Some notions of subharmonicity over the quaternions

This works introduces several notions of subharmonicity for real-valued functions of one quaternionic variable. These notions are related to the theory of slice regular quaternionic functions introduced by Gentili and Struppa in 2006. The interesting properties of these new classes of functions are studied and applied to construct the analogs of Green's functions.Comment: 16 page

Covid-19 and ENT practice: Our experience: ENT outpatient department, ward and operating room management during the SARS-CoV-2 pandemic

Coronavirus COVID-19 SARS-CoV-2 ENT Otolaryngolog

Quality Educational Planning and Senior Secondary Education Goal Attainment in Ilorin Metropolis, Kwara State

This study determined the relationship between quality educational planning and senior secondary education goal attainment in Ilorin metropolis, Kwara State. The study adopted a descriptive design of correlation type while its population comprised all the 3594 teachers across the public secondary schools in Ilorin metropolis. Simple random sampling technique was used to select 346 teachers in the metropolis. An adapted questionnaire titled “Quality Educational Planning Questionnaire” (QEPQ) and “Secondary Education Goal Attainment Proforma” (SEGAP) were used to collect data. Descriptive statistics of frequency count and percentage was used to answer the research questions while inferential statistics of Pearson product-moment correlation statistics was used to test the hypotheses at 0.05 level of significant. The findings of the study revealed that quality educational planning has a significant relationship with secondary education goal attainment in Ilorin metropolis, Kwara State. It was recommended that adequate classrooms and instructional facilities should continue to be adequately planned in order to keep the tempo of academic performance and enhance the level of senior secondary education goal attainment in Kwara State

Role of endoscopy in lateral skull base approaches to the petrous apex

Objective: The aim of this article is to study the role and advantages of combined microscopic/endoscopic procedures or exclusive endoscopic approaches in the treatment of petrous apex pathologies. Methods: The study was designed as a retrospective case series analysis. We included patients affected by pathologies of the petrous apex, who underwent microscopic/endoscopic-assisted or exclusive endoscopic procedures. Patient and pathology characteristics and surgical data (focusing on the involvement of the internal carotid artery (ICA) and facial nerve by the disease) were collected. Residual disease, detected through the endoscopic check, and the feasibility of endoscopic residual tumor removal were also evaluated. Finally, facial nerve and hearing functions were assessed pre- and postoperatively. Results: The records of 75 patients undergoing lateral skull base surgery for petrous apex lesions, from May 2009 to March 2019, were collected. In 17 out of 75 patients, an exclusive endoscopic procedure was possible. The remaining 58 patients underwent a combined microscopic/endoscopic approach. In 15 cases, residual disease was found and removed endoscopically at the end of the microscopic procedure; in eight cases, the residual disease was medial and/or inferior to the horizontal segment of the ICA, while in two cases, it was located in the fundus of the internal auditory canal. In five cases, it involved the labyrinthine segment of the facial nerve. Conclusion: Petrous apex surgery remains a traditional microscopic-based surgery, but the recent advent of endoscopic surgery has permitted an improvement in radicality minimizing the manipulation of neurovascular structures

Random planar trees and the Jacobian conjecture

We develop a probabilistic approach to the celebrated Jacobian conjecture, which states that any Keller map (i.e. any polynomial mapping $F\colon \mathbb{C}^n \to \mathbb{C}^n$ whose Jacobian determinant is a nonzero constant) has a compositional inverse which is also a polynomial. The Jacobian conjecture may be formulated in terms of a problem involving labellings of rooted trees; we give a new probabilistic derivation of this formulation using multi-type branching processes. Thereafter, we develop a simple and novel approach to the Jacobian conjecture in terms of a problem about shuffling subtrees of $d$-Catalan trees, i.e. planar $d$-ary trees. We also show that, if one can construct a certain Markov chain on large $d$-Catalan trees which updates its value by randomly shuffling certain nearby subtrees, and in such a way that the stationary distribution of this chain is uniform, then the Jacobian conjecture is true. Finally, we show that the subtree shuffling conjecture is true in a certain asymptotic sense, and thereafter use our machinery to prove an approximate version of the Jacobian conjecture, stating that inverses of Keller maps have small power series coefficients for their high degree terms.Comment: 36 pages, 4 figures. Section 2.5 added, Section 3 expanded, further minor edit

Factors associated with low rate of exclusive breastfeeding among mothers in Enugu, Nigeria

Background: Exclusive breastfeeding has proven to be beneficial both maternal and child health hence its adopted as a policy for infant feeding in most countries especially developing nations. Its practice has remained low despite the high levels of awareness of exclusive breastfeeding. The study set out to find out the possible reasons that have limited the translation of knowledge of exclusive breastfeeding to action by nursing mothers in an urban city in Nigeria.Methods: A self-administered structured questionnaire was used to collect data from 304 mothers attending immunization clinics of the Institute of maternal and child health in Enugu, Southeast Nigeria.Results: Awareness of exclusive breastfeeding was 98% with an exclusive breastfeeding rate of 26%. The commonest non-human milk given to infant was water- given in the first week of life. Post-natal support from lactation experts and family, beliefs about the sufficiency of human milk and subsequent refusal of complementary foods were major challenges to successful exclusive breastfeeding. Maternal age and education did not determine exclusive breastfeeding.Conclusions: Exclusive breastfeeding rates have remained low in Nigeria. Lack of family support and the belief that human milk is not sufficient food for the less-than-six-months-old infant were major challenges to exclusive breastfeeding

The effectiveness of locally-prepared peritoneal dialysate in the management of children with acute kidney injury in a south-east Nigerian tertiary hospital

Background: Peritoneal dialysis (PD) is the preferred mode of renal replacement therapy (RRT) in children with acute kidney injury (AKI). The gold standard remains the use of commercially-prepared PD fluid. In resource-poor nations, its availability and affordability remain a challenge.Aim: This study aims to report the effectiveness of locally-prepared PD fluid in the management of AKI in a south-east Nigerian tertiary hospital.Subjects and Methods: This was a retrospective study conducted at the paediatric ward of the University of Nigeria Teaching hospital, Enugu. The case records of 36 children seen over three years, diagnosed with AKI and requiring PD were reviewed. The retrieved information comprised biodata, aetiology of AKI, indications for PD, pre-and post-dialysis estimated glomerular filtration rate (eGFR) and patient outcomes.Results: The children (20 males and 16 females) were aged 3 to 36 months with a mean age of 9.92 ± 6.29 months. The common aetiologies of AKI were septicemia (30.6%), hemolytic uremic syndrome (19.4%), and toxic nephropathy (16.7%). The frequent indications for PD were uremic encephalopathy (58.3%) and severe metabolic acidosis (38.8%). The pre-and post-dialysis mean urine flow rate was 0.16 + 0.13 and 2.77 + 0.56 ml/kg/hour respectively. The eGFR before PD, at discontinuation, and a week later was 6.06 + 2.87, 24.44 + 15.71 and 59.07 + 22.22 mls/min/1.73m2 respectively.Conclusion: PD with locally-prepared dialysate is safe, effective and a life-saving alternative in the management of AKI in childrenKeywords: Peritoneal dialysis; renal replacement therapy; acute kidney injury; children; dialysate; developing country

Fácies e superfícies de descontinuidade da barreira regressiva holocênica paranaense

The Holocene regressive barrier of Paraná was formed when the relative sea level was higher than present and is one of the depositional systems that form the coastal plain of Paraná. This work aims to demonstrate the correlation between the barrier bounding surfaces with their sedimentary facies and facies associations. The outcrops were exposed by excavations next Praia de Leste, coast of the state of Paraná. The characterization and interpretation of facies, facies associations and bounding surfaces were performed from the description of 5 geological sections. The barrier is composed of very fine to fine quartz sand which may contain hight concentrate of heavy minerals and plant debris in the form of swaley and hummocky cross stratification. There were identified 13 facies corresponding to the facies associations foreshore, upper shoreface and middle shoreface. Surfaces of 1st, 2nd and 3rd order were identified. The 3rd order surfaces were identified in the three facies associations and were related to architectural elements of the barrier, called: beach face, bars and ebb-tidal delta deposits.A barreira regressiva holocênica paranaense foi formada quando o nível relativo do mar era superior ao atual e é um dos sistemas deposicionais que formam a planície costeira paranaense. O objetivo deste artigo é demonstrar a correlação entre as superfícies de descontinuidade existentes na barreira com as suas fácies sedimentares e associações de fácies. Os afloramentos foram expostos em uma cava de extração de areia nas proximidades de Praia de Leste, litoral do estado do Paraná. Foram realizadas a caracterização e interpretação das fácies, associações de fácies e superfícies de descontinuidade a partir do levantamento e descrição de 5 seções geológicas. A barreira é constituída principalmente por areia quartzosa predominantemente muito fina a fina que pode conter alta concentração de minerais pesados e detritos vegetais na forma de estratificações cruzadas tipo swaley e hummocky. Foram identificadas 13 fácies correspondentes às associações de fácies praia subaérea-intermaré, face litorânea superior e face litorânea média. Superfícies de 1ª, 2ª e 3ª ordem foram identificadas. As superfícies de 3ª ordem foram identificadas nas três associações de fácies e foram relacionadas a elementos arquitetônicos da barreira, denominados: depósitos de face praial, de barras submersas e de delta de maré vazante