We discuss results where information on parts of the discrete spectra of onedimensional Schrödinger operators H = − d2 dx2 + q in L2((0, 1)) or of a finite Jacobi matrix together with partial information on q uniquely determines q a.e. on [0, 1]. These extend classical results of Borg and Hochstadt-Lieberman as well as results in paper II of this series. §

According to Emma Borg, minimalism is (roughly) the view that natural language sentences have truth conditions, and that these truth conditions are fully determined by syntactic structure and lexical content. A principal motivation for her brand of minimalism is that it coheres well with the popular view that semantic competence is underpinned by the cognition of a minimal semantic theory. In t...

The Schrödinger equation is considered on the half line with a selfadjoint boundary condition when the potential is real valued, integrable, and has a finite first moment. It is proved that the potential and the two boundary conditions are uniquely determined by a set of spectral data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral...

OBJECTIVES Bilateral vocal fold abductor paralysis (BVFAP) both deteriorates quality of life and may cause life-threatening respiratory problems. The aim of this study was to reduce respiratory symptoms in BVFAP patients using cricothyroid (CT) botulinum toxin (BTX) injection. METHODS Before and 2 weeks and 4 months after bilateral BTX injection into the CT muscles under electromyography; alt...

The six minute walk test (6MWT) is a standardized test that provides information on exercise capacity in patients with COPD. It is considered a submaximal test in opposition to incremental cardiopulmonary exercise tests (CPET) that provide valuable information on all the systems involved in exercise. OBJECTIVES 1. To compare the perceptive, physiological responses and degree of dynamic hyperi...

Revolutions1 in semiconductor device miniaturization, bioelectronics, and applied neural control technologies are enabling scientists to create machineassisted minds, science fiction’s “cyborgs.” In a paper published in 1999,1 we sought to draw attention to the advances in prosthetic devices, to the myriad of artificial implants, and to the early developments of this technology in cochlear and ...

This paper is about dense regularised mapping using a single camera as it moves through large work spaces. Our technique is, as many are, a depth-map fusion approach. However, our desire to work both at large scales and outdoors precludes the use of RGB-D cameras. Instead, we need to work with the notoriously noisy depth maps produced from small sets of sequential camera images with known inter...

The paper deals with two types of inverse spectral problems for the class of generalized Jacobi matrices introduced in [9]. Following the scheme proposed in [5], we deduce analogs of the Hochstadt–Lieberman theorem and the Borg theorem. Properties of a Weyl function of the generalized Jacobi matrix are systematically used to prove the uniqueness theorems. Trace formulas for the generalized Jaco...