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61.
62.
基于格林函数理论,主要利用Lerray-Schauder抉择定理和上下解方法针对半正定条件下,奇异超线性二阶周期边值问题正解的存在性进行推理证明,获取了奇异超线性二阶周期边值问题的一个正解. 相似文献
63.
In two-phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and, to simplify the analysis, Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. © 2022 Wiley Periodicals, Inc. 相似文献
64.
《Operations Research Letters》2023,51(4):393-400
In this paper, we discuss an application of the Stochastic Dual Dynamic Programming (SDDP) type algorithm to nested risk-averse formulations of Stochastic Optimal Control (SOC) problems. We propose a construction of a statistical upper bound for the optimal value of risk-averse SOC problems. This outlines an approach to a solution of a long standing problem in that area of research. The bound holds for a large class of convex and monotone conditional risk mappings. Finally, we show the validity of the statistical upper bound to solve a real-life stochastic hydro-thermal planning problem. 相似文献
65.
Estimation and control problems with binary-valued observations exist widely in practical systems. However, most of the related works are devoted to finite impulse response (FIR for short) systems, and the theoretical problem of infinite impulse response (IIR for short) systems has been less explored. To study the estimation problems of IIR systems with binary-valued observations, the authors introduce a projected recursive estimation algorithm and analyse its global convergence properties, by using the stochastic Lyapunov function methods and the limit theory on double array martingales. It is shown that the estimation algorithm has similar convergence results as those for FIR systems under a weakest possible non-persistent excitation condition. Moreover, the upper bound for the accumulated regret of adaptive prediction is also established without resorting to any excitation condition. 相似文献
66.
基于分数阶微积分基本定理和三次B样条理论,构造了求解线性Caputo-Fabrizio型分数阶微分方程数值解的三次B样条方法,利用分数阶微积分基本定理将初值问题转化为关于解函数的表达式,再使用三次B样条函数逼近表达式中积分项的被积函数,进而计算了一类Caputo-Fabrizio型分数阶微分方程的数值解.给出了所构造的三次B样条方法的误差估计、收敛性和稳定性的理论证明.数值实验表明,该文数值方法在求解一类Caputo-Fabrizio型分数阶微分方程数值解时具有一定的可行性和有效性,且计算精度和计算效率优于现有的两种数值方法. 相似文献
67.
In this work we consider a poroelastic, flexible material that may deform largely, which is situated in an incompressible fluid driven by the Navier–Stokes equations in two or three space dimensions. By a variational approach we show existence of weak solutions for a class of such coupled systems. We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Fréchet-derivative of a non-convex functional as well as (second order in time) inertia terms. 相似文献
68.
69.
在深海远程正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)水声通信中,信道时延较长,导致信道频率选择性衰落严重,传统的压缩感知信道估计算法性能大幅下降。为此,本文利用深海远程信道在一定时间内具有相关性并呈较稳定簇状分布的特点,在分布式压缩感知信道估计中引入簇区域信息,进行簇约束的多数据块联合稀疏信道估计,提出一种簇约束的分布式压缩感知信道估计方法,并在深海开展了定点远程水声通信实验进行验证,实验结果表明,与传统的分布式压缩感知信道估计算法相比,本方法的能够降低50%左右的误码率。 相似文献
70.
提出了一种基于大气声传播通道的爆炸声源能量估计方法,通过将计算大气声学的传播能量分布结果与大气中传播的声压幅度衰减模型相结合,使用平流层通道与热层通道传播损失能量比例作为修正量,提高了对爆炸声源能量的估计精度。在多次地面爆炸实验得到的数据中,使用观测距离800 km以上且同时存在平流层通道与热层通道的次声接收信号,对比了平流层顶风速修正的能量估计方法与该文提出的基于大气声传播通道的能量估计方法。实验结果验证了相对于传统风速修正的能量估计方法,该方法可显著降低估计误差。 相似文献