On the building dimension of closed cones and Almgren's stratification principle

In this paper we disprove a conjecture stated in [4] on the equality of two notions of dimension for closed cones. Moreover, we answer in the negative to the following question, raised in the same paper. Given a compact family $\mathcal{C}$ of closed cones and a set $S$ such that every blow-up of $S$ at every point $x\in S$ is contained in some element of $\mathcal{C}$, is it true that the dimension of $S$ is smaller than or equal to the largest dimension of a vector space contained is some element of $\mathcal{C}$

Lusin type theorems for Radon measures

We add to the literature the following observation. If $\mu$ is a singular measure on $\mathbb{R}^n$ which assigns measure zero to every porous set and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a Lipschitz function which is non-differentiable $\mu$-a.e. then for every $C^1$ function $g:\mathbb{R}^n\rightarrow\mathbb{R}$ it holds $$\mu\{x\in\mathbb{R}^n: f(x)=g(x)\}=0.$$ In other words the Lusin type approximation property of Lipschitz functions with $C^1$ functions does not hold with respect to a general Radon measure

Khinchin theorem for interval exchange transformations

We define a diophantine condition for interval exchange transformations (i.e.t.s). When the number of intervals is two, that is for rotations on the circle, our condition coincides with classical Khinchin condition. We prove for i.e.t.s the same dichotomy as in Khinchin Theorem. We also develop several results relating the Rauzy-Veech algorithm with homogeneous approximations for i.e.t.s.Comment: 53 page

Residually many BV homeomorphisms map a null set onto a set of full measure

Let $Q=(0,1)^2$ be the unit square in $\mathbb{R}^2$. We prove that in a suitable complete metric space of $BV$ homeomorphisms $f:Q\rightarrow Q$ with $f_{|\partial Q}=Id$, the generical homeomorphism (in the sense of Baire categories) maps a null set in a set of full measure and vice versa. Moreover we observe that, for $1\leq p<2$, in the most reasonable complete metric space for such problem, the family of $W^{1,p}$ homemomorphisms satisfying the above property is of first category, instead

Teaching Value-based Care: A Framework for a Family Medicine Resident Clinic

Milton Family Practice is home to the University of Vermont’s Family Medicine residency program. As efforts to improve the value of health care increase, graduate medical education accreditation organizations may begin to reward and penalize residency programs based on their commitment to teaching and providing value-based care. Residency programs currently lack a clear strategy to prepare residents to assess and deliver value-based care. In this presentation, I present the VALUE Framework (Patel, Davis, & Lypson 2012) for the University of Vermont Family Medicine residency program to teach residents to assess and deliver value-based care for their patients during preceptor sessions.https://scholarworks.uvm.edu/fmclerk/1329/thumbnail.jp

A Chinese Recipe for Curbing the Evasion of Commodity Taxes?

Verbrauchsteuer, Steuerflucht, China, Consumption tax, Tax evasion, China

The limits to growth then and now

In this paper the indications of the 1972 report of the club of Rome about the relationship between environment and economic growth are reviewed and compared to the ideas debated nowadays on the same topic. The implications of the stages of growth approach and of the economic growth models are considered. Market failure has a central role when the environment is considered. Hence the main problems of policy design and evaluation and their implications for international cooperation, as studied in a burgeoning literature, are presented.