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The paper expands the finite difference method to the complex plane, and thus obtains an improvement in the resolution of differential equations with an increase in numerical precision and a generalization in the mathematical modeling of problems. The article begins with a selection of the best techniques for obtaining finite difference coefficients for approximating derivatives in the real domain. Then, the calculation is expanded to the complex domain. The research expands forward, backward, and central difference approximations of the real case by a quadrant approximation in the complex plane, which facilitates the use in boundary conditions of differential equations. The article shows many real and complex finite difference equations with their respective order of error, intended to serve as a basis and reference, which have been tested in practical examples of solving differential equations used in engineering. Finally, a comparison is made between the real and complex techniques of finite difference methods applied in the Theory of Elasticity. As a surprising result, the article shows that the finite difference method has great advantages in numerical precision, diversity of formulas, and modeling generalities in the complex domain when compared to the real domain. [ABSTRACT FROM AUTHOR]

Introduction: There remains a dearth of knowledge concerning the phenomenology of suicidal thoughts, with research focusing on reasons for feeling suicidal rather than their mental expression. While clinical interviews remain the standard phenomenological approach, such exploration of lived experiences may prove challenging for this sensitive topic. As a complementary alternative, the use of naturally-occurring online data is opportune for capturing elaborations on tabooed phenomena. Methods: In this phenomenological study, we present a thematic analysis on lived experiences of suicidal thoughts as spontaneously reported by nonidentified users of a Reddit online board (r/Depression), collecting 668 posts using the search terms "suicidal ideation," "suicidal thoughts," and "suicide." Codes were grouped into descriptive categories summarizing the properties of thoughts, their effects, and their relation to suicide. Then, an interpretative synthesis yielded global themes connecting salient meanings on the experience of suicidal thoughts. Results: With a long-term and recurring nature, thoughts of suicide appear in the form of vivid imagery and daydreaming's, initially bringing relief to adverse feelings but eventually becoming conditioned and all-consuming. Rather than a wonderment, they are experienced as intrusive thoughts by people struggling to make meaning of their occurrence. When conciliating the presence of unwanted thoughts, users express intricate relations to wishing or not to die, as well as varying perceptions of control over actions or fear of suicidal behavior. Discussion: With an innovative application of big qualitative data into phenomenological analysis, this study contributes to an initial characterization of suicidal thoughts, uncovering findings that are not contemplated into current conceptualizations of suicidality. The analysis is limited by a restricted context of posts and unknown demographics, and further research with clinical interviews is warranted for in-depth exploration of suicidal thoughts. [ABSTRACT FROM AUTHOR]

Can governments make courts politically compliant without undermining public confidence in the judicial system? Many studies show a positive relationship between judicial independence and citizens' trust in courts. However, most of them have shown static cross-sectional correlations rather than actual effects of court curbing on trust. Factors such as citizens' level of education and political preferences may also play a role in moderating reactions to court curbing. We analyse how assaults on judicial independence by populist governments in Turkey, Hungary, and Poland affected judicial trust, using a difference-in-differences approach to Eurobarometer data. While we find evidence that court curbing has an adverse effect on judicial trust, this effect is much clearer among citizens who are ideologically distant from their governments. These findings coincide with experimental evidence indicating how citizens tolerate democratic backsliding, suggesting that, for many, trust in the judicial system can subsist even when courts are made politically subservient. [ABSTRACT FROM AUTHOR]

Prior work shows that women are, on average, more risk averse than men. This evidence has been used to theorize about gender differences in elite behavior. However, whether differences in risk aversion hold among the subset of citizens willing to run for office remains an open question. We report a preregistered experiment with parliamentary candidates in Portugal and find that women candidates are less risk averse than men candidates. This effect is driven by risk preferences in public investments and is not explained by gender differences in political experience. The findings are consistent with a process of gendered (self-)selection in which women risk-takers are disproportionately attracted to enter a men-dominated career and run for office. Despite requiring future validation in different contexts, the evidence highlights the challenges of extrapolating from citizen samples to study elite behavior and suggests that risk perceptions are a relevant supply-side determinant of women representation. [ABSTRACT FROM AUTHOR]

The aim of this study was to verify the accuracy of predicting oxygen consumption (O2) in predominantly aerobic activities based on net heart rate (netHR), sex, and body mass index (BMI) in active adults. NetHR is the value of the difference between the resting HR (HRrest) and the average HR value obtained during a given session or period of physical activity. These activities must be continuous, submaximal, and of a stabilized intensity. The magnitude of the netHR depends mainly on the intensity of the exercise. The HR is measured in beats per minute (bpm). A total of 156 participants, 52 women and 104 men, between the ages of 18 and 81, had their netHR and net oxygen intake (netVO2) assessed. There were 79 participants in group 1 (prediction sample) (52 males and 27 females). There were 77 people in group 2 (validation sample) (52 males and 25 females). The results of the multiple linear regression showed that netVO2 (R2 = 85.2%, SEE = 3.38) could be significantly predicted by sex (p < 0.001), netHR (p < 0.001), and BMI (p < 0.001). The Bland–Altman plots satisfied the agreement requirements, and the comparison of the measured and estimated netVO2 revealed non-significant differences with a trivial effect size. We calculated the formula NetVO2 (mL/(kg·min)) = 16 + 3.67 (sex) + 0.27 (netHR) − 0.57 (BMI) to predict netVO2, where netVO2 is the amount of oxygen uptake (mL/(kg·min)) above the resting value, netHR is the heart rate (beats per minute) above the resting value measured during exercise, sex is equal to zero for women and one for men, and BMI is the body mass index. In addition, based on the knowledge of VO2, it was possible to estimate the energy expenditure from a particular training session, and to determine or prescribe the exercise intensity in MET (metabolic equivalent of task). [ABSTRACT FROM AUTHOR]

‘Welfare chauvinism’ (or ‘welfare ethnocentrism,’ when directed against native-born ethnic minorities) is a declination of nativism within the social policy domain and a common element of populist radical right discourse. Previous studies have shown that this rhetoric can influence how people perceive the deservingness and entitlement of certain groups to welfare rights. In this study, we propose it has additional effects by evoking a purported lack of reciprocity in what concerns benefits from, and contributions to, the welfare system, such rhetoric can also justify and legitimize discrimination against out-groups in other domains that are unrelated to welfare. We use a pre-registered experiment embedded in a survey of a nationally representative sample of the Portuguese population to examine whether individuals who are exposed to the issue of illegitimate ‘takers’ of the welfare system become more likely to express discriminatory intentions regarding an out-group’s freedom of movement and establishment. We find that in the Portuguese context, where the populist radical right frequently portrays the Roma minority as welfare abusers, highlighting the issue of reciprocity can trigger a sizeable increase in discriminatory intentions against the Romani even in domains unrelated to welfare rights. [ABSTRACT FROM AUTHOR]