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Multicolored Bipartite Ramsey Numbers of Large Cycles

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 347-357页

作者： Shao-qiang LIU Yue-jian PENG college of mathematics and statistics Hanshan Normal UniversityChaozhou 521041China School of mathematics Hunan UniversityChangsha 410082China

For an integer r≥2 and bipartite graphs Hi,where 1≤i≤r,the bipartite Ramsey number br(H1,H2,…,Hr)is the minimum integer N such that any r-edge coloring of the complete bipartite graph KN;N contains a monochromatic subgraph isomorphic to Hi in color i for some 1≤i≤*** show that if r≥3;α1,α2>0,αj+2≥[(j+2)!-1]Σi=1^(j+1)α1 for j=1,2…r-2,then br(C2[α1n],C2[α2n],…,C2[αrn]=(Σ=j=1^(r)a j+o(1))n.

关键词： ramsey number bipartite ramsey number regularity lemma

A wealth distribution model with a non-Maxwellian collision kernel

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Chinese Physics B 2024年第7期33卷 224-231页

作者：孟俊周霞赖绍永 college of mathematics and statistics Kashi UniversityKashi 844006China college of mathematics and Physics Mianyang Teacher's CollegeMianyang 621000China School of mathematics Southwestern University of Finance and EconomicsChengdu 611130China

A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent *** collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker–Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.

关键词： kinetic theory non-Maxwellian collision kernel wealth distribution Pareto index

Quasi-shadowing for Z^(d)-actions

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1563-1580页

作者： Juan PAN Xian Kun REN Yun Hua ZHOU School of mathematics and statistics Chongqing Technology and Business UniversityChongqing 400067P.R.China college of mathematics and statistics Chongqing UniversityChongqing 401331P.R.China

A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov *** prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of the genera... 详细信息

关键词： Quasi-shadowing Z^(d)-action non-uniformly partially hyperbolic ergodic measure

Empirical likelihood for spatial cross-sectional data models with matrix exponential spatial specification

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Applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 125-139页

作者： LIU Yan RONG Jian-rong QIN Yong-song Nanning University Nanning 530200China Center for Applied mathematics of Guangxi and college of mathematics and statistics Guangxi Normal UniversityGuilin 541004China

In this paper,we study spatial cross-sectional data models in the form of matrix exponential spatial specification(MESS),where MESS appears in both dependent and error *** empirical likelihood(EL)ratio statistics are established for the parameters of the MESS *** is shown that the limiting distributions of EL ratio statistics follow chi-square distributions,which are used to construct the confidence regions of model *** experiments are conducted to compare the performances of confidence regions based on EL method and normal approximation method.

关键词： MESS empirical likelihood con dence region

Pricing Guaranteed Minimum Death Benefits with Dollar Cost Averaging Under Time-changed Le′vy Models

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Acta Mathematicae Applicatae Sinica 2024年

作者： Jia-ming WANG Mei-qiao AI Zhi-min ZHANG college of mathematics and statistics Chongqing University

In this paper, we propose an efficient and accurate method for pricing Guaranteed Minimum Death Benefit (GMDB) under time-changed Le′vy processes. Suppose that the GMDB payoff depends on a dollar cost averaging (DCA) style periodic investment, and the activity rate process in stochastic time change is modeled by a square-root process. We develop a recursive method to derive the closed form valuation formula by using the frame duality projection method. Numerical examples are reported for demonstrating the effectiveness of our approach and illustrating the interplay between contract parameters and the valuation.

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Uniformity of Asymmetric Augmented Designs

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Acta Mathematicae Applicatae Sinica 2024年第4期 1025-1044页

作者： Zhi-qing WANG Xiang-yu FANG Zu-jun OU college of mathematics and statistics Jishou University

Follow-up experimental designs are widely applied to explore the relationship between factors and responses step by step in various fields such as science and engineering. When some additional resources or information become available after the initial design of experiment is carried out, some additional runs and/or factors may be added in the follow-up stage. In this paper, the issue of the uniform row augmented designs and column augmented designs with mixed two-, three-and four-level is investigated. The uniformity of augmented designs is discussed under the wrap-around L2-discrepancy. Some lower bounds of wrap-around L2-discrepancy for the augmented designs are obtained, which can be used to assess uniformity of augmented design. Numerical results show that augmented designs have high efficiency, which have low discrepancy and close to the proposed lower bounds.

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On limit fractional Volterra hierarchies

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Communications in Theoretical Physics 2024年第1期76卷 7-16页

作者： Lixiang Zhang Chuanzhong Li School of mathematics and statistics Ningbo UniversityNingbo315211China college of mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton ***,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative ***,we establish the relationship between new and old solutions of the NCLFV ***,the quasi determinant solutions of the NCLFV hierarchy are obtained.

关键词： limit fractional Volterra hierarchy noncommutative limit fractional Volterra hierarchy Darboux transformation soliton solution quasi determinant solution

New construction of mutually unbiased bases for odd-dimensional state space

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Chinese Physics B 2024年第8期33卷 180-184页

作者：王成红王昆郑驻军 college of mathematics and statistics Zhoukou Normal UniversityZhoukou 466001China School of mathematics South China University of TechnologyGuangzhou 510641China

We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime *** explore the results for composite dimensions which are true for prime power *** then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased *** particular,we present four mutually unbiased bases in C^(15).

关键词： mutually unbiased bases Hilbert space Pauli matrix quantum measurement

MSADCN:Multi-Scale Attentional Densely Connected Network for Automated Bone Age Assessment

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Computers, Materials & Continua 2024年第2期78卷 2225-2243页

作者： Yanjun Yu Lei Yu Huiqi Wang Haodong Zheng Yi Deng college of Computer and Information Science Chongqing Normal UniversityChongqing401331China college of mathematics and statistics Chongqing UniversityChongqing401331China

Bone age assessment(BAA)helps doctors determine how a child’s bones grow and develop in clinical *** BAA methods rely on clinician expertise,leading to time-consuming predictions and inaccurate *** deep learning-based BAA methods feed the extracted critical points of images into the network by providing additional *** operation is costly and *** address these problems,we propose a multi-scale attentional densely connected network(MSADCN)in this *** constructs a multi-scale dense connectivity mechanism,which can avoid overfitting,obtain the local features effectively and prevent gradient vanishing even in limited training ***,MSADCN designs multi-scale structures in the densely connected network to extract fine-grained features at different ***,coordinate attention is embedded to focus on critical features and automatically locate the regions of interest(ROI)without additional *** addition,to improve the model’s generalization,transfer learning is applied to train the proposed MSADCN on the public dataset IMDB-WIKI,and the obtained pre-trained weights are loaded onto the Radiological Society of North America(RSNA)***,label distribution learning(LDL)and expectation regression techniques are introduced into our model to exploit the correlation between hand bone images of different ages,which can obtain stable age *** experiments confirm that our model can converge more efficiently and obtain a mean absolute error(MAE)of 4.64 months,outperforming some state-of-the-art BAA methods.

关键词： Bone age assessment deep learning attentional densely connected network muti-scale