This paper investigates the closability of closed compact linear operators on Hilbert spaces. It establishes that under certain conditions, every closed compact linear operator is closable. Additionally, it investigates the properties of closable operators and highlights their stability under limits and algebraic operations. We establish a non-closability criterion based on sequences in the domain and demonstrate that the limit of bounded compact operators need not be closable. Moreover, we exam...

Algebra 

Healthcare chaplains, alongside those serving in palliative, dementia-care, displacement, and correctional settings, increasingly accompany people whose losses occur while the person still lives—losses that progressively strip away autonomy, agency, identity, and coherent life narrative without offering the closure that bereavement following death affords. Standard spiritual assessment frameworks (FICA, HOPE, SPIRIT, and Spiritual AIM) were designed for broad clinical application rather than for...

Sociology 

Slope failures due to rainfall are one of the main factors that cause damage to transportation infrastructures, embankments, and earth structures even with reinforcement in the tropical and sub-tropical areas. This paper uses combined experimental and numerical methods to study the hydro-mechanical behavior of geosynthetic reinforced slopes as well as the morphing of the damage process as a result of rainfall infiltration. The new research method is making use of instrumented rainfall flume benc...

Environmental Sciences 

Against the backdrop of “Greater Ideological and Political Education”, the systematic integration of ideological and political elements into classroom teaching has become a core educational task for colleges and universities. However, college physics courses are characterized by high abstraction and long logical chains. The traditional “story + slogan” model of ideological and political instruction often leads to issues such as rigid “labeling” and disconnection from real life, resulting in low ...

Pedagogy 

Introduction: Access to healthcare services remains a major challenge in developing countries, particularly in disadvantaged neighborhoods where social inequalities translate into disparities in the use of healthcare services. In Lubumbashi, numerous barriers limit children in disadvantaged neighborhoods’ access to healthcare: precarious socioeconomic conditions, lack of or distance from healthcare services, and geographical disparities, leading to the use of informal alternatives ...

Public Health  Health Policy 

Against the backdrop of rural revitalization and educational equity, rural primary schools face challenges, including teacher shortages, weak oral instruction, and a lack of language environments. Meanwhile, university English majors possess linguistic resources and volunteer enthusiasm but lack practical platforms. This gave rise to the “Smart Linkage for Rural Education” online volunteer teaching program, which explores digital service pathways and a “dual-empowerment” public welfare model. Gu...

Journalism and Communication 

Against the backdrop of a global cocoa price boom (from 1000 to 6100 FCFA/kg between May 2022 and April 2024) and the rapid expansion of sustainable certification (41% of Cameroonian production certified in 2021-2022), this study assesses the socioeconomic effects of Rainforest Alliance (RA) certification on cocoa agroforestry systems in West Cameroon and describes producer behavioural responses to the exceptional price environment. Based on a sample of 105 producers (26 certified, 79 non-certif...

Socioeconomics  Environmental Sciences 

Femoral neck stress fractures (FNSFs) are uncommon injuries that may present with atypical and misleading symptoms, resulting in delayed diagnosis. Although classically associated with athletes and military personnel, these fractures can also occur in non-athletic individuals exposed to repetitive mechanical stress. We report the case of a 35-year-old male who presented with isolated knee pain without antecedent trauma. Initial clinical evaluation suggested primary knee pathology, and knee radio...

Orthopedics 

Based on current data, ultrasound (US) has emerged as an innovative and promising imaging modality for the diagnosis of periapical lesions. Compared to conventional digital radiography and cone-beam computed tomography (CBCT), USG has the advantage of being non-invasive, free of ionizing radiation, and capable of providing additional tissue information. Ultrasound is a histopathological examination, considered the gold standard, particularly in distinguishing between cystic and granulomatous les...

Dentistry 

The study explored pre-service teachers (PSTs) perceived challenges and learning needs in studying general chemistry using an embedded mixed-method design. A purposive sampling technique was used to select three colleges in the Ashanti, Bono, Bono-East, and Ahafo (ASHBA) zone whereas simple random sampling technique was used to select the 258 participants from level 100 primary education students across the selected colleges. Perceived challenges questionnaire (PCQ) and Learning needs questionna...

Pedagogy