Functional equations with division and regular operations

In this paper, we establish Hyers–Ulam–Rassias stability results belonging to two different set valued functional equations in several variables, namely additive and cubic. The results are obtained in the contexts of Banach spaces. The work is in the domain of set valued analysis.

We present a survey of outcomes on Ulam stability of functional equations in non-Archimedean normed spaces. We focus mainly on functional equations in several variables (including the Cauchy equation, the Jordan–von Neumann equation, the Jensen equation, and their generalizations), but we also report a result on a general equation in a single variable, which can be applied to the very important linear functional equation. Let us note that one can observe the symmetry between the presented results and the analogous ones obtained for both classical and two-normed spaces.

Making use of some transparent convolutional approach we consider the sine functional equation in several variables.

A healthy lifestyle is fundamental for the prevention and treatment of cardiovascular disease and other noncommunicable diseases (NCDs). Investment in primary prevention, including modification of health risk behaviors, could result in a 4-fold improvement in health outcomes compared with secondary prevention based on pharmacological treatment. The American Heart Association (AHA) emphasized the importance of lifestyle in its 2020 goals for cardiovascular health promotion and disease reduction. In addition to defining “cardiovascular health” based on criteria for blood pressure and biochemical markers (lipids and glycemia), the AHA Strategic Planning Committee further identified lifestyle characteristics of central importance: nutrition, physical activity, smoking, and maintenance of a healthy body weight.1 The World Health Organization estimated that ≈80% of NCDs could be prevented if 4 key lifestyle practices were followed: a healthy diet, being physically active, avoidance of tobacco, and alcohol intake in moderation.2 To support healthy lifestyle initiatives, major changes are necessary at the societal level to improve population health. Numerous strategies might help to create a culture that promotes and facilitates healthy behaviors, including creating laws and regulations, mounting large-scale public awareness and education campaigns, implementing local community programs, and providing individual counseling.3 Physicians are uniquely positioned to encourage individuals to adopt healthy lifestyle behaviors: Approximately 80% of Americans visit their primary care physician at least once a year. Physicians directly communicate with their patients during clinical encounters across numerous settings, and research indicates that patients highly value recommendations provided by their physicians.4,5 However, data further indicate that lifestyle counseling does not routinely occur in physicians’ offices, thereby representing a lost opportunity. Physicians report that they perform lifestyle counseling during ≈34% of clinic visits.4 Patients, in turn, report an even lower frequency of physician lifestyle counseling. For example, obese patients reported receiving physical activity and …

Axiomatizations of Lovász extensions of pseudo-Boolean functions

Perturbations of a system of general functional equations in several variables

This study is aimed to determine various stabilities of a generalized reciprocal-quadratic functional equation of the form r (Σpj=1 βjuj) = Πpj=1 r (uj) [Σpj=1 βj Πpk=1,k≠j √r(uk)] 2 connected with Ulam, Hyers, T. M. Rassias, J. M. Rassias and Gavruta in non-Archimedean fields, where βj≠0; j = 1,2,..., p are arbitrary real numbers and 0 < β1+β2+...+βp = Σpj=1 βj=β≠1 in non-Archimedean fields by direct and fixed point methods.

Objectives Although Artificial Intelligence (AI) has been a part of the computer science field for many decades, it has only recently been applied to different areas of behavioral and social sciences. This article provides an examination of the applications of AI methodologies to behavioral and social sciences exploring the areas where they are now utilized, the different tools used and their effectiveness. Methods The study is a systematic research examination of peer-reviewed articles (2010–2019) that used AI methodologies in social and behavioral sciences with a focus on children and families. Results The results indicate that artificial intelligence methodologies have been successfully applied to three main areas of behavioral and social sciences, namely (1) to increase the effectiveness of diagnosis and prediction of different conditions, (2) to increase understanding of human development and functioning, and (3) to increase the effectiveness of data management in different social and human services. Random forests, neural networks, and elastic net are among the most frequent AI methods used for prediction, supplementing traditional approaches, while natural language processing and robotics continue to increase their role in understanding human functioning and improve social services. Conclusions Applications of AI methodologies to behavioral and social sciences provide opportunities and challenges that need to be considered. Recommendations for future research are also included.KeywordsArtificial intelligenceBehavioral and social sciencesMachine learningFamiliesChildren

Health and human behavior: areas of interest common to the social and medical sciences.

Increasing blood donor recruitment and retention is of key importance to transfusion services. Research within the social and behavioral science traditions has adopted separate but complementary approaches to addressing these issues. This article aims to review both of these types of literature, examine theoretical developments, identify commonalities, and offer a means to integrate these within a single intervention approach. The social and behavioral science literature on blood donor recruitment and retention focusing on theory, interventions, and integration is reviewed. The role of emotional regulation (anticipated anxiety and vasovagal reactions) is central to both the behavioral and the social science approaches to enhancing donor motivation, yet although intentions are the best predictor of donor behavior, interventions targeting enactment of intentions have not been used to increase donation. Implementation intentions (that is, if-then plans formed in advance of acting) provide a useful technique to integrate findings from social and behavioral sciences to increase donor recruitment and retention. After reviewing the literature, implementation intention formation is proposed as a technique to integrate the key findings and theories from the behavioral and social science literature on blood donor recruitment and retention.

The Society of Behavioral Medicine (SBM) Leadership Institute provides leadership training for mid-career behavioral medicine scientists. As an institute fellow, I explored the experiences of social scientists working in healthcare settings. Exploratory research to describe the experiences, barriers, and facilitators social scientists face working in a healthcare delivery and research system. Our research questions were exploratory, focused on understanding (a) the experiences of social scientists working in a healthcare delivery and research system, (b) barriers that social scientists face working in a healthcare delivery and research system, (c) perceived value of sociological and anthropologic methods to clinicians and other health researchers, and (4) to understand the landscape of organizational models that feature social scientists as part of a larger scientific enterprise. We developed a plan for needs assessment activities. We conducted a design workshop of social scientists (n = 11). Using human-centered design methods, we elicited experiences and asked participants to develop a prototype model where social scientists could find career fulfillment with minimal structural barriers. We found that social scientists feel a strong sense of pride in their social science training and passion for the work they do. They reported occupying multiple disciplines at once, including multiple promotion and reputational expectations. Participants commonly reported that they themselves, as well as collaborators, viewed social science work, particularly qualitative research, as supplemental to quantitative work. Participants described perceptions that social science research is less rigorous or requires less training compared with other disciplines. Participants identified several contextual factors that influenced the perceived value of social science research in healthcare, including the focus of external funding priorities on larger clinical questions, organizational structure, and tangible leadership support of social science. The SBM Leadership Institute created a space for preliminary research into an area that could improve the experiences and research impact of social and behavioral scientists.

Language is a tool for instruction and expressing perspectives (Turetsky et al, 2021). This study aimed to explore the ideologies navigated through translanguaging in Pakistani institutions where English Language instruction is provided as an extra language (EAL). Following an exploratory sequential mixed method design, a survey of 31 items was administered to the language teachers n=100 after conducting non-participant observations of 480 minutes. For this study, the Ideological Model of Literacy (Curiel and Ponzio, 2021) was chosen as the conceptual framework. Observations revealed the involuntary navigation of primarily seven ideologies in the Pakistani classrooms. Quantitative data were analysed through SPSS 20.0, revealing that political ideologies and world Englishes ideologies secured the lowest average score of 2.34. However, racio-linguistic and English-only ideologies were averaged as 3.34. The results indicated that, in contrast, both multilingual ideologies and imperialistic ideologies had a higher mean score of 4.5. This study highlighted learners’ awareness of how their EAL instructors can navigate language ideologies through Translanguaging. References Aghai, L., Sayer, P., &amp; Vercellotti, M. L. (2020). Effects of teachers’ language ideologies on language learners’ translanguaging practices in an intensive English program. In Envisioning TESOL through a translanguaging lens: Global perspectives (pp. 345–362). Agwu Udu, D., Nmadu, J., Uwaleke, C. C., Anudu, A. P., Chukwunonso Okechineke, B., Attamah, P. C., ... &amp; Ogonna, O. C. (2022). Innovative pedagogy and improvement of students’ knowledge retention in science education: Learning activity package instructional approach. Pertanika Journal of Social Sciences &amp; Humanities, 30(3). Ali, I., Azim, M. U., &amp; Rehman, A. U. (2024). Translanguaging as a tool to decolonise English language teaching in Pakistan: Opportunities and challenges. Pakistan Social Sciences Review, 8(1), 246–254. Al-Mutairi, M. A. (2020). Kachru’s three concentric circles model of English language: An overview of criticism &amp; the place of Kuwait in it. English Language Teaching, 13(1), 85–88. Alsuwayhiri, M. M. (2024). The use of translation in English for specific academic purposes classes in Saudi Arabia (Doctoral dissertation, University of Glasgow). Atta, A. (2024). Prospective prognostication: An examination of translanguaging in Pakistan’s educational landscape through the lens of teachers’ and students’ perceptions. Language Teaching Research. https://doi.org/10.1177/13621688241259640 Cárdenas Curiel, L., &amp; Ponzio, C. M. (2021). Imagining multimodal and translanguaging possibilities for authentic cultural writing experiences. Journal of Multilingual Education Research, 11(1), 6. Cenoz, J., &amp; Gorter, D. (2021). Pedagogical Translanguaging. Cambridge University Press. Charalambous, P., Charalambous, C., &amp; Zembylas, M. (2016). Troubling Translanguaging: Language ideologies, superdiversity and interethnic conflict. Applied Linguistics Review, 7(3), 327–352. Cushing, I. (2023). “Miss, can you speak English?”: Raciolinguistic ideologies and language oppression in initial teacher education. British Journal of Sociology of Education, 44(5), 896–911. Fang, F., Jiang, L., &amp; Yang, J. (2023). To impart knowledge or to adhere to policy: Unpacking language ideologies and practices in Chinese EMI courses through a translanguaging lens. Language Teaching Research. https://doi.org/10.1177/13621688231183771 Farahani, M. F., &amp; Maleki, M. (2014). A survey on tendency toward curriculum ideologies among academic board members in educational sciences faculties – Tehran 2010–11. Procedia - Social and Behavioral Sciences, 116, 2392–2396. Galloway, N., &amp; Ruegg, R. (2020). The provision of student support on English medium instruction programmes in Japan and China. Journal of English for Academic Purposes, 45, 100846. Henry, J. (2023). “Say a sentence”: Drawing an interactional link between organisations, language ideologies, and coloniality. Signs and Society, 11(1), 93–114. Hopf, A. (2023). Urdu language ideologies and Pakistani identity. In Language ideologies and the vernacular in colonial and postcolonial South Asia (pp. 34–56). Routledge India. Iversen, J. Y. (2021). Negotiating language ideologies: Pre-service teachers’ perspectives on multilingual practices in mainstream education. International Journal of Multilingualism, 18(3), 421–434. Kachru, B. B. (1996, November). Opening borders with world Englishes: Theory in the classroom. In On JALT96: Crossing borders. The proceedings of the 23rd annual JALT international conference on language teaching/learning, Hiroshima, Japan (pp. 10–20). Khan, I. U., Rahman, G., &amp; Hamid, A. (2021). Poststructuralist perspectives on language and identity: Implications for English language teaching research in Pakistan. SJESR, 4(1), 257–267. Koyama, J., &amp; Kasper, J. (2022). Transworlding and translanguaging: Negotiating and resisting monoglossic language ideologies, policies, and pedagogies. Linguistics and Education, 70, 101010. Mazak, C. M., &amp; Herbas-Donoso, C. (2014). Translanguaging practices and language ideologies in Puerto Rican university science education. Critical Inquiry in Language Studies, 11(1), 27–49. Nadarajan, K., Abdullah, A. H., Alhassora, N. S. A., Ibrahim, N. H., Surif, J., Ali, D. F., ... &amp; Hamzah, M. H. (2022). The effectiveness of a technology-based isometrical transformation flipped classroom learning strategy in improving students’ higher order thinking skills. IEEE Access, 11, 4155–4172. Naheed, M., Azim, M. U., Islam, M., &amp; Imdad, K. (2024). Investigating the necessity of translanguaging in EFL classroom at university level: Perspective of teachers and students. Harf-o-Sukhan, 8(1), 474–487. Paulsrud, B., &amp; Rosén, J. (2020). Translanguaging and language ideologies in education: Northern and Southern perspectives. In Handbook of the changing world language map (pp. 3533–3547). Sahan, K., Rose, H., Paulsrud, B., Tian, Z., &amp; Toth, J. (2021). Problematising the E in EMI: Translanguaging as a pedagogic alternative to English-only hegemony in university contexts. In English-medium instruction and translanguaging (pp. 1–14). Sahar, Y., &amp; Shahbaz, M. (2023). Scope of e-portfolio-based assessment tool: Perceptions and practices of ELT practitioners in Pakistan. International Journal of Innovation in Teaching and Learning (IJITL), 9(1), 75–90. Sahar, Y., Ali, M., &amp; Hussain, M. S. (2024). Emergent bilingual learners’ target language development: A comparison between government policies and school practices. International Journal of Innovation in Teaching and Learning (IJITL), 10(1), 83–98. Strijker, D., Bosworth, G., &amp; Bouter, G. (2020). Research methods in rural studies: Qualitative, quantitative and mixed methods. Journal of Rural Studies, 78, 262–270. Syed, H. (2022). “I make my students’ assignments bleed with red circles”: An autoethnography of translanguaging in higher education in Pakistan. Annual Review of Applied Linguistics, 42, 119–126. Syed, H. (2024). Unravelling the deficit ideologies in English language education in Pakistan: A decolonial perspective. TESOL Journal, e828. Turetsky, K. M., Sinclair, S., Starck, J. G., &amp; Shelton, J. N. (2021). Beyond students: How teacher psychology shapes educational inequality. Trends in Cognitive Sciences, 25(8), 697–709. Uysal, H., &amp; Sah, P. K. (2024). Language ideologies and language teaching in the global world: An introduction to the special issue. International Journal of Bilingualism. https://doi.org/10.1177/13670069241240964 Wei, L., &amp; García, O. (2022). Not a first language but one repertoire: Translanguaging as a decolonising project. RELC Journal, 53(2), 313–324.

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Equations including unknown functions are called function al equations([1]). Among them, functionalequations containing only one independent variable are cal led iterative functional equations([9]). On theother hand, functional equations, like Cauchy's equation( [10]), containing two or more independent vari-ables for unknown functions of a single variable are called f unctional equations of several variables([2]).Among iterative functional equations, the problem of itera tive roots is important. If the n -th iterateof a function f is equal to g, i.e.f

Human health is influenced by multiple interacting biological, psychological, sociocultural, economic, and behavioral factors. Research in behavioral and social sciences informs physicians' approaches to prevention, diagnosis, and patient care. Competent physicians, therefore, require knowledge of society and human behavior to develop essential communication skills, professional conduct, self-awareness, ethical reasoning, and cultural understanding. Consequently, these Social and Behavioral sciences are integral to medical training. This cross-sectional study examines the current state of Social and Behavioral Sciences integration in Libyan medical education programs through a survey of 105 faculty members, curriculum developers, and administrators. Findings reveal strong recognition of SBS importance (84.6% rated it "very important"), yet inconsistencies in curriculum implementation, with 27.9% reporting no formal SBS inclusion. Teaching methods remain lecture-dominated (77.9%), and key challenges include insufficient faculty expertise (59.6%) and curriculum time constraints (40.4%). The study recommended the early curricular integration, faculty development, and enhanced experiential learning.