Key polynomials for simple extensions of valued fields

Let $\iota:K\hookrightarrow L\cong K(x)$ be a simple transcendental extension of valued fields, where $K$ is equipped with a valuation $\nu$ of rank 1. That is, we assume given a rank 1 valuation $\nu$ of $K$ and its extension $\nu'$ to $L$. Let $(R_\nu,M_\nu,k_\nu)$ denote the valuation ring of $\nu$. The purpose of this paper is to present a refined version of MacLane's theory of key polynomials, similar to those considered by M. Vaqui\'e, and reminiscent of related objects studied by Abhyankar and Moh (approximate roots) and T.C. Kuo. Namely, we associate to $\iota$ a countable well ordered set $$\mathbf{Q}=\{Q_i\}_{i\in\Lambda}\subset K[x];$$ the $Q_i$ are called {\bf key polynomials}. Key polynomials $Q_i$ which have no immediate predecessor are called {\bf limit key polynomials}. Let $\beta_i=\nu'(Q_i)$. We give an explicit description of the limit key polynomials (which may be viewed as a generalization of the Artin--Schreier polynomials). We also give an upper bound on the order type of the set of key polynomials. Namely, we show that if $\operatorname{char}\ k_\nu=0$ then the set of key polynomials has order type at most $\omega$, while in the case $\operatorname{char}\ k_\nu=p>0$ this order type is bounded above by $\omega\times\omega$, where $\omega$ stands for the first infinite ordinal.Comment: arXiv admin note: substantial text overlap with arXiv:math/060519

The effect of oil price shocks on the Saudi manufacturing sector

This paper aims to examine the effects of oil price shocks on the manufacturing sector in Saudi Arabia during the period 2002 – 2014, using quarterly data. A unit root test was conducted, in which the data were shown to be non-stationary in the level, and they became stationary in the first difference for all variables. The co-integration model was applied, and the results indicated that no co-integrating equation exists, which means that there is no long run effect of oil price shocks on the manufacturing sector. So, we estimate a Vector Auto Regressive model, the results of which implied that oil price shocks do not affect in the manufacturing sector in the short run, and it may have an effect on the manufacturing sector after 10 quarter according to the impulse response function

Knowledge and attitude towards mental illness among health and non-health university students in Riyadh

Background: Mental illness can affect anyone regardless of age, gender, and residence. Studying the attitude and knowledge about mental illnesses among university students is important, because they are the future decision makers dealing with such problems. The aim of this study was to assess level of knowledge and attitude towards mental illnesses among health and non-health university students in Riyadh.Methods: This study was a cross-sectional study on students of the governmental universities in Riyadh with both health and non-health speciality. The total sample size was 587 students. The questionnaire was designed electronically, and the link was distributed through social media. It included socio-demographic questions, 17 questions to assess knowledge and 22 questions to assess the attitudes. The statistical tests used were chi square, independent sample t-test, spearman’s correlation and multiple linear regression tests.Results: More than half of the participants had a positive attitude toward mental illness (52%). Only 13.46% of university students had good knowledge about mental illness. Significant higher level of good knowledge and positive attitude were reported among health college students compared to non-health (24.7% versus 7.9% for good knowledge and 60.8% versus 48.3 for positive attitude respectively). Attitude towards mental illness can be successfully predicted by using the knowledge score about mental illness and the type of college.Conclusion: Low percentage of university students had good knowledge about mental illness and their attitude towards mental illness was generally positive. Health college students had better attitude and knowledge about mental illness than non-health

Autisme et stress familial : le burn-out parental Défier les barrières sociales pour des perspectives d’épanouissement personnel - regard de psychologie positive

Le mot « autiste » prend son origine de la langue grecque, (autos) signifie soi-même. Il a été employé en 1911 par le psychiatre suisse Eugen Bleuler pour qualifier les patients schizophrènes repliés sur eux-mêmes. L'autisme est un trouble neuro-développemental, caractérisé par des altérations de la communication verbale et non verbale, pendant les relations sociales et lors des comportements et des activités à caractère restreint et répétitif [1]. Ces symptômes apparaissent avant l’âge de 3 ans et sont regroupés sous l’appellation       « triade autistique » et plus précisément des anomalies de comportement.        L'autisme est considéré comme un problème de santé publique. Plusieurs facteurs sont à l'origine de trouble, y compris ceux qui sont de nature génétique.      Les études génétiques des formes mono géniques du trouble du spectre autistique (TSA) ont identifié la fonction synaptique comme l'une des voies moléculaires des troubles neuro-développementaux sous-jacents [2]. Plusieurs gènes sont mis en cause, notamment les gènes des neuroligines, des protéines d'adhésion post-synaptiques des cellules impliquées dans la maturation du système nerveux et la plasticité des réseaux neuronaux [3]

Investigating the Interaction between Soil and Cultivator Blade by Numerical Simulation and Validation of Results by Soil Bin Tests

IntroductionSeedbed preparation, seeding, and transplanting are usually based on mechanical soil tillage. Tillage by cutting, mixing, overturning, and loosening the soil can modify the physical, mechanical, and biological properties of soil. These days, because of soil protection, the use of tillage tools is less and less recommended, and some implements such as cultivators are preferred to primary tillage tools such as plows. Experimental study of soil-tool interaction and field measurements of the mechanics of tillage tools are usually time-consuming and costly. On the other hand, the variety of variables and uncontrolled conditions add other dimensions to the complexity of this method. Also, the experimental and analytical methods do not have a comprehensive view of stress distribution and soil deformation in the soil-tool interaction process.Materials and MethodsThe main purpose of this study is to validate the results of numerical simulations in two phases of experimental tests: in soil bin environment and in finite element computer simulations. Experimental tests were performed in the soil bin environment of the Department of Mechanical Engineering of Biosystems, Urmia University, which has a soil bin facility with dimensions of length and width of 24 and 2 m, respectively, and has clay loam soil. Before experimental tests, soil preparation was performed by using some special tillage implements (harrow, leveler, and roller) which were attached to the soil bin (Figure.1). For experimental tests, a mechanism set consisting of two cultivator blades with a width of 15cm, a length of 20cm, and at a spacing of 35cm from each other was prepared and constructed. The relevant mechanism is designed to have the ability to change the tillage depth. Data were collected at three different soil depth levels of 6, 10, and 14cm in the soil bin with three replications. Data recording was performed using a 10-channel data logger with load cell connectivity and data storage ability. Also, in this study, the Drucker-Prager model as a finite element simulation method was used to calculate the stress during the soil-tool relationship. ABAQUS 6.10.1 software was used to simulate the cultivator tine. To solve the problem, the soil parameters were defined as presented in Table 1, and then the interaction between the soil-tool model and the necessary constraints, including boundary conditions, were defined. In the next step, meshing was applied to the constructed model.Results and DiscussionIn the results section, first, the results related to the amount of traction force required for the tillage tine in the simulation were calculated and then compared with the soil bin experimental tests. The traction force of the finite element simulation results for three tillage depths of 6, 10, and 14 cm in three principal directions is shown in Figure 4. A comparison of simulation and experimental results showed that there is a good agreement between them. In comparison, the simulation error range of the three depths of 6, 10, and 14 cm has shown 7.3, 5.6, and 4.16% at a speed of 2.5 kmh-1, respectively, as the velocity studied in this research. In the next section, the results of stress distribution contours in the soil and finally the overlap of the blade effect were discussed. Figure 6 shows the status of stress contours at three depths. By increasing the depth of the tine at the three depth levels studied, the stress range is shifted from the soil surface to its depth. For this purpose, at the maximum depth studied in this study (14 cm), it shows that the stress propagation to the soil surface is less than at other depths. Also, with decreasing depth, for a depth of 6 cm, the maximum stress was on the top soil surface, in other words, more deformation was seen on the soil surface.ConclusionComparing the simulation results for predicting traction force with the results of experimental tests has led to relatively acceptable results and the maximum traction force prediction error at different depths has been about 7.3%.The distribution of stress in the soil was observed due to the tine depth. The highest intensity of stress propagation was observed at the soil surface; and the highest soil surface deformation at a depth of 6 cm. With increasing depth, both parameters of stress and soil surface deformation have decreased. According to the results of the studied blades, it is better to use these types of tillage tools only at lower depths. Also, in evaluating the overlap of the soil loosening zone in the side-by-side tines, it proves the superiority of the tine performance at lower depths

Prediction of COVID-19 Hospital Length of Stay and Risk of Death Using Artificial Intelligence-Based Modeling

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a highly infectious virus with overwhelming demand on healthcare systems, which require advanced predictive analytics to strategize COVID-19 management in a more effective and efficient manner. We analyzed clinical data of 2017 COVID-19 cases reported in the Dubai health authority and developed predictive models to predict the patient's length of hospital stay and risk of death. A decision tree (DT) model to predict COVID-19 length of stay was developed based on patient clinical information. The model showed very good performance with a coefficient of determination R2 of 49.8% and a median absolute deviation of 2.85 days. Furthermore, another DT-based model was constructed to predict COVID-19 risk of death. The model showed excellent performance with sensitivity and specificity of 96.5 and 87.8%, respectively, and overall prediction accuracy of 96%. Further validation using unsupervised learning methods showed similar separation patterns, and a receiver operator characteristic approach suggested stable and robust DT model performance. The results show that a high risk of death of 78.2% is indicated for intubated COVID-19 patients who have not used anticoagulant medications. Fortunately, intubated patients who are using anticoagulant and dexamethasone medications with an international normalized ratio of <1.69 have zero risk of death from COVID-19. In conclusion, we constructed artificial intelligence–based models to accurately predict the length of hospital stay and risk of death in COVID-19 cases. These smart models will arm physicians on the front line to enhance management strategies to save lives

Study of the Fusion-Fission Process in the 35Cl+24Mg^{35}Cl+^{24}Mg Reaction

Fusion-fission and fully energy-damped binary processes of the $^{35}$Cl+$^{24}$Mg reaction were investigated using particle-particle coincidence techniques at a $^{35}$Cl bombarding energy of E$_{lab}$ $\approx$ 8 MeV/nucleon. Inclusive data were also taken in order to determine the partial wave distribution of the fusion process. The fragment-fragment correlation data show that the majority of events arises from a binary-decay process with a relatively large multiplicity of secondary light-charged particles emitted by the two primary excited fragments in the exit channel. No evidence is observed for ternary-breakup processes, as expected from the systematics recently established for incident energies below 15 MeV/nucleon and for a large number of reactions. The binary-process results are compared with predictions of statistical-model calculations. The calculations were performed using the Extended Hauser-Feshbach method, based on the available phase space at the scission point of the compound nucleus. This new method uses temperature-dependent level densities and its predictions are in good agreement with the presented experimental data, thus consistent with the fusion-fission origin of the binary fully-damped yields.Comment: 30 pages standard REVTeX file, 10 eps Figures; to be published at the European Physical Journal A - Hadrons and Nucle