s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions

We examine the zero-range limit of the finite square well in arbitrary dimensions through a systematic analysis of the reduced, s-wave two-body time-independent Schr\"odinger equation. A natural consequence of our investigation is the requirement of a delta-function multiplied by a regularization operator to model the zero-range limit of the finite-square well when the dimensionality is greater than one. The case of two dimensions turns out to be surprisingly subtle, and needs to be treated separately from all other dimensions

Changes in pain-related beliefs, coping, and catastrophizing predict changes in pain intensity, pain interference, and psychological functioning in individuals with myotonic muscular dystrophy and facioscapulohumeral dystrophy

The primary aim of this study was to test hypothesized associations between changes in psychological variables (i.e., pain beliefs, catastrophizing and coping strategies) and changes in pain intensity and related adjustment (i.e., pain interference and psychological functioning) in individuals with Myotonic Muscular Dystrophy (MMD) and Facioscapulohumeral Muscular Dystrophy (FSHD). Methods: A sample of 107 adults with a diagnosis of MMD or FSHD, reporting pain in the past three months, completed assessments at two time-points, separated by about 24 months. Results showed that changes in pain-related psychological variables were significantly associated with changes in psychological functioning, pain intensity and pain interference. Specifically, increases in the belief that emotion influences pain, and catastrophizing were associated with decreases in psychological functioning. Increases in the coping strategies of asking for assistance and resting, and the increases of catastrophizing were associated with increases in pain intensity. Finally, increases in pain intensity and asking for assistance were associated with increases in pain interference. Discussion: The results support the utility of the biopsychosocial model of pain for understanding pain and its impact in individuals with MMD or FSHD. These findings may inform the design and implementation of psychosocial pain treatments for people with muscular dystrophy and chronic pain

Towards an Ashtekar formalism in eight dimensions

We investigate the possibility of extending the Ashtekar theory to eight dimensions. Our approach relies on two notions: the octonionic structure and the MacDowell-Mansouri formalism generalized to a spacetime of signature 1+7. The key mathematical tool for our construction is the self-dual (antiself-dual) four-rank fully antisymmetric octonionic tensor. Our results may be of particular interest in connection with a possible formulation of M-theory via matroid theory.Comment: 15 pages, Latex, minor changes, to appear in Class. Quantum Gra

Shape invariance approach to exact solutions of the Klein-Gordon equation

Using the shape invariance property we obtain exact solutions of the (1+1)dimensional Klein-Gordon equation for certain types of scalar and vector potentials. We also discuss the possibility of obtaining real energy spectrum with non-Hermitian interaction within this framework

Altered expression of the voltage-gated calcium channel subunit α2δ-1: a comparison between two experimental models of epilepsy and a sensory nerve ligation model of neuropathic pain.

The auxiliary α2δ-1 subunit of voltage-gated calcium channels is up-regulated in dorsal root ganglion neurons following peripheral somatosensory nerve damage, in several animal models of neuropathic pain. The α2δ-1 protein has a mainly presynaptic localization, where it is associated with the calcium channels involved in neurotransmitter release. Relevant to the present study, α2δ-1 has been shown to be the therapeutic target of the gabapentinoid drugs in their alleviation of neuropathic pain. These drugs are also used in the treatment of certain epilepsies. In this study we therefore examined whether the level or distribution of α2δ-1 was altered in the hippocampus following experimental induction of epileptic seizures in rats, using both the kainic acid model of human temporal lobe epilepsy, in which status epilepticus is induced, and the tetanus toxin model in which status epilepticus is not involved. The main finding of this study is that we did not identify somatic overexpression of α2δ-1 in hippocampal neurons in either of the epilepsy models, unlike the upregulation of α2δ-1 that occurs following peripheral nerve damage to both somatosensory and motor neurons. However, we did observe local reorganisation of α2δ-1 immunostaining in the hippocampus only in the kainic acid model, where it was associated with areas of neuronal cell loss, as indicated by absence of NeuN immunostaining, dendritic loss, as identified by areas where microtubule-associated protein-2 immunostaining was missing, and reactive gliosis, determined by regions of strong OX42 staining

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication 20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515