Functions with Prescribed Best Linear Approximations

A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions to such problems. A finite family of subspaces is said to satisfy the \emph{Inverse Best Approximation Property (IBAP)} if there exists a point that admits any selection of points from these subspaces as best approximations. We provide various characterizations of the IBAP in terms of the geometry of the subspaces. Connections between the IBAP and the linear convergence rate of the periodic projection algorithm for solving the underlying affine feasibility problem are also established. The results are applied to problems in harmonic analysis, integral equations, signal theory, and wavelet frames

EuCo2P2: A Model Molecular-Field Helical Heisenberg Antiferromagnet

The metallic compound EuCo2P2 with the body-centered tetragonal ThCr2Si2 structure containing Eu spins 7/2 was previously shown from single-crystal neutron diffraction measurements to exhibit a helical antiferromagnetic (AFM) structure below TN = 66.5 K with the helix axis along the c axis and with the ordered moments aligned within the ab-plane. Here we report crystallography, electrical resistivity, heat capacity, magnetization and magnetic susceptibility measurements on single crystals of this compound. We demonstrate that EuCo2P2 is a model molecular-field helical Heisenberg antiferromagnet from comparisons of the anisotropic magnetic susceptibility chi, high-field magnetization and magnetic heat capacity of EuCo2P2 single crystals at temperature T < TN with the predictions of our recent formulation of molecular field theory. Values of the Heisenberg exchange interactions between the Eu spins are derived from the data. The low-T magnetic heat capacity ~ T^3 arising from spin-wave excitations with no anisotropy gap is calculated and found to be comparable to the lattice heat capacity. The density of states at the Fermi energy of EuCo2P2 and the related compound BaCo2P2 are found from the heat capacity data to be large, 10 and 16 states/eV per formula unit for EuCo2P2 and BaCo2P2, respectively. These values are enhanced by a factor of ~2.5 above those found from DFT electronic structure calculations for the two compounds. The calculations also find ferromagnetic Eu-Eu exchange interactions within the ab-plane and AFM interactions between nearest- and next-nearest planes, in agreement with the MFT analysis of chi{ab}(T < TN).Comment: 20 pages, 17 figures, 3 tables, 46 references. This is an extended replacement of arXiv:1512.02958 with an additional coautho

Sexual Dysfunction among Latino men and women with poorly controlled diabetes

Latinos are the largest minority population in the United States and are diagnosed with diabetes at nearly twice the rate of non-Hispanic whites. Latinos not only suffer disproportionately from diabetes but also from diabetes related complications, including sexual dysfunction. Much of the existing literature on sexual dysfunction among Latinos with diabetes has focused on erectile dysfunction (ED). There is a dearth of information on sexual functioning among Latina women with diabetes or information on both genders in other sexual domains. Our study examined the prevalence of sexual dysfunction among a cohort of 106 poorly controlled Latino diabetics in South Florida who participated in the Miami Healthy Heart Initiative, an NIH/NLBI sponsored clinical trial addressing diabetes management among Latinos. We explored gender differences in various domains of sexual health and examined the role of poor glycemic control and depression on sexual dysfunction. A large proportion of both genders in our sample met the criteria for sexual dysfunction though females exhibited a greater prevalence than males. Depression affected more than one third of our sample, but we did not find any significant associations between sexual dysfunction and depression. We also did not find a linear correlation between glycemic control and sexual dysfunction. We concluded that interventions are needed to address high rates of sexual dysfunction among Latinos with diabetes with particular emphasis on Latina women, who were much more likely than men to report problems with desire and other areas of sexual functioning. Until effective pharmacologic agents to improve desire among women with diabetes become available, clinicians caring for this population should consider behavioral approaches that may limit the impact of sexual dysfunction

cFFR as an alternative to FFR: please do not contrast simplicity!

info:eu-repo/semantics/publishedVersio

The converse problem for the multipotentialisation of evolution equations and systems

We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the {\it converse problem}. Although we mainly study a method for $(1+1)$-dimensional equations/system, we do also propose an extension of the methodology to higher-dimensional evolution equations. An important point is that the proposed converse method allows one to identify certain types of auto-B\"acklund transformations for the equations/systems. In this respect we define the {\it triangular-auto-B\"acklund transformation} and derive its connections to the converse problem. Several explicit examples are given. In particular we investigate a class of linearisable third-order evolution equations, a fifth-order symmetry-integrable evolution equation as well as linearisable systems.Comment: 31 Pages, 7 diagrams, submitted for consideratio