Absence of reflection as a function of the coupling constant

We consider solutions of the one-dimensional equation $-u'' +(Q+ \lambda V) u = 0$ where $Q: \mathbb{R} \to \mathbb{R}$ is locally integrable, $V : \mathbb{R} \to \mathbb{R}$ is integrable with supp$(V) \subset [0,1]$, and $\lambda \in \mathbb{R}$ is a coupling constant. Given a family of solutions $\{u_{\lambda} \}_{\lambda \in \mathbb{R}}$ which satisfy $u_{\lambda}(x) = u_0(x)$ for all $x<0$, we prove that the zeros of $b(\lambda) := W[u_0, u_{\lambda}]$, the Wronskian of $u_0$ and $u_{\lambda}$, form a discrete set unless $V \equiv 0$. Setting $Q(x) := -E$, one sees that a particular consequence of this result may be stated as: if the fixed energy scattering experiment $-u'' + \lambda V u = Eu$ gives rise to a reflection coefficient which vanishes on a set of couplings with an accumulation point, then $V \equiv 0$.Comment: To appear in Journal of Mathematical Physic

Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure

Heat kernel estimates and spectral properties of a pseudorelativistic operator with magnetic field

Based on the Mehler heat kernel of the Schroedinger operator for a free electron in a constant magnetic field an estimate for the kernel of E_A is derived, where E_A represents the kinetic energy of a Dirac electron within the pseudorelativistic no-pair Brown-Ravenhall model. This estimate is used to provide the bottom of the essential spectrum for the two-particle Brown-Ravenhall operator, describing the motion of the electrons in a central Coulomb field and a constant magnetic field, if the central charge is restricted to Z below or equal 86

Connectivity and tree structure in finite graphs

Considering systems of separations in a graph that separate every pair of a given set of vertex sets that are themselves not separated by these separations, we determine conditions under which such a separation system contains a nested subsystem that still separates those sets and is invariant under the automorphisms of the graph. As an application, we show that the $k$-blocks -- the maximal vertex sets that cannot be separated by at most $k$ vertices -- of a graph $G$ live in distinct parts of a suitable tree-decomposition of $G$ of adhesion at most $k$, whose decomposition tree is invariant under the automorphisms of $G$. This extends recent work of Dunwoody and Kr\"on and, like theirs, generalizes a similar theorem of Tutte for $k=2$. Under mild additional assumptions, which are necessary, our decompositions can be combined into one overall tree-decomposition that distinguishes, for all $k$ simultaneously, all the $k$-blocks of a finite graph.Comment: 31 page

The Classification of Obsessive–Compulsive and Related Disorders in the ICD-11

Background To present the rationale for the new Obsessive–Compulsive and Related Disorders (OCRD) grouping in the Mental and Behavioural Disorders chapter of the Eleventh Revision of the World Health Organization’s International Classification of Diseases and Related Health Problems (ICD-11), including the conceptualization and essential features of disorders in this grouping. Methods Review of the recommendations of the ICD-11 Working Group on the Classification for OCRD. These sought to maximize clinical utility, global applicability, and scientific validity. Results The rationale for the grouping is based on common clinical features of included disorders including repetitive unwanted thoughts and associated behaviours, and is supported by emerging evidence from imaging, neurochemical, and genetic studies. The proposed grouping includes obsessive–compulsive disorder, body dysmorphic disorder, hypochondriasis, olfactory reference disorder, and hoarding disorder. Body-focused repetitive behaviour disorders, including trichotillomania and excoriation disorder are also included. Tourette disorder, a neurological disorder in ICD-11, and personality disorder with anankastic features, a personality disorder in ICD-11, are recommended for cross-referencing. Limitations Alternative nosological conceptualizations have been described in the literature and have some merit and empirical basis. Further work is needed to determine whether the proposed ICD-11 OCRD grouping and diagnostic guidelines are mostly likely to achieve the goals of maximizing clinical utility and global applicability. Conclusion It is anticipated that creation of an OCRD grouping will contribute to accurate identification and appropriate treatment of affected patients as well as research efforts aimed at improving our understanding of the prevalence, assessment, and management of its constituent disorders

Mental, behavioral and neurodevelopmental disorders in the ICD-11 : An international perspective on key changes and controversies

The Author(s). 2020Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver(http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.An update of the chapter on Mental, Behavioral and Neurodevelopmental Disorders in the International Classification of Diseases and Related Health Problems (ICD) is of great interest around the world. The recent approval of the 11th Revision of the ICD (ICD-11) by the World Health Organization (WHO) raises broad questions about the status of nosology of mental disorders as a whole as well as more focused questions regarding changes to the diagnostic guidelines for specific conditions and the implications of these changes for practice and research. This Forum brings together a broad range of experts to reflect on key changes and controversies in the ICD-11 classification of mental disorders. Taken together, there is consensus that the WHO's focus on global applicability and clinical utility in developing the diagnostic guidelines for this chapter will maximize the likelihood that it will be adopted by mental health professionals and administrators. This focus is also expected to enhance the application of the guidelines in non-specialist settings and their usefulness for scaling up evidence-based interventions. The new mental disorders classification in ICD-11 and its accompanying diagnostic guidelines therefore represent an important, albeit iterative, advance for the field.Peer reviewedFinal Published versio

On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

We give a variational proof of the existence of infinitely many bound states below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials thus extending the results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007) F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler). Results improved in this versio

Spectral Analysis for Matrix Hamiltonian Operators

In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for the three dimensional cubic equation. Though we focus on a proof of the 3d cubic problem, this work presents a new algorithm for verifying certain spectral properties needed to study soliton stability. Source code for verification of our comptuations, and for further experimentation, are available at http://www.math.toronto.edu/simpson/files/spec_prop_code.tgz.Comment: 57 pages, 22 figures, typos fixe

Imprints of the Quantum World in Classical Mechanics

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless particles is a classical equation which is equivalent to Hamilton's equations.Comment: Paper submitted to Foundations of Physic

Fatally Flawed? : Discursive Evidence from the Movement to Establish Lesbian Studies Programs

While related areas such as Queer Studies and Sexuality Studies have become established as disciplinary formations in North American and British universities, Lesbian Studies has not. This article reports on an analysis of key publications by critics and advocates of Lesbian Studies to explore the possibility that Lesbian Studies was flawed in ways that account for its non-emergence. Charges against Lesbian Studies include naïve essentialism, white middle-classness, separatism, and paranoia. Discourse analysis of books by Lesbian Studies advocates examines evidence of each of these qualities and concludes that Lesbian Studies was above all too lesbian to be successfully integrated into the enduringly heteropatriarchal institution of universities.University of Winnipeghttp://journals.sagepub.com/doi/10.1177/095935351037018