Continuously parametrized Besicovitch sets in R^n

CONVEXITY NUMBERS OF CLOSED SETS IN Rn

Dimension of Besicovitch-eggleston Sets in Countable Symbolic Space

This paper is mainly concerned with Hausdorff dimensions of Besicovitch-Eggleston subsets in countable symbolic space. A notable point is that, the dimension values posses a universal lower bound depending only on the underlying metric. As a consequence of the main results, we obtain Hausdorff dimension formulas for sets of real numbers with prescribed digit frequencies in their Lüroth expansions.

biaccessibility in quadratic julia sets

در این رساله برای چندجمله ای های درجه ی دوم با مجموعه ی ژولیای همبند موضعی; ثابت خواهیم کرد: اندازه برولین مجموعه نقاط از دو سو دست یافتنی در چندجمله ای های درجه دو برابر با صفر است مگر چندجمله ای چبی شف که برابر با یک است. و برای چندجمله ای های درجه دوم با نقاط ثابت خنثی غیر گویا ثابت خواهیم کرد: 1)هر نقطه ی از دو سو دست یافتنی در حالت زیگل نهایتا به نقطه ی بحرانی و در حالت کرمر به نقطه ث...

A New Bound for Finite Field Besicovitch Sets in Four Dimensions

Let F be a finite field with characteristic greater than two. Define a Besicovitch set in F 4 to be a set P ⊆ F 4 containing a line in every direction. The Kakeya conjecture asserts that |P | ≈ |F |. In [19] it was shown that |P | & |F |. In this paper we improve this to |P | ' |F | 1 16 . On the other hand, we show that the bound of |F | is sharp if we relax the assumption that the lines point...

Consistent parameter bounding identification for linearly parametrized model sets

AIrstract--In standard parameter bounding identification a time-domain bound on the noise signal is used to construct parameter bounds. One of the properties of this standard approach is that there is no consistency if a conservative noise bound has been chosen. It is shown that alternative bounds on the noise signal give rise to consistent parameter bounding identification methods; i.e., asymp...