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Improved Upper Bound for Generalized Acyclic Chromatic Number of Graphs

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Acta Mathematicae Applicatae Sinica 2018年第4期34卷 798-800页

作者： jian-sheng cai Xu-ding ZHU School of Mathematics and Information Sciences Weifang University Weifang 261061 China Department of Mathematics Zhejiang Normal University Jinhua 321004 China

A vertex coloring of a graph G is called r-acyclic if it is a proper vertex coloring such that every cycle D receives at least min{｜D｜, r} colors. The r-acyclic chromatic number of G is the least number of colors in an r-acyclic coloring of G. We prove that for any number r ≥ 4, the r-acyclic chromatic number of any graph G with maximum degree △ ≥ 7 and with girth at least（r-1）△ is at most（4r-3）△.

关键词： girth coloring acyclic coloring τ-acyclic coloring Lopsided local lemma

f-Class Two Graphs Whose f-Cores Have Maximum Degree Two

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Acta Mathematica Sinica,English Series 2014年第4期30卷 601-608页

作者： Xia ZHANG Gui Ying YAN jian sheng cai School of Mathematics Science Shandong Normal University Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematics and Information Sciences Weifang University

Abstract An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v ∈ V（G） at most f（v） times. The f-core of G is the subgraph of G induced by the vertices v of degree d（v） = f（v）maxv∈y（G）{ [d（v）/f（v）l}. In this paper, we find some necessary conditions for a simple graph, whose f-core has maximum degree two, to be of class 2 for f-colorings.

关键词： f-Coloring simple graph f-chromatic index f-class 2

A Sufficient Condition for Planar Graphs with Maximum Degree 8 to Be 9-totally Colorable

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Acta Mathematica Sinica,English Series 2014年第6期30卷 993-1006页

作者： jian sheng cai Chang Chun TENG Gui Ying YAN School of Mathematics and Information Sciences Weifang University Academy of Mathematics and Systems Science Chinese Academy of Sciences

A total k-coloring of a graph G is a coloring of V（G） ∪ E（G） using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ＇＇（G） is the smallest integer k such that G has a total k-coloring. It is known that if a planar graph G has maximum degree △≥ 9, then ）χ″（G） =△＋ 1. In this paper, we prove that if O is a planar graph with maximum degree 8 and without a fan of four adjacent 3-cycles, then χ″（G） =- 9.

关键词： Total coloring planar graph a fan of four adjacent 3-cycles

A Note on the Existence of Fractional f-factors in Random Graphs

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 677-680页

作者： jian-sheng cai Xiao-yang WANG Gui-ying YAN School of Mathematics and Information Science Weifang University Beijing Anzhen Hospital Capital Medical University Academy of Mathematics and System Science Chinese Academy of Science

Let G ： Gn,p be a binomial random graph with n vertices and edge probability p = p（n）, and f be a nonnegative integer-valued function defined on V（G） such that 0 〈 a ≤ f（x） ≤ b 〈 np- 2√nplogn for every E V（G）. An fractional f-indicator function is an function h that assigns to each edge of a graph G a number h（e） in [0, 1] so that for each vertex x, we have d^hG（x） = f（x）, where dh（x） = ∑ h（e） is the fractional degree xEe ofx inG. Set Eh = {e ： e e E（G） and h（e） ≠ 0}. IfGh isaspanningsubgraphofGsuchthat E（Gh） = Eh, then Gh is called an fractional f-factor of G. In this paper, we prove that for any binomial random graph Gn,p 2 with p 〉 n^-2/3, almost surely Gn,p contains an fractional f-factor.

关键词： random graph probabilistic method f-factor fractional f-factor

List Injective Coloring of Planar Graphs

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Acta Mathematicae Applicatae Sinica 2022年第3期38卷 614-626页

作者： Yin-dong JIN Lian-ying MIAO School of Mathematics China University of Mining and TechnologyXuzhou 221116China

A k-coloring of a graph G is a mapping c:V(G)→{1,2,···,k}.The coloring c is called injective if any two vertices have a common neighbor get distinct colors.A graph G is injectively k-choosable if for any color list L of admissible colors on V(G)of size k allows an injective coloringφsuch thatφ(v)∈L(v)for each v∈V(G).Letχ;(G),χ;(G)denote the injective chromatic number and injective choosability number of G,*** this paper,we show thatχ;(G)≤△+4 if△≥22 andχ;(G)≤△+5 if△≥15,where G is a triangle-free planar graph and without intersecting 4-cycles.

关键词： planar graph injective coloring list coloring

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最大度为4的图的无圈列表边染色

数学学报（中文版） 2022年第1期65卷 153-160页

作者：王娟苗连英蔡建生曲阜师范大学管理学院日照276826 中国矿业大学数学学院徐州221116 潍坊学院数学与信息科学学院潍坊261061

对于图G=(V(G),E(G)),如果一个映射φ:E(G)→{1,2,…,k},使得G中任意相邻的两边e_(1),e_(2)满足φ(e_(1))≠φ(e_(2)),并且G中不含有双色圈,则称φ为G的一个无圈边染色.对于给定的列表分配L={L(e)|e∈E(G)},如果存在图G的一个无圈边染色... 详细信息

对于图G=(V(G),E(G)),如果一个映射φ:E(G)→{1,2,…,k},使得G中任意相邻的两边e_(1),e_(2)满足φ(e_(1))≠φ(e_(2)),并且G中不含有双色圈,则称φ为G的一个无圈边染色.对于给定的列表分配L={L(e)|e∈E(G)},如果存在图G的一个无圈边染色φ,使得对于任意边e∈E(G),均有φ(e)∈L(e),则称染色φ为G的一个无圈L-边染色.如果对于任意的列表分配L,当对所有的边e∈E(G)满足|L(e)|≥k时,图G均存在无圈L-边染色,那么称G是无圈k-边可选的.使图G无圈k-边可选的最小的正整数k,称为G的无圈列表边色数,用a'_(l)(G)表示.本文证明了对于最大度△≤4的连通图G,如果|E(G)|≤2|V(G)|-1,则a'_(l)(G)≤6,扩展了Basavaraju和Chandran文[*** Theory,2009,61(3):192-209]的结果.

关键词：边染色无圈染色列表染色最大度

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基于DSP的雷达信号采集处理系统

武汉大学学报（理学版） 2001年第5期47卷 573-576页

作者：许丹田建生吴世才武汉大学电子信息学院湖北武汉430072

基于数字信号处理器 (DSP)能实时完成信号处理的特点 ,提出了采用 AD公司生产的定点 DSP芯片ADSP2 181来设计雷达信号采集处理系统的一种方案 .这种方案比传统意义上应用微处理器 (MPU)实现信号采集处理有更快的处理速度 ,更方便的接口... 详细信息

基于数字信号处理器 (DSP)能实时完成信号处理的特点 ,提出了采用 AD公司生产的定点 DSP芯片ADSP2 181来设计雷达信号采集处理系统的一种方案 .这种方案比传统意义上应用微处理器 (MPU)实现信号采集处理有更快的处理速度 ,更方便的接口设计和更高的精度 .作为高频地波雷达的一部分 ,该雷达信号采集处理系统能够满足高频地波雷达要求采样速率快、信号实时处理的要求。

关键词：数字信号处理器高频地波雷达 ADSP2181芯片信号采集 DSP 海洋环境监测 FMICW体制

A nuclide identification method ofγspectrum and model building based on the transformer

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Nuclear Science and Techniques 2025年第1期36卷 80-93页

作者： Fei Li Chu-Yang Luo Ying-Zi Wen sheng Lv Feng Cheng Guo-Qiang Zeng jian-Feng jiang Bing-Hai Li College of Nuclear Technology and Automation Engineering Chengdu University of TechnologyChengdu 610000China Applied Nuclear Technology in Geosciences Key Laboratory of Sichuan Province Chengdu 610000China Department of Physics Universitat Politècnica de CatalunyaBarcelona 08028Spain Airborne Survey and Remote Sensing Center of Nuclear Industry Shijiazhuang 050000China Hebei Key Laboratory of Airborne Detection and Remote Sensing Technology Shijiazhuang 050000China

In current neural network algorithms for nuclide identification in high-background,poor-resolution detectors,traditional network paradigms including back-propagation networks,convolutional neural networks,recurrent neural networks,etc.,have been limited in research on γ spectrum analysis because of their inherent mathematical *** is difficult to make progress in terms of training data requirements and prediction *** contrast to traditional network paradigms,network models based on the transformer structure have the characteristics of parallel computing,position encoding,and deep stacking,which have enabled good performance in natural language processing tasks in recent ***,in this paper,a transformer-based neural network (TBNN) model is proposed to achieve nuclide identification for the first ***,the Geant4 program was used to generate the basic single-nuclide energy spectrum through Monte Carlo simulations.A multi-nuclide energy spectrum database was established for neural network training using random matrices of γ-ray energy,activity,and *** on the encoder–decoder structure,a network topology based on the transformer was built,transforming the 1024-channel energy spectrum data into a 32×32 energy spectrum sequence as the model *** experiments and adjustments of model parameters,including the learning rate of the TBNN model,number of attention heads,and number of network stacking layers,the overall recognition rate reached 98.7%.Additionally,this database was used for training AI models such as back-propagation networks,convolutional neural networks,residual networks,and long shortterm memory neural networks,with overall recognition rates of 92.8%,95.3%,96.3%,and 96.6%,*** indicates that the TBNN model exhibited better nuclide identification among these AI models,providing an important reference and theoretical basis for the practical application of transformers in the qualitative and quantitativ

关键词： Nuclide identification Neural network Transformer

A novel method for simultaneous measurement of^(222)Rn and^(220)Rn progeny concentrations measured by an alpha spectrometer

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Nuclear Science and Techniques 2025年第1期36卷 127-139页

作者： Zhong-Kai Fan Jia-Le Sun Hao-Xuan Li Xiang-Ming cai Hui Yang Shou-Kang Qiu Yan-Liang Tan jian Shan School of Nuclear Science and Technology University of South ChinaHengyang 421001China College of Physics and Electronic Engineering Hengyang Normal UniversityHengyang 421008China

The accumulation of^(222)Rn and^(220)Rn progeny in poorly ventilated environments poses the risk of natural radiation exposure to the public.A previous study indicated that satisfactory results in determining the^(222)Rn and^(220)Rn progeny concentrations by measuring the total alpha counts at five time intervals within 560 min should be expected only in the case of high progeny concentrations in *** complete the measurement within a relatively short period and adapt it for simultaneous measurements at comparatively lower^(222)Rn and^(220)Rn progeny concentrations,a novel mathematical model was proposed based on the radioactive decay *** model employs a nonlinear fitting method to distinguish nuclides with overlapping spectra by utilizing the alpha particle counts of non-overlapping spectra within consecutive measurement cycles to obtain the concentrations of^(222)Rn and^(220)Rn progeny in *** verification experiments were conducted using an alpha *** experimental results demonstrate that the concentrations of^(222)Rn and^(220)Rn progeny calculated by the new method align more closely with the actual circumstances than those calculated by the total count method,and their relative uncertainties are all within±16%.Furthermore,the measurement time was reduced to 90 min,representing an acceleration of 84%.The improved capability of the new method in distinguishing alpha particles with similar energies emitted from ^(218)Po and^(212)Bi,both approximately 6 MeV,contributed to realizing more accurate *** proposed method has the potential advantage of measuring relatively low concentrations of^(222)Rn and^(220)Rn progeny in air more quickly via air filtration.

关键词： ^(222)Rn ^(220)Rn Progeny concentration Nonlinear fitting method Alpha spectrometer