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  • 1
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    Existence of Multispike Positive Solutions for a Nonlocal Problem in ℝ3 (2020)
    Hindawi
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    Publication Date: 2020-07-01
    Description: In this paper, we study the following nonlinear Choquard equation −ϵ2Δu+Kxu=1/8πϵ2∫ℝ3u2y/x−ydyu,x∈ℝ3, where ϵ〉0 and Kx is a positive bounded continuous potential on ℝ3. By applying the reduction method, we proved that for any positive integer k, the above equation has a positive solution with k spikes near the local maximum point of Kx if ϵ〉0 is sufficiently small under some suitable conditions on Kx.
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  • 2
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    Stochastic Representation and Monte Carlo Simulation for Multiterm Time-Fractional Diffusion Equation (2020)
    Hindawi
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    Publication Date: 2020-07-14
    Description: 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.
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  • 3
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    Pinning Synchronization of Nonlinearly Coupled Complex Dynamical Networks on Time Scales (2020)
    Hindawi
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    Publication Date: 2020-07-08
    Description: 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.
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  • 4
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    Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras (2020)
    Hindawi
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    Publication Date: 2020-07-10
    Description: 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.
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  • 5
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    On the Integrability of the SIR Epidemic Model with Vital Dynamics (2020)
    Hindawi
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    Publication Date: 2020-07-06
    Description: In this paper, we study the SIR epidemic model with vital dynamics Ṡ=−βSI+μN−S,İ=βSI−γ+μI,Ṙ=γI−μR, from the point of view of integrability. In the case of the death/birth rate μ=0, 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 μ≠0, 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 μ≠0 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 μ≠0.
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  • 6
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    Mathematical Modelling for Joining Boron Nitride Graphene with Other BN Nanostructures (2020)
    Hindawi
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    Publication Date: 2020-08-30
    Description: 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.
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  • 7
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    Some Properties of Generalized Einstein Tensor for a Pseudo-Ricci Symmetric Manifold (2020)
    Hindawi
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    Publication Date: 2020-07-01
    Description: The object of the paper is to study some properties of the generalized Einstein tensor GX,Y which is recurrent and birecurrent on pseudo-Ricci symmetric manifolds PRSn. Considering the generalized Einstein tensor GX,Y as birecurrent but not recurrent, we state some theorems on the necessary and sufficient conditions for the birecurrency tensor of GX,Y to be symmetric.
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  • 8
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    Multi-Target Robust Waveform Design Based on Harmonic Variance and Mutual Information (2020)
    Hindawi
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    Publication Date: 2020-07-03
    Description: 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.
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  • 9
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    Speech Encryption Algorithm Based on Nonorthogonal Quantum State with Hyperchaotic Keystreams (2020)
    Hindawi
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    Publication Date: 2020
    Description: With the advancement in modern computational technologies like cloud computing, there has been tremendous growth in the field of data processing and encryption technologies. In this contest there is an increasing demand for successful storage of the data in the encrypted domain to avoid the possibility of data breach in shared networks. In this paper, a novel approach for speech encryption algorithm based on quantum chaotic system is designed. In the proposed method, classical bits of the speech samples are initially encoded in nonorthogonal quantum state by the secret polarizing angle. In the quantum domain, encoded speech samples are subjected to bit-flip operation according to the Controlled–NOT gate followed by Hadamard transform. Complete superposition of the quantum state in both Hadamard and standard basis is achieved through Hadamard transform. Control bits for C-NOT gate as well as Hadamard gate are generated with a modified -hyperchaotic system. Secret nonorthogonal rotation angles and initial conditions of the hyperchaotic system are the keys used to ensure the security of the proposed algorithm. The computational complexity of the proposed algorithm has been analysed both in quantum domain and classical domain. Numerical simulation carried out based on the above principle showed that the proposed speech encryption algorithm has wider keyspace, higher key sensitivity and robust against various differential and statistical cryptographic attacks.
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  • 10
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    Lie Symmetry Analysis and Invariant Solutions of a Nonlinear Fokker-Planck Equation Describing Cell Population Growth (2020)
    Hindawi
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    Publication Date: 2020
    Description: In this paper, a complete Lie symmetry analysis is performed for a nonlinear Fokker-Planck equation for growing cell populations. Moreover, an optimal system of one-dimensional subalgebras is constructed and used to find similarity reductions and invariant solutions. A new power series solution is constructed via the reduced equation, and its convergence is proved.
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  • 11
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    A New Complex Network Model with Multiweights and Its Synchronization Control (2020)
    Hindawi
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    Publication Date: 2020
    Description: Based on the weighted complex network model, this paper establishes a multiweight complex network model, which possesses several different weights on the one edge. According to the method of network split, the complex network with multiweights is split into several different complex networks with single weight. Some new static characteristics, such as node weight, node degree, node weight strength, node weight distribution, edge weight distribution, and diversity of weight distribution are defined. Then, by using Lyapunov stability theory, the adaptive feedback synchronization controller is designed, and the complete synchronization of the new complex network model is investigated. Two numerical examples of a triweight network model with the same and diverse structure are given to demonstrate the effectiveness of the control strategies. The synchronization design can achieve good results in the same and diverse structure network models with multiweights, which enrich complex network and control theory, so has certain theoretical and practical significance.
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  • 12
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    Reciprocity and Representation Theorems for Flux- and Field-Normalised Decomposed Wave Fields (2020)
    Hindawi
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    Publication Date: 2020
    Description: We consider wave propagation problems in which there is a preferred direction of propagation. To account for propagation in preferred directions, the wave equation is decomposed into a set of coupled equations for waves that propagate in opposite directions along the preferred axis. This decomposition is not unique. We discuss flux-normalised and field-normalised decomposition in a systematic way, analyse the symmetry properties of the decomposition operators, and use these symmetry properties to derive reciprocity theorems for the decomposed wave fields, for both types of normalisation. Based on the field-normalised reciprocity theorems, we derive representation theorems for decomposed wave fields. In particular, we derive double- and single-sided Kirchhoff-Helmholtz integrals for forward and backward propagation of decomposed wave fields. The single-sided Kirchhoff-Helmholtz integrals for backward propagation of field-normalised decomposed wave fields find applications in reflection imaging, accounting for multiple scattering.
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  • 13
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    New Improvement of Labor Accounting in the Sharing Economy (2020)
    Hindawi
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    Publication Date: 2020
    Description: The investigation of labor is a key aspect of population research, and labor accounting, as its foundation, is an important means to judge the degree of economic development and monitor the changes of the labor market, having always been a focus of scholarly research. At present, the sharing economy is on the rise worldwide and influences labor accounting. In this paper, starting from the context of the sharing economy and the current situation of labor accounting, several important aspects of labor accounting will be discussed. In the context of the sharing economy, household subsistence service production is to be included in the production accounting boundary, which is the root of the changes in labor accounting. On this basis, the following findings are drawn. (1) The scope of accounting for employment should be expanded, which puts higher demands on the labor accounting method. (2) Working time should be remeasured, especially indicators based on pay time. (3) Finally, the design of indicators in labor underutilization also requires the formation of new ideas, especially unemployment should be redefined. Finally, in view of the current status of labor accounting in China, policy suggestions for future improvement under the sharing economy are put forward.
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  • 14
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    Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise (2020)
    Hindawi
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    Publication Date: 2020
    Description: Representation of approximation for manifolds of the stochastic Swift-Hohenberg equation with multiplicative noise has been investigated via non-Markovian reduced system. The approximate parameterizations of the small scales for the large scales are given in the process of seeking for stochastic parameterizing manifolds, which are obtained as pullback limits of some backward-forward systems depending on the time-history of the dynamics of the low modes in a mean square sense through the nonlinear terms. When the corresponding pullback limits of some backward-forward systems are efficiently determined, the corresponding non-Markovian reduced systems can be obtained for researching good modeling performances in practice.
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  • 15
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    Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation (2020)
    Hindawi
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    Publication Date: 2020
    Description: Soliton molecules of the (2 + 1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived by -soliton solutions and a new velocity resonance condition. Moreover, soliton molecules can become asymmetric solitons when the distance between two solitons of the molecule is small enough. Finally, we obtained some novel types of hybrid solutions which are components of soliton molecules, lump waves, and breather waves by applying velocity resonance, module resonance of wave number, and long wave limit method. Some figures are presented to demonstrate clearly dynamics features of these solutions.
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  • 16
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    The Solitary Wave Solution for Quantum Plasma Nonlinear Dynamic Model (2020)
    Hindawi
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    Publication Date: 2020
    Description: In this paper, we discussed the quantum plasma system. A nonlinear dynamic disturbed model is studied. We used the undetermined coefficients method, dimensionless transformation and traveling wave transformation for the hyperbolic functions, and perturbation theory and method; then, the solitary wave solution for the quantum plasma nonlinear dynamic model is solved. Finally, the characteristics of the corresponding physical quantity are described.
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  • 17
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    New Generalized Soliton Solutions for a ()-Dimensional Equation (2020)
    Hindawi
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    Publication Date: 2020
    Description: In this paper, we investigate the nonlinear wave solutions for a ()-dimensional equation which can be reduced to the potential KdV equation. We present generalized -soliton solutions in which some arbitrarily differentiable functions are involved by using a simplified Hirota’s method. Our work extends some previous results.
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  • 18
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    Periodic Coulomb Dynamics of Three Equal Negative Charges in the Field of Equal Positive Charges Fixed in Octagon Vertices (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 19
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    Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 20
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    Blowup of Solutions to the Compressible Euler-Poisson and Ideal MHD Systems (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 21
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    Global Existence for Stochastic Strongly Dissipative Zakharov Equations (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 22
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    On Construction of a Super Hierarchy of the Wadati-Konno-Ichikawa Equation (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 23
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    Pressureless Magnetohydrodynamics System: Riemann Problem and Vanishing Magnetic Field Limit (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 24
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    Error Estimates for the Nearly Singular Momentum-Space Bound-State Equations (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 25
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    Investigation of Viscoelastic-Creep and Mechanical-Hysteresis Behaviors of Hydrostatically Stressed Crystal Using the Phase Field Crystal Method (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 26
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    Lump Solutions of a Nonlinear PDE Combining with a New Fourth-Order Term (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 27
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    Non-Fourier Heat Conduction of a Functionally Graded Cylinder Containing a Cylindrical Crack (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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    Dirichlet Type Problem for 2D Quaternionic Time-Harmonic Maxwell System in Fractal Domains (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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    Adaptive Control Design for Arneodo Chaotic System with Uncertain Parameters and Input Saturation (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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  • 30
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    Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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    Existence and Uniqueness Theorems for a Fractional Differential Equation with Impulsive Effect under Band-Like Integral Boundary Conditions (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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    Residual Symmetries and Bäcklund Transformations of (2 + 1)-Dimensional Strongly Coupled Burgers System (2020)
    Hindawi
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    Publication Date: 2020
    Description: In this article, we mainly apply the nonlocal residual symmetry analysis to a (2 + 1)-dimensional strongly coupled Burgers system, which is defined by us through taking values in a commutative subalgebra. On the basis of the general theory of Painlevé analysis, we get a residual symmetry of the strongly coupled Burgers system. Then, we introduce a suitable enlarged system to localize the nonlocal residual symmetry. In addition, a Bäcklund transformation is derived by Lie’s first theorem. Further, the linear superposition of the multiple residual symmetries is localized to a Lie point symmetry, and an -th Bäcklund transformation is also obtained.
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    PSO–SOM Neural Network Algorithm for Series Arc Fault Detection (2020)
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    Publication Date: 2020
    Description: Self-organizing feature map (SOM) neural network is a kind of competitive neural network with unsupervised learning. It has the strong abilities of self-organization and self-learning. However, the classification accuracy of SOM neural network may decrease when the features of tested object are not obvious. In this paper, the particle swarm optimization (PSO) algorithm is used to optimize the weight values of SOM network. Three indexes, i.e., intra-class density, standard deviation and sample difference, are used to judge the weight value, which can improve the classification accuracy of the SOM network. PSO–SOM network is applied to the detection of series arc fault in electrical circuits and compared with conventional SOM network and learning vector quantization (LVQ) network. The detection accuracy of the PSO–SOM network is 95%, which is higher than conventional SOM network and LVQ network.
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    Fixed Point Problems for Nonexpansive Mappings in Bounded Sets of Banach Spaces (2020)
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    Publication Date: 2020
    Description: It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space. The purpose of this paper is to establish fixed point theorems of nonexpansive mappings for bounded sets in Banach spaces. We study the existence of fixed points for nonexpansive mappings in bounded sets, and we present the iterative process to approximate fixed points. Some examples are given to support our results.
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    Degeneracy in Magneto-Active Dense Plasma (2020)
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    Publication Date: 2020
    Description: Degenerate dense plasmas are of great interest due to their important applications in modern technology and astrophysics. Such plasmas have generated a lot of interest in the last decade owing to their importance in many areas of physics such as semiconductors, metals, microelectronics, carbon nanotubes, quantum dots, and quantum wells. Besides, degenerate plasmas present very interesting features for fusion burning waves’ ignition and propagation. In this paper, we investigated the effects of static magnetic field on energy states and degeneracy of electrons in dense plasma. Using perturbation theory, two cases are considered, strongly and weakly magnetized electrons. Strong magnetic field will not eliminate completely the degeneracy, but it functions to reduce degeneracy. Perturbed energy eigenvalues are calculated to high accuracy. Besides, regardless of whether the perturbed state is degenerate or not, the energy is given by considering the average of orbital and spin coupling with respect to the eigenfunction . Here is the angular momentum vector, is the spin vector of electrons, and is the energy of spin orbit coupling in plasma, which plays a crucial role in the study of energy states and degeneracy of plasma electrons.
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    Edge δ− Graceful Labeling for Some Cyclic-Related Graphs (2020)
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    Publication Date: 2020
    Description: In this paper, we introduce a new type of labeling of a graph with vertices and edges called edge δ− graceful labeling, for any positive integer , as a bijective mapping of the edge set into the set such that the induced mapping , given by , where , is an injective function. We prove the existence of an edge δ− graceful labeling, for any positive integer , for some cycle-related graphs like the wheel graph, alternate triangular cycle, double wheel graph , the prism graph , the prism of the wheel , the gear graph , the closed helm CHn, the butterfly graph , and the friendship Frn.
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    Reconstruction of Velocity Distribution in Partially-Filled Pipe Based on Non-Uniform Under-Sampling (2020)
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    Publication Date: 2020
    Description: In the process of research on the flow velocity distribution in a partially filled pipe, the under-sampling of measurement data often occurs. For the first time, this problem is solved by the improved non-uniform B-spline curve fitting approximation (NBSC) method. The main innovation of this method is to reconstruct the flow velocity distribution fitting curve with a small amount of non-uniform feature points containing flow velocity information. First, the curvature of a whole discrete sampled data is analyzed, then the weighted threshold is set, and the sampled points that satisfy the threshold are extracted as the initial velocity distribution feature points. Next the node vectors were constructed according to the initial feature points, and the initial interpolation fitting curves are generated. Secondly, by using the relative deviation between the initial approximation curve and each sampled point, new feature points were added where the curve allowable deviation exceeded the specified tolerance, and then a new interpolation fitting curve was obtained. The above procedure was repeated until the fitting curve reached expected accuracy, thus the appropriate feature points were determined. Experimental results showed that, in the case of the same approximation deviation, the proposed NBSC method can solve the problem of under-sampling of measurement data better.
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    Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System (2020)
    Hindawi
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    Publication Date: 2020
    Description: An AB modified KdV (AB-mKdV) system which can be used to describe two-place event is studied in this manuscript. Because the AB-mKdV system is considered as a special reduction of the famous AKNS system, the properties of the AKNS system are first revealed by using symmetry analysis. The nonlocal symmetries related to truncated Painlevé expansion, the finite transformation, and the symmetry reduction solutions of the AKNS system are presented. The corresponding Bäcklund transformations and the interaction solutions of the AB-mKdV system are constructed based on the special reduction. The results demonstrate that the AB-mKdV system possesses many kinds of interaction solutions, such as the interactions between kink and soliton and kink and cnoidal waves. The soliton can be changed from bright to dark during propagation.
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    Warped Product Pointwise Semi Slant Submanifolds of Sasakian Space Forms and their Applications (2020)
    Hindawi
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    Publication Date: 2020
    Description: In this study, we attain some existence characterizations for warped product pointwise semi slant submanifolds in the setting of Sasakian space forms. Moreover, we investigate the estimation for the squared norm of the second fundamental form and further discuss the case of equality. By the application of attained estimation, we obtain some classifications of these warped product submanifolds in terms of Ricci soliton and Ricci curvature. Further, the formula for Dirichlet energy of involved warping function is derived. A nontrivial example of such warped product submanifolds is also constructed. Throughout the paper, we will use the following acronyms: “WP” for warped product, “WF” for warping function, “AC” for almost contact, and “WP-PSS” for the warped product pointwise semi slant.
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    Speech Encryption Algorithm Based on Nonorthogonal Quantum State with Hyperchaotic Keystreams (2020)
    Hindawi
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    Publication Date: 2020
    Description: With the advancement in modern computational technologies like cloud computing, there has been tremendous growth in the field of data processing and encryption technologies. In this contest there is an increasing demand for successful storage of the data in the encrypted domain to avoid the possibility of data breach in shared networks. In this paper, a novel approach for speech encryption algorithm based on quantum chaotic system is designed. In the proposed method, classical bits of the speech samples are initially encoded in nonorthogonal quantum state by the secret polarizing angle. In the quantum domain, encoded speech samples are subjected to bit-flip operation according to the Controlled–NOT gate followed by Hadamard transform. Complete superposition of the quantum state in both Hadamard and standard basis is achieved through Hadamard transform. Control bits for C-NOT gate as well as Hadamard gate are generated with a modified -hyperchaotic system. Secret nonorthogonal rotation angles and initial conditions of the hyperchaotic system are the keys used to ensure the security of the proposed algorithm. The computational complexity of the proposed algorithm has been analysed both in quantum domain and classical domain. Numerical simulation carried out based on the above principle showed that the proposed speech encryption algorithm has wider keyspace, higher key sensitivity and robust against various differential and statistical cryptographic attacks.
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    Anti-Synchronization of Fractional-Order Chaotic Circuit with Memristor via Periodic Intermittent Control (2020)
    Hindawi
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    Publication Date: 2020
    Description: In this paper, the anti-synchronization of fractional-order chaotic circuit with memristor (FCCM) is investigated via a periodic intermittent control scheme. Based on the principle of periodic intermittent control and the Lyapunov stability theory, a novel criterion is adopted to realize the anti-synchronization of FCCM. Finally, some examples of numerical simulations are exploited to verify the feasibility of theoretical analysis.
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    Boundary Effect on Asymptotic Behavior of Solutions to the -System with Time-Dependent Damping (2020)
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    Publication Date: 2020
    Description: In this paper, we consider the asymptotic behavior of solutions to the -system with time-dependent damping on the half-line , with the Dirichlet boundary condition , in particular, including the constant and nonconstant coefficient damping. The initial data have the constant state at . We prove that the solutions time-asymptotically converge to as tends to infinity. Compared with previous results about the -system with constant coefficient damping, we obtain a general result when the initial perturbation belongs to . Our proof is based on the time-weighted energy method.
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    Reciprocity and Representation Theorems for Flux- and Field-Normalised Decomposed Wave Fields (2020)
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    Publication Date: 2020
    Description: We consider wave propagation problems in which there is a preferred direction of propagation. To account for propagation in preferred directions, the wave equation is decomposed into a set of coupled equations for waves that propagate in opposite directions along the preferred axis. This decomposition is not unique. We discuss flux-normalised and field-normalised decomposition in a systematic way, analyse the symmetry properties of the decomposition operators, and use these symmetry properties to derive reciprocity theorems for the decomposed wave fields, for both types of normalisation. Based on the field-normalised reciprocity theorems, we derive representation theorems for decomposed wave fields. In particular, we derive double- and single-sided Kirchhoff-Helmholtz integrals for forward and backward propagation of decomposed wave fields. The single-sided Kirchhoff-Helmholtz integrals for backward propagation of field-normalised decomposed wave fields find applications in reflection imaging, accounting for multiple scattering.
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    The Rational Spectral Method Combined with the Laplace Transform for Solving the Robin Time-Fractional Equation (2020)
    Hindawi
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    Publication Date: 2020
    Description: In this paper, the rational spectral method combined with the Laplace transform is proposed for solving Robin time-fractional partial differential equations. First, a time-fractional partial differential equation is transformed into an ordinary differential equation with frequency domain components by the Laplace transform. Then, the spatial derivatives are discretized by the rational spectral method, the linear equation with the parameter is solved, and the approximation is obtained. The approximate solution at any given time, which is the numerical inverse Laplace transform, is obtained by the modified Talbot algorithm. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.
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    Lie Symmetry Analysis and Invariant Solutions of a Nonlinear Fokker-Planck Equation Describing Cell Population Growth (2020)
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    Publication Date: 2020
    Description: In this paper, a complete Lie symmetry analysis is performed for a nonlinear Fokker-Planck equation for growing cell populations. Moreover, an optimal system of one-dimensional subalgebras is constructed and used to find similarity reductions and invariant solutions. A new power series solution is constructed via the reduced equation, and its convergence is proved.
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    Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation (2020)
    Hindawi
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    Publication Date: 2020
    Description: Soliton molecules of the (2 + 1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived by -soliton solutions and a new velocity resonance condition. Moreover, soliton molecules can become asymmetric solitons when the distance between two solitons of the molecule is small enough. Finally, we obtained some novel types of hybrid solutions which are components of soliton molecules, lump waves, and breather waves by applying velocity resonance, module resonance of wave number, and long wave limit method. Some figures are presented to demonstrate clearly dynamics features of these solutions.
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    New Generalized Soliton Solutions for a ()-Dimensional Equation (2020)
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    Publication Date: 2020
    Description: In this paper, we investigate the nonlinear wave solutions for a ()-dimensional equation which can be reduced to the potential KdV equation. We present generalized -soliton solutions in which some arbitrarily differentiable functions are involved by using a simplified Hirota’s method. Our work extends some previous results.
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    New Improvement of Labor Accounting in the Sharing Economy (2020)
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    Publication Date: 2020
    Description: The investigation of labor is a key aspect of population research, and labor accounting, as its foundation, is an important means to judge the degree of economic development and monitor the changes of the labor market, having always been a focus of scholarly research. At present, the sharing economy is on the rise worldwide and influences labor accounting. In this paper, starting from the context of the sharing economy and the current situation of labor accounting, several important aspects of labor accounting will be discussed. In the context of the sharing economy, household subsistence service production is to be included in the production accounting boundary, which is the root of the changes in labor accounting. On this basis, the following findings are drawn. (1) The scope of accounting for employment should be expanded, which puts higher demands on the labor accounting method. (2) Working time should be remeasured, especially indicators based on pay time. (3) Finally, the design of indicators in labor underutilization also requires the formation of new ideas, especially unemployment should be redefined. Finally, in view of the current status of labor accounting in China, policy suggestions for future improvement under the sharing economy are put forward.
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    A New Complex Network Model with Multiweights and Its Synchronization Control (2020)
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    Publication Date: 2020
    Description: Based on the weighted complex network model, this paper establishes a multiweight complex network model, which possesses several different weights on the one edge. According to the method of network split, the complex network with multiweights is split into several different complex networks with single weight. Some new static characteristics, such as node weight, node degree, node weight strength, node weight distribution, edge weight distribution, and diversity of weight distribution are defined. Then, by using Lyapunov stability theory, the adaptive feedback synchronization controller is designed, and the complete synchronization of the new complex network model is investigated. Two numerical examples of a triweight network model with the same and diverse structure are given to demonstrate the effectiveness of the control strategies. The synchronization design can achieve good results in the same and diverse structure network models with multiweights, which enrich complex network and control theory, so has certain theoretical and practical significance.
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    Double Hopf Bifurcation in Microbubble Oscillators with Delay Coupling (2020)
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    Publication Date: 2020
    Description: Using center manifold reduction methodswe investigate the double Hopf bifurcation in the dynamics of microbubble with delay couplingwith main attention focused on nonresonant double Hopf bifurcation. We obtain the normal form of the system in the vicinity of the double Hopf point and classify the bifurcations in a two-dimensional parameter space near the critical point. Some numerical simulations support the applicability of the theoretical results. In particularwe give the explanation for some physical phenomena of the system using the obtained mathematical results.
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    Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise (2020)
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    Publication Date: 2020
    Description: Representation of approximation for manifolds of the stochastic Swift-Hohenberg equation with multiplicative noise has been investigated via non-Markovian reduced system. The approximate parameterizations of the small scales for the large scales are given in the process of seeking for stochastic parameterizing manifolds, which are obtained as pullback limits of some backward-forward systems depending on the time-history of the dynamics of the low modes in a mean square sense through the nonlinear terms. When the corresponding pullback limits of some backward-forward systems are efficiently determined, the corresponding non-Markovian reduced systems can be obtained for researching good modeling performances in practice.
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    The Solitary Wave Solution for Quantum Plasma Nonlinear Dynamic Model (2020)
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    Publication Date: 2020
    Description: In this paper, we discussed the quantum plasma system. A nonlinear dynamic disturbed model is studied. We used the undetermined coefficients method, dimensionless transformation and traveling wave transformation for the hyperbolic functions, and perturbation theory and method; then, the solitary wave solution for the quantum plasma nonlinear dynamic model is solved. Finally, the characteristics of the corresponding physical quantity are described.
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    Multimode Process Monitoring Method Based on Multiblock Projection Nonnegative Matrix Factorization (2020)
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    Publication Date: 2020-04-24
    Description: A multimode process monitoring method based on multiblock projection nonnegative matrix factorization (MPNMF) is proposed for traditional process monitoring methods which often adopt global model of data and ignore local information of data. Firstly, the training data set of each mode is partitioned by the complete link algorithm and the multivariate data space is divided into several subblocks. Then, the projection nonnegative matrix factorization (PNMF) algorithm is used to model each subspace of each mode separately. A joint probabilistic statistic index is defined to identify the running modes of the process data. Finally, the Bayesian information criterion (BIC) is used to synthesize the statistics of each subblock and construct a new statistic for process monitoring. The proposed process monitoring method is applied to the TE process to verify its effectiveness.
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    Characterization of Graphs with an Eigenvalue of Large Multiplicity (2020)
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    Publication Date: 2020-04-29
    Description: Let G be a simple and undirected graph. The eigenvalues of the adjacency matrix of G are called the eigenvalues of G. In this paper, we characterize all the n-vertex graphs with some eigenvalue of multiplicity n−2 and n−3, respectively. Moreover, as an application of the main result, we present a family of nonregular graphs with four distinct eigenvalues.
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    Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations (2020)
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    Publication Date: 2020-04-25
    Description: In this paper, by applying the Jacobian ellipse function method, we obtain a group of periodic traveling wave solution of coupled KdV equations. Furthermore, by the implicit function theorem, the relation between some wave velocity and the solution’s period is researched. Lastly, we show that this type of solution is orbitally stable by periodic perturbations of the same wavelength as the underlying wave.
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    The Rational Spectral Method Combined with the Laplace Transform for Solving the Robin Time-Fractional Equation (2020)
    Hindawi
    Details
    Publication Date: 2020
    Description: In this paper, the rational spectral method combined with the Laplace transform is proposed for solving Robin time-fractional partial differential equations. First, a time-fractional partial differential equation is transformed into an ordinary differential equation with frequency domain components by the Laplace transform. Then, the spatial derivatives are discretized by the rational spectral method, the linear equation with the parameter is solved, and the approximation is obtained. The approximate solution at any given time, which is the numerical inverse Laplace transform, is obtained by the modified Talbot algorithm. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.
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    Double Hopf Bifurcation in Microbubble Oscillators with Delay Coupling (2020)
    Hindawi
    Details
    Publication Date: 2020
    Description: Using center manifold reduction methodswe investigate the double Hopf bifurcation in the dynamics of microbubble with delay couplingwith main attention focused on nonresonant double Hopf bifurcation. We obtain the normal form of the system in the vicinity of the double Hopf point and classify the bifurcations in a two-dimensional parameter space near the critical point. Some numerical simulations support the applicability of the theoretical results. In particularwe give the explanation for some physical phenomena of the system using the obtained mathematical results.
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    On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems (2020)
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    Publication Date: 2020
    Description: 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.
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    Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space (2020)
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    Publication Date: 2020
    Description: 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.
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    The Existence of Normalized Solutions for a Nonlocal Problem in (2020)
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    Publication Date: 2020
    Description: 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.
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    E-Bayesian Prediction for the Burr XII Model Based on Type-II Censored Data with Two Samples (2020)
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    Publication Date: 2020
    Description: 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.
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    Modeling and Estimation of Thermal Flows Based on Transport and Balance Equations (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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    Deviation Effect of Coaxiality on the Rock Brazilian Split (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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    Three Types Generalized -Heisenberg Ferromagnet Models (2020)
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    Publication Date: 2020
    Description: 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.
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    Mixed Rational-Exponential Solutions to the Kadomtsev-Petviashvili-II Equation with a Self-Consistent Source (2020)
    Hindawi
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    Publication Date: 2020
    Description: 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.
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    Characterizations of Trivial Ricci Solitons (2020)
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    Publication Date: 2020-04-10
    Description: Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton. First, on a complete shrinking Ricci soliton, we show that the scalar curvature satisfying a certain inequality gives a characterization of a trivial Ricci soliton. Then, it is shown that the potential field having geodesic flow and length of potential field satisfying certain inequality gives another characterization of a trivial Ricci soliton. Finally, we show that the potential field of constant length satisfying an inequality gives a characterization of a trivial Ricci soliton.
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    Double Stratified Mixed Convective Flow of Couple Stress Nanofluid past Inclined Stretching Cylinder Using Cattaneo-Christov Heat and Mass Flux Model (2020)
    Hindawi
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    Publication Date: 2020-05-08
    Description: 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.
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    Multiparticle Localization at Low Energy for Multidimensional Continuous Anderson Models (2020)
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    Publication Date: 2020-05-05
    Description: We study the multiparticle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multiparticle lower spectral edges are almost surely constant in absence of ergodicity. We stress that this result is not quite obvious and has to be handled carefully. In addition, we prove the spectral exponential and the strong dynamical localization of the continuous multiparticle Anderson model at low energy. The proof based on the multiparticle multiscale analysis bounds needs the values of the external random potential to be independent and identically distributed, whose common probability distribution is at least Log-Hölder continuous.
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    On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term (2020)
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    Publication Date: 2020-05-05
    Description: In the present paper, we consider the following Hamiltonian elliptic system with Choquard’s nonlinear term −Δu+Vxu=∫ΩGvy/x−yβdygv in Ω,−Δv+Vxv=∫ΩFuy/x−yαdyfu in Ω,u=0,v=0 on ∂Ω,where Ω⊂ℝN is a bounded domain with a smooth boundary, 0
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    A Posteriori Error Estimates for Hughes Stabilized SUPG Technique and Adaptive Refinement for a Convection-Diffusion Problem (2020)
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    Publication Date: 2020-05-16
    Description: 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.
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    The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method (2020)
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    Publication Date: 2020-05-15
    Description: 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.
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    Analysis of Heating Effects and Different Wave Forms on Peristaltic Flow of Carreau Fluid in Rectangular Duct (2020)
    Hindawi
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    Publication Date: 2020-05-20
    Description: 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 c 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 β.
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    Theory of Generalized Canonical Transformations for Birkhoff Systems (2020)
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    Publication Date: 2020-05-26
    Description: 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.
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    Indefinite Ruhe’s Variant of the Block Lanczos Method for Solving the Systems of Linear Equations (2020)
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    Publication Date: 2020-05-26
    Description: In this paper, we equip Cn 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.
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    The Existence of the Sign-Changing Solutions for the Kirchhoff-Schrödinger-Poisson System in Bounded Domains (2020)
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    Publication Date: 2020-05-19
    Description: 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 u0 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 u0 as the parameters b↘0 and λ↘0.
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    Scattering Theory for 2N Parameter Models of Finitely Many Relativistic δ-Sphere and δ-Sphere plus Coulomb Interactions Supported by Concentric Spheres in Quantum Mechanics (2020)
    Hindawi
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    Publication Date: 2020-04-15
    Description: We study scattering theory for 2N parameter models of finitely many relativistic δ-sphere and δ-sphere plus Coulomb interactions. We provide the mathematical definitions of the Hamiltonians, solve the resolvent equations, and compute the nonrelativistic limits for both models. We obtain new results related to spectral properties and scattering data.
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    Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data (2020)
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    Publication Date: 2020-04-17
    Description: In this paper, a new three-parameter lifetime distribution is introduced; the new model is a generalization of the log-logistic (LL) model, and it is called the alpha power transformed log-logistic (APTLL) distribution. The APTLL distribution is more flexible than some generalizations of log-logistic distribution. We derived some mathematical properties including moments, moment-generating function, quantile function, Rényi entropy, and order statistics of the new model. The model parameters are estimated using maximum likelihood method of estimation. The simulation study is performed to investigate the effectiveness of the estimates. Finally, we used one real-life dataset to show the flexibility of the APTLL distribution.
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    Joining between Boron Nitride Nanocones and Nanotubes (2020)
    Hindawi
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    Publication Date: 2020-04-30
    Description: Different nanostructures of boron nitride have been observed experimentally such as fullerenes, tubes, cones, and graphene. They have received much attention due to their physical, chemical, and electronic properties that lead them to numerous applications in many nanoscale devices. Joining between nanostructures gives rise to new structures with outstanding properties and potential applications for the design of probes for scanning tunneling microscopy and other nanoscale devices, as carriers for drug delivery and liquid separation. This paper utilizes calculus of variations to model the joining between two types of BN nanostructures, namely, BN nanotubes and BN nanocones. Based on the curvature of the join curve, the joining of these structures can be divided into two models. Model I refers to when the join profile includes positive curvature only, and Model II contains both positive and negative curvatures. The main goal here is to formulate the basic underlying structure from which any such small perturbations can be viewed as departures from an ideal model. For this scenario of joining, we successfully present simple models based on joining BN nanotubes to BN nanocones with five different angles of the cone.
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    Three-Point Boundary Value Problems for the Langevin Equation with the Hilfer Fractional Derivative (2020)
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    Publication Date: 2020-05-04
    Description: We discuss the existence and uniqueness of solutions for the Langevin fractional differential equation and its inclusion counterpart involving the Hilfer fractional derivatives, supplemented with three-point boundary conditions by means of standard tools of the fixed-point theorems for single and multivalued functions. We make use of Banach’s fixed-point theorem to obtain the uniqueness result, while the nonlinear alternative of the Leray-Schauder type and Krasnoselskii’s fixed-point theorem are applied to obtain the existence results for the single-valued problem. Existence results for the convex and nonconvex valued cases of the inclusion problem are derived via the nonlinear alternative for Kakutani’s maps and Covitz and Nadler’s fixed-point theorem respectively. Examples illustrating the obtained results are also constructed. (2010) Mathematics Subject Classifications. This study is classified under the following classification codes: 26A33; 34A08; 34A60; and 34B15.
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    Field Equations and Lagrangian of the Kaluza Energy-Momentum Tensor (2020)
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    Publication Date: 2020-05-04
    Description: We provide an analysis and statement of the source term in the classical Kaluza field equations, by considering the 5-dimensional (5D) energy-momentum tensor corresponding to the 5D geodesic hypothesis that is typically presumed in the Kaluza theory. By providing the 5D matter Lagrangian, this work completes a Lagrangian analysis of the classical Kaluza theory that began by establishing the proper form of the unique Kaluza field Lagrangian. This work considers the transformation properties necessitated by general covariance of the Kaluza source terms, to establish the correct form for the source terms in the field equations, and to establish the 5D matter Lagrangian that corresponds to the 5D geodesic hypothesis. In addition to the effects of a scalar field expected from other scalar-tensor or scalar-electromagnetic theories, a peculiar Kaluza coupling coefficient arises for charged matter which acts to vary the source strengths in ways unknown to conventional physics. We briefly evaluate the implied modifications to source terms in the field equations. We find an ADM-like neutralization of gravity at high specific charge states and a saturation in field strength at high specific charge-to-mass ratios.
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    Entanglement Quantification of Correlated Photons Generated by Three-Level Laser with Parametric Amplifier and Coupled to a Two-Mode Vacuum Reservoir (2020)
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    Publication Date: 2020-05-18
    Description: 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.
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    Rational Solutions and Their Interaction Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation (2020)
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    Publication Date: 2020-04-17
    Description: In this paper, we gave a form of rational solution and their interaction solution to a nonlinear evolution equation. The rational solution contained lump solution, general lump solution, high-order lump solution, lump-type solution, etc. Their interaction solution contained the classical interaction solution, such as the lump-kink solution and the lump-soliton solution. As the example, by using the generalized bilinear method and symbolic computation Maple, we obtained abundant high-order lump-type solutions and their interaction solutions between lumps and other function solutions under certain constraints of the (3+1)-dimensional Jimbo-Miwa equation. Via three-dimensional plots, contour plots and density plots with the help of Maple, the physical characteristics and structures of these waves are described very well. These solutions have greatly enriched the exact solutions of the (3+1)-dimensional Jimbo-Miwa equation on the existing literature.
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    Nonlinear Hydroelastic Interaction among a Floating Elastic Plate, Water Waves, and Exponential Shear Currents (2020)
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    Publication Date: 2020-08-26
    Description: 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.
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    A Comparison of Normal Cone Conditions for Homotopy Methods for Solving Inequality Constrained Nonlinear Programming Problems (2020)
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    Publication Date: 2020-07-04
    Description: 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.
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    Existence of Solution for Double-Phase Problem with Singular Weights (2020)
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    Publication Date: 2020-07-15
    Description: 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.
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    Representations and Deformations of Hom-Lie-Yamaguti Superalgebras (2020)
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    Publication Date: 2020-06-18
    Description: Let L,α 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 L,α and present some properties. Finally, we investigate the deformations of L,α by choosing some suitable cohomology.
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    New Fixed Point Results in F-Quasi-Metric Spaces and an Application (2020)
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    Publication Date: 2020-06-18
    Description: The main goal of the present paper is to obtain several fixed point theorems in the framework of F-quasi-metric spaces, which is an extension of F-metric spaces. Also, a Hausdorff δ-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.
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    Breather Wave Solutions and Interaction Solutions for Two Mixed Calogero-Bogoyavlenskii-Schiff and Bogoyavlensky-Konopelchenko Equations (2020)
    Hindawi
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    Publication Date: 2020-06-16
    Description: 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.
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    The Cauchy Problem for Parabolic Equations with Degeneration (2020)
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    Publication Date: 2020-06-16
    Description: 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.
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    Multiple Lump Solutions of the (4+1)-Dimensional Fokas Equation (2020)
    Hindawi
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    Publication Date: 2020-06-10
    Description: In this paper, we investigate multiple lump wave solutions of the new (4+1)-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.
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  • 91
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    Solovay–Kitaev Approximations of Special Orthogonal Matrices (2020)
    Hindawi
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    Publication Date: 2020-06-24
    Description: 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.
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  • 92
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    The Investigation of MHD Williamson Nanofluid over Stretching Cylinder with the Effect of Activation Energy (2020)
    Hindawi
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    Publication Date: 2020-06-25
    Description: 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.
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    A New Extension of the Rectangular b-Metric Spaces (2020)
    Hindawi
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    Publication Date: 2020-06-01
    Description: In this paper, we introduce a generalization of rectangular b-metric spaces, by changing the rectangular inequality as follows: Dζa,b≤ζa,b,u,vDζa,u+Dζu,v+Dζv,b, for all distinct a,b,u,v∈X. We prove some fixed point theorems, and we use our results to present a nice application in the last section of this paper.
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    Investigating One-, Two-, and Triple-Wave Solutions via Multiple Exp-Function Method Arising in Engineering Sciences (2020)
    Hindawi
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    Publication Date: 2020-06-08
    Description: The multiple Exp-function method is employed for searching the multiple soliton solutions for the new extended (3+1)-dimensional Jimbo-Miwa-like (JM) equation, the extended (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (eCBS) equation, the generalization of the (2+1)-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.
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  • 95
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    Heat Concentration around a Cylindrical Interface Crack in a Composite Tube (2020)
    Hindawi
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    Publication Date: 2020-06-12
    Description: 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.
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    Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance (2020)
    Hindawi
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    Publication Date: 2020-09-26
    Description: 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 T1. Furthermore, the phenomenon of phase locking on the torus T1 is investigated and the parameter condition under which there exists subharmonic motion on the torus T1 is determined.
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    Adaptive Multilevel Collaborative Passenger Flow Control in Peak Hours for a Subway Line (2020)
    Hindawi
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    Publication Date: 2020-09-24
    Description: 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.
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  • 98
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    Broer-Kaup System with Corrections via Inverse Scattering Transform (2020)
    Hindawi
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    Publication Date: 2020-09-15
    Description: 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 ε-order approximate solution of one soliton to the Broer-Kaup system with corrections.
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    Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition (2020)
    Hindawi
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    Publication Date: 2020-09-19
    Description: This paper is devoted to identify a space-dependent source function in a multiterm time-fractional diffusion equation with nonhomogeneous boundary condition from a part of noisy boundary data. The well-posedness of a weak solution for the corresponding direct problem is proved by the variational method. We firstly investigate the uniqueness of an inverse initial problem by the analytic continuation technique and the Laplace transformation. Then, the uniqueness of the inverse source problem is derived by employing the fractional Duhamel principle. The inverse problem is solved by the Levenberg-Marquardt regularization method, and an approximate source function is found. Numerical examples are provided to show the effectiveness of the proposed method in one- and two-dimensional cases.
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    Application of Local Fractional Homotopy Perturbation Method in Physical Problems (2020)
    Hindawi
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    Publication Date: 2020-09-19
    Description: Nonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. The perturbation method is a wave equation solution using HPM compared with the Fourier series method, and both methods results are good agreement. The percentage of error of ux,t with α=1 and 0.33, t =0.1 sec, between the present research and Yong-Ju Yang study for x≥0.6 is less than 10. Also, the % error for x≥0.5 in α=1 and 0.33, t =0.3 sec, is less than 5, whereas for α=1 and 0.33, t =0.8 and 0.7 sec, the % error for x≥0.4 is less than 8.
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