A Sound Field Separation and Reconstruction Technique Based on Reciprocity Theorem and Fourier Transform

We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed.

Categories of Nonlocality in EPR Theories and the Validity of Einstein’s Separation Principle as Well as Bell’s Theorem

Work on quantum entanglement is currently emphasizing the nonlocal nature of theories that attempt to explain spatially separated Einstein-Podolsky-Rosen (EPR) correlation experiments. It is frequently claimed that nonlocal instantaneous influences, or equivalently a breakdown of Einstein’s separation principle, are a signature property of (quantum) entanglement. This paper presents a categorization of the various forms of nonlocality in physical theories. It is shown that, even for Einstein’s theory of relativity, correlations of spatially separated measurements cannot be explained without the involvement of some nonlocal or global knowledge and facts. Instantaneous Influences at a distance are, however, in a special category of nonlocality and, as is well known, Einstein called them spooky. Following a separation of nonlocalities into four distinctly different categories 0, 1, 2, 3, with number 3 corresponding to theories containing instantaneous influences at a distance, I show that any theory of EPR experiments must be at least in category 1 or 2 and does not need to be in category 3. In particular, the Bell theorem, valid for category 0 theories, may be violated for categories 1 and 2 and does not require category 3 theories. Category 0 enforces Bell’s theorem. However, it does not apply to relativistic theories of space like separated measurements.

S-rough sets and knowledge separation

The conceptions of the knowledge screen generated by S-rough sets are given: f- screen and - screen , and then puts forward - filter theorem, - filter theorem of knowledge. At last, the applications of knowledge separation are given according to - screen and - screen.

Rough law generation and its separation-recognition

By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.

Kolmogorov’s Probability Spaces for “Entangled” Data-Subsets of EPRB Experiments: No Violation of Einstein’s Separation Principle

It is demonstrated that the use of Kolmogorov’s probability theory to describe results of quantum probability for EPRB (Einstein-Podolsky-Rosen-Bohm) experiments requires extreme care when different subsets of measurement outcomes are considered. J. S. Bell and his followers have committed critical inaccuracies related to spin-gauge and probability measures of such subsets, because they use exclusively a single probability space for all data sets and sub-sets of data. It is also shown that Bell and followers use far too stringent epistemological requirements for the consequences of space-like separation. Their requirements reach way beyond Einstein’s separation principle and cannot be met by the major existing physical theories including relativity and even classical mechanics. For example, the independent free will does not empower the experimenters to choose multiple independent spin-gauges in the two EPRB wings. It is demonstrated that the suggestion of instantaneous influences at a distance (supposedly “derived” from experiments with entangled quantum entities) is a consequence of said inaccuracies and takes back rank as soon as the Kolmogorov probability measures are related to a consistent global spin-gauge and permitted to be different for different data subsets: Using statistical interpretations and different probability spaces for certain subsets of outcomes instead of probability amplitudes related to single quantum entities, permits physical explanations without a violation of Einstein’s separation principle.

Application of the Separating Theorem

This thesis discusses the theory of nonlinear programming (NLP) including the maths solution to a type of inequality of convex function by utilizing the separating Theorem.

矛盾体分离超演绎方法及应用

作为当前自动定理证明器中常用的推理机制,传统基于二元演绎超归结方法的推理过程限定每次有且只有2个子句参与演绎,这种分离的演绎步骤导致演绎缺失导向性和预判性,演绎效率有待提升。为了提升演绎效率,在理论上,针对传统的超归结方法引入多元演绎思想,提出矛盾体分离超演绎定义和方法,它具有多元性、动态性和导向性的演绎特性;在算法实现中,考虑子句参与演绎具有多元和协同特性,并灵活设定演绎的条件,提出一种具有回溯机制的矛盾体分离超演绎算法。将所提算法应用于Eprover3.1证明器,以国际自动定理证明器2023年竞赛例和TPTP(Thousands of Problems for Theorem Provers)问题库中难度系数为1的问题作为测试对象,在300 s内,应用所提算法的Eprover3.1证明器比原始Eprover3.1多证明了15个定理;当测试相同数量的定理时,所提算法的平均证明时间缩减了1.326 s,能够证明7个难度系数为1的定理。测试结果表明,所提算法能有效地应用于一阶逻辑自动定理证明,提升自动定理证明器的证明能力和效率。

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.

THE EXTENSION THEOREMS OF CONE LINEAR OPERATORS

A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given.

向量平衡问题强有效解集的连通性

本文主要在自反Banach空间中研究向量平衡问题强有效解集的连通性。利用新定义的非线性函数,将1个非凸非闭集合和1个紧致集分离;证明强向量平衡问题的强有效解集可以表示为非线性标量问题解集的并集,从而得到向量平衡问题强有效解集的连通性。

A Separation Theorem for Stochastic Singular Linear Quadratic Control Problem with Partial Information

In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation （GDRE）.

Inequalities and Separation for a Biharmonic Laplace-Beltrami Differential Operator in a Hilbert Space Associated with the Existence and Uniqueness Theorem

In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operatorAu（x） = -△△u（x） ＋ V（x）u（x）,for all x ∈ R^n, in the Hilbert space H = L2（R^n,H1） with the operator potential V（x） ∈ C^1 （R^n, L （H1） ）, where L （H1 ） is the space of all bounded linear operators on the Hilbert space H1, while AAu is the biharmonic differential operator and△u=-∑i,j=1^n 1/√detg δ/δxi[√detgg-1（x）δu/δxj]is the Laplace-Beltrami differential operator in R^n. Here g（x） = （gij（x）） is the Riemannian matrix, while g^-1 （x） is the inverse of the matrix g（x）. Moreover, we have studied the existence and uniqueness Theorem for the solution of the non-homogeneous biharmonic Laplace-Beltrami differential equation Au = - △△u ＋ V（x） u （x） = f（x） in the Hilbert space H where f（x） ∈ H as an application of the separation approach.

基于八叉树的复杂地质体块段模型建模技术

为了有效地减少地质块段模型的数据量，提高建模过程中运算速度及准确性，采用八叉树结构表达块段模型，对三维目标空间进行块段细分；提出八叉树与有向有界箱（OBB）树相交测试算法以提高建模过程中的运算速度，同时改进射线法判断点在多面体内外及点在面状模型上下的算法，以确保复杂地质体块段模型建模的准确性．用C＋＋开发语言实现建模算法并与其它同类软件相比较，结果表明：采用该方法从表面模型到块段模型的转换速度比目前国际上常用的矿业软件要快30％～40％，结果准确，所需存储空间较小，便于空间检索与分析，对于地质模型的工程应用具有重要意义．

换热器管壁圆形泄漏口空间辐射声场分布特征数值研究

根据可分离辐射源的声辐射,利用叠加原理和无穷级数迭代求和,建立了换热器管道壁面圆形口非分离泄漏声辐射源的空间声场分布数学模型。计算了圆形口均匀幅度非分离声辐射源的空间声场远场分布,给出了其远场相对声压级和位相的空间分布图案。与方形口均匀可分离辐射源的空间声场分布特征相比,发现两种情况具有相同的空间指向性特征,在较高频率时辐射声场空间分布出现盲区,在x-y 平面内声场分布与泄漏口形状无关,但与辐射频率有密切关系。

变异粗集与[α/R]知识

利用Z .pawlakroughsets ,提出变异粗集 ,给出变异粗集的数学结构和变异粗集与Z .pawlak粗集之间的关系 ,给出变异粗集与Z .pawlak粗集的变异 -对偶原理 ;利用这些结果 ,提出知识分离的判定定理和知识挖掘准则 ,变异粗集是Z .pawlak粗集中的一个新的研究方向 .

一种新的海量数据分类方法

使用支持向量机对非线性可分数据进行分类的基本思想是将样本集映射到一个高维线性空间使其线性可分。文章则基于Jordan曲线定理,提出了一种通用的基于分类超曲面的分类法,它是通过直接构造分类超曲面,根据样本点关于分类曲面的围绕数的奇偶性进行分类的一种新分类判断算法,不需作升维变换,不需要考虑使用何种核函数,而直接地解决非线性分类问题。对数据分类应用的结果说明:基于分类超曲面的分类法可以有效地解决非线性数据的分类问题,并能够提高分类效率和准确度。

基于改进OBB包围盒的碰撞检测算法

针对车铣复合数控加工仿真碰撞检测精确度低的问题,提出了一种基于改进OBB包围盒的快速碰撞检测算法.该算法基于改进的OBB包围盒算法,利用车铣复合加工仿真碰撞检测的结果,创建碰撞单元组的包围盒及层次包围盒树;通过粗检阶段计算出包围盒树的相交节点集合,计算得到发生碰撞的三角形面片集合;应用回退技术,解得初始碰撞时间及位置.实例验证结果表明,该算法有效提高了车铣复合数控加工碰撞检测的精确度.

基于超曲面的海量数据直接分类方法

使用支持向量机对海量数据的分类是相当困难的 .为了解决这个问题 ,该文讨论了以下问题 :( 1)提出了一种通用的基于超曲面的直接分类方法 ,它是基于Jordan曲线定理 ,根据围绕数的奇偶进行分类判断的一种新算法 ;( 2 )提出了分类超曲面的概念 ,设计出超曲面的构造方法及基于Jordan定理的分类算法 ;( 3)对双螺旋等问题的分类实验结果说明 :分类超曲面可以有效地解决在有限区域分布很复杂的海量的非线性数据分类问题 ,并能够提高分类效率和准确率 .

凸性与度量投影的连续性

本文研究近强凸、近非常凸 Banach空间中度量投影的连续性 .获得如下结果 :若 A是近强凸 (近非常凸 )空间中的逼近凸集 ,则度量投影 PA是范 -范上半连续的(范 -弱上半连续的 ) .此外 ,我们还利用度量投影的连续性给出 Banach空间为近强凸、近非常凸的一些充分必要条件 .

基于等价输入干扰补偿的直流电机定位控制

针对直流电机的高精度定位控制问题,引入等价输入干扰的设计思想设计控制器.该设计方法通过推测一个等价输入干扰,以消除各种扰动对系统输出产生的影响,实现对给定位置指令的高精度定位跟踪.在基于等价输入干扰补偿的控制系统中,采用分离定理将系统分成状态反馈子系统和由状态观测器与低通滤波器构成的子系统两部分进行单独设计,其中的状态观测器与低通滤波器子系统应用了完全调节方法进行设计.仿真和实验结果表明这种方法对于抑制干扰、实现高精度定位的有效性。