Search Results (125)

The main objective of this research is to obtain interesting estimates for Jensen’s gap in the integral sense, along with their applications. The convexity of a fifth-order absolute function is used to established proposed estimates of Jensen’s gap. We performed numerical computations to compare our estimates with previous findings. With the use of the primary findings, we are able to obtain improvements of the Hölder inequality and Hermite–Hadamard inequality. Furthermore, the primary results lead to some inequalities for power means and quasi-arithmetic means. We conclude by outlining the information theory applications of our primary inequalities. Full article

In this paper, we first introduce a parametric identity for generalized differentiable functions using a generalized fractal–fractional integral operators. Based on this identity, we establish several variants of parameterized inequalities for functions whose local fractional derivatives in absolute value satisfy generalized convexity conditions. Furthermore, we demonstrate that our main results reduce to well-known Ostrowski- and Simpson-type inequalities by selecting suitable parameters. These inequalities contribute to finding tight bounds for various integrals over fractal spaces. By comparing the classical Hölder and Power mean inequalities with their new generalized versions, we show that the improved forms yield sharper and more refined upper bounds. In particular, we illustrate that the generalizations of Hölder and Power mean inequalities provide better results when applied to fractal integrals, with their tighter bounds supported by graphical representations. Finally, a series of applications are discussed, including generalized special means, generalized probability density functions and generalized quadrature formulas, which highlight the practical significance of the proposed results in fractal analysis. Full article

Background: Cooking skills represent an important yet often overlooked form of social and cultural capital, influencing dietary quality and health outcomes. As modern societies face growing challenges related to unhealthy eating patterns and a loss of traditional food practices, understanding the societal role of culinary competence becomes critical. This study explored the association between culinary skills, adherence to the Mediterranean diet, and nutritional intake. Methods: Baseline data from 111 adults (60 women; mean age 47.6 ± 10.5 years) participating in the iMC SALT randomized controlled trial (Portugal) were analyzed. Culinary skills were assessed using the Cooking Skills Score, while the dietary intake was evaluated with a Food Frequency Questionnaire and adherence to the Mediterranean diet through the alternative Mediterranean Diet (aMED) Score. Food and beverage processing levels were categorized using the NOVA classification, and the sodium/potassium intake was measured via 24 h urinary excretion. Results: Women demonstrated better culinary skills (5.1 ± 0.9 vs. 4.0 ± 1.1, p < 0.001) and greater adherence to the Mediterranean diet (5.1 ± 1.9 vs. 3.8 ± 1.8, p = 0.001) than men. Better culinary skills were associated with younger age, larger households, and increased adherence to the Mediterranean diet. Culinary skills significantly explained 27.2% of the variance in the Mediterranean diet adherence. Better culinary skills were linked to a greater energy and protein intake; but a lower sodium and potassium intake. Conclusion: These findings highlight culinary skills as a key societal factor shaping dietary behavior and nutritional intake. Promoting culinary education may offer a powerful strategy to address dietary inequalities, support cultural food heritage, and foster healthier, more resilient societies. Full article

This study presents, for the first time, a new class of interval-valued superquadratic stochastic processes and examines their core properties through the lens of the center-radius total order relation on intervals. These processes serve as a powerful tool for modeling uncertainty in stochastic systems involving interval-valued data. By utilizing their intrinsic structure, we derive sharpened versions of Jensen-type and Hermite–Hadamard-type inequalities, along with their fractional extensions, within the framework of mean-square stochastic Riemann–Liouville fractional integrals. The theoretical findings are validated through extensive graphical representations and numerical simulations. Moreover, the applicability of the proposed processes is demonstrated in the domain of information theory by constructing novel stochastic divergence measures and Shannon’s entropy grounded in interval calculus. The outcomes of this work lay a solid foundation for further exploration in stochastic analysis, particularly in advancing generalized integral inequalities and formulating new stochastic models under uncertainty. Full article

In this study, we introduce a new hybrid identity that effectively combines Newton–Cotes and Gauss quadrature, allowing us to recover well-known formulas such as Simpson’s second rule and the left- and right-Radau two-point rules, among others. Building upon this flexible framework, we establish several new biparametrized fractal integral inequalities for functions whose local fractional derivatives are of a generalized convex type. In addition to employing tools from local fractional calculus, our approach utilizes the Hölder inequality, the power mean inequality, and a refined version of the latter. Further results are also derived using the concept of generalized concavity. To support our theoretical findings, we provide a graphical example that illustrates the validity of the obtained results, along with some practical applications that demonstrate their effectiveness. Full article

This study examines the intersection of race, class, and gang violence in Singapore, with a particular focus on the structural dynamics linking racial minorities, street gangs, and institutionalized Chinese secret societies—the archetype of organized crime in the city-state. By integrating race as both an ideology and a system of social relations into the study of gang formation, this research sheds light on why and how racial minorities become disproportionately involved in gang violence. The study revealed that beyond economic marginalization, racialized hierarchies embedded within gang contexts shape the motivations, participation, and mobility of minority individuals in both street gangs and the broader criminal underworld. Drawing on the concept of racialized masculinity, it is argued that racial minorities mobilize their gender and racial resources to compensate for status disparities resulting from structural exclusion in both legitimate and illegitimate spheres. In a postcolonial, multiracial society, like Singapore, where racial and class marginalization intersect, gang affiliation emerges as a means of negotiating power and social standing. The findings contribute to scholarship on race, crime, and social stratification while informing policies aimed at addressing racial inequalities and reducing gang violence. Full article

This article proposes a conversation on the limits and possibilities of collectivizing the way in which we generate and inscribe knowledge within the terms of a political economy of knowledge production and circulation regulated by hierarchies of academic and non-academic classifications, as well as those that demarcate centres and peripheries domestically and internationally through racial–gendered distributions of authority. To this end, it explores a series of collective projects elaborated within the GlobalGRACE network in Brazil (Global Gender and Cultures of Equality), which experiment with residency methodologies designed to create the necessary infrastructure for a redistribution of power, knowledge, and authority in investigations on racial–gendered violence in the peripheries of Rio de Janeiro. As collaborators in this research–action project initiated in 2018 with the Observatory of Favelas of Rio de Janeiro, here, we mobilize two of these collective projects as case studies—the dance residency of Cia Passinho Carioca and the Free School of Arts ELÃ residency—so as to reflect on our ways of knowing and experiencing racial–gendered inequalities in context. In this way, it becomes possible to propose not only questions around the production, erasure, and appropriation of knowledge but also possibilities for the broad-based circulation of dissident knowledge practices and the subsequent displacement of established authorities in the field, notably by means of a disobjectification of subjects of knowledge and exercises in authoring in the first-person plural. This entry point into the conversation on who has the power to know and control the meanings of intersectional inequalities enables a focus on practice, pedagogy, and methods to unpack the ethical and epistemological questions at hand. By centring the problem of authorship, we argue that feminist and decolonial approaches to knowing, teaching, and learning need to effectuate redistributions of power and the construction of politico-epistemic infrastructure if we have any chance of cultivating the conditions needed for liberatory knowledge practices. Full article

Postmodern picture books offer valuable opportunities for children to engage with multiple perspectives and develop critical thinking skills. When used in pedagogical practices that prioritize children’s rights, agency, and voices, these books can effectively challenge dominant social norms and promote justice and equity. Within the framework of the SMOOTH project (Educational Common Spaces, Passing through Enclosures and Reversing Inequalities, Horizon 2020, EU), this qualitative study explores how children aged six to eight attending a public primary school in Lisbon, Portugal, make sense of gender through postmodern picture books. Grounded in the Educational Studies and Sociology of Childhood, the research analyses children’s understandings of gender and the meanings they construct concerning it. A six-month intervention program, consisting of read-aloud sessions, was conducted with children from diverse linguistic and socioeconomic backgrounds. Data were collected through focus groups and observation. Qualitative content analysis highlights how picture books can stimulate critical discussions on the social construction of gender, providing children with opportunities to reflect on differences, power relations, and social change. These findings indicate that embedding a care perspective further strengthens the recognition of children’s lived experiences and enriches educational practices by fostering inclusiveness and deeper understanding. Full article

Sexist ideologies and attitudes perpetuate gender inequalities in both private and public contexts. Traditional views of sexism emphasize hostility, but the phenomenon is more complex, involving interdependent power relations between men and women. The Ambivalent Sexism Theory identifies two forms: hostile sexism (HS) and benevolent sexism (BS). This study aimed to measure the levels of HS and BS among men in a northern Italian town, examining sociodemographic factors associated with elevated sexism scores. A paper questionnaire was administered by a volunteer organization and the Local Health Authority to male individuals over 18 in Cesena from February to April 2023. The convenience sample was recruited from diverse settings, including universities, companies, cafes, and hospitals. The Ambivalent Sexism Inventory (Glick & Fiske) was translated into Italian and used for data collection. A total of 275 participants were included. The mean age was 44.4 years, with a diverse educational background. Regression analyses revealed that higher education levels were associated with lower HS scores with a high school education and a bachelor’s degree or higher showing statistically significant coefficients of −5.33 (SE = 2.26, p = 0.019, and 95% CI: −9.78–−0.88) and −8.64 (SE = 2.51, p = 0.001, and 95% CI: −13.58–−3.69), respectively, if compared to individuals with middle school education or less. Age was a significant predictor of BS, with older individuals showing higher BS scores (Coeff. = 0.20, SE = 0.05, p < 0.001, and 95% CI: 0.10–0.31). Healthcare professionals had higher HS scores, while unionists had both lower HS and BS scores. This study highlighted the levels of both HS and BS in various professional and social contexts. Education appears to be a critical factor in reducing HS, while age influences BS. Full article

The main goal of this study is to provide new q-Fejer and q-Hermite-Hadamard type integral inequalities for uniformly convex functions and functions whose second quantum derivatives in absolute values are uniformly convex. Two basic inequalities as power mean inequality and Holder’s inequality are used in demonstrations. Some particular functions are chosen to illustrate the investigated results by two examples analyzed and the result obtained have been graphically visualized. Full article

The goal of this study is to develop numerous Hermite–Hadamard–Mercer (H–H–M)-type inequalities involving various fractional integral operators, including classical, Riemann–Liouville (R.L), k-Riemann–Liouville (k-R.L), and their generalized fractional integral operators. In addition, we establish a number of corresponding fractional integral inequalities for three-times differentiable convex functions that are connected to the right side of the H–H–M-type inequality. For these results, further remarks and observations are provided. Following that, a couple of graphical representations are shown to highlight the key findings of our study. Finally, some applications on special means are shown to demonstrate the effectiveness of our inequalities. Full article

The intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex stochastic processes simultaneously. We employ weighted quasi-mean, non-negative mapping $\gamma$, and center-radius ordering relations to establish a class of extended $cr$-interval-valued convex stochastic processes. This class yields a combination of innovative convex and non-convex stochastic processes. We characterize our class by illustrating its relationships with other classes as well as certain key attributes and sufficient conditions for this class of processes. Additionally, leveraging Riemann–Liouville stochastic fractional operators and our proposed class, we prove parametric fractional variants of Jensen’s inequality, Hermite–Hadamard’s inequality, Fejer’s inequality, and product Hermite–Hadamard’s like inequality. We establish an interesting relation between means by means of Hermite–Hadamard’s inequality. We utilize the numerical and graphical approaches to showcase the significance and effectiveness of primary findings. Also, the proposed results are powerful tools to evaluate the bounds for stochastic Riemann–Liouville fractional operators in different scenarios for a larger space of processes. Full article

In this paper, a Takagi–Sugeno fuzzy parallel distributed compensation control (TS-PDCC) is proposed for low-frequency oscillation (LFO) suppression in wind energy-penetrated power systems. Firstly, the fuzzy C-mean algorithm (FCMA) is applied to cluster the daily average wind speed of the wind farm, and the obtained wind speed clustering center is used as the premise variable of TS-PDCC, which increases the freedom of parameter setting of the TS fuzzy model and is closer to the actual working environment. Secondly, based on the TS fuzzy model, the TS-PDCC is designed to adjust the active power output of the wind turbine for LFO suppression. To facilitate the computation of controller parameters, the stability conditions are transformed into a set of Linear Matrix Inequalities (LMIs) via the Schur complement. Subsequently, a Lyapunov function is designed to verify the stability of the wind energy-penetrated power system and obtain the parameter ranges. Simulation cases are conducted to verify the validity and superior performance of the proposed TS-PDCC under different operating conditions. Full article

In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for functions whose first-order local fractional derivatives are generalized convex and concave. The obtained results not only represent an extension of certain previously established findings to fractal sets but also a refinement of these when the fractal dimension $\mu$ is equal to one. Finally, to support our findings, we present a practical application to demonstrate the effectiveness of our results. Full article

In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of strongly convex functions, along with some previously known results about strongly convex functions. We are also focused on important applications of the derived results in information theory, deducing estimates for $\chi$-divergence, Kullback–Leibler divergence, Hellinger distance, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence. Additionally, we prove some applications to Mercer-type power means at the end. Full article