Completeness of the Coulomb scattering wave functions

Completeness of the eigenfunctions of a self-adjoint Hamiltonian, which is the basic ingredient of quantum mechanics, plays an important role in nuclear reaction and nuclear structure theory. However, until now, there was no a formal proof of the completeness of the eigenfunctions of the two-body Hamiltonian with the Coulomb interaction. Here we present the first formal proof of the completeness of the two-body Coulomb scattering wave functions for repulsive unscreened Coulomb potential. To prove the completeness we use the Newton's method [R. Newton, J. Math Phys., 1, 319 (1960)]. The proof allows us to claim that the eigenfunctions of the two-body Hamiltonian with the potential given by the sum of the repulsive Coulomb plus short-range (nuclear) potentials also form a complete set. It also allows one to extend the Berggren's approach of modification of the complete set of the eigenfunctions by including the resonances for charged particles. We also demonstrate that the resonant Gamow functions with the Coulomb tail can be regularized using Zel'dovich's regularization method.Comment: 12 pages and 1 figur

Risk mitigation strategies and policy implications for carbon dioxide (CO 2) emission in organically-amended soils in Nigeria

Global food security has been a challenge, especially in Africa. This has attracted the adoption of strategies to improve soil productivity and crop yield. One of such strategies is the use of solid wastes as soil organic matter amendments. An investigation of the effects of soil amendment using poultry manure, sawdust and their mixtures on carbon dioxide (CO 2) emission, maize (Zea mays L.) growth and dry matter yield were assessed under laboratory and greenhouse conditions. Top soil obtained from unfertilized plots at the Obafemi Awolowo University Teaching and Research farm, Ile-Ife, Nigeria was used for the experiments. The organic amendments were added at the rate of 10 g/kg, treatments were in triplicates and treatment means were separated using Duncan’s Multiple Range Test at 95% level of significance. Results obtained revealed that CO 2 emission decreased while maize heights and dry matter yields significantly (P> 0.05) increased with increasing ratios of poultry manure in the poultry manure-sawdust mixtures. The CO 2 emission from poultry manure amended soil was about 61% that from sawdust amended soil while the mean height and dry matter yield in sawdust-amended soils were 84% and 52% respectively those obtained in poultry manure amended soil. This paper concludes that it is essential to design and implement policies that will guide and encourage the use of organic amendments at ratios that can enhance crop yield and mitigate CO 2 emission to the environment

Gradients versus Cycling in Genetic Selection Models

We review the hierarchy of (continuous time) selection models starting with the classical Fisher's viability selection model, and its generalizations when allowing mutations, recombination, sex-dependent viabilities, fertility selection and different mortality rates. We analyse the question in which way Fisher's "Fundamental Theorem of Natural Selection" and Kimura's Maximum Principle can be extended to these more general situations. It turns out that in many cases this is principally impossible since the dynamics becomes cycling or even chaotic

Nonemergent Percutaneous Coronary Intervention on an Unprotected Left Main Coronary Artery Supported with Impella® Heart Pump in Patients Ineligible for Surgical Revascularization

© 2019 Perwaiz M. Meraj et al. Objectives. We sought to assess if ineligibility to coronary artery bypass grafting (CABG) constitutes a risk factor in patients who underwent a nonemergent unprotected left main coronary artery (ULMCA) percutaneous coronary intervention (PCI) with prophylactic Impella® heart pump support. Background. ULMCA PCI in patients not deemed eligible for CABG is associated with significantly worse outcomes compared to ULMCA PCI in eligible patients. Methods. Patients from the cVAD Registry and the PROTECT II trial who underwent a nonemergent ULMCA PCI were identified. We compared in-hospital mortality and major adverse cardiac and cerebrovascular event (MACCE) rates as well as 30-day survival and MACCE rates between CABG ineligible and CABG eligible patients. Results. A total of 331 patients were included (293 Impella 2.5®, 38 Impella CP®); 227 were ineligible for CABG and 104 were eligible. Baseline characteristics were remarkable for a trend toward higher rate of chronic obstructive pulmonary disease in the ineligible patients. In-hospital mortality (3.52% vs. 5.77%; p=0.383) and MACCE (6.61% vs. 7.69%; p=0.816) rates as well as 30-day survival (92.0% vs. 93.4%; Log-Rank p-value =0.781) and MACCE (88.1% vs. 90.1%; Log-Rank p-value=0.648) rates were not different between the two groups. Conclusions. The results of our study suggest that prophylactic Impella support appears to mitigate the risks inherent to surgical ineligibility in patients undergoing a nonemergent ULMCA PCI. Our results require further investigation

Mutation, selection, and ancestry in branching models: a variational approach

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. Here, the variational principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure

Progression of coronary artery calcification in conventional hemodialysis, nocturnal hemodialysis, and kidney transplantation

Introduction Cardiovascular disease is the leading cause of death in end-stage renal disease (ESRD) and is strongly associated with vascular calcification. An important driver of vascular calcification is high phosphate levels, but these become lower when patients initiate nocturnal hemodialysis or receive a kidney transplant. However, it is unknown whether nocturnal hemodialysis or kidney transplantation mitigate vascular calcification. Therefore, we compared progression of coronary artery calcification (CAC) between patients treated with conventional hemodialysis, nocturnal hemodialysis, and kidney transplant recipients. Methods We measured CAC annually up to 3 years in 114 patients with ESRD that were transplantation candidates: 32 that continued conventional hemodialysis, 34 that initiated nocturnal hemodialysis (>= 4x 8 hours/week), and 48 that received a kidney transplant. We compared CAC progression between groups as the difference in square root transformed volume scores per year (Delta CAC SQRV) using linear mixed models. Reference category was conventional hemodialysis. Results The mean age of the study population was 53 +/- 13 years, 75 (66%) were male, and median dialysis duration was 28 (IQR 12-56) months. Median CAC score at enrollment was 171 (IQR 10-647), which did not differ significantly between treatment groups (P = 0.83). Compared to conventional hemodialysis, CAC progression was non-significantly different in nocturnal hemodialysis -0.10 (95% CI -0.77 to 0.57) and kidney transplantation -0.33 (95% CI -0.96 to 0.29) in adjusted models. Conclusions Nocturnal hemodialysis and kidney transplantation are not associated with significantly less CAC progression compared to conventional hemodialysis during up to 3 years follow-up. Further studies are needed to confirm these findings, to determine which type of calcification is measured with CAC in end-stage renal disease, and whether that reflects cardiovascular risk