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1.
高端飞行器的可靠性往往受限于其发动机内部盘、板等构的结构强度和使用寿命,因此对这类部件的无损检测在制造业上具有巨大需求。超声检测作为一种应用广泛、高效、环保的检测方法,常常被应用于这类构件的检测中。但是,大厚度盘、板类构件内的微小缺陷反射能力弱,常规超声脉冲反射法无法进行有效检测。为实现大厚度盘、板类构件内部微小缺陷的识别和定位,采用共线异侧纵波混频法,通过和差频信号特征识别微小缺陷;研究缺陷埋深变化对混频效果的影响,通过测量和差频信号幅值变化,实现微小缺陷的深度定位。结果表明:该方法可有效识别7075铝合金中埋深80mm的φ0.2mm横孔微缺陷,且可实现微小缺陷的深度定位。  相似文献   
2.
To control the temporal profile of a relativistic electron beam to meet requirements of various advanced scientific applications like free-electron-laser and plasma wakefield acceleration, a widely-used technique is to manipulate the dispersion terms which turns out to be one-to-many problems. Due to their intrinsic one-to-many property, current popular stochastic optimization approaches on temporal shaping may face the problems of long computing time or sometimes suggesting only one solution. Here we propose a real-time solver for one-to-many problems of temporal shaping, with the aid of a semi-supervised machine learning method, the conditional generative adversarial network (CGAN). We demonstrate that the CGAN solver can learn the one-to-many dynamics and is able to accurately and quickly predict the required dispersion terms for different custom temporal profiles. This machine learning-based solver is expected to have the potential for wide applications to one-to-many problems in other scientific fields.  相似文献   
3.
The AB system is the basic integrable model to describe unstable baroclinic wave packets in geophysical fluids and the propagation of mesoscale gravity flows in nonlinear optics. On the basis of the spectral analysis of a Lax pair and the inverse scattering method, we establish the Riemann–Hilbert problem of the AB system. Then, the inverse problems are formulated and solved with the aid of the Riemann–Hilbert problem, from which the potentials can be reconstructed according to the asymptotic expansion of the sectional analytic function and the related symmetry relations. As an application, we obtain the multi-bright-dark soliton solutions to the AB system in the reflectionless case and discuss the dynamic behavior of elastic soliton collisions by choosing appropriate free parameters.  相似文献   
4.
The max-cut problem is a fundamental combinatorial optimisation problem, with many applications. Poljak and Turzik found some facet-defining inequalities for the associated polytope, which we call 2-circulant inequalities. We present a more general family of facet-defining inequalities, an exact separation algorithm that runs in polynomial time, and some computational results.  相似文献   
5.
This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.  相似文献   
6.
双边配给问题描述了现实生活中一类带有二部图结构的稀缺资源配置问题, 例如, 在自然灾害期间救援物资的配给; 电力和天然气等自然资源按需分配; 高校引进人才调配等。本文通过求解线性规划, 并从联盟边际贡献的角度出发定义了双边配给问题的一个Shapley解。之后, 通过合作对策模型和解的公理化方法说明新解的合理性。首先, 建立双边配给问题的合作对策模型, 论证了新解与双边配给合作对策的Shapley值一致; 其次, 证明了Shapley解是唯一满足优先一致性的有效配给方案。最后, 将Shapley解应用于博物馆通票问题的研究, 探讨了博物馆合作制定通票后所得单票和通票收益的分配方式。  相似文献   
7.
Given a graph sequence denote by T3(Gn) the number of monochromatic triangles in a uniformly random coloring of the vertices of Gn with colors. In this paper we prove a central limit theorem (CLT) for T3(Gn) with explicit error rates, using a quantitative version of the martingale CLT. We then relate this error term to the well-known fourth-moment phenomenon, which, interestingly, holds only when the number of colors satisfies . We also show that the convergence of the fourth moment is necessary to obtain a Gaussian limit for any , which, together with the above result, implies that the fourth-moment condition characterizes the limiting normal distribution of T3(Gn), whenever . Finally, to illustrate the promise of our approach, we include an alternative proof of the CLT for the number of monochromatic edges, which provides quantitative rates for the results obtained in [7].  相似文献   
8.
在一般的数学模型中,由于要忽略一些次要因素,所建的模型往往是近似的,且对数学模型利用数值算法所求得的解大多是近似解。另一方面,在可行集非紧的情况下,精确解的解集往往是空集,而在较弱的条件下近似解集可以是非空的。在Hausdorff局部凸拓扑线性空间中分别研究了无约束和带约束集值均衡问题近似Benson真有效解。在没有任何凸性假设下,利用非线性泛函分别建立了最优性条件。  相似文献   
9.
In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)αΩ on a bounded open set Ω ■R(N ≥ 2) with C(1,1) boundary ■Ω. We prove that when f ∈ Lp(Ω), and g ∈ C(Ω), the following problem (-△)αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.  相似文献   
10.
The authors consider the short time existence for Ricci-Bourguignon flow on manifolds with boundary. If the initial metric has constant mean curvature and satisfies some compatibility conditions, they show the short time existence of the Ricci-Bourguignon flow with constant mean curvature on the boundary.  相似文献   
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