep, and instability of materials. PubDate: Sat, 08 Aug 2020 13:35:02 +000

Abstract: In this paper, we discuss the representations of -ary multiplicative Hom-Nambu-Lie superalgebras as a generalization of the notion of representations for -ary multiplicative Hom-Nambu-Lie algebras. We also give the cohomology of an -ary multiplicative Hom-Nambu-Lie superalgebra and obtain a relation between extensions of an -ary multiplicative Hom-Nambu-Lie superalgebra by an abelian one and . We also introduce the notion of -extensions of -ary multiplicative Hom-Nambu-Lie superalgebras and prove that every finite-dimensional nilpotent metric -ary multiplicative Hom-Nambu-Lie superalgebra over an algebraically closed field of characteristic not 2 in the case is a surjection is isometric to a suitable -extension. PubDate: Sat, 01 Aug 2020 02:20:07 +000

Abstract: The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian function in the form of polar coordinate was rewritten by using coordinate transformation. (3) By introducing the vector form variables, the two-dimensional M-L oscillator motion differential equation, the first integral, and the Lagrange function are written. Therefore, the two-dimensional M-L oscillator is directly extended to the three-dimensional case, and it is proved that the three-dimensional M-L oscillator can be reduced to the two-dimensional case. (4) The two direct integration methods were provided to solve the two-dimensional M-L oscillator by using polar coordinate Lagrangian and pointed out that the one-dimensional M-L oscillator is a special case of the two-dimensional M-L oscillator. PubDate: Sat, 01 Aug 2020 00:20:09 +000

Abstract: In this paper, we consider an approximate analytical method of optimal homotopy asymptotic method-least square (OHAM-LS) to obtain a solution of nonlinear fractional-order gradient-based dynamic system (FOGBDS) generated from nonlinear programming (NLP) optimization problems. The problem is formulated in a class of nonlinear fractional differential equations, (FDEs) and the solutions of the equations, modelled with a conformable fractional derivative (CFD) of the steepest descent approach, are considered to find the minimizing point of the problem. The formulation extends the integer solution of optimization problems to an arbitrary-order solution. We exhibit that OHAM-LS enables us to determine the convergence domain of the series solution obtained by initiating convergence-control parameter . Three illustrative examples were included to show the effectiveness and importance of the proposed techniques. PubDate: Sun, 26 Jul 2020 07:05:07 +000

Abstract: The aim of this paper is to establish the existence of solutions for singular double-phase problems depending on one parameter. This work improves and complements the existing ones in the literature. There seems to be no results on the existence of solutions for singular double-phase problems. PubDate: Wed, 15 Jul 2020 15:35:02 +000

Abstract: In this paper, we mainly study the solution and properties of the multiterm time-fractional diffusion equation. First, we obtained the stochastic representation for this equation, which turns to be a subordinated process. Based on the stochastic representation, we calculated the mean square displacement (MSD) and time average mean square displacement, then proved some properties of this model, including subdiffusion, generalized Einstein relationship, and nonergodicity. Finally, a stochastic simulation algorithm was developed for the visualization of sample path of the abnormal diffusion process. The Monte Carlo method was also employed to show the behavior of the solution of this fractional equation. PubDate: Tue, 14 Jul 2020 14:35:04 +000

Abstract: In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras, and matching pre-Lie algebras. Moreover, we study the properties and relationships between categories of these matching Hom-algebraic structures. PubDate: Fri, 10 Jul 2020 06:05:00 +000

Abstract: In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results. PubDate: Wed, 08 Jul 2020 16:50:01 +000

Abstract: In this paper, we study the SIR epidemic model with vital dynamics , from the point of view of integrability. In the case of the death/birth rate , the SIR model is integrable, and we provide its general solutions by implicit functions, two Lax formulations and infinitely many Hamilton-Poisson realizations. In the case of , we prove that the SIR model has no polynomial or proper rational first integrals by studying the invariant algebraic surfaces. Moreover, although the SIR model with is not integrable and we cannot get its exact solution, based on the existence of an invariant algebraic surface, we give the global dynamics of the SIR model with . PubDate: Mon, 06 Jul 2020 14:35:02 +000

Abstract: Homotopy methods are powerful tools for solving nonlinear programming. Their global convergence can be generally established under conditions of the nonemptiness and boundness of the interior of the feasible set, the Positive Linear Independent Constraint Qualification (PLICQ), which is equivalent to the Mangasarian-Fromovitz Constraint Qualification (MFCQ), and the normal cone condition. This paper provides a comparison of the existing normal cone conditions used in homotopy methods for solving inequality constrained nonlinear programming. PubDate: Sat, 04 Jul 2020 14:20:00 +000

Abstract: Cognitive radar is an intelligent radar system, and adaptive waveform design is one of the core problems in cognitive radar research. In the previous studies, it is assumed that the prior information of the target is known, and the definition of target spectrum variance has not changed. In this paper, we study on robust waveform design problem in multiple targets scene. We hope that the upper and lower bounds of the uncertainty range of robustness are more close to the actual situation, and establish a finite time random target signal model based on mutual information (MI). On the basis of the optimal transmitted waveform and robust waveform based on MI, we redefine the target spectrum variance as harmonic variance, and propose a novel robust waveform design method based on harmonic variance and MI. We compare its performance with robust waveform based on original variance. Simulation results show that, in the situation of multiple targets, compared to the original variance, the MI lifting rate of robust waveform based on harmonic variance relative to the optimal transmitted waveform in the uncertainty range has great improvement. In certain circumstances, robust waveform based on harmonic variance and MI is more suitable for more targets. PubDate: Fri, 03 Jul 2020 13:35:01 +000

Abstract: The object of the paper is to study some properties of the generalized Einstein tensor which is recurrent and birecurrent on pseudo-Ricci symmetric manifolds . Considering the generalized Einstein tensor as birecurrent but not recurrent, we state some theorems on the necessary and sufficient conditions for the birecurrency tensor of to be symmetric. PubDate: Wed, 01 Jul 2020 11:50:01 +000

Abstract: In this paper, we study the following nonlinear Choquard equation , where and is a positive bounded continuous potential on . By applying the reduction method, we proved that for any positive integer , the above equation has a positive solution with spikes near the local maximum point of if is sufficiently small under some suitable conditions on . PubDate: Wed, 01 Jul 2020 00:50:03 +000

Abstract: In this paper, we discussed the effect of activation energy on mixed convective heat and mass transfer of Williamson nanofluid with heat generation or absorption over a stretching cylinder. Dimensionless ordinary differential equations are obtained from the modeled PDEs by using appropriate transformations. Numerical results of the skin friction coefficient, Nusselt number, and Sherwood number for different parameters are computed. The effects of the physical parameter on temperature, velocity, and concentration have been discussed in detail. From the result, it is found that the dimensionless velocity decreases whereas temperature and concentration increase when the porous parameter is enhanced. The present result has been compared with published paper and found good agreement. PubDate: Thu, 25 Jun 2020 09:50:01 +000

Abstract: The circuit-gate framework of quantum computing relies on the fact that an arbitrary quantum gate in the form of a unitary matrix of unit determinant can be approximated to a desired accuracy by a fairly short sequence of basic gates, of which the exact bounds are provided by the Solovay–Kitaev theorem. In this work, we show that a version of this theorem is applicable to orthogonal matrices with unit determinant as well, indicating the possibility of using orthogonal matrices for efficient computation. We further develop a version of the Solovay–Kitaev algorithm and discuss the computational experience. PubDate: Wed, 24 Jun 2020 16:50:03 +000

Abstract: Let be a Hom-Lie-Yamaguti superalgebra. We first introduce the representation and cohomology theory of Hom-Lie-Yamaguti superalgebras. Also, we introduce the notions of generalized derivations and representations of and present some properties. Finally, we investigate the deformations of by choosing some suitable cohomology. PubDate: Thu, 18 Jun 2020 16:20:01 +000

Abstract: The main goal of the present paper is to obtain several fixed point theorems in the framework of -quasi-metric spaces, which is an extension of -metric spaces. Also, a Hausdorff -distance in these spaces is introduced, and a coincidence point theorem regarding this distance is proved. We also present some examples for the validity of the given results and consider an application to the Volterra-type integral equation. PubDate: Thu, 18 Jun 2020 16:05:01 +000

Abstract: In this paper, based on a bilinear differential equation, we study the breather wave solutions by employing the extended homoclinic test method. By constructing the different forms, we also consider the interaction solutions. Furthermore, it is natural to analyse dynamic behaviors of three-dimensional plots. PubDate: Tue, 16 Jun 2020 03:50:07 +000

Abstract: Annotation. For a second-order parabolic equation, the multipoint in time Cauchy problem is considered. The coefficients of the equation and the boundary condition have power singularities of arbitrary order in time and space variables on a certain set of points. Conditions for the existence and uniqueness of the solution of the problem in Hölder spaces with power weight are found. PubDate: Tue, 16 Jun 2020 03:35:01 +000