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The Monsky Matrices and Non-congruent Numbers

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Algebra Colloquium 2024年第2期31卷 239-262页

作者： Guilin Li Hourong Qin Fei Xu department of mathematics Nanjing UniversityNanjing 210093China 不详

We give some sufficient conditions for non-congruent numbers in terms of the Monsky *** known criteria for non-congruent numbers can be viewed as special cases of our results.

关键词： congruent elliptic curve Selmer group Monsky matrix non-congruent number

Ambarzumyan's Theorem for the Dirac Operator on Equilateral Tree Graphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 568-576页

作者： Dong-Jie WU Xin-Jian XU Chuan-Fu YANG department of mathematics School of Mathematics and StatisticsNanjing University of Science and TechnologyNanjing 210094China

The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x∈[0,π].In this work,the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree *** prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case,then the potential is identically zero.

关键词： dirac operator quantum graph Ambarzumyan’s theorem inverse spectral problem

A KAM theorem for 2-dimensional nonlinear Schrodinger equations with forcing terms and(2p+1)-nonlinearities

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Frontiers of mathematics in China 2024年第2期19卷 75-100页

作者： Shuaishuai XUE School of mathematics Nanjing Audit UniversityNanjing 211815China

In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+φ_(2)(ω_(2)+t)|u|^(2p)u=0,t∈R,x∈T^(2) under periodic boundary conditions. As a result, the existence of a Whitneysmooth family of small-amplitude reducible quasi-periodic solutions is obtained.

关键词： Schrodinger equation reducible KAM tori small divisor quasi-periodic solution

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

A Geometric Based Connection between Fractional Calculus and Fractal Functions

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Acta Mathematica Sinica,English Series 2024年第2期40卷 537-567页

作者： Yong Shun LIANG Wei Yi SU School of mathematics and Statistic Nanjing University of Science and TechnologyNanjing 210094P.R.China department of mathematics Nanjing UniversityNanjing 210023P.R.China

Establishing the accurate relationship between fractional calculus and fractals is an important research content of fractional calculus *** the present paper,we investigate the relationship between fractional calculus and fractal functions,based only on fractal dimension *** dimension of the Riemann-Liouville fractional integral of continuous functions seems no more than fractal dimension of functions *** fractal dimension of the Riemann-Liouville fractional differential of continuous functions seems no less than fractal dimension of functions themselves when they *** further discussion,fractal dimension of the Riemann-Liouville fractional integral is at least linearly decreasing and fractal dimension of the Riemann-Liouville fractional differential is at most linearly increasing for the Holder continuous *** about other fractional calculus,such as the Weyl-Marchaud fractional derivative and the Weyl fractional integral has also been given *** work is helpful to reveal the mechanism of fractional calculus on continuous *** the same time,it provides some theoretical basis for the rationality of the definition of fractional *** is also helpful to reveal and explain the internal relationship between fractional calculus and fractals from the perspective of geometry.

关键词： Fractional calculus fractal functions fractal dimension fractional calculus equation relationship

Pion-photon and kaon-photon transition distribution amplitudes in the Nambu–Jona-Lasinio model

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Chinese Physics C 2024年第8期48卷 94-103页

作者： Jin-Li Zhang Jun Wu department of mathematics and Physics Nanjing Institute of TechnologyNanjing 211167China National Laboratory of Solid State Microstructures Department of PhysicsNanjing UniversityNanjing 210093China

The Nambu–Jona-Lasinio model is utilized to investigate the pion-and kaon-photon leading-twist transition distribution amplitudes using proper time ***,the properties of the vector and axial vector pion-photon transition distribution amplitudes are examined,and the results meet the desired *** study involves sum rule and polynomiality *** vector and axial vector pion-photon transition form factors that are present in theπ^(+)→γe^(+)νprocess are the first Mellin moments of the pion-photon transition distribution *** vector transition form factor originates from the internal structure of hadrons,the axial current can be coupled to a pion,this pion is virtual,and its contribution will be present independently of the external *** kaon transition form factors are *** vector form factor's value at zero momentum transfer is determined by the axial anomaly,while this is not the case for the axial *** vector and axial form factors,as well as the neutral pion vector form factor F_(πγγ)(t),are *** to our findings,the pion axial transition form factor is harder than the vector transition form factor and harder than the electromagnetic form *** also discuss the link betweenπ−γandγ−πtransitions distribution amplitudes.

关键词： transition form factors NJL model transition distribution amplitudes

∞-Tilting Subcategories in Extriangulated Categories

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Chinese Annals of mathematics,Series B 2024年第1期45卷 151-160页

作者： Zhen ZHANG Jiaqun WEI Shance WANG department of mathematics Qilu Normal UniversityJinan 250200China Institution of mathematics School of Mathematics ScienceNanjing Normal UniversityNanjing 210023China

In this paper, the authors introduce a new definition of ∞-tilting(resp. cotilting) subcategories with infinite projective dimensions(resp. injective dimensions) in an extriangulated category. They give a Bazzoni characterization of ∞-tilting(resp. cotilting)subcategories. Also, they obtain a partial Auslander-Reiten correspondence between ∞-tilting(resp. cotilting) subcategories and coresolving(resp. resolving) subcategories with an E-projective generator(resp. E-injective cogenerator) in an extriangulated category.

关键词： Extriangulated category ∞-Tilting subcategory Auslander-Reiten correspondence Bazzoni characterization

Proof of Two Supercongruences of Truncated Hypergeometric Series_(4)F_(3)

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1015-1028页

作者： Guo Shuai MAO department of mathematics Nanjing University of Information Science and TechnologyNanjing 210044P.R.China

In this paper,we prove two supercongruences conjectured by Z.-*** via the Wilf-Zeilberger *** of them is,for any prime p>3,4F3[7/6 1/2 1/2 1/2 1/6 1 1]-1/8]-1/2≡p(-2/p)+p^(3)/4(2/p)Ep-3 (mod p^(4))where(·/p)stands f... 详细信息

关键词： Supercongruence truncated hypergeometric series Wilf–Zeilberger method Euler numbers Legendre symbol

Asymptotics for the joint tail probability of bidimensional randomly weighted sums with applications to insurance

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Science China mathematics 2024年第1期67卷 163-186页

作者： Yang Yang Shaoying Chen Kam Chuen Yuen School of Statistics and Data Science Nanjing Audit UniversityNanjing 211815China department of Statistics and Actuarial Science The University of Hong KongHong Kong 999077China

This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually *** two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence *** applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.

关键词： asymptotic joint tail behavior randomly weighted sum heavy-tailed distribution dependence insurance risk model

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