The Buffon's needle problem for random planar disk-like Cantor sets

On the Dimension of Deterministic and Random Cantor-like Sets

Buffon’s needle estimates for rational product Cantor sets

Let S∞ = A∞ × B∞ be a self-similar product Cantor set in the complex plane, defined via S∞ = ⋃L j=1 Tj(S∞), where Tj : C→ C have the form Tj(z) = 1 Lz+zj and {z1, . . . , zL} = A+iB for some A,B ⊂ R with |A|, |B| > 1 and |A||B| = L. Let SN be the L−N -neighbourhood of S∞, or equivalently (up to constants), its N -th Cantor iteration. We are interested in the asymptotic behaviour as N → ∞ of the...

Recent progress on Favard length estimates for planar Cantor sets

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Random Intersections of Thick Cantor Sets

Let C1, C2 be Cantor sets embedded in the real line, and let τ1, τ2 be their respective thicknesses. If τ1τ2 > 1, then it is well known that the difference set C1 − C2 is a disjoint union of closed intervals. B. Williams showed that for some t ∈ int(C1−C2), it may be that C1∩ (C2 + t) is as small as a single point. However, the author previously showed that generically, the other extreme is tru...