Local-global principles for homogeneous spaces over some two-dimensional geometric global fields

Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains

— Let R be a 2-dimensional normal excellent henselian local domain in which 2 is invertible and let L and k be its fraction field and residue field respectively. Let ΩR be the set of rank 1 discrete valuations of L corresponding to codimension 1 points of regular proper models of Spec R. We prove that a quadratic form q over L satisfies the local-global principle with respect to ΩR in the follo...

Two-dimensional global manifolds of vector fields.

We describe an efficient algorithm for computing two-dimensional stable and unstable manifolds of three-dimensional vector fields. Larger and larger pieces of a manifold are grown until a sufficiently long piece is obtained. This allows one to study manifolds geometrically and obtain important features of dynamical behavior. For illustration, we compute the stable manifold of the origin spirall...

Algebraic Homogeneous Spaces over Fields of Characteristic Two

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...

Quadratic Forms over Global Fields

1. The Hasse Principle(s) For Quadratic Forms Over Global Fields 1 1.1. Reminders on global fields 1 1.2. Statement of the Hasse Principles 2 2. The Hasse Principle Over Q 3 2.1. Preliminary Results: Reciprocity and Approximation 3 2.2. n ≤ 1 6 2.3. n = 2 6 2.4. n = 3 6 2.5. n = 4 8 2.6. n ≥ 5 9 3. The Hasse Principle Over a Global Field 9 3.1. n = 2 10 3.2. n = 3 10 3.3. n = 4 11 3.4. n ≥ 5 12...