Extracting partial decay rates of helium from complex rotation: autoionizing resonances of the one-dimensional configurations

Partial autoionization rates of doubly excited one-dimensional helium in the collinear Zee and eZe configuration are obtained by means of the complex rotation method. The approach presented here relies on a projection of back-rotated resonance wave functions onto singly ionized $\textrm{He}^{+}$ channel wave functions and the computation of the corresponding particle fluxes. In spite of the long-range nature of the Coulomb potential between the electrons and the nucleus, an asymptotic region where the fluxes are stationary is clearly observed. Low-lying doubly excited states are found to decay predomintantly into the nearest single-ionization continuum. This approach paves the way for a systematic analysis of the decay rates observed in higher-dimensional models, and of the role of electronic correlations and atomic structure in recent photoionization experiments

A Riemann-Hilbert Approach to the Kissing Polynomials

Motivated by the numerical treatment of highly oscillatory integrals, this thesis studies a family of polynomials known as the Kissing Polynomials through Riemann-Hilbert techniques. The Kissing Polynomials are a family of non-Hermitian orthogonal polynomials, which are orthogonal with respect to the complex weight function $\exp(i\omega z)$ over the interval $[-1,1]$, where $\omega>0$. Although they have already been used to derive complex quadrature rules, there remain two main questions which this thesis addresses. The first is the existence of such polynomials; the second is the behavior of these polynomials throughout the complex plane. The first two chapters of this thesis provide the necessary background needed for the main results presented in the later chapters. In the first chapter, the connection between the numerical integration of highly oscillatory integrals and the Kissing Polynomials is established. Furthermore, we present the theory of non-Hermitian orthogonal polynomials and provide a more detailed description of the results in this thesis. The second chapter is a review on the formulation of the Kissing Polynomials as a solution to a matrix valued Riemann-Hilbert problem. This formulation is crucial to establishing both the existence of the Kissing Polynomials and its properties throughout the complex plane. Moreover, we also provide an overview of the powerful non-commutative steepest descent technique developed by Deift and Zhou in the mid 1990s used to compute the asymptotics for oscillatory Riemann-Hilbert problems, which will be used extensively in Chapters 4 and 5. In Chapter 3, we utilize the Riemann-Hilbert approach of Fokas, Its, and Kitaev to establish our first main result: the existence of the even degree Kissing polynomials for all values of $\omega>0$. First, we use the Riemann-Hilbert problem to show that the Kissing Polynomials satisfy a certain linear ordinary differential equation. Then, using standard results on differential equations, along with previous results on the Kissing Polynomials found in the literature, we are able to provide the desired result. In Chapter 4, we turn our attention to the behavior of the Kissing Polynomials as both the degree $n$ and parameter $\omega$ become large. To achieve this, we formulate this problem in terms of varying-weight Kissing polynomials, whose asymptotics can be handled with the Deift-Zhou steepest descent analysis. Now, the weight function depends now on $n$, the degree of the underlying polynomial. We are able to provide uniform asymptotics of the Kissing Polynomials as both $n$ and $\omega$ go to infinity at a linear rate such that the ratio $\omega/n >t_c$, where $t_c$ is a to be specified critical value. In Chapter 5, we generalize the results of Chapter 4 and study polynomials which are orthogonal with respect to the varying, complex weight, $\exp(n s z)$, over the interval $[-1,1]$, where now $s\in\mathbb{C}$. We will see that there are curves in the $s$-plane, called breaking curves, which separate regions corresponding to differing asymptotic behavior of the polynomials. In this chapter, we provide the large $n$ behavior of the recurrence coefficients associated to these polynomials. Finally, we also study the behavior of these recurrence coefficients as the parameter $s$ approaches a breaking curve in a specified double scaling limit.PhD Studentship: Cantab Capital Institute for the Mathematics of Informatio

Antimicrobial Use and Stewardship among practicing veterinarians in Uganda

Appropriate, affordable, and readily available veterinary drugs are an essential component of any animal health service. The availability of certain drugs for companion animals (pets), food animals, and wildlife, along with the practitioners\u27 understanding of their use, is crucial in curbing antimicrobial resistance. The aim of this study was to establish categories of drugs commonly used by veterinarians working with companion animals, food animals, and wildlife in Uganda. A cross-sectional study was done to establish common antimicrobial drugs used by practicing veterinarians in Uganda. Fifty-seven veterinarians were purposively selected to participate in the survey. The veterinarians responded to an online questionnaire distributed by a link to their emails and mobile applications. The questionnaire solicited information regarding their demographic traits, expertise pertaining to antimicrobials, and the types of antimicrobials they frequently utilise. Most of the respondents, 53/57 (93%), were male veterinarians, and 29/57 (50.9%), were mixed animal practitioners. Although they were all involved in some kind of practice, only 18/44 (40.9%) confidently understood antimicrobial stewardship. However, the majority, 38/44 (86.4%), agreed on the importance of antimicrobial stewardship in reducing antimicrobial resistance (AMR). The majority, 26/43 (60.5%) of the veterinarians, were aware of the animal owners’ indiscriminate use of the antibiotic without expert prescription. Penicillins and tetracyclines were the most used antimicrobial drugs. Other antimicrobials often used were cephalosporins, fluoroquinolones, aminoglycosides, and chloramphenicol. Field veterinarians need to undergo further training on the current categories of antimicrobial agents, antimicrobial stewardship, and AMR. The Veterinary Formulary should be updated following the WHO list of critically-important-antimicrobials (CIA). The veterinarians should also familiarize themselves with the ‘Essential Veterinary Medicines List for Uganda’

Why honey is effective as a medicine. 1. Its use in modern medicine

Honey has been used as a medicine for thousands of years and its curative properties are well documented. However, modern medicine turned its back on honey and it is only now, with the advent of multi-resistant bacteria, that the antibiotic properties of honey are being rediscovered

THE POSTULATE OF THE HISTORICAL LAW THEORY AND CONFLICT OF LAWS: AN ARTICULATION OF AFRICAN (UKELE) COMMUNAL LEGALISM

This essay is titled "Critique the Postulation of the Historical Law Theory and relate it to African Law. The postulation of the historical law school that law emanates from customs through an ordered pattern of systematized progress into a codified system in relation to African law forms the crust of this essay. To achieve this task, this essay adopts a critical method in exposing c postulation of the historical law school and the African Law (keeping in mind the Ukelle communal Law System). This essay questions whether there can be an independent law made or promulgated without targeting a given people or that there can be a people-free law? This essay claims that like the historical law school, laws emanate from their ground norms but insists that unlike the historical law school, laws in Ukelle Traditional System do not necessarily have to submit to through the rigor of systematic and strict evolutionary pattern of progress. Like Herder, this essay avers that there is a unique character with each culture, and as such Ukelle Traditional Law does not have to submit to any universal character of law

Mercury Contamination and Spill-over at Human-Wildlife-Environment Interface

Man’s quest for energy demands that fuel for running machines and cooking is vital for mankind. Oil and coal have served this energy quest for time immemorial. This oil quest has been present in the Albertine Graben since 1920, threatening biodiversity spots, terrestrial wildlife, and aquatic resources. The current book chapter provides insights into the spatial distribution of potentially toxic elements (Mercury) in terrestrial and marine species and the health risk posed to terrestrial and aquatic species due to oil exploitation

Global‐phase portrait and large‐degree asymptotics for the Kissing polynomials

Funder: Comunidad de Madrid; Id: http://dx.doi.org/10.13039/100012818Funder: Consejería de Educación e Investigación; Id: http://dx.doi.org/10.13039/501100010774Funder: Engineering and Physical Sciences Research Council; Id: http://dx.doi.org/10.13039/501100000266Funder: Cantab Capital Institute for the Mathematics of InformationFunder: Cambridge Centre for AnalysisAbstract: We study a family of monic orthogonal polynomials that are orthogonal with respect to the varying, complex‐valued weight function, exp ( n s z ) , over the interval [ − 1 , 1 ] , where s ∈ C is arbitrary. This family of polynomials originally appeared in the literature when the parameter was purely imaginary, that is, s ∈ i R , due to its connection with complex Gaussian quadrature rules for highly oscillatory integrals. The asymptotics for these polynomials as n → ∞ have recently been studied for s ∈ i R , and our main goal is to extend these results to all s in the complex plane. We first use the technique of continuation in parameter space, developed in the context of the theory of integrable systems, to extend previous results on the so‐called modified external field from the imaginary axis to the complex plane minus a set of critical curves, called breaking curves. We then apply the powerful method of nonlinear steepest descent for oscillatory Riemann–Hilbert problems developed by Deift and Zhou in the 1990s to obtain asymptotics of the recurrence coefficients of these polynomials when the parameter s is away from the breaking curves. We then provide the analysis of the recurrence coefficients when the parameter s approaches a breaking curve, by considering double scaling limits as s approaches these points. We see a qualitative difference in the behavior of the recurrence coefficients, depending on whether or not we are approaching the points s = ± 2 or some other points on the breaking curve

Seroprevalence of Foot and Mouth Disease in apparently healthy beef cattle in Uganda post the 2021 outbreak

Foot-and-mouth disease (FMD) is a highly contagious viral disease of cloven-hoofed animals caused by a picornavirus. There are 7 known serotypes (O, C, A, SAT1, SAT2 and Asia) and more than 60 subtypes of the FMD virus. FMD causes enormous economic losses including reduced animal productivity and restrictions on international trade in animal products. In Uganda, FMD is endemic and caused by mainly O, A, SAT 1, and SAT2 serotypes. The outbreaks are mainly controlled by ring vaccination and restriction of animal movement. These control methods are sometimes not efficient due to lack of regular surveillance. Information on the seroprevalence of FMDV in animal herds post outbreak response is not available to guide policy makers on when to lift quarantine in affected districts. A study was therefore conducted to assess the effectiveness of the 2021 FMD outbreak response in Western Uganda following lifting of the quarantine restrictions. As part of routine herd health checks, blood samples were extracted from sixty-eight apparently healthy beef cattle. Of these, 46 were from Nshaara ranch and 22 from Mbarara city abattoir. The samples were tested for the presence of specific FMDV antibodies using Solid-Phase Competitive Enzyme-Linked Immunosorbent Assay. Overall, out of 68 samples, 51 (75%) tested positive for FMDV. Out of 46 samples taken from Nshaara ranch, 43 (93.5%) were positive and out of 22 samples from Mbarara City abattoir 8 (36.4%) were positive. The study revealed a concerningly high seropositivity of apparently health animals to FMDV antibodies possibly due to early lifting of the quarantine, weak enforcement of control measures or lack of incentive and resources to control the disease. Therefore, the Uganda national outbreak preparedness and response unit should move quickly to put in place a coordinated, effective, and functional preparedness and response mechanism whenever there are such disease outbreaks