In 1987,Alavi,Malde,Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal.Although many researchers have been attracted by it,it is still open.Inspired by this conjecture,in ...In 1987,Alavi,Malde,Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal.Although many researchers have been attracted by it,it is still open.Inspired by this conjecture,in this paper,we prove that rooted products of some trees preserve real-rootedness of independence polynomials.In particular,we can obtain that their independence polynomials are unimodal and log-concave.展开更多
This paper investigates the asymptotic behavior of high-order vector rogue wave(RW)solutions for any multi-component nonlinear Schr¨odinger equation(denoted as n-NLSE)with multiple internal large parameters.We re...This paper investigates the asymptotic behavior of high-order vector rogue wave(RW)solutions for any multi-component nonlinear Schr¨odinger equation(denoted as n-NLSE)with multiple internal large parameters.We report some novel RW patterns,including nonmultiple root(NMR)-type patterns with distinct shapes such as semicircular sector,acute sector,pseudo-hexagram,and pseudo-rhombus shapes,as well as multiple root(MR)-type patterns characterized by right double-arrow and right arrow shapes.We demonstrate that these RW patterns are intrinsically related to the root structures of a novel class of polynomials,termed generalized mixed Adler-Moser(GMAM)polynomials,which feature multiple arbitrary free parameters.The RW patterns can be interpreted as straightforward expansions and slight shifts of the root structures for the GMAM polynomials to some extent.In the(x,t)-plane,they asymptotically converge to a first-order RW at the location corresponding to each simple root of the polynomials and to a lower-order RW at the location associated with each multiple root.Notably,the position of the lower-order RW within these patterns can be flexibly adjusted to any desired location in the(x,t)-plane by tuning the free parameters of the corresponding GMAM polynomials.展开更多
Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three d...Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.展开更多
为构建综合能源系统安全域(integrated energy system security region,IESSR),该文提出一种基于多项式混沌展开(polynomial chaos expansion,PCE)的IESSR边界(IESR boundary,IESSRB)近似方法,借助该方法可得IESSRB的多项式逼近表达式...为构建综合能源系统安全域(integrated energy system security region,IESSR),该文提出一种基于多项式混沌展开(polynomial chaos expansion,PCE)的IESSR边界(IESR boundary,IESSRB)近似方法,借助该方法可得IESSRB的多项式逼近表达式。首先,根据IESSRB的边界拓扑特性,构建系统的IESSR边界点搜索优化模型;然后,根据PCE,对IESSR边界点搜索优化模型进行参数化处理,构建IESSRB搜索的参数化优化模型;进一步地,根据IESSRB搜索的参数化优化模型的KKT条件,将IESSRB的参数化优化模型转化为高维参数化非线性方程组;在此基础上,借助广义Galerkin投影构建关于近似IESSRB的多项式逼近系数的Galerkin投影方程组,通过求解该方程组可得IESSRB的多项式逼近系数,从而获得IESSRB的多项式逼近表达式;为进一步降低Galerkin投影方程组求解复杂度,提出多项式分段近似IESSRB方法,在提高IESSRB近似精度的同时,提升了IESSRB近似的计算效率;最后,通过IES E39-G20测试系统和IES E118-G96测试系统对所提方法进行分析、验证。结果表明,所提方法可实现IESSR的准确、有效构建。展开更多
The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with ...The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.展开更多
本文提出了一种基于调和背景建模的二阶段实例分割方法,可实现复杂遥感图像背景下目标的快速且精细的实例分割。方法包括2个阶段:第1阶段采用可灵活替换的目标检测器,如YOLOv10(You only look once v10)或DINO(DETR with improved denoi...本文提出了一种基于调和背景建模的二阶段实例分割方法,可实现复杂遥感图像背景下目标的快速且精细的实例分割。方法包括2个阶段:第1阶段采用可灵活替换的目标检测器,如YOLOv10(You only look once v10)或DINO(DETR with improved denoising anchor boxes),获取候选目标框;第2阶段设计为“即插即用”的掩膜计算模块,无需额外训练即可基于调和函数模型对背景进行快速回归,并计算前景掩膜,从而提升掩膜计算的精度与鲁棒性。本文方法以调和函数理论及复分析中的相关定理为数学基础,以Dirichlet问题为核心框架,创新性地提出利用局部边界信息推断全局背景的实例掩膜生成策略。通过将Dirichlet问题转化为最小二乘回归形式,算法兼具可实现性与灵活性。在NWPU VHR-10数据集上的实验结果表明,与典型方法相比,本文方法在包围框平均精度(Average precision of boxes,AP-Box)和掩膜平均精度(Average precision of masks,AP-Mask)指标上均取得更优表现,其中AP-Mask指标可以在设定交并比(Intersection over union,IoU)指标为50%时达到92.1%,较现有最佳结果提升2.5个百分点。结果验证了该方法在遥感目标分割任务中的有效性与应用潜力。展开更多
Let Q n denote the class of all polynomials p(z) nonvanishing in the unit disk with deg p≤n and p (0)=1, and let W n denote the class of all polynomials s(z) satisfying deg s≤n and for all...Let Q n denote the class of all polynomials p(z) nonvanishing in the unit disk with deg p≤n and p (0)=1, and let W n denote the class of all polynomials s(z) satisfying deg s≤n and for all p∈Q n, s*p∈Q n , where * denotes the Hadamard product. Some properties for W n and Q n are obtained.展开更多
基金supported by the National Natural Science Foundation of China(No.12271527)。
文摘In 1987,Alavi,Malde,Schwenk and Erdős conjectured that the independence polynomial of any tree or forest is unimodal.Although many researchers have been attracted by it,it is still open.Inspired by this conjecture,in this paper,we prove that rooted products of some trees preserve real-rootedness of independence polynomials.In particular,we can obtain that their independence polynomials are unimodal and log-concave.
基金supported by the NSFC(12471236)the Guangzhou Municipal Science and Technology Project(Guangzhou Science and Technology Plan,No.2024A04J6245)Guangdong Natural Science Foundation(2025A1515011868)。
文摘This paper investigates the asymptotic behavior of high-order vector rogue wave(RW)solutions for any multi-component nonlinear Schr¨odinger equation(denoted as n-NLSE)with multiple internal large parameters.We report some novel RW patterns,including nonmultiple root(NMR)-type patterns with distinct shapes such as semicircular sector,acute sector,pseudo-hexagram,and pseudo-rhombus shapes,as well as multiple root(MR)-type patterns characterized by right double-arrow and right arrow shapes.We demonstrate that these RW patterns are intrinsically related to the root structures of a novel class of polynomials,termed generalized mixed Adler-Moser(GMAM)polynomials,which feature multiple arbitrary free parameters.The RW patterns can be interpreted as straightforward expansions and slight shifts of the root structures for the GMAM polynomials to some extent.In the(x,t)-plane,they asymptotically converge to a first-order RW at the location corresponding to each simple root of the polynomials and to a lower-order RW at the location associated with each multiple root.Notably,the position of the lower-order RW within these patterns can be flexibly adjusted to any desired location in the(x,t)-plane by tuning the free parameters of the corresponding GMAM polynomials.
基金Supported by the National Natural Science Foundation of China (Grant No.12161074)the Talent Introduction Research Foundation of Suqian University (Grant No.106-CK00042/028)+1 种基金Suqian Sci&Tech Program (Grant No.M202206)Sponsored by Qing Lan Project of Jiangsu Province and Suqian Talent Xiongying Plan of Suqian。
文摘Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.
文摘为构建综合能源系统安全域(integrated energy system security region,IESSR),该文提出一种基于多项式混沌展开(polynomial chaos expansion,PCE)的IESSR边界(IESR boundary,IESSRB)近似方法,借助该方法可得IESSRB的多项式逼近表达式。首先,根据IESSRB的边界拓扑特性,构建系统的IESSR边界点搜索优化模型;然后,根据PCE,对IESSR边界点搜索优化模型进行参数化处理,构建IESSRB搜索的参数化优化模型;进一步地,根据IESSRB搜索的参数化优化模型的KKT条件,将IESSRB的参数化优化模型转化为高维参数化非线性方程组;在此基础上,借助广义Galerkin投影构建关于近似IESSRB的多项式逼近系数的Galerkin投影方程组,通过求解该方程组可得IESSRB的多项式逼近系数,从而获得IESSRB的多项式逼近表达式;为进一步降低Galerkin投影方程组求解复杂度,提出多项式分段近似IESSRB方法,在提高IESSRB近似精度的同时,提升了IESSRB近似的计算效率;最后,通过IES E39-G20测试系统和IES E118-G96测试系统对所提方法进行分析、验证。结果表明,所提方法可实现IESSR的准确、有效构建。
文摘The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.
文摘本文提出了一种基于调和背景建模的二阶段实例分割方法,可实现复杂遥感图像背景下目标的快速且精细的实例分割。方法包括2个阶段:第1阶段采用可灵活替换的目标检测器,如YOLOv10(You only look once v10)或DINO(DETR with improved denoising anchor boxes),获取候选目标框;第2阶段设计为“即插即用”的掩膜计算模块,无需额外训练即可基于调和函数模型对背景进行快速回归,并计算前景掩膜,从而提升掩膜计算的精度与鲁棒性。本文方法以调和函数理论及复分析中的相关定理为数学基础,以Dirichlet问题为核心框架,创新性地提出利用局部边界信息推断全局背景的实例掩膜生成策略。通过将Dirichlet问题转化为最小二乘回归形式,算法兼具可实现性与灵活性。在NWPU VHR-10数据集上的实验结果表明,与典型方法相比,本文方法在包围框平均精度(Average precision of boxes,AP-Box)和掩膜平均精度(Average precision of masks,AP-Mask)指标上均取得更优表现,其中AP-Mask指标可以在设定交并比(Intersection over union,IoU)指标为50%时达到92.1%,较现有最佳结果提升2.5个百分点。结果验证了该方法在遥感目标分割任务中的有效性与应用潜力。
文摘Let Q n denote the class of all polynomials p(z) nonvanishing in the unit disk with deg p≤n and p (0)=1, and let W n denote the class of all polynomials s(z) satisfying deg s≤n and for all p∈Q n, s*p∈Q n , where * denotes the Hadamard product. Some properties for W n and Q n are obtained.
