Abstract: We consider the following double phase problem with variable exponents: . By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some assumptions. Moreover, infinitely many pairs of solutions are provided by applying the Fountain Theorem, Dual Fountain Theorem, and Krasnoselskii’s genus theory. PubDate: Mon, 23 Mar 2020 14:20:04 +000

Abstract: In this paper, the existence and uniqueness of response solutions, which has the same frequency with the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequency form a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed-point methods and the -property of quasiperiodic functions. PubDate: Sat, 21 Mar 2020 04:50:06 +000

Abstract: In this study, we have constructed a new model for competitive knowledge diffusion in organization based on the statistical thermodynamics of physics. In order to achieve the purpose of research, we newly define the absorptive capacity coefficient, the creativity ability coefficient, the depreciation coefficient of knowledge, the ambiguity coefficient of knowledge, and the knowledge affinity coefficient of organizational culture. And various knowledge quantities such as knowledge energy, knowledge temperature, and diffusion coefficient for the knowledge diffusion equation were defined and simulations were carried out by the lattice kinetic method. And, based on the new model, we have successfully studied the impact of the characteristics of members, knowledge itself, and organizational culture on the diffusion of competitive knowledge. The results show that the diffusion velocity of knowledge in the organization increases as the knowledge absorbing ability of the members is larger, and the ambiguity of knowledge has a negative impact on the diffusion of knowledge. The degree of knowledge affinity of organizational culture is a decisive factor in the diffusion and accumulation of knowledge in the organization, and the cultural characteristics of the organization have a much greater influence on the diffusion of competitive knowledge than the personal characteristics of members. Therefore, the organization manager needs to pay more attention to building a better organizational culture than improving personal characteristics. Our research is helpful in analyzing the factors affecting competitive knowledge diffusion and constructing an effective knowledge management system. PubDate: Sat, 21 Mar 2020 04:50:04 +000

Abstract: Let be a simple graph with vertices. Let , where and and denote the adjacency matrix and degree matrix of , respectively. is called the -Estrada index of , where denote the eigenvalues of . In this paper, the upper and lower bounds for are given. Moreover, some relations between the -Estrada index and -energy are established. PubDate: Mon, 16 Mar 2020 06:50:06 +000

Abstract: This paper deals with a class of one element -degree polynomial differential equations. By the fixed point theory, we obtain periodic solutions of the equation. This paper generalizes some related conclusions of some papers. PubDate: Mon, 16 Mar 2020 06:05:03 +000

Abstract: This paper is devoted to the numerical scheme for a class of fractional order integrodifferential equations by reproducing kernel interpolation collocation method with reproducing kernel function in the form of Jacobi polynomials. Reproducing kernel function in the form of Jacobi polynomials is established for the first time. It is implemented as a reproducing kernel method. The numerical solutions obtained by taking the different values of parameter are compared; Schmidt orthogonalization process is avoided. It is proved that this method is feasible and accurate through some numerical examples. PubDate: Wed, 11 Mar 2020 04:05:21 +000

Abstract: In this paper, we give two Lichnerowicz-type formulas for modified Novikov operators. We prove Kastler-Kalau-Walze-type theorems for modified Novikov operators on compact manifolds with (respectively without) a boundary. We also compute the spectral action for Witten deformation on 4-dimensional compact manifolds. PubDate: Fri, 06 Mar 2020 15:50:19 +000

Abstract: The fractional telegraph equation is a kind of important evolution equation, which has an important application in signal analysis such as transmission and propagation of electrical signals. However, it is difficult to obtain the corresponding analytical solution, so it is of great practical value to study the numerical solution. In this paper, the alternating segment pure explicit-implicit (PASE-I) and implicit-explicit (PASI-E) parallel difference schemes are constructed for time fractional telegraph equation. Based on the alternating segment technology, the PASE-I and PASI-E schemes are constructed of the classic explicit scheme and implicit scheme. It can be concluded that the schemes are unconditionally stable and convergent by theoretical analysis. The convergence order of the PASE-I and PASI-E methods is second order in spatial direction and 3-α order in temporal direction. The numerical results are in agreement with the theoretical analysis, which shows that the PASE-I and PASI-E schemes are superior to the classical implicit schemes in both accuracy and efficiency. This implies that the parallel difference schemes are efficient for solving the time fractional telegraph equation. PubDate: Mon, 02 Mar 2020 14:50:02 +000

Abstract: Periodic solutions of the Coulomb equation motion for three equal negative point charges in the field of six equal positive point charges fixed in vertices of a convex octagon are found. The system possesses an equilibrium configuration. The Lyapunov center theorem is applied. PubDate: Fri, 28 Feb 2020 16:50:07 +000

Abstract: We investigate the use of Hamilton-Jacobi approaches for the purpose of state reconstruction of dynamic systems. First, the classical formulation based on the minimization of an estimation functional is analyzed. Second, the structure of the resulting estimator is taken into account to study the global stability properties of the estimation error by relying on the notion of input-to-state stability. A condition based on the satisfaction of a Hamilton-Jacobi inequality is proposed to construct estimators with input-to-state stable dynamics of the estimation error, where the disturbances affecting such dynamics are regarded as input. Third, the so-developed general framework is applied to the special case of high-gain observers for a class of nonlinear systems. PubDate: Wed, 26 Feb 2020 09:35:04 +000

Abstract: In the present paper, we study the blowup of the solutions to the full compressible Euler system and pressureless Euler-Poisson system with time-dependent damping. By some delicate analysis, some Riccati-type equations are achieved, and then, the finite time blowup results can be derived. PubDate: Fri, 21 Feb 2020 16:50:06 +000

Abstract: Two new orthogonal functions named the left- and the right-shifted fractional-order Legendre polynomials (SFLPs) are proposed. Several useful formulas for the SFLPs are directly generalized from the classic Legendre polynomials. The left and right fractional differential expressions in Caputo sense of the SFLPs are derived. As an application, it is effective for solving the fractional-order differential equations with the initial value problem by using the SFLP tau method. PubDate: Fri, 21 Feb 2020 16:50:03 +000

Abstract: In this paper, tracking controller and synchronization controller of the Arneodo chaotic system with uncertain parameters and input saturation are considered. An adaptive tracking control law and an adaptive synchronization control law are proposed based on backstepping and Lyapunov stability theory. The adaptive laws of the unknown parameters are derived by using the Lyapunov stability theory. To handle the effect caused by the input saturation, an auxiliary system is used to compensate the tracking error and synchronization error. The proposed adaptive tracking control and synchronization schemes ensure the effects of tracking and synchronization. Several examples have been detailed to illuminate the design procedure. PubDate: Thu, 13 Feb 2020 13:50:03 +000

Abstract: The stochastic strongly dissipative Zakharov equations with white noise are studied. On the basis of the time uniform a priori estimates, we prove the existence and uniqueness of solutions in energy spaces and , by using the standard Galerkin approximation method of stochastic partial differential equations. PubDate: Thu, 13 Feb 2020 13:50:02 +000

Abstract: This paper focuses on efficiently numerical investigation of two-dimensional heat conduction problems of material subjected to multiple moving Gaussian point heat sources. All heat sources are imposed on the inside of material and assumed to move along some specified straight lines or curves with time-dependent velocities. A simple but efficient moving mesh method, which continuously adjusts the two-dimensional mesh dimension by dimension upon the one-dimensional moving mesh partial differential equation with an appropriate monitor function of the temperature field, has been developed. The physical model problem is then solved on this adaptive moving mesh. Numerical experiments are presented to exhibit the capability of the proposed moving mesh algorithm to efficiently and accurately simulate the moving heat source problems. The transient heat conduction phenomena due to various parameters of the moving heat sources, including the number of heat sources and the types of motion, are well simulated and investigated. PubDate: Tue, 11 Feb 2020 11:05:01 +000

Abstract: In this paper, a super Wadati-Konno-Ichikawa (WKI) hierarchy associated with a matrix spectral problem is derived with the help of the zero-curvature equation. We obtain the super bi-Hamiltonian structures by using of the super trace identity. Infinitely, many conserved laws of the super WKI equation are constructed by using spectral parameter expansions. PubDate: Fri, 07 Feb 2020 17:05:02 +000

Abstract: In this paper, we consider Cauchy problem of space-time fractional diffusion-wave equation. Applying Laplace transform and Fourier transform, we establish the existence of solution in terms of Mittag-Leffler function and prove its uniqueness in weighted Sobolev space by use of Mikhlin multiplier theorem. The estimate of solution also shows the connections between the loss of regularity and the order of fractional derivatives in space or in time. PubDate: Fri, 07 Feb 2020 10:50:02 +000

Abstract: In this paper, we study the following fractional Schrödinger equation in , in with and . By using the constrained variational method, we show the existence of solutions with prescribed norm for this problem. PubDate: Wed, 05 Feb 2020 15:20:02 +000

Abstract: We present errors of quadrature rules for the nearly singular integrals in the momentum-space bound-state equations and give the critical value of the nearly singular parameter. We give error estimates for the expansion method, the Nyström method, and the spectral method which arise from the near singularities in the momentum-space bound-state equations. We show the relations amongst the near singularities, the odd phenomena in the eigenfunctions, and the unreliability of the numerical solutions. PubDate: Sat, 01 Feb 2020 07:35:05 +000

Abstract: The phase field crystal (PFC) method is a density-functional-type model with atomistic resolution and operating on diffusive time scales which has been proven to be an efficient tool for predicting numerous material phenomena. In this work, we first propose a method to predict viscoelastic-creep and mechanical-hysteresis behaviors in a body-centered-cubic (BCC) solid using a PFC method that is incorporated with a pressure-controlled dynamic equation which enables convenient control of deformation by specifying external pressure. To achieve our objective, we use constant pressure for the viscoelastic-creep study and sinusoidal pressure oscillation for the mechanical-hysteresis study. The parametric studies show that the relaxation time in the viscoelastic-creep phenomena is proportional to temperature. Also, mechanical-hysteresis behavior and the complex moduli predicted by the model are consistent with those of the standard linear solid model in a low-frequency pressure oscillation. Moreover, the impact of temperature on complex moduli is also investigated within the solid-stabilizing range. These results qualitatively agree with experimental and theoretical observations reported in the previous literature. We believe that our work should contribute to extending the capability of the PFC method to investigate the deformation problem when the externally applied pressure is required. PubDate: Sat, 01 Feb 2020 07:05:03 +000

Abstract: This paper proposes the pressureless magnetohydrodynamics (MHD) system by neglecting the effect of pressure difference in the MHD system. Firstly, the Riemann problem for the pressureless MHD system is solved with five kinds of structures of solutions consisting of combinations of shock, rarefaction wave, contact discontinuity, and vacuum state. Secondly, the limit behavior of the obtained Riemann solutions as the magnetic field drops to zero is studied. It is shown that, as the magnetic field vanishes, the Riemann solutions of the pressureless MHD system just tend to the corresponding Riemann solutions of the Euler equations for pressureless fluids. The formation processes of delta shocks and vacuum states are clarified. For the delta shock, both the intermediate density and internal energy simultaneously develop delta measures. PubDate: Sat, 01 Feb 2020 01:05:06 +000

Abstract: A nonlinear PDE combining with a new fourth-order term is studied. Adding three new fourth-order derivative terms and some second-order derivative terms, we formulate a combined fourth-order nonlinear partial differential equation, which possesses a Hirota’s bilinear form. The class of lump solutions is constructed explicitly through Hirota’s bilinear method. Their dynamical behaviors are analyzed through plots. PubDate: Sat, 01 Feb 2020 00:35:09 +000

Abstract: Type-II censored data is an important scheme of data in lifetime studies. The purpose of this paper is to obtain E-Bayesian predictive functions which are based on observed order statistics with two samples from two parameter Burr XII model. Predictive functions are developed to derive both point prediction and interval prediction based on type-II censored data, where the median Bayesian estimation is a novel formulation to get Bayesian sample prediction, as the integral for calculating the Bayesian prediction directly does not exist. All kinds of predictions are obtained with symmetric and asymmetric loss functions. Two sample techniques are considered, and gamma conjugate prior density is assumed. Illustrative examples are provided for all the scenarios considered in this article. Both illustrative examples with real data and the Monte Carlo simulation are carried out to show the new method is acceptable. The results show that Bayesian and E-Bayesian predictions with the two kinds of loss functions have little difference for the point prediction, and E-Bayesian confidence interval (CI) with the two kinds of loss functions are almost similar and they are more accurate for the interval prediction. PubDate: Sat, 01 Feb 2020 00:35:08 +000

Abstract: Heat transfer in counterflow heat exchangers is modeled by using transport and balance equations with the temperatures of cold fluid, hot fluid, and metal pipe as state variables distributed along the entire pipe length. Using such models, boundary value problems can be solved to estimate the temperatures over all the length by means of measurements taken only at the boundaries. Conditions for the stability of the estimation error given by the difference between the temperatures and their estimates are established by using a Lyapunov approach. Toward this end, a method to construct nonlinear Lyapunov functionals is addressed by relying on a polynomial diagonal structure. This stability analysis is extended in case of the presence of bounded modeling uncertainty. The theoretical findings are illustrated with numerical results, which show the effectiveness of the proposed approach. PubDate: Sat, 01 Feb 2020 00:35:06 +000

Abstract: The present work investigates the problem of a cylindrical crack in a functionally graded cylinder under thermal impact by using the non-Fourier heat conduction model. The theoretical derivation is performed by methods of Fourier integral transform, Laplace transform, and Cauchy singular integral equation. The concept of heat flux intensity factor is introduced to investigate the heat concentration degree around the crack tip quantitatively. The temperature field and the heat flux intensity factor in the time domain are obtained by transforming the corresponding quantities from the Laplace domain numerically. The effects of heat conduction model, functionally graded parameter, and thermal resistance of crack on the temperature distribution and heat flux intensity factor are studied. This work is beneficial for the thermal design of functionally graded cylinder containing a cylindrical crack. PubDate: Sat, 01 Feb 2020 00:35:05 +000

Abstract: Tension failure is one of the main forms of instability in geotechnical engineering. Aiming at the calculation error caused by the loading direction deviation of the Brazilian disc splitting method, a mechanical model of a disc under chord loading was constructed firstly. Based on the theory of complex variable function, the analytic solutions of stresses in a circular disc were deduced, and the calculation error of the tensile strength under chord loading was characterized by defining the error impact rate. And the stress distribution of a disc and the law of rock fracture under chord loading were detailed analyzed through numerical calculation. Through numerical calculation, the stress distribution of the disc and rock failure law under chordwise loading are discussed in detail. The results show that the stress concentration near the loading point is stronger under the chordwise loading comparing with the radial loading, which makes the disc more vulnerable to produce compression failure near the loading point. The disc exhibits a maximum tensile stress and a minimum compressive stress at the intersection of the loaded string and the horizontal diameter, so that tensile rupture damage is likely to occur here. With the increase of deviation angle, the tensile strength measured by the Brazilian splitting test decreases gradually, and the influence rate of error increases significantly. The proposed analytical solution under chord loading provides theoretical guiding significance for nonradial splitting failure of a disc. PubDate: Sat, 01 Feb 2020 00:35:04 +000

Abstract: Explicit rational-exponential solutions for the Kadomtsev-Petviashvili-II equation with a self-consistent source (KPIIESCS) are studied by the Hirota bilinear method. One typical feature for this hybrid type of solutions is that they contain two arbitrary functions of time variable which affect the amplitudes and propagation trajectories. The dynamics of solutions are demonstrated by the three-dimensional figures. The method used here is quite general and can be applied to other equations with self-content sources. PubDate: Fri, 31 Jan 2020 13:50:09 +000

Abstract: By taking values in a commutative subalgebra , we construct a new generalized -Heisenberg ferromagnet model in (1+1)-dimensions. The corresponding geometrical equivalence between the generalized -Heisenberg ferromagnet model and -mixed derivative nonlinear Schrödinger equation has been investigated. The Lax pairs associated with the generalized systems have been derived. In addition, we construct the generalized -inhomogeneous Heisenberg ferromagnet model and -Ishimori equation in (2+1)-dimensions. We also discuss the integrable properties of the multi-component systems. Meanwhile, the generalized Zn-nonlinear Schrödinger equation, Zn-Davey–Stewartson equation and their Lax representation have been well studied. PubDate: Fri, 31 Jan 2020 13:50:08 +000

Abstract: We investigate an electromagnetic Dirichlet type problem for the 2D quaternionic time-harmonic Maxwell system over a great generality of fractal closed type curves, which bound Jordan domains in . The study deals with a novel approach of -summability condition for the curves, which would be extremely irregular and deserve to be considered fractals. Our technique of proofs is based on the intimate relations between solutions of time-harmonic Maxwell system and those of the Dirac equation through some nonlinear equations, when both cases are reformulated in quaternionic forms. PubDate: Fri, 31 Jan 2020 13:50:07 +000

Abstract: In this paper, we consider a class of nonlinear Caputo fractional differential equations with impulsive effect under multiple band-like integral boundary conditions. By constructing an available completely continuous operator, we establish some criteria for judging the existence and uniqueness of solutions. Finally, an example is presented to demonstrate our main results. PubDate: Tue, 28 Jan 2020 13:35:07 +000