Search

A coordinated control strategy for a variable-coefficient wind power full DC system to address problems such as reduced system inertia and insufficient frequency regulation abilities in the AC grid caused by the integration of wind power full DC systems is proposed. In terms of inertia response, the grid-side converter station adopts inertial synchronization control, while the DC-boost converter station adopts constant variable-ratio control to provide inertia support to the grid through DC capacitor and perceive the AC system frequency through the DC voltage on the low-voltage side. Additionally, a virtual inertia control scheme is introduced by adding a variable virtual inertia coefficient to the DC wind turbine (DCWT), enabling the wind power full DC system to have different equivalent inertia in different frequency response stages. As for frequency regulation, the DCWT operates in a load-reducing mode combining overspeed and variable-pitch control, adjusting its active power output through variable droop control. This approach fully utilizes the available capacity at different wind speeds, allowing the wind power full DC system to participate more effectively in frequency regulation. Simulation results demonstrate that this strategy improves the inertial response and primary frequency modulation of the power system after the integration of the wind-powered full DC system.

In this work, analytic solutions of initial value problems for fractional Langevin equations involving Hilfer fractional derivatives and variable coefficients are studied. Firstly, the equivalence of an initial value problem to an integral equation is proved. Secondly, the existence and uniqueness of solutions for the above initial value problem are obtained without a contractive assumption. Finally, a formula of explicit solutions for the proposed problem is derived. By using similar arguments, corresponding conclusions for the case involving Riemann–Liouville fractional derivatives and variable coefficients are obtained. Moreover, the nonlinear case is discussed. Two examples are provided to illustrate theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Engineering Technology is the property of Editorial Department of Electric Power Engineering Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this article, we investigated new travelling wave solutions for the modified Burgers equation with additional time-dependent variable coefficient via the functional variable method. The performance of this method is reliable and effective and gives the exact solitary wave solutions. All solutions of this equation have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab program. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena. This method presents a wider applicability for handling nonlinear wave equations. [ABSTRACT FROM AUTHOR]

Nondegenerate solitons were reported in the localized case, and yet partially nonlocal nonautonomous nondegenerate vector solitons are hardly studied. Our work aims to study the nonlinear tunnelling of 3D partially nonlocal nonautonomous nondegenerate vector solitons based on a 3D coupled nonautonomous Gross–Pitaevskii equation with a linear external potential. With the aid of a simplified transformation and solutions of this model by way of the bilinear method, we reveal 3D partially nonlocal nonautonomous nondegenerate vector solitons and study their nonlinear tunnelling effect under the exact balance conditions among functions for the diffraction, nonlinearity, linear potential and linear phase. After tunnelling through the barrier/well, two vector components both magnify/attenuate their amplitudes to form the peaks/dips, then attenuate/increase their amplitudes and recover their original shapes, respectively. These results may be helpful to further comprehend all-optical switches and logic. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the viscoelastic wave equation with variable coefficients and a delay, which is subject to nonlinear and nonlocal boundary dissipation. The existence of strong and weak solutions is obtained by means of Faedo-Galerkin approximation and denseness argument. By introducing an equivalent energy functional and using the Riemannian geometry method, we show the general decay rate of energy when kernel function satisfies some sufficient small conditions that we provide the range accurately. [ABSTRACT FROM AUTHOR]

In this paper, a fully-discrete alternating direction implicit (ADI) difference method is proposed for solving three-dimensional (3D) fractional subdiffusion equations with variable coefficients, whose solution presents a weak singularity at $ t = 0 $. The proposed method is established via the L1 scheme on graded mesh for the Caputo fractional derivative and central difference method for spatial derivative, and an ADI method is structured to change the 3D problem into three 1D problems. Using the modified Grönwall inequality we prove the stability and $ \alpha $-robust convergence. The results presented in numerical experiments are in accordance with the theoretical analysis.

Copyright of Journal of Shanghai University / Shanghai Daxue Xuebao is the property of Journal of Shanghai University (Natural Sciences) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, a second-order difference scheme is developed to solve two-dimensional two-sided space distributed-order fractional diffusion equation with variable coefficients. In the spatial direction, a second-order difference scheme is proposed, the distribution-order integral is discretized by the Gauss–Legendre quadrature formula and the space fractional derivative is approximated by the weighted and shifted Grünwald–Letnikov operators. In addition, the time direction is discretized into a second-order difference scheme by the Crank–Nicolson method. Therefore, the main numerical scheme is developed. Furthermore, a small perturbation is added to the main difference scheme to construct an alternating-direction implicit scheme. Also, the stability and convergence of the numerical scheme are proved. Finally, some numerical results are provided to show the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we derive an explicit formula of solutions to Hilfer linear fractional integro-differential equations with a variable coefficient in a weighted space, and obtain the existence and uniqueness of solutions for fractional kinetic equations and fractional integro-differential equations with a generalized Mittag–Leffler function. An example is given to illustrate the result obtained. [ABSTRACT FROM AUTHOR]

Freak wave triplets have been studied in the localized situation, however 3D partially nonlocal ring-like freak wave triplets are hardly reported. This work aims to analyze the excitation of ring-like freak wave triplets based on a 3D partially nonlocal coupled NLS system with a linear potential. With the benefit of the ψ -to- Ψ correlation, we find analytical approximate solution of partially nonlocal ring-like freak wave triplets and study their excitation behaviors. The inchoate shape and full shape of partially nonlocal ring-like freak wave triplets can be modulated by comparing values of the maximum accumulated time and excited location in the autonomous system. [ABSTRACT FROM AUTHOR]

This study explores the Ulam stability of third-order differential equation h (t) x ′ ′ ′ + e (t) x ′ ′ + f (t) x ′ + g (t) x = 0 with a new approach, where e, f, g and h are real-valued variable coefficients. The claim of the main result is that if two differential equations different from the above equation have a complex-valued solution on an interval I, then Ulam stability for the above equation is guaranteed on I. In addition, an explicit Ulam constant is also derived. The results are applied to Euler differential equations and constant coefficients differential equations. [ABSTRACT FROM AUTHOR]

The stabilization issue for a nonlinear piezoelectric beam system with variable coefficients and time-varying delay in the control input is considered. The system is constituted by two strongly coupled nonlinear hyperbolic equations, in one of which a kind of distributed control is actuated and time-varying delay exists in the control input. The feedback gains are also time-varying ones. We first apply Kato's variable norm technique to show the well-posedness of the system without nonlinear terms and based on which, the well-posedness of the whole nonlinear system is proved by the fixed-point theory. The exponential stability of the nonlinear time-delay coupled PDEs' system is further proved by the energy estimates together with multiplier techniques under certain conditions. The stability of its corresponding electrostatic/quasi-static model is also investigated. Finally, some numerical simulations are given to illuminate the results obtained in this work. [ABSTRACT FROM AUTHOR]

The goal of this article is to obtain soliton cluster solutions of (2 + 1)-dimensional nonlinear variable coefficient Schrödinger equations through computerized symbolic computation. By applying the self-similarity method, one soliton solution is constructed for the NLS equations with variable coefficient, which provide a model of the propagation of the soliton waves. Consequently, the solitonary cluster solution is achieved in different structures. Additionally, the propagation of the obtaining solitonary cluster solutions is analyzed and discussed. The results are useful to explain the soliton phenomena in nonlinear optics.

We investigate regularity and stability of wave equations with variable coefficients and the frictional damping, where the damping effect is only on Wentzell boundary and there is no interior damping at all. Based on the spectral approach and the Reimannian geometry method, we present a new way of studying the challenging Wentzell-type problem concerning "the lack of interior damping" and the variable coefficients a div (A (x) ∇ u). First, we establish a high-order regularity estimate for the solution of variable coefficient Wentzell problem and a spectral theorem for the operator derived from this problem. And then, after a series of specialized analysis and investigation on the special structure and basic properties of some auxiliary systems, the lower-order term and the resolvent of the operator associated to the variable coefficient Wentzell system by virtue of the Riemannian geometry method and other ideas, we prove eventually that the energies of the system decay with the rate 1 / t. As can be seen, even for the constant coefficient case, the decay rate 1 / t obtained in this paper is essentially better than the decay rate t − 4 / 5 given in the previous work. [ABSTRACT FROM AUTHOR]

In this paper, a class of variable coefficient coupled Schrödinger equations with gain or loss terms is studied, which can be used to describe soliton excitation in non-uniform trihydrogen chain α -helix proteins. The N-soliton solutions of this equation are obtained by using the Hirota bilinear method, the 1,2, 3-soliton solutions are numerically simulated, and their dynamic properties are analyzed. On this basis, the asymptotic behavior of soliton solutions is discussed. Besides, the influence of variable coefficient function and other parameters on solitons is studied, the corresponding rules are summarized. [ABSTRACT FROM AUTHOR]

In this work, analytic solutions of initial value problems for fractional Langevin equations involving Hilfer fractional derivatives and variable coefficients are studied. Firstly, the equivalence of an initial value problem to an integral equation is proved. Secondly, the existence and uniqueness of solutions for the above initial value problem are obtained without a contractive assumption. Finally, a formula of explicit solutions for the proposed problem is derived. By using similar arguments, corresponding conclusions for the case involving Riemann–Liouville fractional derivatives and variable coefficients are obtained. Moreover, the nonlinear case is discussed. Two examples are provided to illustrate theoretical results.

In this paper, two compact difference schemes are established for solving two-dimensional (2D) and three-dimensional (3D) nonlinear wave equations with variable coefficients, respectively, by using the local one-dimensional (LOD) method and the fourth-order compact difference approximation formulas of the second-order derivatives. Firstly, a four-step fourth-order compact scheme is derived to solve the 2D nonlinear wave equation. The stability of the scheme 2for solving the linear equation is analyzed by the discrete Fourier method, which shows that it is conditionally stable. Then, the method is extend to solve the 3D nonlinear wave equation and stability condition for the linear equation is also analyzed. Finally, numerical experiments are conducted to verify the accuracy and stability of the proposed schemes. [ABSTRACT FROM AUTHOR]

In this work, the homotopy analysis method (HAM) is proposed to obtain semi-analytical solutions of timefractional fourth-order partial differential equations (PDEs) with variable coefficients, by the Caputo fractional derivative in the time direction. Convergence of this method has been considered and some illustrative examples show the effect of changing homotopy auxiliary parameter h¯ on the convergence of the approximate solution. Comparison of obtained results with other techniques such as Adomian decomposition method and modified variational iteration method, in literature demonstrate that our utilized method is powerful and reliable technique. Moreover, the absolute errors of considered problems in the integer differential order cases, show that the reported results are very closed to the exact solutions.

We establish an accurate and efficient scheme with four-order accuracy for solving three-dimensional (3D) acoustic wave equation. First, the local one-dimensional method is used to transfer the 3D wave equation into three one-dimensional wave equations. Then, a new scheme is obtained by the Padé formulas for computation of spatial second derivatives and the correction of the truncation error remainder for discretization of temporal second derivative. It is compact and can be solved directly by the Thomas algorithm. Subsequently, the Fourier analysis method and the Lax equivalence theorem are employed to prove the stability and convergence of the present scheme, which shows that it is conditionally stable and convergent, and the stability condition is superior to that of most existing numerical methods of equivalent order of accuracy in the literature. It allows us to reduce computational cost with relatively large time step lengths. Finally, numerical examples have demonstrated high accuracy, stability, and efficiency of our method.

Block pulse functions (BPFs) are constant functions on each subinterval and not so smooth. This property makes BPFs incapable of approximating function accurately. Therefore, the existing BPFs method is insufficiently accurate to numerically solve variable coefficients fractional differential equations (VCFDEs). To obtain highly accurate solutions with fewer computational burden, we propose an efficient numerical method to find the approximate solutions of VCFDEs. The proposed method uses a hybrid of Bernoulli polynomials and BPFs (HBPBPFs) to overcome the disadvantage that BPFs are piecewise constant and smooth enough. For this aim, a fractional integral operational matrix of HBPBPFs is derived and used to convert VCFDEs into a system of algebraic equations. The solutions of VCFDEs are obtained by solving the algebraic equations. Some simulation examples are presented to verify the effectiveness of our proposed method. Numerical results from our proposed method are compared with those from the existing BPFs numerical method. It is demonstrated that our method can obtain more accurate approximate solutions than the BPFs method. [ABSTRACT FROM AUTHOR]

In this paper, a variable coefficient (3+1)-dimensional Gross–Pitaevskii equation is used to study the propagation properties of solitons in Bose–Einstein condensation, as well as the influence of nonlinear terms of time modulation on the properties of solitons. Under reasonable assumptions, the 1-, 2-, 3-soliton solutions of Gross–Pitaevskii equation are constructed by Hirota bilinear method. The results indicate that they can be transformed into special soliton solutions (bright, dark and periodic) under certain conditions. On this basis, the figures of various soliton solutions are displayed, and the influence of coefficient function on soliton solutions is discussed. It is found that the influence of variable coefficients on the physical quantities of several types of soliton solutions has different emphases, and specific laws of influence are derived. In addition, in order to better understand the dynamic properties of soliton solutions, the asymptotic behavior of 2-, 3-soliton solutions is analyzed. Our research can provide a theoretical basis for the dynamics problem in Bose–Einstein condensation. [ABSTRACT FROM AUTHOR]

In a ball screw feed system of high-speed/high-acceleration machine tools, large frictional and inertial forces may change the real contact state of the kinematic joints, resulting in changes in the contact and transmission stiffnesses and, hence, changes in the dynamic characteristics of the system. In this study, a variable–coefficient dynamic modeling method for a ball screw feed system is proposed, considering the influence of changes in the no-extra-load running states, such as position, speed, and acceleration. Based on Timoshenko beam elements with two nodes and four DOFs, an equivalent dynamic model of a ball screw feed system is established using the hybrid element method. The expression for the equivalent axial stiffness of individual kinematic joints is derived, considering the influence of the feed speed/acceleration under the no-extra-load running state of the system. In addition, the stiffness and mass of the screw shafts on both sides of the screw nut are calculated, considering the influence of the system's feed position. Hence, we obtain the total stiffness and mass of the system in the no-extra-load running state and analyze the natural frequency. Finally, we conduct validation experiments on a ball screw feed system of a large gantry-type machine tool with different no-extra-load running states. [ABSTRACT FROM AUTHOR]

In this paper, we derive an explicit formula of solutions to Hilfer linear fractional integro-differential equations with a variable coefficient in a weighted space, and obtain the existence and uniqueness of solutions for fractional kinetic equations and fractional integro-differential equations with a generalized Mittag–Leffler function. An example is given to illustrate the result obtained.

The Kirchhoff model is derived from the vibration problem of stretchable strings. In this paper, the Kirchhoff equation with thermal effects and memory terms is studied. First, the existence and uniqueness of the solution to the equation are obtained using the Faedo–Galerkin method. Then, the existence of a global attractor is established by proving the existence of a bounded absorbing set and the asymptotic smoothness of the semigroup. This paper innovatively considers the long-term dynamic behavior of the Kirchhoff model under the simultaneous action of variable coefficients, memory, and thermal effects comprehensively. It also promotes the relevant conclusions of the Kirchhoff model. The findings of this paper provide a theoretical basis for subsequent application and research.

Aiming at the difficult problem of solving nonlinear ordinary differential equation with variable coefficients, In this paper, the definition of elastic transformation is introduced, and the elastic transformation method for solving differential equations with variable coefficients is proposed. By this method, a class of nonhomogeneous nonlinear first-order and a class of nonlinear third-order ordinary differential equations with variable coefficients can be transformed into the homogeneous linear special equations (Associated Legendre equation, Gegenbauer equation, Hypersphere equation) which the general solutions can be found. Then, according to the definition of elasticity and the general solution of the special equation, the general solution of the original differential equations are obtained. The elastic transformation method not only expands the solvable classes of ordinary differential equation, but also promotes the application of special equation. More importantly, the elastic transformation method provides a new idea for solving low-order and high-order nonlinear ordinary differential equation with variable coefficients. [ABSTRACT FROM AUTHOR]

In the present paper, we are interested in the blow-up condition and upper bound estimates of lifespan for a class of semilinear wave equations with power nonlinearity in R n , which includes time- and space-dependent coefficients. With the use of an iteration procedure and some time-dependent functionals, we derive blow-up results for all dimensional cases. Particularly, optimal result in one-dimensional case and a threshold to distinguish different blow-up behaviors for the range of power exponent in two-dimensional case are obtained. Finally, we give some remarks to behaviors for lifespan estimates. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic stability and instability of solutions to a variable coefficient logarithmic wave equation with nonlinear damping and memory term. Such model describes wave traveling through nonhomogeneous viscoelastic materials. By choosing appropriate multiplier and using weighted energy method, we prove the exponential decay of the energy. Moreover, we also obtain the instability of the solutions at the infinity in the presence of the nonlinear damping. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical approximations for the variable coefficient fourth-order fractional sub-diffusion equations subject to the second Dirichlet boundary conditions. We construct two effective difference schemes with second order accuracy in time by applying the second order approximation to the time Caputo derivative and the sum-of-exponentials approximation. By combining the discrete energy method and the mathematical induction method, the proposed methods proved to be unconditional stable and convergent. In order to overcome the possible singularity of the solution near the initial stage, a difference scheme based on non-uniform mesh is also given. Some numerical experiments are carried out to support our theoretical results. The results indicate that the our two main schemes has the almost same accuracy and the fast scheme can reduce the storage and computational cost significantly. [ABSTRACT FROM AUTHOR]

Aiming at the initial value problems of variable coefficient nonlinear ordinary differential equations, this paper introduces the elastic transformation method into the process of solving the initial value problems of nonlinear ordinary differential equations with variable coefficients. A class of first-order and a class of third-order nonlinear ordinary differential equations with variable coefficients can be transformed into Chebyshev equations through elastic upgrading transformation and elastic reduction transformation respectively. According to the properties of Chebyshev polynomials and the initial conditions, the solutions to the initial value problems of the original first-order and third- order differential equations can be obtained through the elastic inverse transformation, and then the curves of the solutions can be drawn. The introduction of the elastic transformation method not only provides a new idea for solving the initial value problems of nonlinear differential equations, but also expands the solvable classes of ordinary differential equations.

In this paper, a high order compact finite difference is established for the time multi-term fractional sub-diffusion equation. The derived numerical differential formula can achieve second order accuracy in time and four order accuracy in space. A unconditionally stable and convergent difference scheme is presented, and a rigorous proof for the stability and convergence is given. Numerical results demonstrate the efficiency of the proposed difference schemes.

In this paper, the stochastic asymptotic behavior of the nonautonomous stochastic higher-order Kirchhoff equation with variable coefficients is studied. By using the Galerkin method, the solution of this kind of equation is obtained, and stochastic dynamical system under this kind of equation is obtained; by using the uniform estimation, the existence of the family of Dk{{\mathcal{D}}}_{k}-absorbing sets of the stochastic dynamical system Φk{\Phi }_{k} is obtained, and the asymptotic compactness of Φk{\Phi }_{k} is proved by the decomposition method. Finally, the Dk{{\mathcal{D}}}_{k}-stochastic attractor family of the stochastic dynamical system Φk{\Phi }_{k} in Vm+k(Ω)×Vk(Ω){V}_{m+k}\left(\Omega )\times {V}_{k}\left(\Omega ) is obtained.

The Conventional model predictive control (C-MPC) uses only a single voltage vector in each control period, resulting in poor control performance. In addition, the computational burden in discrete space state generated by three-level inverter cannot be ignored. To improve the control performance, this paper proposes a variable coefficient virtual vector MPC (VC-VV-MPC) method, a five-level virtual space voltage vector is constructed to improve the control performance, and a scaling coefficient is used to further improve the control performance. In addition, a voltage vector pre-selection method is used to reduce the computational burden. The simulation and experiment results shown that, compare with C-MPC and adjacent vector MPC (AV-MPC), the proposed VC-VV-MPC can achieve the improvement of control performance under lower computational burden.

Aiming at the problem of solving nonlinear ordinary differential equations with variable coefficients, this paper introduces the elastic transformation method into the process of solving ordinary differential equations for the first time. A class of first-order and a class of third-order ordinary differential equations with variable coefficients can be transformed into the Laguerre equation through elastic transformation. With the help of the general solution of the Laguerre equation, the general solution of these two classes of ordinary differential equations can be obtained, and then the curves of the general solution can be drawn. This method not only expands the solvable classes of ordinary differential equations, but also provides a new idea for solving ordinary differential equations with variable coefficients.

In this paper, we study the numerical results of the Burgers equation with the variable coefficient in space and time and then put forward a lattice Boltzmann model of backward difference solution of nonlinear system. The macroscopic equation is recovered by using the Chapman-Enskog method and the direct Taylor-series expansion method. These two methods can recover the same hydrodynamic equations and analyze various nonlinear systems. In particular, it is much easier to perform error analysis by using the direct Taylor method. In this study, the two methods are used to analyze the Burgers equation with variable coefficient in space and time, the numerical results are discussed and are compared with the analytical solution. The numerical results verify the effectiveness of the model. The stability of the model ensures that we can use larger time step lengths. The improvement of lattice speed can improve the computational performance of the model, and the D1Q7 lattice performance is much better than the D1Q5 lattice performance.

We consider a variable coefficient wave equation with memory-type acoustic boundary conditions. The polynomially decay rate of the system is established when the memory kernel decays polynomially to zero. We apply the Riemannian geometry method to deal with the variable coefficients. [ABSTRACT FROM AUTHOR]

We consider direct and inverse abstract Cauchy problems with time-dependent coefficients. We give an explicit representation of the unique solution operator of the direct abstract Cauchy problem. We use the obtained solution and a new method to recover time-dependent coefficients for the inverse abstract Cauchy problem. [ABSTRACT FROM AUTHOR]

Fractional-order calculus has become a useful mathematical framework to describe the complex super-diffusive process; however, numerical solutions of the two-sided space-fractional super-diffusive model with variable coefficients are difficult to obtain, and almost no method can obtain an analytical solution. In this paper, a class of new fractional dimensional reproducing kernel spaces (RKS) based on Caputo fractional derivatives is given, and we give analytical and numerical solutions of the two-sided space-fractional super-diffusive model based on the class of new RKS. The analytical solution is represented in the form of series in the reproducing kernel space. Numerical experiments indicate that the piecewise reproducing kernel method is more accurate than the traditional reproducing kernel method (RKM), and these new fractional reproducing kernel spaces are efficient for the two-sided space-fractional super-diffusive model. [ABSTRACT FROM AUTHOR]

In this paper, rogue wave solutions of a sixth-order focusing nonlinear Schrödinger (NLS) equation with variable coefficients are investigated on a periodic background. To get the results, we take advantage of Darboux transformation approach and the nonlinearization of spectral problem and we firstly find one kind of rogue wave solution that evolves periodically with time on a periodically spatial background. Besides, we also find this kind of rogue wave solution dissipates over time. Modulation instability (MI) of the sixth-order focusing NLS equation with variable coefficients is also studied. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Introduction of residue number systems (RNS) into hardware realization of high dynamic range FIR filters is known to be advantageous. However, deciding on the number and forms of the moduli, and nature of the filter coefficients is a critical issue, wherein all the previous relevant works lean on RNS multiplication schemes that only work with restricted forms of moduli (e.g., only prime numbers) or only constant FIR coefficients; hence considerably tightening the design space. As a remedy, we propose a modulo-( 2 n - δ ) multiplier/accumulator scheme (The parameter n represents the bit-width of the corresponding residue channels wherein the other parameter δ determines the exact value of the corresponding modulo) with no restriction on the value of δ (except that δ < 2 n - 1 , for balancing the widths of residue channel), nor on the constant/variable nature of the coefficients. The key to this liberty of choice is the especial handling of the end-around carries of modular operations that results in performing only regular non-modular operations, except for the last two that yield the final result. Simulation and synthesis of the proposed circuits show speed, cost and power gains. [ABSTRACT FROM AUTHOR]

Abstract We establish the Ulam stability of a first-order linear nonautonomous quantum equation with Cayley parameter in terms of the behavior of the nonautonomous coefficient function. We also provide details for some cases of Ulam instability.

Soils with spatial variability are the product of natural history. The mechanical properties tested by soil samples from boreholes in the same soil layer may be different. Underground structure service in surrounding soils, their seismic response is controlled by the deformation of the surrounding soils. The variability of soil mechanical parameters was not considered in the current research on the seismic response of underground structures. Therefore, a random field model was established to describe the spatial variability of surrounding soils based on the random field theory. Then the seismic response of underground structures in the random field was simulated based on the time-domain explicit global FEM analysis, and the soil mechanical parameters and earthquake intensity influencing the seismic response of surrounding soils and underground structures were studied. Numerical results presented that, the randomness of soil parameters does not change the plastic deformation mode of surrounding soils significantly. The variation coefficients of inter-story deformation of structures and lateral deformation of columns are much smaller than that of mechanical parameters, and the randomness of soil parameters has no obvious effect on the structural deformation response.

An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form ∑ i = 1 ℓ q i (t) D t α i u (x , t) , where the q i are continuous functions, each D t α i is a Caputo derivative, and the α i lie in (0, 1]. Maximum/comparison principles for this problem are proved under weak hypotheses. A new positivity result for the multinomial Mittag-Leffler function is derived. A posteriori error bounds are obtained in L 2 (Ω) and L ∞ (Ω) , where the spatial domain Ω lies in R d with d ∈ { 1 , 2 , 3 } . An adaptive algorithm based on this theory is tested extensively and shown to yield accurate numerical solutions on the meshes generated by the algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with a Cauchy problem of the inhomogeneous parabolic equation ut=Δu+〈x〉γup+tσw(x) in ℝN×(0,T), where constants γ>0,p>1, and σ>−1. The Japanese brackets 〈x〉γ:=1+|x|2γ; w(≥,≢0) and the initial data are continuous functions in ℝN. We determine the Fujita exponent for global and non‐global solutions of the problem, depending strictly on N,γ and σ, which complete the ones for the nonnegative solutions in J. Math. Anal. Appl. 251 (2000) 624–648 for N=1,2. It is so interesting that the inhomogeneous term leads to the discontinuity of this critical exponent with respect to σ at zero. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global adaptive stabilization of a nonlinear axially moving string. The adopted model is of Kirchhoff type and with variable density. The aim is to formulate a control in case no velocity feedback is available. We show that the suggested control is able to stabilize asymptotically the system in spite of the longitudinal movement of the string. The proof is based on LaSalle's invariance principle. [ABSTRACT FROM AUTHOR]