Abstract: 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. PubDate: Tue, 14 Jan 2020 11:05:01 +000

Abstract: 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. PubDate: Mon, 13 Jan 2020 10:50:01 +000

Abstract: 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. PubDate: Mon, 13 Jan 2020 08:05:07 +000

Abstract: 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. PubDate: Mon, 13 Jan 2020 08:05:06 +000

Abstract: 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. PubDate: Mon, 13 Jan 2020 08:05:04 +000

Abstract: 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. PubDate: Thu, 09 Jan 2020 08:50:03 +000

Abstract: 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. PubDate: Wed, 08 Jan 2020 15:20:00 +000

Abstract: 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. PubDate: Tue, 07 Jan 2020 14:20:01 +000

Abstract: 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. PubDate: Mon, 06 Jan 2020 15:50:01 +000

Abstract: 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. PubDate: Fri, 03 Jan 2020 08:50:03 +000

Abstract: 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. PubDate: Thu, 02 Jan 2020 14:20:04 +000

Abstract: The purpose of this paper is to establish the necessary conditions for a fuzzy optimal control problem of several variables. Also, we define fuzzy optimal control problems involving isoperimetric constraints and higher order differential equations. Then, we convert these problems to fuzzy optimal control problems of several variables in order to solve these problems using the same solution method. The main results of this paper are illustrated throughout three examples, more specifically, a discussion on the strong solutions (fuzzy solutions) of our problems. PubDate: Sun, 29 Dec 2019 18:05:02 +000

Abstract: In this paper, we study the following Schrödinger-Poisson equations where the parameter and . When the parameter is small and the weight function fulfills some appropriate conditions, we admit the Schrödinger-Poisson equations possess infinitely many negative energy solutions by using a truncation technology and applying the usual Krasnoselskii genus theory. In addition, a byproduct is that the set of solutions is compact. PubDate: Sun, 29 Dec 2019 17:50:03 +000

Abstract: In this paper, with the help of symbolic computation, three types of rational solutions for the ()-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation are derived. By means of the truncated Painlevé expansion, we show that the ()-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation can be written as a trilinear-linear equation, from which we get explicit representation for rational solutions of the ()-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation. PubDate: Sun, 29 Dec 2019 16:50:06 +000

Abstract: In the current work, a combination between a new integral transform and the homotopy perturbation method is presented. This combination allows to obtain analytic and numerical solutions for linear and nonlinear systems of partial differential equations. PubDate: Sun, 22 Dec 2019 09:20:01 +000

Abstract: The physics of gyroscopic effects are more complex than presented in existing mathematical models. The effects presented by these models do not match the real forces acting on gyroscopic devices. New research in this area has demonstrated that a system of inertial torques, which are generated by the rotating mass of spinning objects, acts upon a gyroscope. The actions of the system of inertial forces are validated by practical tests of the motions of a gyroscope with one side support. The action of external load torque on a gyroscope with one side support demonstrates that the gyroscope’s upward motion is wrongly called an “antigravity” effect. The upward motion of a gyroscope is the result of precession torque around its horizontal axis. The novelty of the present work is related to the mathematical models for the upward and downward motions of gyroscopes influenced by external torque around the vertical axis. This analytical research describes the physics of gyroscopes’ upward motion and validates that gyroscopes do not possess an antigravity property. PubDate: Fri, 20 Dec 2019 07:35:04 +000

Abstract: In this paper, we investigate the Lorentzian generalized Sasakian-space-form. We give the necessary and sufficient conditions for the Lorentzian generalized Sasakian-space-form to be projectively flat, conformally flat, conharmonically flat, and Ricci semisymmetric and their relationship between each other. As the application of our theorems, we study the Ricci almost soliton on conformally flat Lorentzian generalized Sasakian-space-form. PubDate: Thu, 19 Dec 2019 12:50:05 +000

Abstract: It is of great practical significance to figure out the propagation mechanism and outbreak condition of rumor spreading on online social networks. In our paper, we propose a multi-state reinforcement diffusion model for rumor spreading, in which the reinforcement mechanism is introduced to depict individual willingness towards rumor spreading. Multiple intermediate states are introduced to characterize the process that an individual's diffusion willingness is enhanced step by step. We study the rumor spreading process with the proposed reinforcement diffusion mechanism on two typical networks. The outbreak thresholds of rumor spreading on both two networks are obtained. Numerical simulations and Monte Carlo simulations are conducted to illustrate the spreading process and verify the correctness of theoretical results. We believe that our work will shed some light on understanding how human sociality affects the rumor spreading on online social networks. PubDate: Tue, 17 Dec 2019 08:05:03 +000

Abstract: By using the complex variable function theory and the conformal mapping method, the scattering of plane shear wave (SH-wave) around an arbitrary shaped nano-cavity is studied. Surface effects at the nanoscale are explained based on the surface elasticity theory. According to the generalized Yong–Laplace equations, the boundary conditions are given, and the infinite algebraic equations for solving the unknown coefficients of the scattered wave solutions are established. The numerical solutions of the stress field can be obtained by using the orthogonality of trigonometric functions. Lastly, the numerical results of dynamic stress concentration factor around a circular hole, an elliptic hole and a square hole as the special cases are discussed. The numerical results show that the surface effect and wave number have a significant effect on the dynamic stress concentration, and prove that our results from theoretical derivation are correct. PubDate: Sun, 15 Dec 2019 11:20:05 +000

Abstract: A fractional Hardy–Sobolev inequality with a magnetic field is studied in the present paper. Under appropriate conditions, the achievement of the best constant of the fractional magnetic Hardy–Sobolev inequality is established. PubDate: Thu, 12 Dec 2019 10:35:05 +000

Abstract: In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the - approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results. PubDate: Wed, 21 Aug 2019 13:05:11 +000

Abstract: Using a resonance nonlinear Schrödinger equation as a bridge, we explore a direct connection of cold plasma physics to two-dimensional black holes. Namely, we compute and diagonalize a metric attached to the propagation of magnetoacoustic waves in a cold plasma subject to a transverse magnetic field, and we construct an explicit change of variables by which this metric is transformed exactly to a Jackiw-Teitelboim black hole metric. PubDate: Mon, 19 Aug 2019 08:05:13 +000

Abstract: In this paper, a prey-predator model and weak Allee effect in prey growth and its dynamical behaviors are studied in detail. The existence, boundedness, and stability of the equilibria of the model are qualitatively discussed. Bifurcation analysis is also taken into account. After incorporating the searching delay and digestion delay, we establish a delayed predator-prey system with Allee effect. The results show that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values. Finally, we present some numerical simulations to illustrate our theoretical analysis. PubDate: Tue, 06 Aug 2019 10:05:17 +000

Abstract: The Davey-Stewartson Equation (DSE) is an equation system that reflects the evolution in finite depth of soft nonlinear packets of water waves that move in one direction but in which the waves’ amplitude is modulated in spatial directions. This paper uses the Generalized Elliptic Equation Rational Expansion (GEERE) technique to extract fresh exact solutions for the DSE. As a consequence, solutions with parameters of trigonometric, hyperbolic, and rational function are achieved. To display the physical characteristics of this model, the solutions obtained are graphically displayed. Modulation instability assessment of the outcomes acquired is also discussed and it demonstrates that all the solutions built are accurate and stable. PubDate: Tue, 06 Aug 2019 10:05:13 +000

Abstract: The principal pivoting algorithm is a popular direct algorithm in solving the linear complementarity problem, and its block forms had also been studied by many authors. In this paper, relying on the characteristic of block principal pivotal transformations, a block principal pivoting algorithm is proposed for solving the linear complementarity problem with an -matrix. By this algorithm, the linear complementarity problem can be solved in some block principal pivotal transformations. Besides, both the lower-order and the higher-order experiments are presented to show the effectiveness of this algorithm. PubDate: Tue, 30 Jul 2019 10:05:11 +000

Abstract: Solving nonclassical symmetry of partial differential equations (PDEs) is a challenging problem in applications of symmetry method. In this paper, an alternative method is proposed for computing the nonclassical symmetry of PDEs. The method consists of the following three steps: firstly, a relationship between the classical and nonclassical symmetries of PDEs is established; then based on the link, we give three principles to obtain additional equations (constraints) to extend the system of the determining equations of the nonclassical symmetry. The extended system is more easily solved than the original one; thirdly, we use Wu’s method to solve the extended system. Consequently, the nonclassical symmetries are determined. Due to the fact that some constraints may produce trivial results, we name the candidate constraints as “potential” ones. The method gives a new way to determine a nonclassical symmetry. Several illustrative examples are given to show the efficiency of the presented method. PubDate: Thu, 18 Jul 2019 13:05:14 +000

Abstract: Let be a -Jordan Lie supertriple system. We first introduce the notions of generalized derivations and representations of and present some properties. Also, we study the low-dimensional cohomology and the coboundary operator of , and then we investigate the deformations and Nijenhuis operators of by choosing some suitable cohomologies. PubDate: Thu, 11 Jul 2019 09:05:15 +000

Abstract: In this paper, we present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems. We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological structure. We also found that the equilibrium point generated by the fractional order system belongs to the unstable saddle point through the prediction correction method and the fractional order stability theory. The complexity of fractional order chaotic system is given by spectral entropy algorithm and algorithm. We concluded that the fractional order chaotic system has a higher complexity. The fractional order system can generate rich dynamic behavior phenomenon with the values of the parameters and the order changed. We applied the finite time stability theory to design the finite time synchronous controller between drive system and corresponding system. The numerical simulations demonstrate that the controller provides fast and efficient method in the synchronization process. PubDate: Wed, 03 Jul 2019 08:05:08 +000

Abstract: We analyze the appearance of delta shock wave and vacuum state in the vanishing pressure limit of Riemann solutions to the non-isentropic generalized Chaplygin gas equations. As the pressure vanishes, the Riemann solution including two shock waves and possible one contact discontinuity converges to a delta shock wave solution. Both the density and the internal energy simultaneously present a Dirac delta singularity. And the Riemann solution involving two rarefaction waves and possible one contact discontinuity converges to a solution involving vacuum state of the transport equations. PubDate: Wed, 03 Jul 2019 08:05:06 +000

Abstract: In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation. Furthermore, the upper semicontinuity of random attractors is discussed when the intensity of noise approaches zero. The main difficulty is to prove the asymptotic compactness for establishing the existence of tempered pullback random attractor. PubDate: Thu, 27 Jun 2019 15:05:07 +000