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An Extension of the Win Theorem: Counting the Number of Maximum Independent Sets

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Chinese Annals of Mathematics,Series B 2019年第3期40卷 411-428页

作者： Wanpeng LEI Liming XIONG Junfeng DU Jun YIN school of Mathematics and statistics Beijing Institute of Technology school of computer science Qinghai Normal University

Win proved a well-known result that the graph G of connectivity κ(G) withα(G) ≤κ(G) + k-1(k ≥ 2) has a spanning k-ended tree, i.e., a spanning tree with at most k leaves. In this paper, the authors extended the Win theorem in case when κ(G) = 1 to the following: Let G be a simple connected graph of order large enough such that α(G) ≤ k + 1(k ≥ 3) and such that the number of maximum independent sets of cardinality k + 1 is at most n-2k-2. Then G has a spanning k-ended tree.

关键词： k-ended tree Connectivity Maximum independent set

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ON A LEMMA OF BOWEN

Acta Mathematica Scientia 2014年第3期34卷 932-940页

作者：李名田马际华 school of Mathematics and statistics Wuhan University school of Mathematics and computer science Fujian Normal University

We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, whic... 详细信息

关键词： Quasi generic point Billingsley dimension measure theoretic entropy symbolic dynamical system

Finite p-Groups with Few Non-major k-Maximal Subgroups

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Chinese Annals of Mathematics,Series B 2018年第1期39卷 59-68页

作者： Boyan WEI Haipeng QU Yanfeng LUO school of Mathematics and statistics Lanzhou University school of Mathematics and computer science Shanxi Normal University

A subgroup of index p^k of a finite p-group G is called a k-maximal subgroup of *** by d(G) the number of elements in a minimal generator-system of G and by δ_k(G) the number of k-maximal subgroups which do not contain the Frattini subgroup of *** this paper,the authors classify the finite p-groups with δ_(d(G))(G) ≤ p^2 and δ_(d(G)-1)(G) = 0,respectively.

关键词： Finite p-groups k-Maximal subgroups k-Major subgroups Frattini subgroup The number of non-major k-maximal subgroups

A Note on the Strong Edge-coloring of Outerplanar Graphs with Maximum Degree 3

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Acta Mathematicae Applicatae Sinica 2016年第4期32卷 883-890页

作者： Shun-yi LIU He-ping ZHANG Hong-liang LU Yu-qing LIN school of Mathematics and statistics Lanzhou University College of science Chang’an University school of Mathematics and statistics Xi’an Jiaotong University school of Electrical Engineering and computer science The University of Newcastle

A strong k-edge-coloring of a graph G is an assignment of k colors to the edges of G in such a way that any two edges meeting at a common vertex, or being adjacent to the same edge of G, axe assigned different colors. The strong chromatic index of G is the smallest integer k for which G has a strong k-edge-coloring. In this paper, we have shown that the strong chromatic index is no larger than 6 for outerplanax graphs with maximum degree 3.

关键词： strong edge-coloring strong chromatic index outerplanar graphs

Elliptic curve with Optimal mixed Montgomery-Edwards model for low-end devices

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science China(Information sciences) 2015年第11期58卷 67-74页

作者： LIU Zhe HU Zhi WU Wei University of Luxembourg school of Mathematics and statistics Central South University school of Mathematics and computer science Fujian Normal University

This paper introduces a special family of twisted Edwards curve named Optimal mixed MontgomeryEdwards(OME) curves. The OME curve is proposed by exploiting the fact that every twisted Edwards curve is birationally equivalent to some elliptic curve in Montgomery form. The OME curves achieve optimal group arithmetic for both of twisted Edwards model and Montgomery model. In particular, the Montgomery model of OME curves only requires 3M + 2S and 1M + 3S + 3C to perform the point addition and point doubling operations, while 7M and 3M + 4S are needed for executing a point addition and point doubling for the twisted Edwards model of them. We also make effort to carefully choose the curve parameters and the underlying implementation field to achieve high performance. An example of OME curve is E /Fp:-x2+y2= 1-27822·x2y2over p = 2192- 264- 1. Our implementation results on the widely used 8-bit micro-controller platforms(i.e.,AVR Atmega128) further demonstrate and highlight the practical benefits of proposed OME curve on low-end device. In particular, our implementation, performed in constant-time, reduces the execution time by up to14% and 18% for fixed point and random point scalar multiplication, respectively, when comparing with the state-of-the-art implementation on the identical platform.

关键词： cryptography elliptic curve scalar multiplication efficient implementation 8-bit AVR processors

Stability of second-order stochastic neutral partial functional differential equations driven by impulsive noises

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science China(Information sciences) 2016年第11期59卷 117-127页

作者： Feng JIANG Hua YANG Yi SHEN school of statistics and Mathematics Zhongnan University of Economics and Law school of Automation Huazhong University of Science and Technology school of Mathematics and computer science Wuhan Polytechnic University

This paper investigates the stability of second-order stochastic neutral partial functional differential equations driven by impulsive noises. Some sufficient conditions ensuring pth moment exponential stability of the second-order stochastic neutral partial functional differential equations driven by impulsive noises are obtained by establishing a new impulsive-integral inequality. These existing results are generalized and improved by the present study. Finally, an example is given to show the effectiveness of our results.

关键词： second-order stochastic neutral partial functional differential equations exponential stability impulsive noises sine family cosine family

Extensions and Deformations of 3-Lie Algebras with Higher Derivations

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Journal of Mathematical Research with Applications 2025年第1期 20-32页

作者： Shuangjian GUO school of Mathematics and statistics Guizhou University of Finance and Economics

In this paper, we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair. We introduce a cohomology theory of 3-LieHDer pairs. Next, we interpret the second cohomology group as the space of all isomorphism classes of abelian extensions. Finally,we consider formal deformations of 3-LieHDer pairs that are governed by the cohomology with self-coefficient.

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Weak Finite Determinacy of Relative Map-Germs

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Chinese Annals of Mathematics,Series B 2014年第6期35卷 991-1000页

作者： Changmei SHI Donghe PEI school of Mathematics and statistics Northeast Normal University school of Mathematics and computer science Guizhou Normal College

The weak finite determinacy of relative map-germs is studied. The authors first give the concept of weak finite determination, and then give several sufficient conditions for a relative map-germ to be weak finitely determined, which is an important complement to Mather＇s work. Moreover, us an application, it is proven that the relative stable map-germs are weak finitely determined.

关键词： Relative map-germs Weak finite determinacy Relative stability

Early identification of stroke through deep learning with multi-modal human speech and movement data

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Neural Regeneration Research 2025年第1期20卷 234-241页

作者： Zijun Ou Haitao Wang Bin Zhang Haobang Liang Bei Hu Longlong Ren Yanjuan Liu Yuhu Zhang Chengbo Dai Hejun Wu Weifeng Li Xin Li school of computer science and Engineering Sun Yat-sen UniversityGuangzhouGuangdong ProvinceChina Department of Neurology Guangdong Neuroscience InstituteGuangdong Provincial People’s Hospital(Guangdong Academy of Medical Sciences)Southern Medical UniversityGuangzhouGuangdong ProvinceChina Department of Emergency Medicine Guangdong Provincial People’s Hospital(Guangdong Academy of Medical Sciences)Southern Medical UniversityGuangzhouGuangdong ProvinceChina

Early identification and treatment of stroke can greatly improve patient outcomes and quality of *** clinical tests such as the Cincinnati Pre-hospital Stroke Scale(CPSS)and the Face Arm Speech Test(FAST)are commonly used for stroke screening,accurate administration is dependent on specialized *** this study,we proposed a novel multimodal deep learning approach,based on the FAST,for assessing suspected stroke patients exhibiting symptoms such as limb weakness,facial paresis,and speech disorders in acute *** collected a dataset comprising videos and audio recordings of emergency room patients performing designated limb movements,facial expressions,and speech tests based on the *** compared the constructed deep learning model,which was designed to process multi-modal datasets,with six prior models that achieved good action classification performance,including the I3D,SlowFast,X3D,TPN,TimeSformer,and *** found that the findings of our deep learning model had a higher clinical value compared with the other ***,the multi-modal model outperformed its single-module variants,highlighting the benefit of utilizing multiple types of patient data,such as action videos and speech *** results indicate that a multi-modal deep learning model combined with the FAST could greatly improve the accuracy and sensitivity of early stroke identification of stroke,thus providing a practical and powerful tool for assessing stroke patients in an emergency clinical setting.

关键词： artificial intelligence deep learning diagnosis early detection FAST screening stroke