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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 coefficients.Eremenko 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 C.Examples 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

Competitive Resource Allocation Among Urban Congestion Areas in a Modern Big City

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Journal of the Operations research Society of China 2024年第1期12卷 133-153页

作者： Alexander Krylatov Anastasiya Raevskaya Institute of Applied mathematical research of the Karelian research centre of the Russian Academy of sciences Petrozavodsk185910Russia Saint Petersburg State University Saint Petersburg199034Russia

The continuing growth of modern big cities leads to their spatial expansion and the emergence of new road connections and urban areas.Areas where large transportation flows of pedestrians,passengers,and drivers come together create demand points,which attract business companies that strive to allocate their resources in the most sought-after places.However,the law of supply and demand restrains companies from allocating all their resources solely in the most popular congestion areas since the more valuable an urban area,the higher the cost to be paid for a resource unit allocation there.As a result,companies act in a non-cooperative manner and try to minimize their own overall costs when allocating resources across available commercial areas in a big city.Non-cooperative behavior of companies leads to the problem of Nash equilibrium search in the game of competing entrepreneurs.In this paper,we study the corresponding resource allocation game under affine cost functions and obtain Nash equilibrium strategies in explicit form.These findings allow us to develop a simple procedure for computing Nash equilibria in the game of companies allocating their resources among urban congestion areas.The computational study demonstrates the dependence of the average price for resource allocation on the number of players and their resource volumes.The outcome of the paper contributes to flow theory and seems to be fresh and useful for managers.

关键词： Resource allocation Nash equilibrium Affine costs

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

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Chinese Annals of Mathematics,Series B 2024年第3期45卷 413-440页

作者： Yachun LI Zhaoyang SHANG Chenmu WANG Liang ZHAO School of mathematical sciences CMA-ShanghaiMOE-LSC and SHL-MACShanghai Jiao Tong University School of Finance Shanghai Lixin University of Accounting and Finance School of mathematical sciences Shanghai Jiao Tong University School of mathematical sciences Harbin Engineering University mathematical Modelling&Data Analytics Center Oxford Suzhou Centre for Advanced Research

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics(MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Ampe`re law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.

关键词： Planar MHD equations Relaxation limits Global convergence Stream function 35B25 35L45 35K45 76W05

On asymptotic stability of the 3D Boussinesq equations without heat conduction

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Science China Mathematics 2024年第2期67卷 253-280页

作者： Lihua Dong Yongzhong Sun School of physical and mathematical sciences Nanjing Tech UniversityNanjing 211816China Department of Mathematics Nanjing UniversityNanjing 210093China

We investigate the asymptotic stability of the solutions to Boussinesq equations without heat conduction with the initial data near a specific stationary solution in the three-dimensional domain Ω=R^(2)×(0,1).It is shown that the solution starting from a small perturbation to the stationary solution converges to it with explicit algebraic rates as time tends to infinity.

关键词： Boussinesq equations stationary solutions asymptotic stability decay rates

Trace inequalities, isocapacitary inequalities, and regularity of the complex Hessian equations

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Science China Mathematics 2024年第3期67卷 557-576页

作者： Jiaxiang Wang Bin Zhou Beijing International Center for mathematical research Peking UniversityBeijing 100871China School of mathematical sciences Peking UniversityBeijing 100871China

In this paper, we study the relations between trace inequalities(Sobolev and Moser-Trudinger types), isocapacitary inequalities, and the regularity of the complex Hessian and Monge-Amp`ere equations with respect to a general nonnegative Borel measure. We obtain a quantitative characterization for these relations through the properties of the capacity-minimizing functions.

关键词： complex Monge-Ampère equations plurisubharmonic functions Sobolev inequality Moser-Trudinger inequality

Color-kinematics duality and dual conformal symmetry for a four-loop form factor in N=4 SYM

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Science China(Physics,Mechanics & Astronomy) 2024年第4期67卷 64-71页

作者： Guanda Lin Gang Yang Siyuan Zhang CAS Key Laboratory of Theoretical Physics Institute of Theoretical PhysicsChinese Academy of SciencesBeijing 100190China School of physical sciences University of Chinese Academy of SciencesBeijing 100049China School of Fundamental Physics and mathematical sciences Hangzhou Institute for Advanced StudyUCASHangzhou 310024China International centre for Theoretical Physics Asia-Pacific Beijing/Hangzhou 310024China

We obtain the integrand of full-color four-loop three-point form factor of the stress-tensor supermultiplet in N=4 SYM,based on the color-kinematics(CK)duality and generalized unitarity method.Our result not only manifests all dual Jacobi relations via CK duality but also contains 133 free parameters.This suggests the constructibility of the form factor at even higher loops via CK duality.We also find that the planar form factor has a hidden dual conformal symmetry in the lightlike limit of the operator momentum,which is checked up to four loops.

关键词： S-matrix supersymmetric model perturbative calculations

Achieving high-performance sodium metal anodes: From structural design to reaction kinetic improvement

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Nano research 2024年第3期17卷 1288-1312页

作者： Jing Xu Jianhao Yang Yashuang Qiu Yang Jin Tianyi Wang Bing Sun Guoxiu Wang research Center of Grid Energy Storage and Battery Application School of Electrical and Information EngineeringZhengzhou UniversityZhengzhou 450001China College of Chemistry and Chemical Engineering Yangzhou University Yangzhou 225009China centre for Clean Energy Technology School of Mathematical and Physical SciencesFaculty of ScienceUniversity of Technology SydneyUltimoNSW 2007Australia

Sodium metal is one of the ideal anodes for high-performance rechargeable batteries because of its high specific capacity(~1166 mAh·g^(-1)),low reduction potential(-2.71 V compared to standard hydrogen electrodes),and low cost.However,the unstable solid electrolyte interphase,uncontrolled dendrite growth,and inevitable volume expansion hinder the practical application of sodium metal anodes.At present,many strategies have been developed to achieve stable sodium metal anodes.Here,we systematically summarize the latest strategies adopted in interface engineering,current collector design,and the emerging methods to improve the reaction kinetics of sodium deposition processes.First,the strategies of constructing protective layers are reviewed,including inorganic,organic,and mixed protective layers through electrolyte additives or pretreatments.Then,the classification of metal-based,carbon-based,and composite porous frames is discussed,including their function in reducing local deposition current density and the effect of introducing sodiophilic sites.Third,the recent progress of alloys,nanoparticles,and single atoms in improving Na deposition kinetics is systematically reviewed.Finally,the future research direction and the prospect of high-performance sodium metal batteries are proposed.

关键词： sodium metal anodes interface engineering current collector design reaction kinetics sodium deposition processes

Data-Driven Direct Adaptive Risk-Sensitive Control of Stochastic Systems

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Journal of Systems Science & Complexity 2024年第4期37卷 1446-1469页

作者： QIAO Nan LI Tao School of mathematical sciences East China Normal University Shanghai Key Laboratory of Pure Mathematics and mathematical Practice School of Mathematical SciencesEast China Normal University

The authors propose a data-driven direct adaptive control law based on the adaptive dynamic programming(ADP) algorithm for continuous-time stochastic linear systems with partially unknown system dynamics and infinite horizon quadratic risk-sensitive indices. The authors use online data of the system to iteratively solve the generalized algebraic Riccati equation(GARE) and to learn the optimal control law directly. For the case with measurable system noises, the authors show that the adaptive control law approximates the optimal control law as time goes on. For the case with unmeasurable system noises, the authors use the least-square solution calculated only from the measurable data instead of the real solution of the regression equation to iteratively solve the GARE. The authors also study the influences of the intensity of the system noises, the intensity of the exploration noises, the initial iterative matrix, and the sampling period on the convergence of the ADP algorithm.Finally, the authors present two numerical simulation examples to demonstrate the effectiveness of the proposed algorithms.

关键词： Adaptive dynamic programming direct adaptive control generalized algebraic Riccati equation risk-sensitive control

Design consideration of phthalocyanines as sensitizers for enhanced sono-photodynamic combinatorial therapy of cancer

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Acta Pharmaceutica Sinica B 2024年第3期14卷 1077-1097页

作者： Lindokuhle Cindy Nene Heidi Abrahamse Laser research centre Faculty of Health SciencesUniversity of JohannesburgDoornfontein 2028South Africa

Cancer remains one of the diseases with the highest incidence and mortality globally.Conventional treatment modalities have demonstrated threatening drawbacks including invasiveness,noncontrollability,and development of resistance for some,including chemotherapy,radiation,and surgery.Sono-photodynamic combinatorial therapy(SPDT)has been developed as an alternative treatment modality which offers a non-invasive and controllable therapeutic approach.SPDT combines the mechanism of action of sonodynamic therapy(SDT),which uses ultrasound,and photodynamic therapy(PDT),which uses light,to activate a sensitizer and initiate cancer eradication.The use of phthalocyanines(Pcs)as sensitizers for SPDT is gaining interest owing to their ability to induce intracellular oxidative stress and initiate toxicity under SDT and PDT.This review discusses some of the structural prerequisites of Pcs which may influence their overall SPDT activities in cancer therapy.

关键词： Sonodynamic therapy Photodynamic therapy Combinatorial therapy Phthalocyanines Sensitizer Cancer