کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4946023 | 1364079 | 2017 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On ramification indices of formal solutions of constructive linear ordinary differential systems
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
هوش مصنوعی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: On ramification indices of formal solutions of constructive linear ordinary differential systems On ramification indices of formal solutions of constructive linear ordinary differential systems](/preview/png/4946023.png)
چکیده انگلیسی
We consider full rank linear ordinary differential higher-order systems whose coefficients are computable power series. It is shown that the algorithmic problems connected with the ramification indices of irregular formal solutions of a given system are mostly undecidable even if we fix a conjectural value r of the ramification index. This enables us to obtain a strengthening of the theorem which has been proven earlier and states that we are not able to compute algorithmically the dimension of the space of all formal solutions although we can construct a basis for the subspace of regular solutions. In fact, it is impossible to compute algorithmically this dimension even if, in addition to the system, we know the list of all values of the ramification indices. However, there is nearby an algorithmically decidable problem: if a system S and integers r, d are such that for S the existence of d linearly independent formal solutions of ramification index r is guaranteed then one can compute such d solutions of S.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 79, Part 2, MarchâApril 2017, Pages 475-481
Journal: Journal of Symbolic Computation - Volume 79, Part 2, MarchâApril 2017, Pages 475-481
نویسندگان
S.A. Abramov,