Geometry is a very interesting, applicable and beautiful part of mathematics. However, geometry is often difficult for students to understand and demanding for teachers to teach [1]. Constructing proofs in geometric problems turns out to be particularly difficult, even for high attaining students [2]. Sometimes, students do not even know where to start when trying to solve these [3].

A simple polygon that either has equal all sides or all interior angles is called a semi-regular nonagon. In terms of this definition, we can distinguish between two types of semi-regular polygons: equilateral polygons (that have equal all sides and different interior angles) and equiangular polygons (that have equal interior angles and different sides). Unlike regular polygons, one characteristic element is not enough to analyze the metric properties of semi-regular polygons, and an additional one is needed. To select this additional characteristic element, note that the following regular triangles can be inscribed to a semi-regular equilateral nonagon by joining vertices: ∆A1 A4A7, △ A2 A5 A8, △A3 A6 A9. Now have a look at triangle △A1 A4A7. Let us use the mark φ=∡(a,b1) to mark the angle between side a of the semi-regular nonagon and side b1 of the inscribed regular triangle. In interpreting the metric properties of a semi-regular equilateral nonagon, in addition to its side, we also use the angle that such side creates with the side of one of the three regular triangles that can be inscribed to such semi-regular nonagon. We consider the way in which convexity, possibility of construction, surface area, and other properties depend on a side of the semi-regular nonagon and angle φ=∡(a,b1).

A simple polygon that either has equal all sides or all interior angles is called a semi-regular polygon. In terms of this definition, we can distinguish between two types of semi-regular polygons: equilateral polygons (that have equal all sides and different interior angles) and equiangular polygons (that have equal interior angles and different sides). To analyze the metric properties of semi-regular polygons, knowing only one basic element, e.g. the length of a side, as in regular polygons, is not enough. Therefore, in addition to the side of a semi-regular polygon, we use another characteristic element of it to analyze the metric features, and that is the angle δ=∠(a,b) between the side of a semi-regular polygon PN and the side b of its inscribed regular polygon PN. Some metric properties of a semi-regular equilateral 2n-sides polygon are analyzed in this paper with respect to these two characteristic elements. Some of the problems discussed in the paper are: convexity, calculation of surface area, dependence on the length of sides a and δ, calculation of the radius of the inscribed circle depending on the sides a and angles δ, and calculation of the surface area in which the radius of the inscribed circle is known, as well as the relationship between them. It has been shown that the formula for calculating the surface area of regular polygons results from the formula for the surface area of 2n-side semi-regular, equilateral polygons. Further, by using these results, it has been shown that the cross-sections of regular polygons inscribed to semi-regular equilateral polygons, the vertices of equiangular semi-regular polygons, as well as the sides of the regular polygons inscribed to it, intersect in the same manner at the vertices of the equilateral semi-regular polygon. It has further been shown that the sides of the equiangular semi-regular polygon refer to each other as the sines of the angles created by the sides of the inscribed polygons and the side of the semi-regular polygon.

Recently, Leung et al. [1] proposed that α7-subtype nicotinic acetylcholine receptor (α7-nAChR) antagonists might decrease angiotensin-converting enzyme (ACE)2 receptor expression in respiratory epithelium and, hence, prevent severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) invasion of pulmonary epithelial cells. Let us further theoretically evaluate this assertion and contribute to the quest for potential medications that might reduce virulence and pathogenicity of coronavirus disease 2019 (COVID-19). Smoking may be associated with progression and negative outcome of COVID-19 [1]. The receptor-binding domain of the S protein (spike) on the surface of SARS-CoV-2 interacts with the ACE2 receptor, which is an entry point of the virus into host respiratory cells [2]. Memantine, as an antagonist of α7-nAChR and NMDA receptors, may decrease ACE2 receptor expression and reduce oxidative stress and inflammation. Hence, memantine may potentially reduce SARS-CoV-2 virulence. https://bit.ly/2AZHiVg

OBJECTIVES The Dark Triad traits (i.e., narcissism, psychopathy, Machiavellianism) capture individual differences in aversive personality to complement work on other taxonomies, such as the Big Five traits. However, the literature on the Dark Triad traits relies mostly on samples from English-speaking (i.e., Westernized) countries. We broadened the scope of this literature by sampling from a wider array of countries. METHOD We drew on data from 49 countries (N = 11,723; 65.8% female; AgeMean = 21.53) to examine how an extensive net of country-level variables in economic status (e.g., Human Development Index), social relations (e.g., gender equality), political orientations (e.g., democracy), and cultural values (e.g., embeddedness) relate to country-level rates of the Dark Triad traits, as well as variance in the magnitude of sex differences in them. RESULTS Narcissism was especially sensitive to country-level variables. Countries with more embedded and hierarchical cultural systems were more narcissistic. Also, sex differences in narcissism were larger in more developed societies: Women were less likely to be narcissistic in developed (vs. less developed) countries. CONCLUSIONS We discuss the results based on evolutionary and social role models of personality and sex differences. That higher country-level narcissism was more common in less developed countries, whereas sex differences in narcissism were larger in more developed countries, is more consistent with evolutionary than social role models.

Abstract We apply deep kernel learning (DKL), which can be viewed as a combination of a Gaussian process (GP) and a deep neural network (DNN), to compression ignition engine emissions and compare its performance to a selection of other surrogate models on the same dataset. Surrogate models are a class of computationally cheaper alternatives to physics-based models. High-dimensional model representation (HDMR) is also briefly discussed and acts as a benchmark model for comparison. We apply the considered methods to a dataset, which was obtained from a compression ignition engine and includes as outputs soot and NOx emissions as functions of 14 engine operating condition variables. We combine a quasi-random global search with a conventional grid-optimization method in order to identify suitable values for several DKL hyperparameters, which include network architecture, kernel, and learning parameters. The performance of DKL, HDMR, plain GPs, and plain DNNs is compared in terms of the root mean squared error (RMSE) of the predictions as well as computational expense of training and evaluation. It is shown that DKL performs best in terms of RMSE in the predictions whilst maintaining the computational cost at a reasonable level, and DKL predictions are in good agreement with the experimental emissions data.

Arylmethylenebis(3-hydroxy-5,5-dimethyl-2-cyclohexen-1-one) derivatives (aryl=2-hydroxynaphthyl ( 1 ) and 3,4-dihydroxyphenyl ( 2 ) have been synthesized and their structures have been elucidated. Both compounds were examined for their antioxidant, antimicrobial and cytotoxic activity. Antioxidative activities of synthesized compounds were evaluated by 2,2-diphenyl-1-picryl-hydrazyl (DPPH) and ferric reducing antioxidant power (FRAP) methods. The microbial screening was performed by diffusion method on bacterial strains Staphylococcus aureus , Enterococcus faecalis , Bacillus subtilis and Candida albicans . Cytotoxic activity was tested on liver hepatocellular carcinoma cell line (Hep G2) by Neutral red assay. Compared to compound 2 , compound 1 showed better antimicrobial and antifungal activity, while compound 2 showed better antioxidant activity with IC 50 of 0.0156 mM and FRAP value 50469.44 µmol/l Fe 2+ . Both compounds showed cytotoxic activity. Obtained results implicate the importance of arylmethylenebis(3-hydroxy-5,5-dimethyl-2-cyclohexen-1-on) derivatives as a potential antioxidant, antimicrobial and cytotoxic agents.

According to the report of the World Health Organization, the city of Tuzla is the second in the world, and the first in Europe in terms of the number of diseases caused by air pollution. Tuzla Canton since 2003 has continuous air monitoring. Concentrations of individual pollutants exceed hourly, daily and annual limit values. In this paper, based on the existing results of air monitoring and meteorological data, using statistical methods and neural network modeling methods, unique and reliable models for predicting the concentration of NO2 in the air for the City of Tuzla have been developed. The results obtained using these models can be used in strategic decision-making processes and activities related to air quality control and management. This paper, on the example of the City of Tuzla, showed that using existing air monitoring data, concentrations of pollutants can be predicted for a longer period of time, using artificial intelligence methods. Reliable models with a high correlation coefficient can be obtained. In the case of a short or long interruption of the measurement of pollutant concentrations for the City of Tuzla with the help of models, which are the result of this work, it is possible to predict the concentrations of pollutants and plan to take measures based on them.

A simulation of a single-stage evaporator system integrated with a mechanical com- pressor for a case study (concentrating the electrolytic system KNO3 – H2O) was performed. A mathematical model of the subsystem of a single-stage evaporator, a mechanical compressor, and superheated steam seeding is presented. Microsoft Excel with VBA (Visual Basic for Application) was used to solve the mathematical model. The model was solved by an iterative method where the values of the in- let stream temperature and the salt concentration in the concentrated stream at the evaporator outlet were assumed. The process parameters of the system have been determined. Since the goal of any industrial process is to minimize costs and maximize products, the impact of mean temperature difference changes on satu- ration water consumption and molar salt content in the concentrated stream was presented. 106.92 kg/h of freshwater are required to obtain 18% by weight of salt in a concentrated stream, while 432.30 kg/h of fresh water are required to obtain 25% by weight of salt in a concentrated stream. Consumption of heating steam ranged from 1760.31 to 4473.4 kg/h depending on the average temperature dif- ference. By increasing the temperature differences from 10 to 25 ◦C, the amount of transferred upper lines increases from 1025 to 2750 kW, which is an advantage of increasing the mean temperature difference. The disadvantage of the larger tem- perature difference is the increase in the power of the mechanical compressor from 97.02 to 384.12 kW.

The aim of this study was to examine foreign language classroom anxiety and motivation to speak in English as a foreign language with respect to gender and grade level as well as their effects on students' EFL performance. The research sample comprised 160 (middle and high school) students. Foreign Language Classroom Anxiety Scale (FLCAS) and the Speaking Motivation Scale were used to collect the data. The results showed that foreign language classroom anxiety and intrinsic motivation were negatively associated with each other, while extrinsic motivation and a motivation were significantly positively associated with foreign language classroom anxiety. Even though there was an insignificant difference between the males’ and females’ motivation to speak English as a foreign language, foreign language classroom anxiety was significantly affected by gender. The outcomes of a one-way MANOVA revealed that grade level had no effect on the combined dependent variables of foreign language classroom anxiety, while it had a significant effect on speaking motivation. Furthermore, the findings indicated that overall intrinsic motivation and intrinsic motivation to experience stimulation were significant predictors of the students’ EFL achievement, whereas communication apprehension as a foreign language classroom anxiety factor was in a negative association with the students’ EFL achievement. The study provides instructors with guidelines on how to make their classrooms an environment conducive to the development of higher levels of speaking motivation and lower levels of anxiety with the aim of improving their students’ performance.

Cloud point extraction (CPE) is an attractive technique that reduces solvent con- sumption and exposure, disposal costs, and process time. This method has an im- portant practical application and is used to separate and concentrate the analyte as a step before its determination, and after the formation of a poorly water-soluble complex. Use of nonionic surfactants as ”green solvents” which represent an effec- tive alternative to toxic organic solvents (in classical extraction), along with other advantages, such as low cost and low flammability, makes this method attractive and worth further research and optimization. This paper presents a detailed de- scription of the principles, procedure, advantages, disadvantages and application of CPE.