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convolution semigroups associated with measure-valued branching processes

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Chinese Science Bulletin 1996年第4期41卷 276-280页

作者：李增沪 Department of Mathematics Beijing Normal University Beijing 100875 China

Suppose that E is a Lusin topological space. We let (?)(E) denote the σ-algebra on E generated by all open sets, which is referred to as the Borel σ-algebra on E. B(E) denotes the set of all bounded (?)(E)-measurable functions on E and B(E)^+ denotes the subspace of B(E) comprising non-negative elements. Let M(E) be the totality of finite measures on (E, (?)(E)). Topologize M(E) by the weak convergence topology, so it also becomes a

关键词： measure-valued branching process entrance law convolution semigroup.

Ultracompact meta-imagers for arbitrary all-optical convolution

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Light(Science & Applications) 2022年第4期11卷 595-607页

作者： Weiwei Fu Dong Zhao Ziqin Li Songde Liu Chao Tian Kun Huang Department of Optics and Optical Engineering University of Science and Technology of ChinaHefeiAnhui 230026China Institute of Artificial Intelligence Hefei Comprehensive National Science CenterHefeiAnhui 230088China. Department of Precision Machinery and Precision Instrumentation University of Science and Technology of ChinaHefeiAnhui 230026China

Electronic digital convolutions could extract key features of objects for data processing and information identification in artificial intelligence,but they are time-cost and energy consumption due to the low response of *** massless photons enable high-speed and low-loss analog convolutions,two existing all-optical approaches including Fourier fItering and Green's function have either limited functionality or bulky volume,thus restricting their applications in smart ***,we report aloptical convolutional computing with a metasurface-singlet or-doublet imager,considered as the third approach,where its point spread function is modified arbitrarily via a complex-amplitude meta-modulator that enables functionality-unlimited *** one-and two-dimensional spatial differentiation,we demonstrate real-time,parallel,and analog convolutional processing of optical and biological specimens with challenging pepper-salt denoising and edge enhancement,which significantly enrich the toolkit of all-optical *** meta-imager approach bridges multi-functionality and high-integration in all-optical convolutions,meanwhile possessing good architecture compatibility with digital convolutional neural networks.

关键词： convolution enable arbitrary

Revisions of convolution Model of Reflected Seismic Wave

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Chinese Physics Letters 1998年第11期15卷 851-853页

作者： HUANG Guang-yuan Institute of Mathematics Shandong UniversityJi’nan 250100

The convolution model of reflected wave used in exploration physics has no serious physical concept and mathematical *** phenomena should be characterized by instantaneous spectrum in physics and a complex function of three real variables(*** frequency)in *** coefficient is also a complex function of place and *** new formulas instead of convolution model are *** on wavelet transform and a method of“3 basis colors”,new color sectional image is obtained from practical data.

关键词： convolution sectional Wave

Multi-Axis Attention With convolution Parallel Block for Organoid Segmentation

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IEEE/CAA Journal of Automatica Sinica 2024年第5期11卷 1295-1297页

作者： Pengwei Hu Xun Deng Feng Tan Lun Hu Xinjiang Technical Institute of Physics and Chemistry Chinese Academy of SciencesUrumqi 830011 University of Chinese Academy of Sciences Beijing 100049 Xinjiang Laboratory of Minority Speech and Language Information Processing Urumqi 830011China Merck KGaA Darmstadt 64293Germany

Dear Editor,This letter presents an organoid segmentation model based on multi-axis attention with convolution parallel *** adeptly captures dynamic dependencies within bright-field microscopy images,improving global ... 详细信息

关键词： letter convolution organo

A convolution-type semi-analytic DQ approach to transient response of rectangular plates

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Applied Mathematics and Mechanics(English Edition) 2009年第9期30卷 1143-1151页

作者：彭建设杨杰袁玉全罗光兵 School of Physics and Electronic Information China West Normal University Chengdu University School of Aerospace Mechanical and Manufacturing Engineering RMIT University School of Science Sichuan University of Science & Engineering

The convolution-type Gurtin variational principle is known as the only variational principle that is, from the mathematics point of view, totally equivalent to the initial value problem system. In this paper, the equation of motion of rectangular thin plates is first transformed to a new governing equation containing initial conditions by using a convolution method. A convolution-type semi-analytical DQ approach, which involves differential quadrature （DQ） approximation in the space domain and an analytical series expansion in the time domain, is proposed to obtain the transient response solution. This approach offers the same advantages as the Gurtin variational principle and, at the same time, is much simpler in calculation. Numerical results show that it is very accurate yet computationally efficient for the dynamic response of plates.

关键词： convolution transient response differential quadrature method semianalytical method

PROPERTIES OF THE convolution WITH PRESTARLIKE FUNCTIONS

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Acta Mathematica Scientia 2013年第6期33卷 1685-1694页

作者： Jacek DZIOK Institute of Mathematics University of Rzeszów

In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known clas... 详细信息

关键词： analytic functions prestarlike functions starlike functions linear operator convolution

Averages of shifted convolution sums for arithmetic functions

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Frontiers of Mathematics in China 2019年第1期14卷 123-134页

作者： Miao LOU School of Mathematics Shandong University Jinan 250100 China

Let f be a full-level cusp form for GLm(Z) with Fourier coefficients Af(cm-2,…, c1, n): Let λ(n) be either the von Mangoldt function Λ(n) or the k-th divisor function τk(n): We consider averages of shifted convolu... 详细信息

关键词： Average shifted convolution sum arithmetic function

SOME ASYMPTOTIC PROPERTIES OF THE convolution TRANSFORMS OF FRACTAL MEASURES

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Acta Mathematica Scientia 2012年第6期32卷 2096-2104页

作者：曹丽 School of Mathematics Hefei University of Technology School of Mathematics and Statistics Wuhan University

We study the asymptotic behavior near the boundary of u（x, y） = Ky ＊ μ （x）, defined on the half-space R^＋ x RN by the convolution of an approximate identity Ky （.）（y 〉 0） and a measure μ on IRN. The Poisson and the heat kernel are unified as special cases in our setting. We are mainly interested in the relationship between the rate of growth at boundary of u and the s-density of a singular measure μ. Then a boundary limit theorem of Fatou＇s type for singular measures is proved. Meanwhile, the asymptotic behavior of a quotient of Kμ and Ku is also studied, then the corresponding Fatou-Doob＇s boundary relative limit is obtained. In particular, some results about the singular boundary behavior of harmonic and heat functions can be deduced simultaneously from ours. At the end, an application in fractal geometry is given.

关键词： fractal density harmonic function convolution singular measure

Relating brain structure images to personality characteristics using 3D convolution neural network

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CAAI Transactions on Intelligence Technology 2021年第3期6卷 338-346页

作者： Lixian Cao Yanchun Liang Wei Lv Kaechang Park Yasuhiro Miura Yuki Shinomiya Shinichi Yoshida Zhuhai Laboratory of Key Laboratory of Symbol Computation and Knowledge Engineering of Ministry of Education Zhuhai College of Jilin UniversityZhuhaiChina Key Laboratory of Symbol Computation and Knowledge Engineering of Ministry of Education College of Computer Science and TechnologyJilin UniversityChangchunChina School of Information&Research Institute Kochi University of TechnologyKochiJapan

The Keras deep learning framework is employed to study MRI brain data in a preliminary analysis of brain structure using a convolutional neural *** results obtained are matched with the content of personality *** Big Five personality traits provide easy differentiation for dividing personalities into different *** now,the highest accuracy obtained from the results of personality prediction from the analysis of brain structure is about 70%.Although there is still no effective evidence to prove a clear relationship between brain structure and personality,the obtained results could prove helpful in understanding the basic relationship between brain structure and personality characteristics.

关键词： convolution structure dividing