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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 {1. sciences Nanjing Tech UniversityNanjing 211816China school of {1. 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 1.98 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 {1. 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 {1. 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 81.45 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 {1. 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 {1. sciences Zhejiang Normal UniversityJinhua 321004China school of {1. 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 with the initial(angular) velocity being located in sub-critical Sobolev spaces H^(s)(R^(2))(01. and the initial density being bounded from above and below by some positive constants. The global unique solvability of the 2D incompressible inhomogeneous asymmetric fluids with the initial data in the critical Besov space(u_(0), w_(0))∈˙B^(0)_(2,1.(R^(2))andρ^(−1.−1.˙B^(ε)_(2/ε),1.R^(2))is established. In particular, the uniqueness of the solution is also obtained without any more regularity assumptions on the initial density which is an improvement on the recent result of Abidi and Gui(2021. for the 2D inhomogeneous incompressible NavierStokes system.

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 {1. sciences Nankai University school of {1. 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 {1. sciences Tianjin Normal UniversityTianjin300387China school of {1. 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

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 {1. 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

Presentation of the Berry-Tabor conjecture in Levy plates

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Chinese Physics B 2024年第10期33卷 240-247页

作者： Chao Li Guo-Lin Hou school of {1. sciences Inner Mongolia UniversityHohhot 010021China

The Berry-Tabor(BT)conjecture is a famous statistical inference in quantum chaos,which not only establishes the spectral fluctuations of quantum systems whose classical counterparts are integrable but can also be used to describe other wave *** this paper,the BT conjecture has been extended to Lévy *** predicted by the BT conjecture,level clustering is present in the spectra of Lévy *** consequence of level clustering is studied by introducing the distribution of nearest neighbor frequency level spacing ratios P(r),which is calculated through the analytical solution obtained by the Hamiltonian *** work investigates the impact of varying foundation parameters,rotary inertia,and boundary conditions on the frequency spectra,and we find that P(r)conforms to a Poisson distribution in all *** reason for the occurrence of the Poisson distribution in the Lévy plates is the independence between modal frequencies,which can be understood through mode functions.

关键词： Berry-Tabor conjecture frequency spectra Hamiltonian approach Lévy plates