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Recurrent Neural Network Inspired Finite-Time Control Design

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IEEE/CAA Journal of Automatica Sinica 2024年第6期11卷 1527-1529页

作者： Jianan Liu Shihua Li Rongjie Liu School of Automation Southeast UniversityNanjing 210096China department of statistics Florida State UniversityFL 32304 USA IEEE

Dear Editor,This letter is concerned with the role of recurrent neural networks(RNNs)on the controller design for a class of nonlinear *** by the architectures of RNNs,the system states are stacked according to the dynamic along with time while the controller is represented as the neural network *** build the bridge between RNNs and finite-time controller,a novel activation function is imposed on RNNs to drive the convergence of states at finite-time and propel the overall control process *** stability proof is briefly provided for the convergence of the proposed finite-time *** last,a numerical simulation example is presented to illustrate the efficiency of the proposed *** networks can be classified as static(feedforward)and dynamic(recurrent)nets[1].The former nets do not perform well in dealing with training data and using any information of the local data structure[2].In contrast to the feedforward neural networks,RNNs are constituted by high dimensional hidden states with dynamics.

关键词： dynamics finite proof

Data-driven slicing for dimension reduction in regressions:A likelihood-ratio approach

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Science China Mathematics 2024年第3期67卷 647-664页

作者： Peirong Xu Tao Wang Lixing Zhu department of statistics Shanghai Jiao Tong UniversityShanghai 200240China Center for statistics and Data Science Beijing Normal University at ZhuhaiZhuhai 519087China

To efficiently estimate the central subspace in sufficient dimension reduction,response discretization via slicing its range is one of the most used methodologies when inverse regression-based methods are ***,existing slicing schemes are almost all ad hoc and not widely ***,how to define datadriven schemes with certain optimal properties is a longstanding problem in this *** research described here is then ***,we introduce a likelihood-ratio-based framework for dimension reduction,subsuming the popularly used methods including the sliced inverse regression,the sliced average variance estimation and the likelihood acquired ***,we propose a regularized log likelihood-ratio criterion to obtain a data-driven slicing scheme and derive the asymptotic properties of the estimators.A simulation study is carried out to examine the performance of the proposed method and that of existing methods.A data set concerning concrete compressive strength is also analyzed for illustration and comparison.

关键词： full-likelihood approach adaptive slicing regularization second-order method

Equitable Cluster Partition of Planar Graphs with Girth at Least 12

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Journal of Mathematical Research with Applications 2024年第2期44卷 152-160页

作者： Xiaoling LIU Lei SUN Wei ZHENG department of Mathematics and statistics Shandong Normal University

An equitable(Ok1, Ok2,..., Okm)-partition of a graph G, which is also called a k cluster m-partition, is the partition of V(G) into m non-empty subsets V1, V2,..., Vm such that for every integer i in {1, 2,..., m}, G[Vi] is a graph with components of order at most k, and for each distinct pair i, j in {1,..., m}, there is-1 ≤ |Vi|-|Vj| ≤ 1. In this paper, we proved that every planar graph G with minimum degree δ(G) ≥ 2 and girth g(G) ≥ 12 admits an equitable(O71, O72,..., O7m)-partition, for any integer m ≥ 2.

关键词： equitable cluster partition planar graph girth discharging

Trends in colorectal cancer incidence according to an increase in the number of colonoscopy cases in Korea

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World Journal of Gastrointestinal Oncology 2024年第1期16卷 51-60页

作者： Ga Hee Kim Yeong Chan Lee Tae Jun Kim Sung Noh Hong Dong Kyung Chang Young-Ho Kim Dong-Hoon Yang Chang Mo Moon Kyunga Kim Hyun Gun Kim Eun-Ran Kim Division of Gastroenterology Department of Internal MedicineAsan Medical CenterUniversity of Ulsan College of MedicineSeoul 05505South Korea department of Digital Health Samsung Advanced Institute for Health Science and TechnologySungkyunkwan University School of MedicineSeoul 06351South Korea Division of Gastroenterology Department of Internal MedicineSamsung Medical CenterSungkyunkwan University School of MedicineSeoul 06351South Korea Division of Gastroenterology Department of Internal MedicineEwha Womans UniversitySeoul 07985South Korea Biomedical statistics Center Samsung Medical CenterSeoul 06351South Korea Division of Gastroenterology Department of Internal MedicineSoonchunhyang University College of MedicineSeoul 04401South Korea

BACKGROUND The incidence of colorectal cancer(CRC)and preinvasive CRC(e.g.,early colon cancer and advanced adenoma)is gradually increasing in several *** To evaluate the trend in incidence of CRC and preinvasive CRC according to the increase in the number of colonoscopies performed in *** This retrospective cohort study enrolled Korean patients from 2002 to 2020 to evaluate the incidence of CRC and preinvasive CRC,and assess the numbers of diagnostic colonoscopies and colonoscopic ***-related complications by age group were also *** The incidence of CRC showed a rapid increase,then decreased after 2012 in the 50-75 year-age *** the study period,the rate of incidence of preinvasive CRC increased at a similar level in patients under 50 and 50-75 years of *** 2009,the increase has been rapid,showing a pattern similar to the increase in *** rate of colonoscopic polypectomy in patients aged under 50 was similar to the rate in patients over 75 years of age after *** rate of complications after colonoscopy and related deaths within 3 mo was high for those over 75 years of *** The diagnosis of preinvasive CRC increased with the increase in the number of colonoscopies *** the risk of colonoscopy-related hospitalization and death is high in the elderly,if early lesions at risk of developing CRC are diagnosed and treated under or at the age of 75,colonoscopy-related complications can be reduced for those aged 76 years or over.

关键词： Colorectal cancer Preinvasive colorectal cancer Colorectal polypectomy Colonoscopy

Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1059-1098页

作者： Donald A.DAWSON Jean VAILLANCOURT Hao WANG School of Mathematics and statistics Carleton UniversityOttawaCanada department of Decision Sciences HECMontrealCanada department of Mathematics University of OregonEugeneUSA

We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),... 详细信息

关键词： Measure-valued diffusions stochastic partial differential equations superprocesses branching processes local time Tanaka formula

Ding Projective Modules and Dimensions over Formal Triangular Matrix Rings

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Journal of Mathematical Research with Applications 2024年第5期 617-632页

作者： Wenhui ZHANG Ting LIU department of Mathematics and statistics Northwest Normal University

Let T be a formal triangular matrix ring. We prove that, if for each 1 ≤ j < i ≤ n, Uijis flat on both sides, then a left T-module ■ is Ding projective if and only if M1is a Ding projective left A1-module and for each 1 ≤ k ≤ n-1 the mapping Фk+1,k : Uk+1,k■AkMk→Mk+1is injective with cokernel Ding projective over Ak+1. As a consequence, we describe Ding projective dimension of a left T-module.

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Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

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Applied Mathematics and Mechanics(English Edition) 2024年第1期45卷 197-216页

作者： C.G.PAVITHRA B.J.GIREESHA M.L.KEERTHI department of PG Studies and Research in Mathematics Kuvempu UniversityShankaraghatta 577451India department of Mathematics and statistics M.S.Ramaiah University of Applied SciencesBengaluru 560058India

The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.

关键词： convection radiation moving longitudinal fin Adomian decomposition Sumudu transform method(ADSTM) trihybrid nanofluid magnetic field

Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories

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Science China Mathematics 2024年第8期67卷 1735-1760页

作者： Ji Lin Liangang Peng department of Mathematics and statistics Fuyang Normal UniversityFuyang 236037China School of Mathematics Sichuan UniversityChengdu 610064China

Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness *** define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall ***,we describe the semiderived Ringel-Hall algebra by the generators and defining *** particular,if t is an odd integer,we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.

关键词： hereditary abelian categories the categories of Z/t-graded complexes semi-derived Ringel-Hall algebras derived Hall algebras

A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES

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Acta Mathematica Scientia 2024年第4期44卷 1337-1346页

作者： Xiaosong LIU Taishun LIU School of Mathematics and statistics Lingnan Normal UniversityZhanjiang 524048China department of Mathematics Huzhou UniversityHuzhou 313000China

In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of *** next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of *** results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.

关键词： refined Schwarz-Pick estimate bounded holomorphic mapping Carathéodory metric first order Fréchet derivative higher order Fréchet derivatives