Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is continuous at zero energy. An explicit formula is provided for the scattering matrix at zero energy. The small-energy asymptotics are established also for the corresponding Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems.Comment: This published version has been edited to improve the presentation of the result

Exact Solutions to the Sine-Gordon Equation

A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable $x$ and the temporal variable $t,$ and they are exponentially asymptotic to integer multiples of $2\pi$ as $x\to\pm\infty.$ The solution formulas are expressed explicitly in terms of a real triplet of constant matrices. The method presented is generalizable to other integrable evolution equations where the inverse scattering transform is applied via the use of a Marchenko integral equation. By expressing the kernel of that Marchenko equation as a matrix exponential in terms of the matrix triplet and by exploiting the separability of that kernel, an exact solution formula to the Marchenko equation is derived, yielding various equivalent exact solution formulas for the sine-Gordon equation.Comment: 43 page

Exercise decreases PP2A-specific reversible thiol oxidation in human erythrocytes:Implications for redox biomarkers

New readily accessible systemic redox biomarkers are needed to understand the biological roles reactive oxygen species (ROS) play in humans because overtly flawed, technically fraught, and unspecific assays severely hamper translational progress. The antibody-linked oxi-state assay (ALISA) makes it possible to develop valid ROS-sensitive target-specific protein thiol redox state biomarkers in a readily accessible microplate format. Here, we used a maximal exercise bout to disrupt redox homeostasis in a physiologically meaningful way to determine whether the catalytic core of the serine/threonine protein phosphatase PP2A is a candidate systemic redox biomarker in human erythrocytes. We reasoned that: constitutive oxidative stress (e.g., haemoglobin autoxidation) would sensitise erythrocytes to disrupted ion homeostasis as manifested by increased oxidation of the ion regulatory phosphatase PP2A. Unexpectedly, an acute bout of maximal exercise lasting ˜16 min decreased PP2A-specific reversible thiol oxidation (redox ratio, rest: 0.46; exercise: 0.33) without changing PP2A content (rest: 193 pg/ml; exercise: 191 pg/ml). The need for only 3-4 μl of sample to perform ALISA means PP2A-specific reversible thiol oxidation is a capillary-fingertip blood-compatible candidate redox biomarker. Consistent with biologically meaningful redox regulation, thiol reductant-inducible PP2A activity was significantly greater (+10%) at rest compared to exercise. We establish a route to developing new readily measurable protein thiol redox biomarkers for understanding the biological roles ROS play in humans

Power logics of consumers’ gendered (in)justices: reading reproductive health interventions through the Transformative Gender Justice Framework

Global gender asymmetries in marketing and consumer behavior were recently exemplified by the Transformative Gender Justice Framework (TGJF). The TGJF, however, lacks an explicit reference to power—an aspect that becomes apparent when it is used to assess a consumer phenomenology. In this article we augment the TGJF by building out the power logics and by empirically testing it through an assessment of the reproductive market in Uganda. We capture macro-, meso-, and micro-level power asymmetries, and explore how bio-power and control over resources melds with local gender relations and agentic practices that i) leave social marketing efforts misaligned with embodied realities, and ii) result in dichotomies and tensions in the reproductive health market as the North-South strive to define the modern-traditional, medical-pleasurable, and women-men nature of contraceptives

Analytical evaluation of the MoM matrix elements

Derivation of the closed-form Green's functions has eliminated the computationally expensive evaluation of the Sommerfeld integrals to obtain the Green's functions in the spatial domain. Therefore, using the closed-form Green's functions in conjunction with the method of moments (MoM) has unproved the computational efficiency of the technique significantly. Further improvement can be achieved on the calculation of the matrix elements involved in the MoM, usually double integrals for planar geometries, by eliminating the numerical integration. The contribution of this paper is to present the analytical evaluation of the matrix elements when the closed-form Green's functions are used, and to demonstrate the amount of improvement in computation time. © 1996 IEEE

Explicit solutions to the Korteweg-de Vries equation on the half line

Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schr\"odinger equation. In the reflectionless case such solutions reduce to pure $N$-soliton solutions. An illustrative example is provided.Comment: 17 pages, no figure

Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectru

A unified approach to Darboux transformations

We analyze a certain class of integral equations related to Marchenko equations and Gel'fand-Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution. We show how this result provides a unified approach to Darboux transformations associated with various systems of ordinary differential operators. We illustrate our theory by deriving the Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a discrete eigenvalue is added to the spectrum.Comment: final version that will appear in Inverse Problem

Three-dimensional chromatin interactions remain stable upon CAG/CTG repeat expansion

Expanded CAG/CTG repeats underlie 13 neurological disorders, including myotonic dystrophy type 1 (DM1) and Huntington's disease (HD). Upon expansion, disease loci acquire heterochromatic characteristics, which may provoke changes to chromatin conformation and thereby affect both gene expression and repeat instability. Here, we tested this hypothesis by performing 4C sequencing at the DMPK and HTT loci from DM1 and HD-derived cells. We find that allele sizes ranging from 15 to 1700 repeats displayed similar chromatin interaction profiles. This was true for both loci and for alleles with different DNA methylation levels and CTCF binding. Moreover, the ectopic insertion of an expanded CAG repeat tract did not change the conformation of the surrounding chromatin. We conclude that CAG/CTG repeat expansions are not enough to alter chromatin conformation in cis. Therefore, it is unlikely that changes in chromatin interactions drive repeat instability or changes in gene expression in these disorders