A Schwarz lemma for the pentablock

In this paper we prove a Schwarz lemma for the pentablock. The set $$\mathcal{P}=\{(a_{21}, \text{tr} \ A, \det A) : A=[a_{ij}]_{i,j=1}^2 \in \mathbb{B}^{2\times 2}\}$$ where $\mathbb{B}^{2\times 2}$ denotes the open unit ball in the space of $2\times 2$ complex matrices, is called the pentablock. The pentablock is a bounded nonconvex domain in $\Bbb{C}^3$ which arises naturally in connection with a certain problem of $\mu$-synthesis. We develop a concrete structure theory for the rational maps from the unit disc $\Bbb{D}$ to the closed pentablock $\overline{\mathcal{P}}$ that map the unit circle ${\mathbb{T}}$ to the distinguished boundary $b\overline{\mathcal{P}}$ of $\overline{\mathcal{P}}$. Such maps are called rational ${\overline{\mathcal{P}}}$-inner functions. We give relations between penta-inner functions and inner functions from $\Bbb{D}$ to the symmetrized bidisc. We describe the construction of rational penta-inner functions $x = (a, s, p) : \Bbb{D} \rightarrow \overline{\mathcal{P}}$ of prescribed degree from the zeroes of $a, s$ and $s^2-4p$. The proof of this theorem is constructive: it gives an algorithm for the construction of a family of such functions $x$ subject to the computation of Fej\'er-Riesz factorizations of certain non-negative trigonometric functions on the circle. We use properties and the construction of rational ${\overline{\mathcal{P}}}$-inner functions to prove a Schwarz lemma for the pentablock.Comment: 35 pages. This version includes minor revisions. It has been accepted for publication by the Journal of Geometric Analysi

Impact of Knowledge and Attitude on Saudis’ Physical Activity Practice and Inactivity Barriers: A Questionnaire-based Study

BACKGROUND: Community participation in physical activity is considered a major public health preference of WHO. Saudi Arabia in the last decades faced many tremendous economic changes leading to adoption of western dietary habits associated with sedentary lifestyle. AIM: We aimed to study the relationship between both physical activity knowledge and attitude of community to the practice of individuals. METHODS: We used a questionnaire consists of a mixture of closed-ended questions. Participants were recruited through direct meetings in local markets, schools, and workplaces. Seven hundred and sixty six individuals agreed to participate. RESULTS: Overall correct answers to questions about importance of physical activity were 76.58%. The predominance of participants’ attitude was to establish public places for physical activity in each neighborhood (92.1%). Participants acknowledged that they exercise to improve their health (47.5%). Participants mainly perform light exercises (47.2%) on basis of 1–3 times weekly (48.9%). About 90.8% of participants admitted that they like to increase duration of their physical activity. CONCLUSIONS: Overall physical activity practice of participants’ needs encourage overcoming obstacles that prevent individuals from practicing especially lack of time

Experimental Investigation on Heat Transfer in a Prismatic Modular Reactor under Cosine Heat Flux

The current study has investigated natural convection heat during pressurized conduction cooldown (PCC) accident scenario to understand the passive safety features of prismatic modular reactors (PMR) under different intensities of nonuniform center peaking step heat flux distributions (approximating cosine shape) using an advanced fast-response heat transfer technique. A scaled-down PMR module was designed and developed at Missouri S&T by the research team of the Multiphase Reactors Engineering and Applications Laboratory (mReal). The module consists of upper and lower plena connected by heated and cooled channels. Nonuniform heat flux distribution was applied to the heated channel under nonuniform heating center peaking step (approximating cosine shape), simulating nonuniform heat distribution within the core of PMR. Air was used as the coolant to study the effect of nonuniform heating under a range of heat flux intensity (four sets of nonuniform heat flux and one set of uniform heat flux were tested) at 413.7 kPa (60 psi). At an axial position of Z/L = 0.409 along the heated channel, the heat transfer coefficient is increased by 35% for nonunifor libJo2O18*m heat flux distributions of set 1 (0.25*2.579 kW.m-2+0.50*3.152 kW.m-2+0.25*2.579 kW.m-2) and set 2 (0.25*2.292 kW.m-2+0.50*2.865 kW.m-2+0.25*2.292 kW.m-2) with respect to the the uniform heat flux set 5(2.865 kW.m-2), and it is decreased by 56% for nonuniform heat flux distributions of set 3 (0.25*2.006 kW.m-2+0.50*2.579 kW.m-2+0.25*2.006 kW.m-2) and set 4 (0.25*1.719 kW.m-2+0.50*2.292 kW.m-2+0.25*1.719 kW.m-2) with respect to the uniform heat flux set (set 5). There is a significant reorder in the heat transfer coefficients distribution curves in descending order along the heated channel after the inflection point (after Z/L =0.773)

A Comparison Between Students’ Performance In Multiple Choice and Modified Essay Questions in the MBBS Pediatrics Examination at the College of Medicine, King Khalid University, KSA

Objectives: To investigate the relation between the students' scores in MCQs and MEQs of the summative assessment in pediatrics at the College of medicine KKU. Introduction: Student assessment is the most difficult task in medicine since it is ultimately related to human life and safety. Assessment can take different types of formats with advantages and disadvantages and there is no single prescribed method of choice. Research Methods: This is a quantitative, observational retrospective study enrolling 50 students who completed the final MBBS examination in pediatrics in 2015.The medical students’ scores in MCQs and MEQs in the final MBBS pediatrics examination were collected and SPSS used for analysis. Results: 52% of the students scored A and B, 46% scored C and 2% scored D and nobody scored F. The mean percentage scores in MCQs, MEQs and the combined are75.03%, 79.99% and 76.68% respectively. The standard deviation (SD) for MCQs, MEQs and combined are 0.0753, 0.0763 and 0.0559 respectively.There are no significant differences in means and SD. The correlation (CR) between MCQs and MEQs is -1.73%. The CR between MCQs and MEQs for those who scored A and B is 7.38% which could indicate a weak but significant +ve CR (p value 0.017), (table3). For those who scored C inverse CR (-74.38%) was observed between MCQs and MEQs. Discussion: The main finding of this study was the weakly negative CR between students' performance on MCQs and MEQs. Good performance in MCQs is not necessary correlated with good performance in LEQs. This is not in agreement with Oyebola et al. and Moqattash et al findings, who reported positive CR in the performance of their students. The discrepancy observed in performance between MCQs and MEQs could be explained by the subjectivity and the difficulty in avoiding bias in setting and marking essay questions.   Key Words: multiple choice questions, Modified long essay questions, correlation

Acute effects of cigarette smoking on the cardiac diastolic functions

AbstractBackgroundSmoking is an independent risk factor for coronary heart diseases and it increases all causes of cardiovascular morbidity and mortality.Aim of the workTo assess the acute effect of cigarette smoking on ventricular diastolic functions (LV and RV) in healthy, young, and slim smokers.MethodsThirty volunteers who had recently commenced smoking (less than one year) and who smoked 1–2 cigarettes per day, underwent ECG, 2D and M-mode echocardiography, standard Doppler echocardiography, pulsed TDI (tissue Doppler imaging) on septal and lateral side of mitral annulus and lateral tricuspid annulus. Vp values were measured. The investigator asked them to hold smoking for at least two days after which echocardiographic examination was conducted before smoking one cigarette and the second examination conducted immediately after smoking one cigarette containing at least 0.4mg of nicotine.ResultsDoppler findings over the mitral valve showed the E wave was significantly reduced from 82.7±10.4 to 74.6±10.4 after smoking; the A wave increased; the E/A ratio was reduced from 1.5±0.3 to 1.2±0.2; the E′ septal significantly decreased (15.3±2.4 vs. 11.2±1.1) after smoking, and the E/E′ ratio increased from 5.5±1.1 to 6.7±1.1. Doppler findings over the tricuspid valve showed the E wave was reduced from 60.6±9.7 to 52.7±9.6; the A wave increased from 42.2±6.5 to 50.1±6.6; and the E/A ratio decreased (1.45±0.25 vs. 1.06±0.19). The E′ significantly decreased from 14.1±1.8 to 10.9±2.4, while the A′ increased (10.2±2.4 vs. 12.7±3.6) after smoking; and the IVRT of the RV was significantly prolonged from 62.9±7.5 to 68.7±7.9 after smoking. The Vp was markedly reduced from 67.8±8 to 55.2±3.5 after smoking. These findings reflected on the LV filling pressure (LVFvp) which increased from 9.8±1.4 to 10.5±1.3 after smoking. All changes were statistically significant at P<0.001.ConclusionsOur study reveals that cigarette smoking can result in significant acute alteration in the diastolic functions of both ventricles

Developing a simulated intelligent instrument to measure user behavior toward cybersecurity policies

Institutions struggle to protect themselves from threats and cybercrime. Therefore, they devote much attention to improving information security infrastructures. Users’ behaviors were explored via a traditional questionnaire research instrument in a data collocate process. The questionnaire explores users’ behaviors theoretically, so the respondents’ answers to the questionnaire are insufficiently reliable, and the responses might not reflect actual behavior based on the human bias when facing theoretical problems. This study aims to solve unreliable responses to the questionnaire by developing a simulated intelligent instrument to measure users’ behaviors toward cybersecurity policies in an experimental study using gamification

Active vibration suppression of a nonlinear electromechanical oscillator system with simultaneous resonance

In this paper, we explored the nonlinear dynamics behavior and vibration suppression of a nonlinear electromechanical oscillator system under harmonic and parametric excitation. The model comprises of an electrical part coupled to mechanical part and displayed by a coupled nonlinear ordinary differential equations. The analytical up to second order approximate solutions are sought applying the method of multiple scales method. We utilized the time-series and method of averaging to analyze the response and stability of the solutions at the worst resonance cases. We checked the results of perturbation solution through numerical simulations and the effects of different system parameters have been reported. Comparison between analytical and numerical solutions is obtained. Also, the numerical results are obtained using MAPLE and MATLAB algorisms

Evaluation of The Quality of E-Learning Platforms Used in Educating Kindergarten Children Distantly During the Coronavirus Pandemic

During the coronavirus pandemic, and for the first time, ministries of education in many countries have resorted to electronic education platforms for kindergarten children as a safe alternative to face-to-face education. This shift to distance education is still used partly in the education process, even after the end of the pandemic. The current study aimed to consider this unique experience by evaluating the quality of the Rawdaty platform, which is one of the e-learning platforms launched by the Saudi Ministry of Education during the coronavirus pandemic, to ensure the continuation of the educational process in kindergartens. The analytical descriptive approach was used, and a scale derived from the Saudi National E-Learning Center (NELC) standards was designed to achieve the studys objectives. The scale includes four main dimensions: Design, Interaction, Equity and accessibility, Measurement and Evaluation. The research sample consisted of (94) mothers and (67) kindergarten teachers. The results of the study were as follows: The quality standards of the Rawdaty platform were achieved to a high degree from the point of view of mothers, with an arithmetic mean of (55.93) and an average weight of (2.664). It also showed the high-quality standards of the kindergarten platform from the point of view of the teachers, with an arithmetic mean of (58.35) and an average weight of (2.78). The study recommended the possibility of adopting e-learning platforms to teach kindergarten children distantly during exceptional circumstances