A note on the fractional perimeter and interpolation

We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter and the Hausdorff content and implies several known inequalities involving the Gagliardo seminorm of the Sobolev spaces $W^{\alpha, 1}$ of order $0 < \alpha < 1$

Unlikely Estimates of the Ex Ante Real Interest Rate: Another Dismal Performance from the Dismal Science1

The ex ante real rate of interest is one of the most important concepts in economics and finance. Because the universally-used Fisher theory of interest requires positive ex ante real interest rates, empirical estimates of the ex ante real interest rate derived from the Fisher theory of interest should also be positive. Unfortunately, virtually all estimates of the ex ante real interest rate published in economic journals and textbooks or used in macroeconomic models and policy discussions for the past 35 years contain negative values for extended time periods and, thus, are theoretically flawed. Moreover, the procedures generally used to estimate ex ante real interest rates were shown to produce biased estimates of the ex ante real rate over 30 years ago. In this article, we document this puzzling chasm between the Fisherian theory that mandates positive ex ante real interest rates and the practice of macroeconomists who generate and use ex ante real interest rate estimates that violate this theory. We explore the reasons that this problem exists and assess some alternative approaches for estimating the ex ante real interest rate to determine whether they might resolve this problem.ex ante real interest rate, Fisher theory of interest, biased real interest rate estimates

Applications of Partial Supersymmetry

I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of this theory. This method reveals an intriguing equivalence between two formulations of this theory, one of which is one-dimensional, and the other of which is infinite-dimensional. Second, I demonstrate the use of partial supersymmetry as a tool to obtain the asymptotic energy levels in non-relativistic quantum mechanics in an exceptionally easy way. In the end, I discuss possible extensions of this work, including the possible connections between partial supersymmetry and renormalization group arguments.Comment: 11 pages, harvmac, no figures; typo corrected in identifying info on title pag

Contributory Negligence of Automobile Passengers

What is the duty of a passenger when the auto in which he is riding is approaching a railroad crossing, or an intersection, or when the auto is going at an excessive rate of speed, or if the driver is intoxicated? When does the passenger have a duty to remonstrate with the driver and when may he rely on the skill and care of the driver? May the contributory negligence of the driver be imputed to the passenger? Note that this article deals with contributory negligence as such, and does not attempt to distinguish between results in guest statute or non-guest-statute situations

Contributory Negligence of Automobile Passengers

What is the duty of a passenger when the auto in which he is riding is approaching a railroad crossing, or an intersection, or when the auto is going at an excessive rate of speed, or if the driver is intoxicated? When does the passenger have a duty to remonstrate with the driver and when may he rely on the skill and care of the driver? May the contributory negligence of the driver be imputed to the passenger? Note that this article deals with contributory negligence as such, and does not attempt to distinguish between results in guest statute or non-guest-statute situations

A decomposition by non-negative functions in the Sobolev space Wk,1W^{k, 1}

We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space $W^{k,1}(\mathbb{R}^d)$ as the difference of two non-negative functions in the same space with control of their norms