This article presents a mathematical model designed to simulate the impact of targeted interventions aimed at preventing HIV transmission among female sex workers (FSWs) and their clients, while also analyzing their effects on the health of the general population. The compartmental model distinguishes between high-risk populations (FSWs and their clients) and low-risk populations (sexually active men and women in the general population), and links prevention efforts in high-risk groups to the evolution of the epidemic in the low-risk population. The fundamental properties of the model, such as the positivity of solutions and the boundedness of the system, have been verified, and the basic reproduction number R₀ has been calculated. Finally, the stability of the model was studied using Varga’s theorem and the Lyapunov method. Simulation results show that targeted prevention among FSWs and their clients reduces HIV incidence in the general population. This framework provides a valuable tool for guiding policymakers in the design of effective strategies to combat the epidemic, especially relevant in the context of suspension of USAID funding.

A residual-set framework is introduced for analyzing additive prime conjectures, with particular emphasis on the Strong Goldbach Conjecture (SGC). For each even integer $E_n\ge 4$, the residual set $ℛ\left(E_n\right)=\{E_n-p\mid$ $p<E_n,p\in \mathbb{P}\}$ is defined, and the universal residual set ${ℛ}_{\mathbb{E}}={{{\displaystyle \cup }}^{\text{}}}_{E_n}ℛ\left(E_n\right)$ is constructed. It is shown that ${ℛ}_{\mathbb{E}}$ contains infinitely many primes. A nontrivial constructive lower bound is derived, establishing that the number of Goldbach partitions satisfies $G\left(E\right)\ge 2$ for all $E\ge 8$, and that the cumulative partition count satisfies ${\displaystyle \sum }_{E\le N}G\left(E\right)\gg \frac{N^2}{{\text{log}}^{4}N}$. An optimized deterministic algorithm is implemented to verify the SGC for even integers up to 16,000 digits. Each computed partition $E_n=p+q$ is validated using elliptic curve primality testing, and no exceptions are observed. Runtime variability observed in the empirical tests corresponds with known fluctuations in prime density and modular residue distribution. A recursive construction is formulated for generating Goldbach partitions, using residual descent and leveraging properties of the residual sets. The method extends naturally to Lemoine's Conjecture, asserting that every odd integer $n\ge 7$ can be expressed as $n=p+2q$, where $p,q\in \mathbb{P}$. A corresponding residual formulation is developed, and it is proven that at least two valid partitions exist for all $n\ge 9$. Comparative analysis with the Hardy-Littlewood and Chen estimates is provided to contextualize the cumulative growth rate. The residual-set methodology offers a deterministic, scalable, and structurally grounded approach to additive problems in prime number theory, supported by both theoretical results and large-scale computational evidence.

With an increasing diversity of learners in today’s educational set-ups, there is an insurmountable need to cater for individual differences including the cultural variations among learners. It is therefore necessary for educators to develop culturally responsive teaching that enhances intercultural competencies of learners. As educators strive to provide inclusive learning environments in which learners from diverse cultural backgrounds learn equitably, differentiated instruction becomes a practical tool. This paper explores how differentiated instruction can support and enhance culturally responsive teaching by examining how tailored instructional approaches can bridge cultural gaps and enhance educational outcomes. The aim is to provide a comprehensive understanding of how educators can effectively integrate differentiated instructional methodologies to achieve the goals of Culturally Responsive Teaching. The study used a descriptive survey design to determine the use of differentiated instruction by junior school teachers in Kenya and a systematic review of literature, practical examples, and studies on teachers’ practices in culturally responsive teaching. The study outcomes indicated that teachers used various differentiated instructional strategies with flexible grouping being the most commonly used strategy. However, there arises a concern, that teachers were not very familiar with cultural variations of learners in their classrooms even as they developed their differentiated instructional strategies. Literature provided the principles and practices of culturally responsive teaching. The combination of these results were used to formulate a conceptual framework for Culturally Responsive Differentiated Instruction (CRDI) that provides insights for practitioners to develop and implement culturally responsive differentiated instructional strategies. The study recommends that a framework to support teachers in the implementation of inclusive and equitable curriculum through CRDI be developed, CRDI be integrated into the teaching processes and the teachers be trained on providing for learner differences through CRDI.

Artificial Immune Systems (AIS) are bio-inspired computational frameworks that emulate the adaptive mechanisms of the human immune system, such as self/non-self discrimination, clonal selection, and immune memory. These systems have demonstrated significant potential in addressing complex challenges across optimization, anomaly detection, and adaptive system control. This paper provides a comprehensive exploration of AIS applications in domains such as cybersecurity, resource allocation, and autonomous systems, highlighting the growing importance of hybrid AIS models. Recent advancements, including integrations with machine learning, quantum computing, and bioinformatics, are discussed as solutions to scalability, high-dimensional data processing, and efficiency challenges. Core algorithms, such as the Negative Selection Algorithm (NSA) and Clonal Selection Algorithm (CSA), are examined, along with limitations in interpretability and compatibility with emerging AI paradigms. The paper concludes by proposing future research directions, emphasizing scalable hybrid frameworks, quantum-inspired approaches, and real-time adaptive systems, underscoring AIS's transformative potential across diverse computational fields.

The Chinese film Wolf Warrior II floats all the way at the domestic box office, and jumps into the top 100 of the world's film box office rankings. It has achieved great economic success and ratings are overwhelmingly positive in China. Nevertheless, in stark contrast to this, Wolf Warrior II is cold at the box office abroad, and the word of mouth is not satisfactory. Transcreation is the re-creation or adaptation of content for a group of specific target audience. As an inter-related process of translation, a successful and holistic transcreation can arouse the same emotions as well as connotations produced in the target language as the source language. There are different perspectives to detailed translation analysis of China’s identity as a prominent character of contemporary society. Insofar as this research probes into the branding and in subtitle translation, it also constructs a binary theoretical model based on triadic signs of intersemiotic translation and metafunctional framework of multimodal analysis to testify China’s core values in this film and beyond.

This paper investigates the constructability of angles multiples of 3 within the framework of Euclidean geometry. It makes a significant contribution by presenting the first geometric construction for all such angles, offering a rigorous solution to a longstanding geometric problem. The paper reaffirms the efficacy of Euclidean geometry in providing precise constructions and robust proofs for these angles, demonstrating the enduring strength of Euclidean principles from classical to modern times. The presented workflow goes beyond Euclidean geometry to examine non-Euclidean methods, particularly analytical approaches, revealing misconceptions that compromise the genetic and geometric rigor of Euclidean principles. The paper exposes incongruities when algebraic proofs related to angle constructability are applied to the Euclidean system, emphasizing the misalignment of fundamental geometric concepts. A notable result in the paper is the construction of a angle, introducing the “ angle chord” as a novel geometric property. This property challenges assumptions made by non-Euclidean methods and highlights the nuanced geometric properties crucial for rigorous constructions. The paper refutes the fallacy of relying solely on algebra for solutions to angles multiples of , emphasizing the necessity of embracing Euclidean geometry for geometric discoveries. The paper underscores the merits and resilience of Euclidean geometry, showcasing its independence and depth across historical and modern perspectives. The newly presented geometric construction not only resolves a longstanding question but also emphasizes the intrinsic strength and uniqueness of Euclidean principles in contrast to alternative methodologies.

With the current sources of US supply chains being more diversified than before, China’s share in US goods imports is declining while Mexico becomes the largest exporter to the US market in 2023. However, can Mexico use this trade diversion to successfully outweigh China in US supply chains? This paper thus investigates whether the Mexico manufacturing sector is competitive enough to completely replace its Chinese counterparts and rise to a strategically vital supplier for the US economy. Based on multiple empirical evidence, we find that although US supply chain sources are shifting from China to Mexico, the major part of the value added of Mexican exports to the US market is generated in China. Moreover, our evidence shows that Mexico’s exports to the US concentrate on low-skill sectors, while China’s mainly consists of high-skill goods. Further discussion shows that the current US trade shift is highly likely due to China’s FDI inflows to Mexico’s traditionally strong export sector, motor vehicles. However, this shift is not significant enough for Mexico to become a capable substitute for China in the US supply chains. We conclude that the "trade diversion" strategy alone cannot support Mexico’s role in reducing the US supply chain dependence on China. Therefore, the US should better consider how to establish a sustainable trade framework that fosters stable cooperation with China.

Background: By rediscovering the medical field spiritual foundation, clinicians sought to balance their care and realize that spirituality is frequently associated with healthcare, thus one’s spiritual beliefs influence patients' decisions between aggressive care and complementary therapies in oncology care. Aim: This study investigates clinicians’ experiences and perceptions of spirituality in oncology care that clinicians can utilize to improve cancer and spiritual care provision. Methods: A thematic, qualitative synthesis. Results: Four main themes emerged from the synthesis of the 11 included studies that can steer future framework and policies to make clinicians more inept in providing care to address spiritual well-being of the patients and their family from a clinician's point of view of spirituality: “Maintaining Hope and Spiritual Wellness, Clinician’s Sensitivity to Cancer Patients, Provision of Culturally Respectful Spiritual Care, and Education in Providing Spiritual Care”. Conclusion: Cancer patients, cancer survivors, and clinicians’ quality of life is correlated with measures of spirituality and spiritual well-being. Spirituality also fulfill these oncologic patients has been linked to improved emotional and spiritual adjustment. Implications: Clinicians with different proficiencies, novice or expert, develop a strong spiritual belief can also be a strength when it comes to caring for those terminally ill patients, to be able to aid them in their sufferings. Amidst the challenges of spiritual care, these clinicians provide a patient strategy approach that is holistic to the care.

There have been various concerns about the environmental impact of construction works. This generates a need to take a more proactive approach in evaluating the environmental impacts of construction operations and further explore ways to reduce the environmental impacts. Enormous opportunities exist within the building industry to achieve a reduction in greenhouse gas emissions. The aim of the study is to develop a framework for the evaluation of improvement opportunities for environmental impact for onsite and offsite building construction works using life cycle assessment (LCA) and value-stream-mapping concepts. Various tools for LCA exist; however, there is a need for the development of an LCA framework and improvement opportunities that can be localized to various communities to evaluate improvement opportunities for building construction. This study conducts a review of methods to evaluate the LCA of buildings on local construction sites. A procedure for establishing improvement opportunities is also developed. Based on the author’s knowledge and experience, including site visits, using value stream mapping (VSM) techniques, a conceptual framework of the present state map and future state map of residential construction works was developed. The study presents a procedure for the evaluation of improvement opportunities for the environmental impacts of construction operations.