On regular tangent covectors, regular differential forms, and smooth vector fields on a differential space

Differential Arcs and Regular Types in Differential Fields

We introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety is determined by its arcs at a point. Using differential arcs, we show that if (K,+,×, δ1, . . . , δn) is a differentially closed field of characteristic zero with n commuting derivations and p ∈ S(K) is a regular type over K, then either p is locally modular or there is a definable ...

Cohomology of regular differential forms for affine curves

Let C be a complex affine reduced curve, and denote by H1(C) its first truncated cohomology group, i.e. the quotient of all regular differential 1-forms by exact 1-forms. First we introduce a nonnegative invariant μ(C, x) that measures the complexity of the singularity of C at the point x, and we establish the following formula: dim H(C) = dim H1(C) + ∑

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...

On Regular and Logarithmic Solutions of Ordinary Linear Differential Systems

Metrically Regular Differential Generalized Equations

In this paper we consider a control system coupled with a generalized equation, which we call Differential Generalized Equation (DGE). This model covers a large territory in control and optimization, such as differential variational inequalities, control systems with constraints, as well as necessary optimality conditions in optimal control. We study metric regularity and strong metric regulari...