串联系统可靠性虚拟系统法置信下限的小样本性质

本文讨论了具有r个成败型元件串联系统可靠性的置信下限问题。研究了虚拟系统法置信下限的小样本性质,证明了,在通常情况下虚拟系统法置信下限要大于常见的L-M法置信下限.更一般地,本文证明了在成败型试验中,当成功数与试验数之比保持不变时,试验次数的增加将直接缩小成功率置信区间的长度。     

Hypersurface with Constant Main Curvature Symmetric Functions

ＨｙｐｅｒｓｕｒｆａｃｅｗｉｔｈＣｏｎｓｔａｎｔＭａｉｎＣｕｒｖａｔｕｒｅＳｙｍｍｅｔｒｉｃＦｕｎｃｔｉｏｎｓ￥ＷｕＢａｏｑｉａｎｇ；ＳｏｎｇＨｏｎｇｚａｏ（ＸｕｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，２２１００９）（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，...     

A COMPLETE METRIC OF POSITIVE CURVATURE ON R~n AND EXISTENCE OF CLOSED GEODESICS

ＡＣＯＭＰＬＥＴＥＭＥＴＲＩＣＯＦＰＯＳＩＴＩＶＥＣＵＲＶＡＴＵＲＥＯＮＲ~ｎＡＮＤＥＸＩＳＴＥＮＣＥＯＦＣＬＯＳＥＤＧＥＯＤＥＳＩＣＳ￥ＺＨＵＤＡＸＩＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙｌＴｉａｎｊ?..     

关于3维Minkowski空间中类空曲面的若干结果

在本文，我们证明２维黎曼流形能实现为Ｌ３中的类空极大曲面的充要条件是相应的Ｒｉｃｃｉ条件成立，此外还确定了Ｌ３中其平均曲率向量ｈ满足条件△ｈ＝λｈ（λ∈Ｒ）的类空曲面     

Projected gradient methods for linearly constrained problems

The aim of this paper is to study the convergence properties of the gradient projection method and to apply these results to algorithms for linearly constrained problems. The main convergence result is obtained by defining a projected gradient, and proving that the gradient projection method forces the sequence of projected gradients to zero. A consequence of this result is that if the gradient projection method converges to a nondegenerate point of a linearly constrained problem, then the active and binding constraints are identified in a finite number of iterations. As an application of our theory, we develop quadratic programming algorithms that iteratively explore a subspace defined by the active constraints. These algorithms are able to drop and add many constraints from the active set, and can either compute an accurate minimizer by a direct method, or an approximate minimizer by an iterative method of the conjugate gradient type. Thus, these algorithms are attractive for large scale problems. We show that it is possible to develop a finite terminating quadratic programming algorithm without non-degeneracy assumptions. Work supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38. Work supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38.     

Error bounds for asymptotic expansions of the distribution of the MLE in a GMANOVA model

Summary In this paper we obtain asymptotic expansions for the distribution function and the density function of a linear combination of the MLE in a GMANOVA model, and for the density function of the MLE itself. We also obtain certain error bounds for the asymptotic expansions.     

Twin-field quantum key distribution based on twisted photon

Quantum key distribution (QKD) is a promising application to establish unconditional secure communications by quantum mechanics. However, its widespread application still faces a great challenge, that is, the fundamental linear key-rate constraint called Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound. Recently, twin-field QKD (TF-QKD) was proposed (Lucamarini et al., 2018 [4]), it overcomes the constraint mentioned above. However, the original TF-QKD is based on the phase-encoding strategy, which requires active alignment. In this paper, we improve the original TF-QKD with the photon orbital angular momentum (OAM), and propose a novel reference frame independent protocol to overcome the reference frame dependence. No more alignment procedure is needed, and the intrinsic misalignment errors are eliminated by utilizing the rotation-invariance of OAM photons. Besides, the security performance is also improved.     

D = 5, N = 2 Geometric Higher Curvature Supergravity in the Second-Order Canonical Theory

The supersymmetric extension of the five-dimensional Chern–Simons gravity is studied from the Hamiltonian point of view. This model containing the Gauss–Bonnet term quadratic in the Riemann curvature is the gauge theory of the supergroup SU(2,2/1). In the first order, the theory has a polynomial structure, but the second-order leads to a nonpolynomial structure for both the Hamiltonian and the supersymmetry transformation rules of the fields. The second-order theory has the advantage that the apparent gauge degrees of freedom are unambiguously removed leaving only the physical ones. This important feature is analyzed by constructing the second-order Hamiltonian theory. The gauge invariances of the model and the generator of time evolution are found.     

Invariant surfaces of a three-dimensional manifold with constant Gauss curvature

We give a reduction procedure to determine (locally) the surfaces with constant Gauss curvature in a three-dimensional manifold which are invariant under the action of a one-parameter subgroup of the isometry group of the ambient space. We apply this procedure to describe the invariant surfaces with constant Gauss curvature in $H^2\times R$ and in $H_3$.