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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]

The power output in cycling is one of the most important factors for athletes and coaches. The cycling community has several commercial gears that can be used. One of the most used is the TACX Neo 2T (TN2T) smart trainer. The objective of this study was to investigate the metrological proprieties of the TN2T (accuracy and reliability), as well as its agreement with the Garmin Vector 3 (GV3) pedals at different power stages. The sample consisted of ten regional-level cyclists with a mean age of 45.6 ± 6.4 years, who regularly participated in regional and national competitions. Residual relative differences were found between the two devices. Both devices showed good reliability with coefficients of variation and intraclass correlation coefficients ranging from 0.03% to 0.15% and from 0.731 to 0.968, respectively. Independent samples t-test comparison between devices showed no significant differences in all power stages (p > 0.05). Bland–Altman plots showed that more than 80% of the plots were within the 95% confidence intervals in all power stages. The present data showed that there were non-significant differences between the two devices at power stages between 100 W and 270 W, with a strong agreement. Therefore, they can be used simultaneously. [ABSTRACT FROM AUTHOR]

This study examined whether sleep disturbance predicted or moderated responses to psychotherapy in participants who participated in STEP-BD, a national, multisite study that examined the effectiveness of different treatment combinations for bipolar disorder. Participants received either a brief psychosocial intervention called collaborative care (CC; n = 130) or intensive psychotherapy (IP; n = 163), with study-based pharmacotherapy. Participants (N = 243) were defined as current (past week) short sleepers (

This research note investigates how different sources of economic information affected citizens' approval of the government in Portugal from 2001 to 2018. It compares the predictive power of the revised and most accurate data on GDP growth with other economic indicators that were available to the public at the time, such as the first estimates of recent growth and the forecasts of future growth. It finds that approval is best predicted by information about forecasted growth for the current year. These results provide further indirect evidence that the state of the economy, as it plays out directly in people's lives and experiences, may be less consequential for evaluations of the government than the mediated information about it that is conveyed to the public. [ABSTRACT FROM AUTHOR]