Abstract

This paper introduces a pure geometric proof for Ptolemy’s Theorem, without using trigonometry, coordinate geometry, complex numbers, vectors or any other geometric inversion techniques focusing on cyclic quadrilaterals and employing a generalized identity in relation to a cevian of an arbitrary Euclidean plane triangle. Additionally, the paper provides proofs to the converse of Ptolemy’s Theorem to which almost no pure geometric complete proof is available, and to the standard Ptolemy’s Inequality, to fulfil the research gap in the proofs to some extent. It also includes applications, new corollaries, derived from Ptolemy’s Theorem and its converse.

Keywords: Cyclic quadrilaterals, Equilateral triangles, Inequalities, Mathematical logic, Perpendiculars, Similar triangles

Download

Abstract

Gene expression studies on gene transcription to synthesize functional gene products have been used extensively to understand biological differences between different disease conditions. Thus, this study determines differentially expressed genes in dengue infection during disease progression following the three phases: Febrile, Defervescence and Convalescent. Integrative data analysis of two publicly available longitudinal datasets in Gene Expression Omnibus (GEO) database has been employed to accomplish the prime objective of exploring temporal gene expression patterns. The Friedman test was given more emphasis due to the non-normality distributions of data. Repeated measures analysis of variance (ANOVA) and linear mixed models were also implemented to examine the potential of detecting differentially expressed genes despite non-normality. The Friedman test revealed significant differences in gene expression levels across different phases in dengue disease over time. This led to a notably higher count of genes showing differential expression compared to the other two methods: Repeated measures ANOVA and linear mixed models. The pathway analysis approach consists of significant differentially expressed genes derived from the Friedman test. The results identified upregulated pathways with any significant change in the overall expression of genes within pathways over time for the Febrile and Defervescence phases considering the Convalescent phase as a baseline. Moreover, genes available in pathways were not identified by the two parametric tests for non-normal data implying that the parametric approaches resulted in the least significance for data with non-normal distributions.

Keywords: Dengue, Friedman test, Gene expression studies, Longitudinal data, Non-normality

Download

Abstract

Studies on the role of administrative law in the realization of the public policy of a country has been the subject for numerous studies, but rarely has it been observed through the prism of natural justice. Therefore, the present study aims to address this dearth in research by focusing on the role principles of natural justice can play in the exercise of discretion by public administrators, the agents whose work helps realize the public policy of a country. To achieve this objective, this study has conducted a review of the major administrative law cases that were decided in Sri Lanka along with the local and international literature that relates to this subject. Thus, this study argues that there is a discernable hesitancy in the early administrative law decisions to recognize the role natural justice principles can play when safeguarding the rights of the public from the abuse of discretionary powers by the administrators. However, a more receptive attitude towards recognizing the role of natural justice in public administration could be observed towards the late twentieth century in Sri Lanka, a shift that is probably brought forth by the changing welfarist policies and socio-economical instabilities in the country. Therefore, this study contends that the role natural justice principles can play when curving the discretionary powers of the administrative authorities has now been well established in Sri Lanka, creating a legal tradition that continues to gain prominence within the country’s public policy developments. However, this study also has identified some criticisms that can be levelled against the incorporation of natural justice principles in the public administration of Sri Lanka which in turn may prevent the general public from reaping the full benefits of those progressive changes that continue to take place.

Keywords: Administrative law, Natural justice principles, Public administration, Public policy, Sri Lanka

Download

Abstract

Principles of natural justice, including fair hearings and unbiased decision-makers, should apply in employee disciplinary procedures. However, Sri Lankan labor law does not statutorily require employers to conduct domestic inquiries before imposing disciplinary punishments. This study investigated whether courts continue to uphold principles of natural justice in the absence of a legal mandate requiring domestic inquiries, thereby assessing the necessity for legal reforms. Through examining legislation, case law, and academic literature, this study found courts generally only consider if a valid reason exists for the punishment, not whether fair procedures were followed. Further discrimination arises between public and private sector employees in applying natural justice principles. Reforming labor law to mandate domestic inquiries before employee punishment would strengthen natural justice rules and align with international standards like ILO Convention 158. This reform is needed to universally uphold procedural fairness in workplace discipline. Until then, the judiciary cannot fully ensure employees’ rights to fair disciplinary procedures are protected. Courts have upheld natural justice primarily under writ or fundamental rights jurisdiction, mainly benefiting public sector employees. Private sector employees lack that protection. Requiring domestic inquiries before punishment through amending the Industrial Disputes Act would fill this gap. This suggested legal reform would bolster the rule of law in Sri Lanka’s employment relations. As the law stands, employers currently have full discretion on disciplinary procedures. Statutorily mandating domestic inquiries would check that unilateral authority. This study demonstrates the need to embed fair process requirements into labor legislation to fully realize principles of natural justice.

Keywords:Disciplinary punishments, Domestic inquiry, Labor law, Natural justice

Download

Abstract

The prevalence of depression, stress, and anxiety symptoms among Sri Lankan undergraduates has increased over the years, especially among females. However, there is limited research on the impact of romantic relationships on these symptoms as well as their quality of life. This study aims to compare the difference in levels of depression, anxiety, stress, and quality of life of female Sri Lankan undergraduates based on their relationship status. A random sample of 295 female undergraduates (18-29 years) purposively selected from Sri Lankan universities, which consist of 152 having no relationship (‘single’) and 143 having romantic relationship (‘relationship’) was taken for this study. An online survey that included a demographic questionnaire, the Sinhala translated version of the Depression Anxiety Stress Scale (DASS-21), and the World Health Organization Quality of Life – BREF (WHOQOL-BREF) was utilized to obtain the necessary information. Results showed that there is a strong positive multicollinearity among depression, anxiety, and stress in female undergraduates. There are no significant differences in the mean score of anxiety and stress between the two groups even at the 10% level, but the mean score of depression of the single group (13.16) is significantly higher than that of the relationship group (10.74) at 10% level. Positive significant correlations were also found among six pairs within the four variables: physical, psychological, social relationships and environment in QoL among female undergraduates irrespective of the type of groups. The mean score for social relationship in ‘relationship’ group (63.69) is significantly higher (p < 0.05) than that of ‘single’ group (50.05). This study reveals the intricate nature of relationships and mental health and highlights the need for investigations that consider different cultures.

Keywords: Anxiety, Depression, Quality of life, Romantic relationships, Sri Lankan undergraduates

Download