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

Abstract: The effect of the structure parameter on the compressibility of dust grains and soliton behavior in a dusty plasma system consisting of Maxwellian electrons, ions, and dust grains charged with a negative charge has been studied. In the theoretical study, a reductive perturbation technique was used to derive the Korteweg-de Vries (KdV) equation and employ the Hirota bilinear method to obtain multisoliton solution. It is found that coupling and structure parameters have a clear effect on the compressibility. These changes in the compressibility affected the amplitude and width of interactive solitons, in addition to the phase shifts resulting from the interaction. These results can be used to understand the behavior of solitary waves that occur in various natural and laboratory plasma environments with dust impurity situations. PubDate: Mon, 16 Nov 2020 06:50:01 +000

Abstract: We present new results regarding the long-range scalar field that emerges from the classical Kaluza unification of general relativity and electromagnetism. The Kaluza framework reproduces known physics exactly when the scalar field goes to one, so we studied perturbations of the scalar field around unity, as is done for gravity in the Newtonian limit of general relativity. A suite of interesting phenomena unknown to the Kaluza literature is revealed: planetary masses are clothed in scalar field, which contributes 25% of the mass-energy of the clothed mass; the scalar potential around a planet is positive, compared with the negative gravitational potential; at laboratory scales, the scalar charge which couples to the scalar field is quadratic in electric charge; a new length scale of physics is encountered for the static scalar field around an electrically-charged mass, ; the scalar charge of elementary particles is proportional to the electric charge, making the scalar force indistinguishable from the atomic electric force. An unduly strong electrogravitic buoyancy force is predicted for electrically-charged objects in the planetary scalar field, and this calculation appears to be the first quantitative falsification of the Kaluza unification. Since the simplest classical field, a long-range scalar field, is expected in nature, and since the Kaluza scalar field is as weak as gravity, we suggest that if there is an error in this calculation, it is likely to be in the magnitude of the coupling to the scalar field, not in the existence or magnitude of the scalar field itself. PubDate: Mon, 09 Nov 2020 15:20:01 +000

Abstract: This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). The suggested technique is implemented to obtain the solutions of space-time Kolmogorov Petrovskii Piskunov (KPP) equation and its derived equations, namely, Fitzhugh Nagumo (FHN) equation and Newell-Whitehead (NW) equation. The considered models are significant in biology. The KPP equation describes genetic model for spread of dominant gene through population. The FHN equation is imperative in the study of intercellular trigger waves. Similarly, the NW equation is applied for chemical reactions, Faraday instability, and Rayleigh-Benard convection. The proposed technique FIM can be applied to find the exact solutions of PDEs. PubDate: Mon, 09 Nov 2020 15:20:00 +000

Abstract: This paper deals with the existence and uniqueness of solutions for a new class of coupled systems of Hilfer fractional pantograph differential equations with nonlocal integral boundary conditions. First of all, we are going to give some definitions that are necessary for the understanding of the manuscript; second of all, we are going to prove our main results using the fixed point theorems, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem; in the end, we are giving two examples to illustrate our results. PubDate: Fri, 06 Nov 2020 07:50:00 +000

Abstract: The present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order . Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional derivative which is used to get many solitary wave solutions by changing various parameters. The obtained solutions include three classes of soliton wave solutions in terms of hyperbolic function, trigonometric function, and rational function solutions. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of nonlinearity. Some of the nonlinear equations arise in fluid dynamics and nonlinear phenomena. PubDate: Wed, 04 Nov 2020 07:20:00 +000

Abstract: In this work, we give sufficient conditions to investigate the existence and uniqueness of solution to fractional-order Langevin equation involving two distinct fractional orders with unprecedented conditions (three-point boundary conditions including two nonlocal integrals). The problem is introduced to keep track of the progress made on exploring the existence and uniqueness of solution to the fractional-order Langevin equation. As a result of employing the so-called Krasnoselskii and Leray-Schauder alternative fixed point theorems and Banach contraction mapping principle, some novel results are presented in regarding to our main concern. These results are illustrated through providing three examples for completeness. PubDate: Fri, 30 Oct 2020 14:05:01 +000

Abstract: This paper considers a system of fractional differential equations involving -Laplacian operators and two parameters where ,, and are the standard Riemann-Liouville derivatives, ,,,, and and and are two positive parameters. We obtain the existence and uniqueness of positive solutions depending on parameters for the system by utilizing a recent fixed point theorem. Furthermore, an example is present to illustrate our main result. PubDate: Fri, 30 Oct 2020 06:50:01 +000

Abstract: Quenching characteristics based on the two-dimensional (2D) nonlinear unsteady convection-reaction-diffusion equation are creatively researched. The study develops a 2D compact finite difference scheme constructed by using the first and the second central difference operator to approximate the first-order and the second-order spatial derivative, Taylor series expansion rule, and the reminder-correction method to approximate the three-order and the four-order spatial derivative, respectively, and the forward difference scheme to discretize temporal derivative, which brings the accuracy resulted meanwhile. Influences of degenerate parameter, convection parameter, and the length of the rectangle definition domain on quenching behaviors and performances of special quenching cases are discussed and evaluated by using the proposed scheme on the adaptive grid. It is feasible for the paper to offer potential support for further research on quenching problem. PubDate: Thu, 29 Oct 2020 14:05:01 +000

Abstract: In this paper, we show the existence of solutions for an indefinite fractional Schrödinger equation driven by the variable-order fractional magnetic Laplace operator involving variable exponents and steep potential. By using the decomposition of the Nehari manifold and variational method, we obtain the existence results of nontrivial solutions to the equation under suitable conditions. PubDate: Wed, 28 Oct 2020 07:05:01 +000

Abstract: In this paper, we report a novel memristor-based cellular neural network (CNN) without equilibrium points. Dynamical behaviors of the memristor-based CNN are investigated by simulation analysis. The results indicate that the system owns complicated nonlinear phenomena, such as hidden attractors, coexisting attractors, and initial boosting behaviors of position and amplitude. Furthermore, both heterogeneous multistability and homogenous multistability are found in the CNN. Finally, Multisim circuit simulations are performed to prove the chaotic characteristics and multistability of the system. PubDate: Tue, 27 Oct 2020 06:20:01 +000

Abstract: Our objective of this investigation is to mainly focus on the behavior of a plasma gas that is bounded by a moving rigid flat plate; its motion is damping with time. The effects of an external magnetic field on the electrons collected with each other, with positive ions, and with neutral atoms in the plasma fluid are studied. The BGK type of the Boltzmann kinetic equation is used to study the gas dynamics various regimes with Maxwellian velocity distribution functions. An analytical solution of the model equations for the unsteady flow was given using the moment and the traveling wave methods. The manner of the mean velocity of plasmas is illustrated, which is compatible with the variation of the shear stress, viscosity coefficient, and the initial and boundary conditions. Besides, the thermodynamic prediction is investigated by applying irreversible thermodynamic principles and extended Gibbs formula. Finally, qualitative agreements with previous related papers were demonstrated using 3-dimensional graphics for calculating the variables. The significance of this study is due to its vast applications in numerous fields such as in physics, engineering, commercial, and industrial applications. PubDate: Thu, 22 Oct 2020 15:05:01 +000

Abstract: The Dirac delta function and its integer-order derivative are widely used to solve integer-order differential/integral equation and integer-order system in related fields. On the other hand, the fractional-order system gets more and more attention. This paper investigates the fractional derivative of the Dirac delta function and its Laplace transform to explore the solution for fractional-order system. The paper presents the Riemann-Liouville and the Caputo fractional derivative of the Dirac delta function, and their analytic expression. The Laplace transform of the fractional derivative of the Dirac delta function is given later. The proposed fractional derivative of the Dirac delta function and its Laplace transform are effectively used to solve fractional-order integral equation and fractional-order system, the correctness of each solution is also verified. PubDate: Tue, 20 Oct 2020 08:20:00 +000

Abstract: Methods known as fractional subequation and sine-Gordon expansion (FSGE) are employed to acquire new exact solutions of some fractional partial differential equations emerging in plasma physics. Fractional operators are employed in the sense of conformable derivatives (CD). New exact solutions are constructed in terms of hyperbolic, rational, and trigonometric functions. Computational results indicate the power of the method. PubDate: Sat, 17 Oct 2020 13:35:00 +000

Abstract: We have analyzed the squeezing and statistical properties of the cavity light beam produced by a coherently driven degenerate three-level laser with a degenerate parametric amplifier (DPA) in an open cavity and coupled to a vacuum reservoir via a single-port mirror. We have carried out our analysis by putting the noise operators associated with the vacuum reservoir in normal order. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equation for the cavity mode operator, the mean photon number and the quadrature squeezing of the cavity light are calculated. And a large part of the mean photon number is confined in a relatively small frequency interval. Furthermore, we also obtain the antinormally ordered characteristic function defined in the Heisenberg picture. With the aid of the resulting characteristic function, we determine the function which is then used to calculate the photon number distribution. PubDate: Mon, 12 Oct 2020 08:20:01 +000

Abstract: Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of Cho and Kimura. PubDate: Mon, 12 Oct 2020 08:20:01 +000

Abstract: In this paper, we focus on high-order approximate solutions to two-level systems with quasi-resonant control. Firstly, we develop a high-order renormalization group (RG) method for Schrödinger equations. By this method, we get the high-order RG approximate solution in both resonance case and out of resonance case directly. Secondly, we introduce a time transformation to avoid the invalid expansion and get the high-order RG approximate solution in near resonance case. Finally, some numerical simulations are presented to illustrate the effectiveness of our RG method. We aim to provide a mathematically rigorous framework for mathematicians and physicists to analyze the high-order approximate solutions of quasi-resonant control problems. PubDate: Tue, 06 Oct 2020 14:20:01 +000

Abstract: In this paper, the symmetry classification and symmetry reduction of a two-component reaction-diffusion system are investigated, the reaction-diffusion system can be reduced to system of ordinary differential equations, and the solutions and numerical simulation will be showed by examples. PubDate: Mon, 05 Oct 2020 13:05:02 +000

Abstract: Through the method of -KP hierarchy, we propose a new ()-dimensional weakly coupled B-KP equation. Based on the bilinear form, we obtain the lump and rational solutions to the dimensionally reduced cases by constructing a symmetric positive semidefinite matrix. Then, we do numerical analysis on the rational solutions and fit the trajectory equation of the crest. Furthermore, we verify the accuracy of the trajectory equation by numerical analysis. This method of solving the lump and rational solutions can also be applied to other nonlinear evolution equations. PubDate: Wed, 30 Sep 2020 14:20:01 +000

Abstract: With the help of Maple, the precise traveling wave solutions of three fractal-order model equations related to water waves, including hyperbolic solutions, trigonometric solutions, and rational solutions, are obtained by using function expansion method. An isolated wave solution is selected from the solution of each nonlinear dispersive wave model equation, and the influence of fractional order change on these isolated wave solutions is discussed. The results show that the fractional derivatives can modulate the waveform, local periodicity, and structure of the isolated solutions of the three model equations. We also point out the construction rules of the auxiliary equations of the extended ()-expansion method. In the “The Explanation and Discussion” section, a more generalized auxiliary equation is used to further emphasize the rules, which has certain reference value for the construction of the new auxiliary equations. The solutions of fractional-order nonlinear partial differential equations can be enriched by selecting other solvable equations as auxiliary equations. PubDate: Wed, 30 Sep 2020 12:50:02 +000

Abstract: In this paper, we present a common fixed point result for a pair of mappings defined on a b-metric space, which satisfies quasi-contractive inequality with nonlinear comparison functions. An application in solving a class of integral equations will support our results. PubDate: Tue, 29 Sep 2020 07:35:01 +000

Abstract: The aim of this paper is to give existence results for a class of coupled systems of fractional integrodifferential equations with Hilfer fractional derivative in Banach spaces. We first give some definitions, namely the Hilfer fractional derivative and the Hausdorff’s measure of noncompactness and the Sadovskii’s fixed point theorem. PubDate: Tue, 29 Sep 2020 06:05:02 +000

Abstract: The Neimark-Sacker bifurcation of a forced vibration system is considered in this paper. The series solution to the motion equation is obtained, and the Poincaré map is established. The fixed point of the Poincaré map is guaranteed by the implicit function theorem. The map is transformed into its normal form at the fifth-order resonance case. For some parameter values, there exists the torus . Furthermore, the phenomenon of phase locking on the torus is investigated and the parameter condition under which there exists subharmonic motion on the torus is determined. PubDate: Sat, 26 Sep 2020 14:50:02 +000

Abstract: Due to contradiction of large-scale passenger demand and limited transportation capacity, the passengers who cannot be transported away in time accumulate and congest in stations. To ensure travel safety, improve travel efficiency, and ameliorate waiting environments for passengers, this paper proposes an adaptive multilevel collaborative passenger flow control strategy integrating the control of station entrance and station hall. An integer linear programming model is constructed, which aims at minimizing the total passenger waiting time and taking the safe capacity of each key area of all stations as the necessary constraints. The model is applied in two scenarios with different scales of passenger demand in the morning peak of the Batong line. The results show that the proposed model can adaptively activate the appropriate control level, limit the amount of accumulated passengers in each key area of the station within its safe capacity, and shorten the total passenger waiting time. PubDate: Thu, 24 Sep 2020 14:20:01 +000