Generalized exterior boundary-value problems and optimization for the Helmholtz equation

A class of radiation problems is considered for the Helmholtz equation in exterior domains bounded by a smooth surface on which Dirichlet, Neumann, or Robin boundary conditions are imposed. The problem of finding the boundary data which maximizes far field power in a restricted subset of far field directions is formulated as a constrained maximization problem. Existence of an optimal solution in a variety of control domains is established. The particular case when the boundary is circular and the control domain is the unit ball inL ² is treated in detail. An algorithm for constructing the optimal solution is derived and used to obtain explicit numerical results.This work was supported by the US Air Force under Grant No. AFOSR 81-0156. The work was completed while the first author was on leave to the Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, BRD.     

Estimation of the Multivariate Normal Precision Matrix under the Entropy Loss

Let X ₁, , X _n (n > p) be a random sample from multivariate normal distribution N _p (, ), where R ^p and is a positive definite matrix, both and being unknown. We consider the problem of estimating the precision matrix ^–1. In this paper it is shown that for the entropy loss, the best lower-triangular affine equivariant minimax estimator of ^–1 is inadmissible and an improved estimator is explicitly constructed. Note that our improved estimator is obtained from the class of lower-triangular scale equivariant estimators.     

Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions

A new class of generalized convex set-valued functions, termed nearly-subconvexlike functions, is introduced. This class is a generalization of cone-subconvexlike maps, nearly-convexlike set-valued functions, and preinvex set-valued functions. Properties for the nearly-subconvexlike functions are derived and a theorem of the alternative is proved. A Lagrangian multiplier theorem is established and two scalarization theorems are obtained for vector optimization.     

电子稳像技术中的坐标变换及像偏移函数分析

为了进行图像偏移的数字补偿 ,需要分析图像的偏移函数 ,要对定坐标系O0 X0 Y0 Z0 ,CCD摄像机载体坐标系O1X1Y1Z1和像空间坐标系O2 X2 Y2 Z2 进行坐标变换 ,从而得出图像偏移与载体运动速度的关系 ,为数字电子稳像奠定基础。     

一类非线性算子的带误差的Ishikawa迭代程序及其稳定性

建立了任意实Banach空间中带误差的Ishikawa迭代程序逼近Lipschitz强伪压缩算子的不动点的一般性定理,指出已被广泛广泛研究的Ishikawa迭代序列的稳定性问题仅是带误差的Ishikawa迭代程序的特例,作为直接的应用,用不同于通常的方法证得任意实Banach空间中的Ishikawa迭代序列关于Lipschitz强伪压缩算子是稳定的,这些推广或发展了近期许多相应的结果。     

物联网环境下的差异网络数据库异常数据检测

当前的物联网环境下,各个智能网络的数据库的使用没有统一标准,不同生产商的数据库中的异常数据标准也不同,这就使得传统的以模式识别为基础的网络数据库异常检测方法在进行异常阀值设置时,无法形成统一标准,数据库数据量庞大且存在无序性,无法保证检测的准确性和检测效率。提出基于混沌特征分析算法的物联网环境下的差异网络数据库异常数据检测方法。依据混沌特征分析相关理论构建物联网环境下的差异网络数据库模型,构建一种异常数据的偏差函数,对不同数据库下的异常数据进行偏差统计,通过对偏差函数的统计结果进行最小值求解,根据求解描述最小化的阀值请求,实现物联网环境下的差异网络数据库异常数据的检测。实验结果表明,利用改进算法进行异常数据检测,能够提高检测的有效性与准确性。     

A novel technique for scaffold fabrication: SLUP (salt leaching using powder)

In this study, we proposed a novel salt-leaching method using PCL and NaCl powders, known as the SLUP (salt leaching using powder) technique, which has several advantages: this technique does not require solvent, pressure, or unnecessary expensive devices. First, PCL powder (100–180 μm size) and NaCl powder (350–400 μm size) were prepared. Second, the PCL and NaCl powders were mixed at a certain ratio, and then the mixed powder was poured into a mold. Afterward, the mold was heated to melt the PCL powder in an oven at 80 °C for 15 min. Subsequently, after the PCL/NaCl mixture was separated from the mold, the PCL/NaCl mixture was soaked in D.I. water for 24 h to leach out the NaCl particles. Consequently, the remaining PCL structure was porous and could be used as a scaffold. To analyze the compressive modulus of the fabricated scaffold, a uniaxial compression test was performed using a UTM (universal testing machine), and the surface characteristics of the scaffold were observed using an SEM (scanning electron microscope). Additionally, cell-culture experiments were performed using hMSCs (human mesenchymal stem cells), and the cell-culture characteristics were assessed and compared with the characteristics from a conventional salt-leaching scaffold.     

On Rearrangements of the Haar System in L p

In this paper we study operators rearranging the Haar system in each bundle. It is proved that the norm of any nonidentical rearrangement admits a nontrivial lower bound in L ^p spaces, .     

On the Law of The Iterated Logarithm for Rapidly Increasing Subsequences

The usual law of the iterated logarithm states that the partial sums S_n of independent and identically distributed random variables can be normalized by the sequence a_n = √nlog log n, such that limsup_n→∞ S_n/a_n = √2 a.s. As has been pointed out by Gut (1986) the law fails if one considers the limsup along subsequences which increase faster than exponentially. In particular, for very rapidly increasing subsequences {n_k≥1} one has limsup_k→∞ S_nk/a_nk = 0 a.s. In these cases the normalizing constants a_nk have to be replaced by √nk log k to obtain a non-trivial limiting behaviour: limsup_k→∞ S_nk/ √nk log k = √2 a.s. We will present an intelligible argument for this structural change and apply it to related results.