SUSY transformation of the Green function and a trace formula

An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuous spectra. It is shown that when the continuous spectrum is present the trace of the difference of the Green functions for SUSY partners is a finite quantity which may or may not be equal to zero despite the divergence of the traces of each Green function. Our findings are illustrated by using the free particle example considered both on the whole real line and on a half line

Tuberculosis: through the artist’s eye

The history of medicine and art have intersected at several instances over time. Centuries ago, even when many diseases were obscure, art has shed some light over early clinical features and signs of many diseases. This article describes Leonardo Da Vinci’s famous sketch, “The Five Grotesque Heads” and highlights the hints of reference to the age-old infection of tuberculosis. Da vinci’s eye for detail has been known to capture several startling anatomical and pathological features of diseases, which were largely unknown at his time. However, these subtle references give us insight into the clinical presentation of the timeless disease of tuberculosis through the ages

Second Order Darboux Displacements

The potentials for a one dimensional Schroedinger equation that are displaced along the x axis under second order Darboux transformations, called 2-SUSY invariant, are characterized in terms of a differential-difference equation. The solutions of the Schroedinger equation with such potentials are given analytically for any value of the energy. The method is illustrated by a two-soliton potential. It is proven that a particular case of the periodic Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the corresponding Schroedinger equation equation are found for any value of the energy. A simple analytic expression for a family of two-gap potentials is derived

On an error term related to the Jordan totient function Jk(n)

AbstractWe investigate the error terms Ek(x)=∑n⩽xJk(n)−xk+1(k+1)ζ(k+1) for k⩾2, where Jk(n) = nkΠp|n(1 − 1pk) for k ≥ 1. For k ≥ 2, we prove ∑n⩽xEk(n)∼xk+12(k+1)ζ(k+1). Also, lim infn→∞Ek(x)xk⩽Dζ(k+1), where D = .7159 when k = 2, .6063 when k ≥ 3. On the other hand, even though lim infn→∞Ek(x)xk⩽−12ζ(k+1), Ek(n) > 0 for integers n sufficiently large

Connection between the Green functions of the supersymmetric pair of Dirac Hamiltonians

The Sukumar theorem about the connection between the Green functions of the supersymmetric pair of the Schr\"odinger Hamiltonians is generalized to the case of the supersymmetric pair of the Dirac Hamiltonians.Comment: 12 pages,Latex, no figure

Shoulder pain and disability index: its effectiveness and reliability in an outpatient setting in Indian population

Background: One of the most common joints to be treated in the clinic is the shoulder joint. An orthopedic surgeon and physical therapists should be knowledgeable about the proper assessment of the shoulder joint to effectively evaluate and design a treatment program in shoulder pathologies. Shoulder pain and disability index (SPADI) is a questionnaire designed to measure pain and disability associated with shoulder pathologies in a clinical setting. SPADI’s effectiveness as a tool needed to be validated in Indian population hence this study. The objectives of this study were to measure effectiveness of SPADI in our setting and to measure the reliability and acceptability of SPADI in Indian population.Methods: 60 patients with shoulder pain between the age of 25-50 years who attended the orthopaedic OPD during the time period of April 2017 to April 2018 were included. The subjects were evaluated with SPADI and oxford shoulder score (OSS) questionnaires. The data was analyzed by paired sample T test and alpha coefficient level.Results: The data statistically analysed revealed that the scales are reliable as the Cronbach's alpha was high (>0.7) and was effective to measure the pain and disability of the shoulder joint in our clinical set up.Conclusions: It can be concluded from our statistical analysis that both SPADI and OSS are equally effective tools in measuring pain and disability in our clinical set up, the only difference being that SPADI is operationally very simple and lucid for our population

How the timing of police evidence disclosure impacts custodial legal advice

Presently, the police in England and Wales disclose their evidence at different points during the arrest and detention of a suspect. While the courts have not objected to this, past field research suggests that lawyers can only advise their clients accurately when the police disclose their evidence before the police interview. To examine this from a law – psychology perspective, we recruited 100 criminal defence lawyers to participate in an online study. Lawyers read fictional scenarios and provided custodial legal advice to a hypothetical client (Christopher) when given either pre-interview disclosure or disclosure at various points during the police interview (early, gradually, or late). Lawyers given pre-interview disclosure provided considerably more informed legal advice compared to those who were only provided with disclosure during the hypothetical police interview. Using an interdisciplinary approach, this paper provides further evidence that pre-interview disclosure is essential for lawyers to deliver case-specific legal advice to suspects