Herman's Theory Revisited

We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\delta<\alpha\le1$, is $C^{1+\alpha-\delta}$-smoothly conjugate to a rigid rotation. We also derive the most precise version of Denjoy's inequality for such diffeomorphisms.Comment: 10 page

COVID-19 Antibody Testing as a Precondition for Employment: Ethical and Legal Considerations

Employers and governments are interested in the use of serological (antibody) testing to allow people to return to work before there is a vaccine for SARS-CoV-2. We articulate the preconditions needed for the implementation of antibody testing, including the role of the U.S. Food & Drug Administration

Preventive analgesia and novel strategies for the prevention of chronic post-surgical pain

Chronic post-surgical pain (CPSP) is a serious complication of major surgery that can impair a patient’s quality of life. The development of CPSP is a complex process which involves biologic, psychosocial, and environmental mechanisms that have yet to be fully understood. Currently perioperative pharmacologic interventions aim to suppress and prevent sensitization with the aim of reducing pain and analgesic requirement in acute as well as long-term pain . Despite the detrimental effects of CPSP on patients, the body of literature focused on treatment strategies to reduce CPSP remains limited and continues to be understudied. This article reviews the main pharmacologic candidates for the treatment of CPSP, discusses the future of preventive analgesia, and considers novel strategies to help treat acute postoperative pain and lessen the risk that it becomes chronic. In addition, this article highlights important areas of focus for clinical practice including: multimodal management of CPSP patients, psychological modifiers of the pain experience, and the development of a Transitional Pain Service specifically designed to manage patients at high risk of developing chronic post-surgical pain.HC is supported by a Merit Award (Department of Anaesthesia, University of Toronto) and the STAGE Training Program in Genetic Epidemiology (Canadian Institutes of Health Research, CIHR) and a grant by the Physicians Services Incorporated Foundation. JK is supported by a Canada Research Chair in Health Psychology. The authors of this manuscript have no conflicts of interest to declare

Convergence and Stability of the Inverse Scattering Series for Diffuse Waves

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the serie

Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

On Local Behavior of Holomorphic Functions Along Complex Submanifolds of C^N

In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of \Co^{N}. As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein type inequalities on transcendental curves in \Co^{2}.Comment: minor changes in the formulation and the proof of Lemma 8.

Time Asymmetric Quantum Physics

Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.Comment: Tex file with 2 figure