Symmetries of Itô and Stratonovich Dynamical Systems and Their Conserved Quantities

A new definition for the symmetries of Itô and Stratonovich dynamicalsystem is given. Determining systems of symmetries for Itô andStratonovich systems have been obtained, and their relation has beendiscussed. It has been shown that some of the Lie point symmetries ofthe Fokker–Planck equation can be constructed using the symmetries ofItô dynamical systems. Conserved quantities can be found from thesymmetries of stochastic dynamical systems which do not arise from aHamiltonian. The results have been applied to an example.     

Random rotations of the Wiener path

Summary Let (W, H, ) be an abstract Wiener space and letR(w) be a strongly measurable random variable with values in the set of isometries onH. Suppose that Rh is smooth in the Sobolev sense and that it is a quasi-nilpotent operator onH for everyhH. It is shown that (R(w)h) is again a Gaussian (0, |h| _H ² )-random variable. Consequently, if (e _i ,i)W ^* is a complete, orthonormal basis ofH, then defines a measure preserving transformation, a rotation, onW. It is also shown that if for some strongly measurable, operator valued (onH) random variableR, (R(w+k)h) is (0, |h| _H ² )-Gaussian for allk, hH, thenR is an isometry and Rh is quasi-nilpotent for allHH. The relation between the stochastic calculi for these Wiener pathsw and , as well as the conditions of the inverbibility of the map are discussed and the problem of the absolute continuity of the image of the Wiener measure under Euclidean motion on the Wiener space (i.e. composed with a shift) is studied.The research of the second author was supported by the Fund for the Promotion of Research at the TechnionDedicated to the memory of Albert Badrikian     

Symmetric orbits of orthogonal veronese actions and their second order envelopes

The orbits of Lie groups acting in Euclidean spaces by isometries are extrinsically symmetric iff they are parallel, i.e. satisfy ${\overline \nabla} h =0 $ Submanifolds characterized by the integrability condition $ {\overline R}\o\ h =0 $ of this system ${\overline \nabla} h =0$ are called semi-parallel (or semi-symmetric, extrinsically); they are the 2nd order envelopes of the symmetric orbits. For the orthogonal Veronese action, corresponding to the map well-known from the algebraic geometry, all symmetric orbits will be determined, as well as their 2nd order envelopes. The results are essential for the classification of the semi-parallel submanifolds.     

湍流边界层激励下腔体内水动力自噪声预报与测量

循环水槽中试验测量了腔体内水动力自噪声,并与模态法建立的湍流脉动压力引起腔体自噪声预报进行比较验证。透声窗振动以简支边界为条件,腔体内部声波以刚性边界为条件模态展开,通过辐射边界条件建立模态耦合振动方程。在随机湍流脉动压力作用下,推导了模态振动方程在随机力激励下的自噪声功率谱响应。对循环水槽中5 m/s和8 m/s两种流速工况下的腔体水动力自噪声和湍流脉动压力进行了测试,结合测量的脉动压力预报方法可以计算腔体水动力自噪声量值,理论预报与试验测量结果大致吻合,趋势一致,为声呐罩材料选取及声学环境控制提供了一种分析方法。     

基于改进U-Net++的CT影像肺结节分割算法

卷积神经网络的语义分割模型未有效利用特征权重信息,导致在医学图像复杂场景中分割边界出现欠分割现象.针对该问题,基于融合自适应加权聚合策略提出一种改进的U-Net++网络,并将其应用于电子计算机断层扫描影像肺结节分割.该模型首先在卷积神经网络中提取出不同深度特征语义级别的信息,再结合权重聚合模块,自适应地学习各层特征的权...     

Some results about the spectrum of commutative Banach algebras under the weak topology and applications

LetA be a commutative Banach algebra with a nonempty spectrum A. By weak we denote the relative weak topology induced on A by (A ^*,A ^**). In this note we study some properties of the topological space (A, weak) and present some applications of the results obtained and tools used to amenability, weakly compact homomorphisms, weakly compact subsets of the spectrum of the uniform algebras and to a characterization of the synthesizable ideals of the algebraA.     

Multiscale expansions in discrete world

In this paper, we show the attainability of KdV equation from some types of nonlinear Schrödinger equation by using multiscale expansions discretely. The power of this manageable method is confirmed by applying it to two selected nonlinear Schrödinger evolution equations. This approach can also be applied to other nonlinear discrete evolution equations. All the computations have been made with Maple computer packet program.     

One Spot Microwave Synthesis and Characterization of Nitrogen-Doped Carbon Dots with High Oxygen Content for Fluorometric Determination of Banned Sudan II Dye in Spice Samples

Journal of Fluorescence - A simple microwave-assisted synthesis of nitrogen-doped carbon dots with high oxygen content (O-N-CDs) was carried out with citric acid as a carbon source and...     

光纤水听器解调技术研究进展

光纤水听器是水声研究领域的关键技术,在实际应用中具有显著优势,广泛应用于AUV导航定位、资源勘探、海水警戒等场景.光纤水听器将声信号转化为光信号传播,在接收信号时就需要对光信号进行解调提取出声压信号.总结了几种常用的信号解调算法及关键技术,包括PGC解调法、3×3耦合器解调法和外差解调法;介绍了各种解调算法的基本原理和...     

食品中三聚氰胺的光谱检测与分析技术研究进展

三聚氰胺是豆、乳类制品中的非法食品添加剂,曾作为蛋白质的廉价代替物被非法添加进奶粉等食品中,造成了严重的社会危害,极大地威胁人民生命财产安全。目前光谱技术已成为识别和定量检测非法食品添加剂的有效手段,为质量监管部门提供了可靠的研究方法和鉴定依据。光谱检测技术的时效性、无损性和准确性提高了食品中三聚氰胺的检测效率,促进了精准化、自动化食品质量检测的发展。近年来有大量研究围绕着三聚氰胺的光谱检测新技术,如开发新型增强底物或传感器,降低三聚氰胺的检测限,提高检测精度;开发更加便携的自动化光谱快检设备,降低检测成本,提高检测效率。这些光谱技术各具优势,但很难形成标准化、统一化的检测规范,使得各种光谱检测技术仅仅停留在试验阶段,无法应用于实战。另一方面,随着人工智能与模式识别技术的发展,光谱数据分析方法在近年来也有着长足的进步,各种光谱预处理和数据建模方法被不断提出,大大提高了光谱检测技术的灵敏性和稳定性。综述了近十年光谱技术（拉曼光谱、近红外光谱、荧光光谱、光谱成像等）在三聚氰胺检测中的应用现状,总结了不同仪器检测限、定量范围和样品前处理方法;分析了各种光谱预处理和光谱数据建模方法在不同光谱数据中的适用性,归纳出这些方法的优劣与适配的仪器,并对其应用前景和研究趋势进行了展望。