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951.
In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
952.
Liming Zhang Tao Qian Weixiong Mai Pei Dang 《Mathematical Methods in the Applied Sciences》2017,40(8):2815-2833
The Dirac‐type time‐frequency distribution (TFD), regarded as ideal TFD, has long been desired. It, until the present time, cannot be implemented, due to the fact that there has been no appropriate representation of signals leading to such TFD. Instead, people have been developing other types of TFD, including the Wigner and the windowed Fourier transform types. This paper promotes a practical passage leading to a Dirac‐type TFD. Based on the proposed function decomposition method, viz., adaptive Fourier decomposition, we establish a rigorous and practical Dirac‐type TFD theory. We do follow the route of analytic signal representation of signals founded and developed by Garbo, Ville, Cohen, Boashash, Picinbono, and others. The difference, however, is that our treatment is theoretically throughout and rigorous. To well illustrate the new theory and the related TFD, we include several examples and experiments of which some are in comparison with the most commonly used TFDs. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
953.
Marius Buliga 《Journal of Elasticity》1998,52(3):201-238
954.
Singularly perturbed systems with structural perturbations are analyzed for stability. New sufficient conditions of asymptotic stability and uniform asymptotic stability are established. The systems in question are widely used in control theory, engineering, etc 相似文献
955.
Fan Xijun 《Acta Mechanica Sinica》1992,8(4):295-306
The constitutive equation for a semiconcentrated fibre suspension in the Oldroyd-B fluid has been derived from a statistical
model of such a suspension by employing the molecular theory for polymeric liquids. To circumvent theoretical difficulties
in viscoelastic fluid mechanics, several simplified models are used to account for the interactions of fibres and polymer
molecules. Some of material functions are calculated in terms of the constitutive equation.
The project Supported by the University of Melbourne of Australia, the National Natural Science Foundation of China and Zhejiang
Province 相似文献
956.
Alex Elías-Züñiga 《Nonlinear dynamics》2007,49(1-2):307-315
The aim of this paper is to show how Jacobi elliptic functions in combination with the averaging and the harmonic balance
methods can be applied to obtain the approximate solution of two coupled, ordinary differential equations having a spring
with cubic nonlinearity and subjected to driving forces of elliptic type. By an appropriate choice of the system parameter
values, it is possible to show that our derived solution represents the exact steady-state solution of the undamped Duffing
equation with driving force of elliptic type. At the end of this work, we also demonstrate the validity of our derived solution
by comparing the amplitude–time response curves with those of the numerical integration solutions. 相似文献
957.
K. S. Matviichuk 《International Applied Mechanics》2006,42(6):699-713
Sufficient conditions for the technical stability in measure of a nonstationary control system with variable structure are
established. The controller of the system has feedback-switched filters functioning together with shaper and actuator. It
is assumed that the nonstationary parameters of the system vary within given ranges, at a finite rate, with appropriate control
laws, with adjustment against mismatch signal, its derivatives of finite order, and all variable parameters of the filter.
The parameters of the switching hyperplane remain constant. This approach for analysis of technical stability does not involve
sliding mode conditions. Criteria of technical instability in measure for the control system under consideration are formulated
using the properties of systems of comparison from below. The general criteria of technical stability and instability are
applied to nonstationary filtered-control systems of variable structure of the third order. The comparison method based on
normalized Lyapunov functions is used
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 110–127, June 2006. 相似文献
958.
Analytical solutions for cohesive zone models 总被引:2,自引:0,他引:2
Solutions are given for a cantilever beam specimen using a beam on elastic foundation model to incorporate various cohesive zone traction laws. These included both positive and negative linear slopes and constant stresses. Negative slopes give rise to multiple solutions. However, all the solutions give very similar results for energy release rate and beam root rotation confirming insensitivity to the form of the traction law. The use of these solutions to analyse peeling is discussed. 相似文献
959.
改进的移动最小二乘法 总被引:4,自引:2,他引:4
近年来发展的无网格方法大多采用移动员小二乘法来构造试函数,而应用移动最小二乘法形成的方程组有时会是病态的甚至奇异的,从而限制了它的发展和应用。本文采用带权正交函数作为基函数对移动最小二乘法做了改进,避免出现病态方程组,且在计算过程中不需要进行短阵求逆运算,提高了计算速度。之后,借鉴牛顿法、平衡法和摄动法对由移动最小二乘法得到的非线性代数方程组提出了新的求解方法。 相似文献
960.
Equilibrium and bicontinuum nonequilibrium formulations of the advection–dispersion equation (ADE) have been widely used to describe subsurface solute transport. The Green's Function Method (GFM) is particularly attractive to solve the ADE because of its flexibility to deal with arbitrary initial and boundary conditions, and its relative simplicity to formulate solutions for multidimensional problems. The Green's functions that are presented can be used for a wide range of problems involving equilibrium and nonequilibrium transport in semiinfinite and infinite media. The GFM is applied to analytically model multidimensional transport from persistent solute sources typical of nonaqueous phase liquids (NAPLs). Specific solutions are derived for transport from a rectangular source (parallel to the flow direction) of persistent contamination using first, second, or thirdtype boundary or source input conditions. Away from the source, the first and thirdtype condition cannot be expected to represent the exact surface condition. The secondtype condition has the disadvantage that the diffusive flux from the source needs to be specified a priori. Near the source, the thirdtype condition appears most suitable to model NAPL dissolution into the medium. The solute flux from the pool, and hence the concentration in the medium, depends strongly on the mass transfer coefficient. For all conditions, the concentration profiles indicate that nonequilibrium conditions tend to reduce the maximum solute concentration and the total amount of solute that enters the porous medium from the source. On the other hand, during nonequilibrium transport the solute may spread over a larger area of the medium compared to equilibrium transport. 相似文献