Geometric patterns identified in spatial data after inspection are difficult to evaluate statistically. When hypotheses are formulated a posteriori, conventional tests can overestimate significance because exploratory choices are not accounted for. This problem is pronounced in small-N spatial point sets, where model flexibility and feature selection strongly influence outcomes.A constrained evaluation framework is applied to assess a posteriori geometric hypotheses in spatial data. The approach limits the geometric degrees of freedom and conditions tests on a fixed set of candidate points. It is intended for situations in which a geometric pattern is first observed and then formally assessed. Point-to-curve deviations are used to compare the observed configuration with alternative spatial and geometric arrangements subject to specified constraints.The framework is demonstrated using a summit landscape in Central Bosnia, where a constrained logarithmic curve pattern has been proposed to link a small set of named summit locations derived from LiDAR data. The observed configuration occupies an extreme position relative to alternative constrained configurations within the defined summit set.The analysis is limited to spatial geometry and does not address origin or interpretation. The contribution is a transparent method for evaluating a posteriori geometric hypotheses in small-N spatial datasets.
Vol. 13, Issue 03, March, 2026
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ABSTRACT:DOI:https://doi.org/10.64485/ijramr.6464.03.2026
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ABSTRACT:
This paper examines the critical and evolving role of environmental sustainability in the English Premier League (EPL), using Manchester United Football Club (MUFC) as an in-depth case study. Amid growing global pressure for corporate environmental responsibility, the professional sports industry, and elite football in particular, faces increasing scrutiny over its substantial environmental footprint. This research investigates the key barriers and drivers shaping the adoption of sustainable practices at one of the world’s most iconic football clubs. It specifically explores the potential for circular economy (CE) principles to be integrated into large-scale stadium operations, infrastructure renovation, and broader club strategies to foster long-term ecological and financial resilience. The study employs a mixed-methods approach, triangulating quantitative data from a large-scale survey of 857 football community members with qualitative insights from semi-structured interviews with eight senior stakeholders from MUFC, UEFA, the Premier League, and other expert organisations. The findings reveal strong stakeholder support for sustainability initiatives, even in the face of financial costs, yet also highlight a significant awareness gap regarding existing club efforts. Key statistical correlations demonstrate a powerful link between environmental consciousness and support for corporate responsibility, as well as a willingness to accept the practical implications of sustainable infrastructure projects. The research synthesises these findings to provide a nuanced understanding of the complex interplay between governance, finance, stakeholder expectations, and operational realities in shaping the sustainability agenda of elite football clubs. It concludes with a set of strategic, evidence-based recommendations for Manchester United and other Premier League clubs to advance their environmental performance, arguing that a proactive and deeply integrated sustainability strategy is not merely a reputational asset but a fundamental component of modern, responsible business practice in the 21st century, essential for securing the long-term social license and commercial viability of the sport.
DOI:https://doi.org/10.64485/ijramr.6469.03.2026 -
ABSTRACT:
Introduction: Premenstrual Syndrome (PMS) is a prevalent cyclical gynecological condition characterized by recurrent physical, psychological, and behavioral symptoms that occur during the luteal phase of the menstrual cycle and subside with the onset of menstruation. Although PMS is not described as a distinct disease entity in Unani medicine, its symptom complex closely corresponds to conditions such as Ihtebās-e-Ṭams (retention of menses), Sudāʿ Qabl al-Ḥayḍ (premenstrual headache), and Tashannuj al-Raḥim (uterine spasm). These conditions are attributed to sūʾ-e-mizāj (deranged temperament), imtilāʾ (congestion), and fasād-e-dam (impurity of blood), resulting in humoral imbalance and altered uterine function. Meterial and Method s: This narrative review examines the Unani conceptualization of PMS through classical medical texts such as Al-Qānūn fī al-Ṭibb, Al-Ḥāwī, Kulliyāt-e-Nafīsī, and Zakhīra Khwārazm Shāhī, along with contemporary scientific literature. The Unani framework is critically compared with modern biomedical explanations emphasizing hormonal and neurochemical mechanisms. Results and Discussion: Unani management of PMS focuses on restoring humoral balance and normalizing temperament through Ilāj bil-Tadbīr (regimenal therapy), Ilāj bil-Ghizā (dietotherapy), and Ilāj bil-Dawā (pharmacotherapy). Medicinal plants such as Asgandh (Withania somnifera), Bābūna (Matricaria chamomilla), and Saunf (Foeniculum vulgare) exhibit musakkin, mudirr-e-ṭams, and muḥallil-e-waram properties, providing symptomatic relief and hormonal regulation. Conclusion: The Unani system offers a holistic and individualized approach to PMS by addressing both physiological and psychological dimensions. Integration of classical Unani therapeutics with contemporary scientific research may lead to safe, effective, and patient-centered strategies for managing PMS.
DOI:https://doi.org/10.64485/ijramr.6490.03.2026 -
ABSTRACT:
The present Decision-making is a fundamental cognitive process that underlies nearly every domain of human behaviour. The present study examined the psychological foundations of decision-making by investigating the contributions of personal values and moral reasoning to rational and intuitive decision-making styles. A sample of 201 emerging adults completed standardised questionnaires measuring decision-making style, value orientations, and moral reasoning capacity. Correlation and regression analyses were employed to examine the relationships among these variables. Results indicated significant associations between moral reasoning and rational decision-making, and between value orientations and intuitive decision-making styles. These findings suggest that decision-making is not a purely cognitive event but is deeply embedded within an individual's moral and value framework. Theoretical and practical implications for psychological research and applied settings are discussed.
DOI:https://doi.org/10.64485/ijramr.6523.03.2026