Abstract: By energy estimate approach and the method of upper and lower solutions, we give the conditions on the occurrence of the extinction and nonextinction behaviors of the solutions for a quasilinear parabolic equation with nonlinear source. Moreover, the decay estimates of the solutions are studied. PubDate: Sat, 20 Feb 2021 14:35:01 +000

Abstract: This paper is concerned with a problem of a logarithmic nonuniform flexible structure with time delay, where the heat flux is given by Cattaneo’s law. We show that the energy of any weak solution blows up infinite time if the initial energy is negative. PubDate: Thu, 11 Feb 2021 08:20:01 +000

Abstract: In this paper, the stochastic resonance (SR) phenomenon of four kinds of noises (the white noise, the harmonic noise, the asymmetric dichotomous noise, and the Lévy noise) in underdamped bistable systems is studied. By applying theory of stochastic differential equations to the numerical simulation of stochastic resonance problem, we simulate and analyze the system responses and pay close attention to stochastic control in the proposed systems. Then, the factors of influence to the SR are investigated by the Euler-Maruyama algorithm, Milstein algorithm, and fourth-order Runge-Kutta algorithm, respectively. The results show that the SR phenomenon can be generated in the proposed system under certain conditions by adjusting the parameters of the control effect with different noises. We also found that the type of the noise has little effect on the resonance peak of the output power spectrum density, which is not observed in conventional harmonic systems driven by multiplicative noise with only an overdamped term. Therefore, the conclusion of this paper can provide experimental basis for the further study of stochastic resonance. PubDate: Thu, 11 Feb 2021 08:05:01 +000

Abstract: A generalization of the Lambert function called the logarithmic Lambert function is introduced and is found to be a solution to the thermostatistics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor series, approximation formula, and branches of the function are obtained. The heat functions and specific heats are computed using the “unphysical” temperature and expressed in terms of the logarithmic Lambert function. PubDate: Tue, 09 Feb 2021 14:35:01 +000

Abstract: Evaluating efficiency according to the different states of returns to scale (RTS) is crucial to resource allocation and scientific decision for decision-making units (DMUs), but this kind of evaluation will become very difficult when the DMUs are in an uncertain random environment. In this paper, we attempt to explore the uncertain random data envelopment analysis approach so as to solve the problem that the inputs and outputs of DMUs are uncertain random variables. Chance theory is applied to handling the uncertain random variables, and hence, two evaluating models, one for increasing returns to scale (IRS) and the other for decreasing returns to scale (DRS), are proposed, respectively. Along with converting the two uncertain random models into corresponding equivalent forms, we also provide a numerical example to illustrate the evaluation results of these models. PubDate: Mon, 08 Feb 2021 06:50:02 +000

Abstract: The Painlevé integrability of the higher-order Boussinesq equation is proved by using the standard Weiss-Tabor-Carnevale (WTC) method. The multisoliton solutions of the higher-order Boussinesq equation are obtained by introducing dependent variable transformation. The soliton molecule and asymmetric soliton of the higher-order Boussinesq equation can be constructed by the velocity resonance mechanism. Lump solution can be derived by solving the bilinear form of the higher-order Boussinesq equation. By some detailed calculations, the lump wave of the higher-order Boussinesq equation is just the bright form. These types of the localized excitations are exhibited by selecting suitable parameters. PubDate: Thu, 04 Feb 2021 07:05:00 +000

Abstract: In this paper, we consider the KP-MEW(3,2) equation by the bifurcation theory of dynamical systems when integral constant is considered. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. The phase portrait for ,, and is drawn. Exact parametric representations of periodic peakon solutions and smooth periodic solution are presented. PubDate: Wed, 03 Feb 2021 07:05:01 +000

Abstract: In the present paper, we define -cone metric spaces over a Banach algebra which is a generalization of -metric space (-MS) and cone metric space (CMS) over a Banach algebra. We give new fixed-point theorems assuring generalized contractive and expansive maps without continuity. Examples and an application are given at the end to support the usability of our results. PubDate: Mon, 01 Feb 2021 06:20:01 +000

Abstract: Let be a separable symmetric space on and the corresponding noncommutative space. In this paper, we introduce a kind of quasimartingale spaces which is like but bigger than and obtain the following interpolation result: let be the space of all bounded -quasimartingales and . Then, there exists a symmetric space on with nontrivial Boyd indices such that . PubDate: Sun, 31 Jan 2021 11:20:01 +000

Abstract: In this paper, we study the Kirchhoff-type equation: where ,,, and . and are vanishing at infinity. With the aid of the quantitative deformation lemma and constraint variational method, we prove the existence of a sign-changing solution to the above equation. Moreover, we obtain that the sign-changing solution has exactly two nodal domains. Our results can be seen as an improvement of the previous literature. PubDate: Sun, 31 Jan 2021 10:35:00 +000

Abstract: In this article, Box-Cox and Yeo-Johnson transformation models are applied to two time series datasets of monthly temperature averages to improve the forecast ability. An application algorithm was proposed to transform the positive original responses using the first model and the stationary responses using the second model to improve the nonparametric estimation of the functional time series. The Box-Cox model contributed to improving the results of the nonparametric estimation of the original data, but the results become somewhat confusing after attempting to make the transformed response variable stationary in the mean, while the functional time series predictions were more accurate using the transformed stationary datasets using the Yeo-Johnson model. PubDate: Sat, 30 Jan 2021 14:35:01 +000

Abstract: In this paper, the quantum properties of a two-level atom interaction with squeezed vacuum reservoir is throughly analyzed. With the aid of the interaction Hamiltonian and the master equation, we obtain the time evolution of the expectation values of the atomic operators. Employing the steady-state solution of these equations, we calculate the power spectrum and the second-order correlation function for the interaction of two-level atom with squeezed vacuum reservoir. It is found that the half width of the power spectrum of the light increases with the squeeze parameter, . Furthermore, in the absence of decay constant and interaction time, it enhances the probability for the atom to be in the upper level. PubDate: Fri, 29 Jan 2021 07:50:01 +000

Abstract: The classifications and reductions of radially symmetric diffusion system are studied due to the conditional Lie-Bäcklund symmetry method. We obtain the invariant condition, which is the so-called determining system and under which the radially symmetric diffusion system admits second-order conditional Lie-Bäcklund symmetries. The governing systems and the admitted second-order conditional Lie-Bäcklund symmetries are identified by solving the nonlinear determining system. Exact solutions of the resulting systems are constructed due to the compatibility of the original system and the admitted differential constraint corresponding to the invariant surface condition. For most of the cases, they are reduced to solving four-dimensional dynamical systems. PubDate: Mon, 18 Jan 2021 08:35:01 +000

Abstract: In this article, the exact wave structures are discussed to the Caudrey-Dodd-Gibbon equation with the assistance of Maple based on the Hirota bilinear form. It is investigated that the equation exhibits the trigonometric, hyperbolic, and exponential function solutions. We first construct a combination of the general exponential function, periodic function, and hyperbolic function in order to derive the general periodic-kink solution for this equation. Then, the more periodic wave solutions are presented with more arbitrary autocephalous parameters, in which the periodic-kink solution localized in all directions in space. Furthermore, the modulation instability is employed to discuss the stability of the available solutions, and the special theorem is also introduced. Moreover, the constraint conditions are also reported which validate the existence of solutions. Furthermore, 2-dimensional graphs are presented for the physical movement of the earned solutions under the appropriate selection of the parameters for stability analysis. The concluded results are helpful for the understanding of the investigation of nonlinear waves and are also vital for numerical and experimental verification in engineering sciences and nonlinear physics. PubDate: Sat, 16 Jan 2021 09:20:01 +000

Abstract: In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar structure as other integrable systems possess in the AKNS scheme. Finally, we generalize the Darboux transformation of the classical Painlevé second equation to the -th form in terms of Wranskian. PubDate: Fri, 15 Jan 2021 08:05:01 +000

Abstract: Let be a BiHom-Hopf algebra and be an -module BiHom-algebra. Then, in this paper, we study some properties on the BiHom-smash product . We construct the Maschke-type theorem for the BiHom-smash product and form an associated Morita context . PubDate: Fri, 15 Jan 2021 07:05:01 +000

Abstract: In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extended -expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers. PubDate: Fri, 08 Jan 2021 13:20:01 +000

Abstract: The study focuses on extending the fast mean-reversion volatility, which was developed by the author in a previous work, to the multiscale volatility model so that it can express a well-separated time scale. The leading-order term and first-order correction terms are analytically computed using the perturbation theory based on the Lie–Trotter operator splitting method. Finally, the study is concluded by deriving the numerical results that further validate the effectiveness of the model. PubDate: Wed, 06 Jan 2021 14:05:00 +000

Abstract: In this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product whose fiber has -parabolic universal covering. Furthermore, applications to the weighted hyperbolic space are given. In particular, we also study the special case when the ambient space is weighted product space and provide some results by Bochner’s formula. As a consequence of this parametric study, we also establish Bernstein-type properties of the entire graphs in weighted Riemannian warped products. PubDate: Sat, 02 Jan 2021 12:05:01 +000

Abstract: In this study, an attempt has been made to investigate the mass and heat transfer effects in a BLF through a porous medium of an electrically conducting viscoelastic fluid subject to a transverse magnetic field in the existence of an external electric field, heat source/sink, and chemical reaction. It has been considered the effects of the electric field, viscous and Joule dissipations, radiation, and internal heat generation/absorption. Closed-form solutions for the boundary layer equations of viscoelastic, second-grade, and Walters’ fluid models are considered. The method of the solution includes similarity transformation. The converted equations of thermal and mass transport are calculated using the optimal homotopy asymptotic method (OHAM). The solutions of the temperature field for both prescribed surface temperature (PST) and prescribed surface heat flux (PHF) are found. It is vital to remark that the interaction of the magnetic field is found to be counterproductive in enhancing velocity and concentration distribution, whereas the presence of chemical reaction, as well as a porous matrix with moderate values of the magnetic parameter, reduces the temperature and concentration fields at all points of the flow domain. PubDate: Mon, 28 Dec 2020 06:50:02 +000

Abstract: The existence, nonexistence, and multiplicity of vector solutions of the linearly coupled Choquard type equations are proved, where ,, are positive functions, and denotes the Riesz potential. PubDate: Mon, 21 Dec 2020 06:20:01 +000

Abstract: The paper mainly focuses on the synchronization of multiple-weight Markovian switching complex networks under nonlinear coupling mode. Based on the finite-time stability theory, Itô’s lemma, and some inequality technologies, the synchronization criterion of network models in the nonlinear coupling mode is obtained; at the same time, unknown parameters of networks are also identified by an effective controller. In addition, several corollaries are given to illustrate the general applicability of the control rules in the paper. Finally, two typical numerical simulations are given to prove the rationality and feasibility of theoretical analysis of network models. PubDate: Fri, 11 Dec 2020 07:50:03 +000

Abstract: In the current manuscript, the notion of a cone -metric space over Banach’s algebra with parameter is introduced. Furthermore, using -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations. PubDate: Tue, 08 Dec 2020 05:50:01 +000

Abstract: In this paper, we consider the problem of the rotational motion of a rigid body with an irrational value of the frequency . The equations of motion are derived and reduced to a quasilinear autonomous system. Such system is reduced to a generating one. We assume a large parameter proportional inversely with a sufficiently small component of the angular velocity which is assumed around the major or the minor axis of the ellipsoid of inertia. Then, the large parameter technique is used to construct the periodic solutions for such cases. The geometric interpretation of the motion is obtained to describe the orientation of the body in terms of Euler’s angles. Using the digital fourth-order Runge-Kutta method, we determine the digital solutions of the obtained system. The phase diagram procedure is applied to study the stability of the attained solutions. A comparison between the considered numerical and analytical solutions is introduced to show the validity of the presented techniques and solutions. PubDate: Mon, 07 Dec 2020 07:05:02 +000

Abstract: The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally unbounded infinitesimal generators. In conclusion, the concept of module over a Banach algebra is proposed as the generalization of the Banach algebra. As an application to mathematical physics, the rigorous formulation of a rotation group, which consists of unbounded operators being written by differential operators, is provided using the module over a Banach algebra. PubDate: Sun, 29 Nov 2020 14:20:00 +000

Abstract: In this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entropy solutions through vanishing viscosity method and compensated compactness framework. Based on the uniform estimates of density, we then prove the entropy solutions converge to the corresponding unique stationary solution exponentially with time. We generalize the existing results to the variable coefficient damping case. PubDate: Mon, 23 Nov 2020 06:35:01 +000

Abstract: The aim of this paper is to introduce a notion of -contraction defined on a metric space with -distance. Moreover, fixed-point theorems are given in this framework. As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations. Some illustrative examples are provided to advocate the usability of our results. PubDate: Thu, 19 Nov 2020 06:05:01 +000

Abstract: The extended complex method is investigated for exact analytical solutions of nonlinear fractional Liouville equation. Based on the work of Yuan et al., the new rational, periodic, and elliptic function solutions have been obtained. By adjusting the arbitrary values to the constants in the constructed solutions, it can describe the physical phenomena to the traveling wave solutions, since traveling wave has significant value in applied sciences and engineering. Our results indicate that the extended complex technique is direct and easily applicable to solve the nonlinear fractional partial differential equations (NLFPDEs). PubDate: Thu, 19 Nov 2020 05:35:00 +000

Abstract: A Riemann-Hilbert approach is developed to the multicomponent Kaup-Newell equation. The formula is presented of -soliton solutions through an identity jump matrix related to the inverse scattering problems with reflectionless potential. PubDate: Wed, 18 Nov 2020 07:50:01 +000

Abstract: In this paper, the concept of sequential -metric spaces has been introduced as a generalization of usual metric spaces, -metric spaces and specially of -metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to examine the validity of the underlying space and in respect to our proven fixed point theorems. PubDate: Tue, 17 Nov 2020 14:35:02 +000