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
Abstract: Cracks always form at the interface of discrepant materials in composite structures, which influence thermal performances of the structures under transient thermal loadings remarkably. The heat concentration around a cylindrical interface crack in a bilayered composite tube has not been resolved in literature and thus is investigated in this paper based on the singular integral equation method. The time variable in the two-dimensional temperature governing equation, derived from the non-Fourier theory, is eliminated using the Laplace transformation technique and then solved exactly in the Laplacian domain by the employment of a superposition method. The heat concentration degree caused by the interface crack is judged quantitatively with the employment of heat flux intensity factor. After restoring the results in the time domain using a numerical Laplace inversion technique, the effects of thermal resistance of crack, liner material, and crack length on the results are analyzed with a numerical case study. It is found that heat flux intensity factor is material-dependent, and steel is the best liner material among the three potential materials used for sustaining transiently high temperature loadings. PubDate: Fri, 12 Jun 2020 16:35:01 +000
Abstract: In this paper, we investigate multiple lump wave solutions of the new ()-dimensional Fokas equation by adopting a symbolic computation method. We get its 1-lump solutions, 3-lump solutions, and 6-lump solutions by using its bilinear form. Moreover, some basic characters and structural features of multiple lump waves are explained by depicting the three-dimensional plots. PubDate: Wed, 10 Jun 2020 14:35:00 +000
Abstract: The multiple Exp-function method is employed for searching the multiple soliton solutions for the new extended ()-dimensional Jimbo-Miwa-like (JM) equation, the extended ()-dimensional Calogero-Bogoyavlenskii-Schiff (eCBS) equation, the generalization of the ()-dimensional Bogoyavlensky-Konopelchenko (BK) equation, and a variable-coefficient extension of the DJKM (vDJKM) equation, which contain one-soliton-, two-soliton-, and triple-soliton-kind solutions. The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in figures by selecting suitable values. PubDate: Mon, 08 Jun 2020 15:50:02 +000
Abstract: In this paper, we introduce a generalization of rectangular -metric spaces, by changing the rectangular inequality as follows: , for all distinct We prove some fixed point theorems, and we use our results to present a nice application in the last section of this paper. PubDate: Mon, 01 Jun 2020 08:35:03 +000
Abstract: Transformation is an important means to study problems in analytical mechanics. It is often difficult to solve dynamic equations, and the use of variable transformation can make the equations easier to solve. The theory of canonical transformations plays an important role in solving Hamilton’s canonical equations. Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics. This paper attempts to extend the canonical transformation theory of Hamilton systems to Birkhoff systems and establish the generalized canonical transformation of Birkhoff systems. First, the definition and criterion of the generalized canonical transformation for the Birkhoff system are established. Secondly, based on the criterion equation and considering the generating functions of different forms, six generalized canonical transformation formulas are derived. As special cases, the canonical transformation formulas of classical Hamilton’s equations are given. At the end of the paper, two examples are given to illustrate the application of the results. PubDate: Tue, 26 May 2020 16:35:03 +000
Abstract: In this paper, we equip with an indefinite scalar product with a specific Hermitian matrix, and our aim is to develop some block Krylov methods to indefinite mode. In fact, by considering the block Arnoldi, block FOM, and block Lanczos methods, we design the indefinite structures of these block Krylov methods; along with some obtained results, we offer the application of this methods in solving linear systems, and as the testifiers, we design numerical examples. PubDate: Tue, 26 May 2020 09:20:08 +000
Abstract: The existing analysis deals with heat transfer occurrence on peristaltic transport of a Carreau fluid in a rectangular duct. Flow is scrutinized in a wave frame of reference moving with velocity away from a fixed frame. A peristaltic wave propagating on the horizontal side walls of a rectangular duct is discussed under lubrication approximation. In order to carry out the analytical solution of velocity, temperature, and pressure gradient, the homotopy perturbation method is employed. Graphical results are displayed to see the impact of various emerging parameters of the Carreau fluid and power law index. Trapping effects of peristaltic transport is also discussed and observed that number of trapping bolus decreases with an increase in aspect ratio . PubDate: Wed, 20 May 2020 09:05:03 +000
Abstract: In this paper, we study a class of the Kirchhoff-Schrödinger-Poisson system. By using the quantitative deformation lemma and degree theory, the existence result of the least energy sign-changing solution is obtained. Meanwhile, the energy doubling property is proved, that is, we prove that the energy of any sign-changing solution is strictly larger than twice that of the least energy. Moreover, we also get the convergence properties of as the parameters and . PubDate: Tue, 19 May 2020 11:05:02 +000
Abstract: In this paper, the detailed inseparability criteria of entanglement quantification of correlated two-mode light generated by a three-level laser with a coherently driven parametric amplifier and coupled to a two-mode vacuum reservoir is thoroughly analyzed. Using the master equation, we obtain the stochastic differential equation and the correlation properties of the noise forces associated with the normal ordering. Next, we study the squeezing and the photon entanglement by considering different inseparability criteria. The various criteria of entanglement used in this paper show that the light generated by the quantum optical system is entangled and the amount of entanglement is amplified by introducing the parametric amplifier into the laser cavity and manipulating the linear gain coefficient. PubDate: Mon, 18 May 2020 11:05:01 +000
Abstract: The motive of the present work is to propose an adaptive numerical technique for singularly perturbed convection-diffusion problem in two dimensions. It has been observed that for small singular perturbation parameter, the problem under consideration displays sharp interior or boundary layers in the solution which cannot be captured by standard numerical techniques. In the present work, Hughes stabilization strategy along with the streamline upwind/Petrov-Galerkin (SUPG) method has been proposed to capture these boundary layers. Reliable a posteriori error estimates in energy norm on anisotropic meshes have been developed for the proposed scheme. But these estimates prove to be dependent on the singular perturbation parameter. Therefore, to overcome the difficulty of oscillations in the solution, an efficient adaptive mesh refinement algorithm has been proposed. Numerical experiments have been performed to test the efficiency of the proposed algorithm. PubDate: Sat, 16 May 2020 09:50:02 +000
Abstract: In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in the Caputo’s sense by a simple quadrature formula. This RBFs approach was theoretically proved with different problems of two numerical examples: time step arbitrage bubble case and time linear arbitrage bubble case. Then, the numerical results were compared with the semiclassical solution in case of fractional order close to 1. As a result, both numerical examples showed that the option prices from RBFs method satisfy the semiclassical solution. PubDate: Fri, 15 May 2020 13:05:01 +000
Abstract: In this exploration, a double stratified mixed convective flow of couple stress nanofluid past an inclined stretching cylinder using a Cattaneo-Christov heat and mass flux model is considered. The governing partial differential equation of the boundary layer flow region is reduced to its corresponding ordinary differential equation using a similarity transformation technique. Then, the numerical method called the Galerkin finite element method (GFEM) is applied to solve the proposed fluid model. We performed a grid-invariance test or grid-convergence test to confirm the convergence of the series solution. The effects of the different noteworthy variables on velocity, temperature, concentration, local skin friction, local Nusselt number, and local Sherwood number are analyzed in both graphical and tabular forms. We have compared our result with the existing results in the literature, and it is shown that GFEM is accurate and efficient. Moreover, our result shows that the velocity field is retarded when the angle of inclination enhances and the heat transfer rate is reduced with larger values of the curvature of the cylinder. PubDate: Fri, 08 May 2020 12:50:02 +000
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