Effective definability of Kolchin polynomials

KOLCHIN SEMINAR IN DIFFERENTIAL ALGEBRA Differential Dimension Polynomials

An Effective Lojasiewicz Inequality for Real Polynomials

Example 1. Set f1 = x d 1 and fi = xi−1 − x d i for i = 2, . . . , n. Then Φ(x) := maxi{|fi(x)|} > 0 for x 6= 0. Let p(t) = (t d , t n−2 , . . . , t). Then limt→0 ||p(t)||/|t| = 1 and Φ(p(t)) = t d . Thus the Lojasiewicz exponent is ≥ d. (In fact it equals d.) This works both over R and C. In the real case set F = ∑ f 2 i . Then degF = 2d, F has an isolated real zero at the origin and the Lojas...

Effective identifiability criteria for tensors and polynomials

A tensor T , in a given tensor space, is said to be h-identifiable if it admits a unique decomposition as a sum of h rank one tensors. A criterion for h-identifiability is called effective if it is satisfied in a dense, open subset of the set of rank h tensors. In this paper we give effective h-identifiability criteria for a large class of tensors. We then improve these criteria for some symmet...

investigation of effective parameters on the rigidity of light composite diaphragms (psscb) by fem

در این رساله با معرفی سقف های psscb متشکل از ترکیب ورق های فولادی ذوزنقه ای و تخته های سیمانی الیافی به عنوان سقف های پیش ساخته (سازگار با سیستم سازه ای قاب های فولادی سبک) به بررسی پارامترهای موثر بر صلبیت سقف، پرداخته می شود. در تحقیق حاضر ابتدا به مدل سازی دو نمونه سقف آزمایش شده، به روش اجزاء محدود با استفاده از نرم افزار تحلیلی abaqus ver 6.10 پرداخته شده است. نمونه های ساخته شده تحت اعما...

Delta1-Definability

Boban Veli ckovi c y Jensen's Coding Theorem provides a method for making a class of ordinals 2-deenable in a real. In this paper we explore the possibility of obtaining a 1-deenition. While this is not possible in general, we show that by assuming enough condensation, a class can be made 1 in a real parameter in a class-generic extension. Our main application is the following. Theorem There is...