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Rational Solutions of First Order Algebraic Ordinary Differential Equations

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Journal of Systems Science & Complexity 2024年第2期37卷 567-580页

作者： FENG Shuang SHEN Liyong school of Physical and mathematical sciences Nanjing Tech UniversityNanjing 211816China school of mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Let f(t,y,y')=∑ _(i=0)^(n )a_(i)(t,y)y'^(i)=0 be an irreducible first order ordinary differential equation with polynomial *** in 1998 proved that there exists a constant C such that every rational solution of f(t,y,y')=0 is of degree not greater than *** show that this degree bound C depends not only on the degrees of f in t,y,y' but also on the coefficients of f viewed as the polynomial in t,y,y'.In this paper,the authors show that if f satisfies deg(f,y)0,then the degree bound C only depends on the degrees of f in t,y,y',and furthermore we present an explicit expression for C in terms of the degrees of f in t,y,y'.

关键词： Degree bound first order AODE height rational solution

A Note on the Entropy for Heisenberg Group Actions on the Torus

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2324-2336页

作者： Yu ZHANG Yu Jun ZHU school of mathematical sciences Xiamen University

In this paper,the entropy of discrete Heisenberg group actions is *** α be a discrete Heisenberg group action on a compact metric space *** types of entropies,■ and h(α)are introduced,in which ■ is defined in Ruelle’s way and h(α) is defined via the natural extension of α.It is shown that when X is the torus and α is induced by integer matrices then ■ is zero and h(α) can be expressed via the eigenvalues of the matrices.

关键词： Entropy Heisenberg group action natural extension torus

Uncertainty Principles on Clifford Modules

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2537-2570页

作者： Pan LIAN school of mathematical sciences Tianjin Normal University

In this paper, we derive the optimal Cauchy–Schwarz inequalities on a class of Hilbert and Krein modules over a Clifford algebra, which heavily depend on the Clifford algebraic *** obtained inequalities further lead to very general uncertainty inequalities on these modules. Some new phenomena arise, due to the non-commutative nature, the Clifford-valued inner products and the Krein geometry. Taking into account applications, special attention is given to the Dirac operator and the Howe dual pair Pin(m) × osp(1|2). Moreover, it is surprisingly to find that the recent highly nontrivial uncertainty relation for triple observables is indeed a direct consequence of our Cauchy–Schwarz inequality. This new observation leads to refined uncertainty relations in terms of the Wigner–Yanase–Dyson skew information for mixed states and other generalizations. These show that the obtained uncertainty inequalities on Clifford modules can be considered as new uncertainty relations for multiple observables.

关键词： 30G35 81P45 Clifford algebra Fischer decomposition Krein space uncertainty principle Wigner–Yanase–Dyson skew information

The Strategic Analysis of Demand Forecast-Sharing in a Hybrid-Format Online Platform Supply Chain

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Journal of Systems Science and Systems Engineering 2024年第3期33卷 281-310页

作者： Jing Zhao Zijun Yin Guobiao Zhou school of mathematical sciences Tiangong UniversityTianjin300387China

This paper examines the optimal forecast-sharing strategy in a hybrid-format online platform supply chain where a supplier sells a product through agency format and reselling format provided by a platform retailer who possesses demand forecasts from two *** asymmetry and co-opetitive relationship arise between the platform retailer and the supplier,which affect their operational decisions and the supply chain’s *** improve supply chain efficiency,we compare different forecast-sharing strategies(i.e.,no forecast sharing,sharing a single forecast,and sharing two forecasts),and analyze the effects of co-opetitive parameters on the optimal forecast-sharing *** analysis shows that forecast sharing is always beneficial to the supplier,and sharing two forecasts is more beneficial than sharing a single *** for the platform retailer and the whole supply chain,forecast sharing is beneficial only under certain conditions,depending on the co-opetitive *** optimal forecast-sharing strategy is the result of a combination of the negative effect of double marginalization in reselling channel and the positive effect of responding pricing to demand uncertainty in agency *** illustrate the parameter regions of the platform retailer’s voluntary sharing,contract sharing,and no sharing,and also find that higher channel competition intensity,higher market share of agency channel,and higher commission rate can promote the platform retailer’s voluntary *** study extends the research scope of demand forecast-sharing and sheds light on the decision-making processes for managing a hybrid-format online platform supply chain.

关键词： Supply chain management hybrid-format online platform demand forecast-sharing co-opetitive relationship channel competition intensity

Global well-posedness for 2D inhomogeneous asymmetric fluids with large initial data

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Science China Mathematics 2024年第3期67卷 527-556页

作者： Chenyin Qian Beibei He Ting Zhang school of mathematical sciences Zhejiang Normal UniversityJinhua 321004China school of mathematical sciences Zhejiang UniversityHangzhou 310058China

In this paper, by using time-weighted global estimates and the Lagrangian approach, we first investigate the global existence and uniqueness of the solution for the 2D inhomogeneous incompressible asymmetric fluids wi... 详细信息

关键词： inhomogeneous asymmetric fluids Littlewood-Paley theory Besov spaces global well-posedness

PROPERTIES OF THE POSITIVE SOLUTIONS OF FRACTIONAL P&Q-LAPLACE EQUATIONS WITH A SIGN-CHANGING POTENTIAL

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Acta Mathematica Scientia 2024年第6期44卷 2422-2442页

作者：段雨博魏雅薇 school of mathematical sciences Nankai University school of mathematical sciences and LPMC Nankai University

In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing *** model is inspired by the De Giorgi *** are two main results in this ***,in the bounded domain,we use the moving plane method to show that the solution is radially ***,for the unbounded domain,in view of the idea of the sliding method,we find the existence of the maximizing sequence of the bounded solution,then obtain that the solution is strictly monotone increasing in some direction.

关键词： fractional p&q-Laplacian moving plane method sliding method

Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth

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Science China Mathematics 2024年第7期67卷 1525-1554页

作者： Lingwei Ma Zhenqiu Zhang school of mathematical sciences Tianjin Normal UniversityTianjin300387China school of mathematical sciences and LPMC Nankai UniversityTianjin300071China

This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,Du)+■π=f,div u=0,where Du is the symmetric part of the gradient■*** first establish anε-regularity criterion involving both the excess functional of the symmetric gradient Du and Wolff potentials of the nonhomogeneous term f to guarantee the local vanishing mean oscillation(VMO)-regularity of Du in an open subset Ω_(u) of Ω with full *** anε-regularity criterion leads to a pointwise Wolff potential estimate of Du,which immediately infers that Du is partially C^(0)-regular under appropriate ***,we give a local continuous modulus estimate of Du.

关键词： nonlinear Stokes system partial regularity Wolff potential estimates continuous modulus estimates

Materials design and preparation of ultrathin two-dimensional metal halide perovskites

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Nano Research 2024年第7期17卷 6231-6246页

作者： Xiaomin Zhang Sihan Zhao Junran Zhang Lin Wang school of Flexible Electronics(Future Technologies)and Institute of advanced Materials Key Laboratory of Flexible ElectronicsJiangsu National Synergetic Innovation Center for Advanced MaterialsSchool of Physical and Mathematical SciencesNanjing Tech UniversityNanjing 211816China

Metal halide perovskites(MHPs)have emerged as highly promising candidates for the next generation of photonics and optoelectronic devices,owing to their prominent optical and excitonic properties,as well as the convenience of ***,ultrathin two-dimensional(2D)MHPs,which are generally prepared by exfoliation,solution growth,and chemical vapor deposition method,have attracted dramatically increasing attentions owing to their combined features of ultrathin 2D morphology and superior performance of *** the growing interest in ultrathin 2D MHPs,there is currently a lack of a comprehensive and systematic overview of the distinct advantages offered by each growth method for producing these *** review critically assesses the preliminary studies on the materials design and preparation of ultrathin ***,it explores heterostructures based on ultrathin MHPs and offers insights into the challenges and opportunities that lie ahead for this enticing class of 2D materials.

关键词： ultrathin perovskites material preparation exfoliation solution growth chemical vapor deposition

Flocking Effects of the Stochastic Cucker-Smale System with Noise

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Journal of Systems Science & Complexity 2024年第5期37卷 1978-1994页

作者： HAN Ning GE Bin LI Lin school of mathematical sciences Harbin Engineering UniversityHarbin 150001China

In this paper,the flocking behavior of a Cucker-Smale model with a leader and noise is studied in a finite *** authors present a Cucker-Smale system with two nonlinear controls for a complex network with stochastic synchronization in *** on the finite-time stability theory of stochastic differential equations,the sufficient conditions for the flocking of stochastic systems in a finite time are obtained by using the Lyapunov function ***,the numerical simulation of the particle system is carried out for the leader and noise,and the correctness of the results is verified.

关键词： Cucker-Smale model flocking behavior leader noise