Asymptotic analytical study of differential equations

A.复域微分方程的渐近分析。Uchiyama证明了一类具有正则奇点的非线性偏微分方程的形式解用主级数法收敛。Ouchi证明了某半线性1^<st>阶奇异PDE形式解的Borel可和性及其在向量场正规形式中的应用，并证明了某PDE形式解的多重可和性。Tahara得到了Fuchsian非线性PDE解的奇异性结构、一阶正规型PDE解奇异性存在的充分必要条件和全特征型非线性PDE解的（非）奇异性和唯一性。实域微分方程的渐近分析及相关分析。Uchiyama证明了2^<和>阶一维p-椭圆方程径向解的局部唯一性，并利用L.Paredes从4^< >阶p-椭圆方程的一维模型中获得了一个具有正则奇异性的非线性偏微分方程候选。Yoshino与M. Suwa对指数型分布进行了刻画，并给出了一些应用结果。Hirata给出了3^<rd>阶非线性偏微分方程的椭圆函数解族的具体表示。Goto做了关于渐近包含的研究。Aoyagi给出了非解析学习机随机复杂度的渐近展开式。

A. Asymptotic analysis of differential equations in complex domain.Uchiyama showed that formal solutions to a certain nonlinear PDE with regular singularity converge by the method of majorant series. Ouchi showed Borel summability of formal solutions to a certain semilinear 1^<st> order singular PDE and its application to normal form of vector fields and multi-summability of formal solution to a certain PDE regarded as perturbation of ODE. Tahara obtained the structure of singularities of solutions to Fuchsian nonlinear PDE, necessary or sufficient conditions for existence of singular solutions to 1St order PDE's of normal type and (non)existence of singularities and uniqueness of solutions to nonlinear PDE of totally characteristic type.B. Asymptotic analysis of differential equations in real domain and related analysis.Uchiyama showed local uniquness of radial solutions to 2^<nd> order one dimensional p-elliptic equations and obtained with L.Paredes a candidate of nonlinear PDEs with regular singularity from one dimensinal model of 4^<th> order p-elliptic equations. Yoshino, with M. Suwa, characterized distribution of exponential type with applications and obtained results on positive definite distribution. Hirata gave a concrete representation of a family of solutions through elliptic functions to 3^<rd> order nonlinear PDE. Goto did reserch on asymptotic inclusion. Aoyagi gave asymptotic expasion of the stochastic comlexity of non-analytic learning machines.