SEEKING FURTHER POSSIBILITIES OF MATHEMATICS

寻求数学的更多可能性

• 批准号: 08304013
• 负责人: YOSHIKAWA Atsushi
• 金额: $ 8.83万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08304013/
• 关键词: Real Analytic Methods; Nonlinear evolution equations; Types and Proof Theory; Cone Manifolds; Hyperbolic Geometries; Hyperplanes Arrangements; Concentration Phenomena; Inverse Problems; 錐多様体; 迷問題; 型図子; 量子アフィン代数; 型・証明論; モーメント写像; 反応拡散系; 非線型発展

Through the present research project, we have obtained fruitful results in the following fields :(1) Applications of methods of real analysis to non-linear evolution equation(2) Theories of types and proofs(3) Cone manifolds and hyperbolic geometry(4) Mathematical arrangements of hyperplanes configurations(5) Concentration phenomena in elliptic and parabolic partial differential equations(6) Mathematical theory of inverse problems and their numerical analysis.Detailed reports (or lecture notes) have been arranged to be published by the Mathematical Society of Japan. That our project did contribute to so many fields conforms to our original objective, firstly, to encourage non-conventional mathematical challenges, promoting small group research sessions (Regional Workshops or RW's), and secondly, thus to assure relevant activities.

通过本研究项目，我们在以下领域取得了丰硕的成果：（1）实分析方法在非线性演化方程中的应用（2）类型与证明理论（3）锥流形与双曲几何（4）超平面构形的数学排列（5）椭圆和抛物型偏微分方程中的集中现象（6）反问题的数学理论及其数值模拟 详细的报告（或讲义）已由日本数学会安排出版。我们的项目确实对如此多的领域做出了贡献，这符合我们最初的目标，首先，鼓励非常规数学挑战，促进小组研究会议（区域研讨会或RW），其次，从而确保相关活动。

项目成果

吉川 敦: "Modulation Equations for planer phases and asymptotic weak solutions" Kyushu Journal of Methemetics. 52-1. 99-148 (1998)

Atsushi Yoshikawa：“平面相位和渐近弱解的调制方程”《九州数学杂志》52-148（1998）。

三輪哲二: "The monodromy matrices of the XYZ model in the infinite volume limit" J.Phys.A.Math.Gen.30. 7509-7523 (1997)

Tetsuji Miwa：“无限体积极限中 XYZ 模型的单向矩阵”J.Phys.A.Math.Gen.30 7509-7523 (1997)。

YOSHIKAWA,A: "Modulation equations for planar phases and asymptotic weak solutions" Kyushu Journal of Mathematics. 52. 99-148 (1998)

YOSHIKAWA,A：“平面相位和渐近弱解的调制方程”九州数学杂志。

YAMAMOTO,M.: "Lipschitz stability in inverse parabolic problems by the Carleman estimate" Inverse Problems. 14. 1229-1245 (1998)

YAMAMOTO,M.：“卡尔曼估计的反抛物线问题中的利普希茨稳定性”反问题。

岡 睦雄: "Geometry of Cuspidal sextics and their dual curves" Proc.Singalarity.Conf.Sapporo. (印刷中). (1998)

Mutsuo Oka：“尖牙六角几何及其对偶曲线”Proc.Singalarity.Conf.Sapporo（正在出版）。