Badly approximable vectors on a vertical Cantor set

For $i, j > 0, i + j = 1$, the set of badly approximable vectors with weight $(i, j)$ is defined by $Bad(i, j) = \{(x, y) \in \R^2 : \exists c > 0 \forall q\in\N, \;\; \max\{q||qx||^{1/i}, q||qy||^{1/j} \} > c\}$, where $||x||$ is the distance of $x$ to the nearest integer. In 2010 Badziahin-Pollington-Velani solved Schmidt's conjecture which was stated in 1982, proving that $Bad(i, j) \cap Bad(j, i)$ is nonempty. Using Badziahin-Pollington-Velani's technique with reference to fractal sets, we were able to improve their results: Assume that we are given a sequence $(i_t, j_t)$ with $i_t, j_t > 0, i_t + j_t = 1$. Then, the intersection of $Bad(i_t, j_t)$ over all t is nonempty

Experimental Studies of Electroweak Physics

Some experimental new Electroweak physics results measured at the LEP/SLD and the TEVATRON are discussed. The excellent accuracy achieved by the experiments still yield no significant evidence for deviation from the Standard Model predictions, or signal to physics beyond the Standard Model. The Higgs particle still has not been discovered and a low bound is given to its mass.Comment: 10 pages, 5 figures, Invited talk at "Fundemental Particles and Interactions", Vanderbilt University, Nashville, Tennessee, May 199

In for a Penny, or: If You Disapprove of Investment Migration, Why Do You Approve of High-Skilled Migration?

While many argue investment-based criteria for immigration are wrong or at least problematic, skill-based criteria remain relatively uncontroversial. This is normatively inconsistent. This article assesses three prominent normative objections to investment-based selection criteria for immigrants: that they wrongfully discriminate between prospective immigrants that they are unfair, and that they undermine political equality among citizens. It argues that either skill-based criteria are equally susceptible to these objections, or that investment-based criteria are equally shielded from them. Indeed, in some ways investment-based criteria are less normatively problematic than skill-based criteria. Given this analysis, the resistance to investment-based migration criteria, but not to skill-based criteria, is inconsistent