Entropy dissipation estimates for the linear Boltzmann operator

We prove a linear inequality between the entropy and entropy dissipation functionals for the linear Boltzmann operator (with a Maxwellian equilibrium background). This provides a positive answer to the analogue of Cercignani's conjecture for this linear collision operator. Our result covers the physically relevant case of hard-spheres interactions as well as Maxwellian kernels, both with and without a cut-off assumption. For Maxwellian kernels, the proof of the inequality is surprisingly simple and relies on a general estimate of the entropy of the gain operator due to Matthes and Toscani (2012) and Villani (1998). For more general kernels, the proof relies on a comparison principle. Finally, we also show that in the grazing collision limit our results allow to recover known logarithmic Sobolev inequalities

The Probability of the Truth on a Truth Table

In symbolic (or mathematical) logic the truth table is used to establish the truth or falsity (falsehood) of both simple and compound statements (or arguments). However, the use of the term “truth table” falsely suggests that all arguments through the table are true. It is known that the table contains both true and false arguments. So the use of “truth table” is indiscriminate. Consequently, this study was focused on solving this problem by finding out the probability of having a true argument associated with every one of the four binary proposition connectives- “and”, “double implication” “inclusive v”, single implication”  used in the arguments. The obtained probabilities are ordered as 1/4, ½ and ¾ respectfully for “and”, “double implication”, and (“inclusive v” and “single implication”). So the “truth tables” are discriminately decomposed into “falsehood tables”, “neutral tables” and “truth tables” at probabilities of ¼, ½ and ¾ respectively. These probabilities are independent of the number of statements, n, greater than unity

Comparing Two Examination Results using Means of Sample Means and Control Charts

Some examination candidates submit their scripts first, sometimes, for recognition as being brilliant, and some do for not knowing what to write. However, some equally submit last because they want to dot i’s and cross t’s. The objective of this research is to compare the results of both the earliest and latest submissions with the aim of finding out whether or not there is a significant difference between the two. The examination results of students of the Departments of Accounting, Business Administration and Industrial Relations and Personnel Management of the Faculty of Business Administration and the Department of Mathematics, Faculty of Science,  University of Lagos were  compared using means of sample means and two statistical quality control charts. The results showed that, generally, the early submissions seemed to be an indication of being more brilliant than the last submissions in the Faculty of Business Administration. In the Mathematics Department, however, the last to submit appeared to be more brilliant. Keywords:measures of brilliance, statistical quality control, two-sample test, ordered-data-control charts,  time sequence of exam-script submission, competition assessmen

Strong Convergence towards homogeneous cooling states for dissipative Maxwell models

We show the propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for small inelasticity. This result together with the weak convergence towards the homogenous cooling state present in the literature implies the strong convergence in Sobolev norms and in the $L^1$ norm towards it depending on the regularity of the initial data. The strategy of the proof is based on a precise control of the growth of the Fisher information for the inelastic Boltzmann equation. Moreover, as an application we obtain a bound in the $L^1$ distance between the homogeneous cooling state and the corresponding Maxwellian distribution vanishing as the inelasticity goes to zero.Comment: 2 figure

Schwannoma vestibular (neurinoma do acústico) imitando desordens temporomandibulares: um relato de caso

Aproximadamente 6 a 16% dos pacientes com sintomas de neuralgia trigeminal apresentam tumores intracranianos, sendo mais comum o schwannoma vestibular (neurinoma do acústico). Alguns sintomas relatados pelos pacientes são perda da audição, zumbido, dores de cabeça, vertigens e distúrbios trigeminais. Uma resposta muscular aumentada na musculatura associada da cabeça e do pescoço também pode ser observada, o que pode mimetizar sinais e sintomas de desordens temporomandibulares. Nestes casos é de grande valia o uso de imagem de ressonância magnética (IRM) para detecção de tumores. É importante, também, a diferenciação de dores miofasciais e neurálgicas, pois ambas podem apresentar características semelhantes, mas com origens e tratamentos diferentes. O objetivo desse trabalho foi demonstrar através de relato de caso clínico a associação entre sintomas de neuralgia trigeminal, tumores intracranianos e disfunção temporomandibular.Approximately 6 to 16% of patients with trigeminal neuralgia symptoms present intracranial tumors, the most common being the vestibular schwannoma (acoustic neuroma). Some symptoms reported by patients include hearing loss, tinnitus, headaches, vertigo and trigeminal disturbances. An increased muscle response in the surrounding head and neck musculature may also be observed, which mimics signs and symptoms of temporomandibular disorders. In these cases, magnetic resonance imaging (MRI) has proved to be a useful tool in tumor diagnosis. The differential diagnosis between myofascial and neuralgic pain is important, as both may present similar characteristics, while being of different origin, and demanding special treatment approaches. The purpose of this paper is to demonstrate the relationship among trigeminal neuralgia symptoms, intracranial tumors and temporomandibular dysfunction by presenting a clinical case

Flavonoid-inspired vascular disrupting agents: Exploring flavone-8-acetic acid and derivatives in the new century

Naturally occurring flavonoids are found as secondary metabolites in a wide number of plants exploited for both medicine and food and have long been known to be endowed with multiple biological activities, making them useful tools for the treatment of different pathologies. Due to the versatility of the scaffolds and the vast possibilities of appropriate decoration, they have also been regarded as fruitful sources of lead compounds and excellent chemical platforms for the development of bioactive synthetic compounds. Flavone-8-acetic acid (FAA) and 5,6-dimethylxanthone acetic acid (DMXAA) emerged for their antitumour potential due to the induction of cytokines and consequent rapid haemorrhagic necrosis of murine tumour vasculature, and different series of derivatives have been designed thereafter. Although the promising DMXAA failed in phase III clinical trials because of strict species-specificity, a boost in research came from the recent identification of the stimulator of interferon genes (STING), responsible for supporting tumoural innate immune responses, as a possible biological target. Consequently, in the last decade a renewal of interest for these flavonoid-based structures was noticed, and novel derivatives have been synthesised and evaluated for a deeper understanding of the molecular features needed for affecting human cells. Un-doubtedly, these natural-derived molecules deserve further investigation and still appear attractive in an anticancer perspective

Regular vs. classical M\"obius transformations of the quaternionic unit ball

The regular fractional transformations of the extended quaternionic space have been recently introduced as variants of the classical linear fractional transformations. These variants have the advantage of being included in the class of slice regular functions, introduced by Gentili and Struppa in 2006, so that they can be studied with the useful tools available in this theory. We first consider their general properties, then focus on the regular M\"obius transformations of the quaternionic unit ball B, comparing the latter with their classical analogs. In particular we study the relation between the regular M\"obius transformations and the Poincar\'e metric of B, which is preserved by the classical M\"obius transformations. Furthermore, we announce a result that is a quaternionic analog of the Schwarz-Pick lemma.Comment: 14 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

Planejamento Estratégico Como Prática Managerialista em Organizações Hospitalares

Hospitais são caracterizados como Sistemas Adaptativos Complexos (SAC) por apresentarem significativa presença de características como: não linearidade, imprevisibilidade, dinamicidade das interações e agentes autônomos, os quais fazem com que o sistema aprenda e evolua continuamente, desafiando seus gestores. Visando maior profissionalização da gestão, essas organizações têm adotado metodologias de gestão tais como o Planejamento Estratégico (PE) voltadas, principalmente, ao desempenho financeiro, nem sempre observando as peculiaridades organizacionais, caracterizando-se como uma prática reconhecida como managerialism. Diante desse contexto, este estudo questiona: Quais as implicações do Planejamento Estratégico no desempenho organizacional de hospitais, como Sistemas Adaptativos Complexos? Para tanto, investigou-se as características e a influência de elementos tais como interações, não linearidade e aprendizado, no Planejamento Estratégico de duas organizações hospitalares da Região Sudeste. Esse estudo tem base em conceitos de Estratégia em Organizações e da Teoria da Complexidade. Trata-se de um estudo comparativo de casos, com corte transversal e de natureza qualitativa. Os dados foram coletados por meio de entrevistas em profundidade, observação não participante e documentos, os quais foram analisados por meio de técnicas de análise de narrativa e análise documental. Resultados evidenciaram que o PE adotado nos Hospitais segue a orientação tradicional, ou seja, apresenta características managerialistas que tem no desempenho financeiro o seu foco principal. A não observação das especificidades organizacionais limitou a efetividade do PE nos hospitais investigados. As características de SAC permitiram compreender as razões das dificuldades encontradas: 1) a não linearidade é potencializada pela autonomia dos agentes e grupos de agentes por tratar-se de organização profissional; 2) as decisões são fortemente influenciadas pela imprevisibilidade do hospital e, por isso, a dinamicidade das interações informais se torna mais efetiva do que o planejamento deliberado; 3) a capacidade de aprendizado dos agentes demonstrou ser essencial para lidarem com o imprevisto, contribuindo para a gestão estratégica das organizações, não necessariamente por meio do Planejamento Estratégico. A partir desses resultados, conclui-se que, embora algumas estratégias planejadas tenham sido implementadas, prevalece na gestão estratégica de hospitais as estratégias emergentes, muito influenciadas pela multiplicidade e pluralidade de agentes, pelos interesses divergentes entre grupos (especialmente administrativo e profissional), e pela constante necessidade de adaptação dos agentes para promover mudanças. Por tratar-se de um hospital, o desempenho assume uma vertente social que, juntamente com a financeira, além de não equilibrado se torna motivo de conflito para o público interno, especialmente, junto aos profissionais especialistas. Por fim, o Planejamento Estratégico demonstrou cumprir um papel simbólico, legitimando a gestão dos hospitais perante o mercado