Differential Galois theory III: Some inverse problems
نویسندگان
چکیده
منابع مشابه
global results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Differential Galois Theory
The aim of the talk is to explain how to make these statements precise and prove them, using differential Galois theory. The reference to all of the material here is [vdPS03]. By solving a differential equation we mean obtaining a solution via a finite number of operations of the following kind (starting with a rational function): • Adding a function algebraic over the functions we already have...
متن کاملDifferential Galois Theory
Differential Galois Theory is a branch of abstract algebra that studies fields equipped with a derivation function. In much the same way as ordinary Galois Theory studies field extensions generated by solutions of polynomials over a base field, differential Galois Theory studies differential field extensions generated by solutions to differential equations over a base field. In this paper, we w...
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Assuming the generalized Riemann hypothesis, we prove the following complexity bounds: The order of the Galois group of an arbitrary polynomial f(x) ∈ Z[x] can be computed in P#P. Furthermore, the order can be approximated by a randomized polynomial-time algorithm with access to an NP oracle. For polynomials f with solvable Galois group we show that the order can be computed exactly by a random...
متن کاملNotes on Galois Theory III
Clearly F ≤ EH ≤ E. On the other hand, given an intermediate field K between F and E, i.e. a subfield of E containing F , so that F ≤ K ≤ E, we can define Gal(E/K) and Gal(E/K) is clearly a subgroup of Gal(E/F ), since if σ(a) = a for all a ∈ K, then σ(a) = a for all a ∈ F . Thus we have two constructions: one associates an intermediate field to a subgroup of Gal(E/F ), and the other associates...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1997
ISSN: 0019-2082
DOI: 10.1215/ijm/1255985739