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.

The Mambaka watershed is extends between latitudes 1 3°45'E and 14°15'E and longitudes 7°16'N and 6°45'N. The geology, various tectonic and structural events that have affected the Adamawa Plateau in Cameroon make it rich in multi-substance mining. The objective of this study is to map rare earth (REE) geochemical anomalies in the sediments of the watershed streams west of Mambaka, and to trace their origins and geochemical processes. Predictive maps from inverse distance interpolations (IDW), factor analysis (F1) or principal component analysis (PCA) and hierarchical bottom-up classification maps provided a better understanding of the central tendency, distribution and dispersion of REE in the samples and in the study area, based on standard deviation and variance values that generated two factors F1 (Ho-Tm-Er-Yb-Lu-Dy-Tb-Gd-Eu-Sm) and F2 (Pr-Nd-Ce-La-Sm) representing 92.44% of the total cumulative variance. The ratios Ce/Ce* > 0.78 and Eu/Eu* > 1 demonstrate positive anomalies in Ce and Eu, and clear differentiation. The normalized concentrations used to calculate fractionation ratios show that the values for LaN/YbN (0.58 to 1.34), LaN/SmN (0.61 to 0.88) and LaN/LuN (0.62 to 1.43) suggest higher fractionation in SS09 and lower fractionation in SS01. Similarly, the ratios La/Lu (61.71 to 143.46), La/Yb (9.00 to 20.72), La/Sm (4.02 to 5.83) and La/ Lu (61.71 to 143.46) confirm these higher ratios in SS09 and lower in SS01. The REE in the study area comes from hydrothermal processes based on high lineament densities at sampling points in igneous rocks with a mean ∑REE value of between 174-219 ppm.

Opuntia ficus-indica (L.) Mill., commonly known as prickly pear, is a versatile plant widely used for food, medicinal, and cosmetic purposes in various regions of the Mediterranean and North Africa. This study provides a comparative ethnobotanical review of prickly pear uses in Algeria, Morocco, Tunisia, and Italy. In total, 74 articles were selected from ethnobotanical uses in Italy, Algeria, Morocco and Tunisia. In the Maghreb, the plant is used for fruit production and processed products, such as jams, oils, and flours, as well as for traditional medicinal purposes. In Algeria and Morocco, the fruits and cladodes are used to treat digestive disorders, diabetes, and skin diseases. In Tunisia, products derived from O. ficus-indica are also applied in the cosmetic industry and for erosion control. In Italy, particularly in Sicily and Calabria, the prickly pear is a vital resource, used for both food consumption and for medicinal purposes. The cladodes, rich in mucilage, are applied as topical remedies for skin problems, while the fruits are a key ingredient in the preparation of traditional desserts. Furthermore, O. ficus-indica has historically been used as forage and to produce natural dyes. Results indicate that the versatility of this species, combined with its ability to adapt to extreme climates, makes it a valuable resource for the development of new nutraceutical and cosmetic products. However, further scientific research is necessary to explore the bio-functional potential of this plant and to promote its broader and more sustainable use, especially in arid and semi-arid regions.

Background: Financial well-being is a key domain of overall well-being, encompassing an individual's ability to meet financial obligations, secure their financial future, and maintain a sense of financial freedom. Education is often viewed as a critical pathway to enhancing financial well-being. However, the returns of education on financial well-being are not uniform across racial, ethnic, and nativity groups. The theory of Minorities’ Diminished Returns (MDRs) suggests that the positive effects of education on outcomes such as income and financial security are weaker for marginalized groups, including Black individuals, Latinos, and immigrants. Objective: This study examines the diminished returns of education on financial well-being among Black, Latino, and immigrant populations in the United States. We aim to investigate how structural inequalities contribute to weaker financial returns on education for these groups compared to their White and native-born counterparts. Methods: We utilized data from the Understanding America Study (UAS 2014) to conduct a cross-sectional analysis of adult respondents. The study assessed financial well-being outcomes (e.g., income, savings, and financial security) and their association with educational attainment across racial, ethnic, and nativity groups. Regression models were employed to test for interaction effects between education and race/ethnicity/nativity, adjusting for sociodemographic factors such as age, gender, employment, and family structure. Results: Our analysis included 8,121 individuals. The mean age of the respondents was 48 years (SD = 16). High education was associated with higher financial well-being (B = 1.284, 95% CI: 1.157, 1.410). The interaction terms between education and immigrant status (B = -0.507, 95% CI: -0.930, -0.084), race (Black) (B = -0.770, 95% CI: -1.208, -0.331), and ethnicity (Hispanic) (B = -0.589, 95% CI: -0.969, -0.210) were all significant, suggesting that immigrant, Black, and Hispanic individuals experience diminished returns on education in terms of financial well-being, relative to US-born non-Hispanic White individuals. The significant negative interactions between education and minority statuses (Black, Hispanic, and immigrant) indicate that while education generally improves financial well-being, the magnitude of this improvement is substantially smaller for these marginalized groups. Conclusion: Understanding how education translates to financial well-being across different racial, ethnic, and nativity groups is critical for addressing persistent financial disparities.

A persistent problem in the pharmaceutical industry that has existed for centuries is the prevalence of counterfeit drugs, and the World Health Organization (WHO) estimates that millions of people are affected by this issue each year. In particular, 4 out of 10 drugs in poor or underdeveloped countries may be adulterated, which can lead to severe adverse events. To address this problem, many countries have implemented regulatory compliance measures such as pharmaceutical drug serialization, which requires the unique identification of every drug package manufactured. This enables tracking and tracing of individual packages throughout the supply chain and helps to prevent counterfeit drugs from entering the market. In this paper, we conduct a systematic review of the serialization process evaluation and its impact on the pharmaceutical industry. We discuss the benefits of pharmaceutical drug serialization, including its ability to improve drug security and reduce adverse events and investigations. We also examine the challenges associated with implementing serialization processes and the regulatory requirements necessary for compliance. Finally, we explore the various tracking and tracing technologies used in serialization processes and their effectiveness in preventing the distribution of counterfeit drugs. Overall, this paper highlights the importance of pharmaceutical drug serialization in ensuring the safety and efficacy of drugs in the healthcare industry, particularly in poor or underdeveloped countries where the problem of adulterated drugs is especially prevalent.

This work presents the results of an ethnobotanical research carried out in the territory of Serre Calabre, province of Vibo Valentia (Calabria, southern Italy). In this territory, the bond between the residents and the rural environment is still strong, because the small urban centers are placed in a predominantly agricultural and forestry environment still managed in a traditional way. The survey took place between January 2019 and July 2021. Data were collected through semi-structured interviews with locals. As many as 17 informants were interviewed and a total of 185 interviews were recorded. Plant specimens were collected under the indication of the informants and then deposited at the herbarium of the Mediterranean University of Reggio Calabria (REGGIO). The data were stored on a digital database and then statistically analyzed some synthetic indexes have also been calculated, such as Relative Frequency of Citation (RFC) and the Cultural Importance Index (CI). The investigation allowed to identify 84 taxa belonging to 39 different families, among which the most represented are Lamiaceae (23 interviews, 9 taxa), Asteraceae (22 interviews, 12 taxa). The identified taxa were prevalently cited for alimentary (46 interviews, 32 taxa) and healing (55, 27) uses. The results obtained show how the traditional knowledge about plants in the Serre Calabre area is still alive, however it is exclusive heritage of elderly people and often only in one or just a few informants. In fact, many practices are no longer in use and will not be transferred to the new generations.

Addressing adolescent and sexual reproductive healthcare is essential to providing young patients with the resources they need to navigate and empower themselves with. However, there is limited data about how often this occurs. Several studies have previously indicated that there is a large gap in accessing this gap in low-income neighborhoods. Our study aims to identify the establishment of gynecologic care among adolescent cisgender women and elucidate potential reasons for seeking or not seeking out care. We approached women in the pediatric emergency room that matched the inclusion criteria set out. Qualitative surveys were conducted until thematic saturation was reached and a cross-section study design was employed. Interviews were analyzed through modified ground theory. The study was conducted at the pediatric emergency department at University Hospital located in Newark, NJ. In 2018 estimates, the Newark population consists of 47.0% Black and 39.2% Hispanic or Latinos. Semi-structured interviews were conducted with 27 cisgendered, English-speaking females between ages 18 to 25 presenting to the pediatric emergency room who may or may not have previously established primary care with a gynecologist. Transcriptions were analyzed using modified grounded theory and themes were identified using inductive coding of patient interviews.

Using a desktop review of literature, the effect of illegal capital flows on the economic performance of Sub-Saharan Africa is examined. The review focus on articles with attention to illegal capital flows and their effects on the economic performance of Sub-Saharan Africa as a whole. By way of sampling method, purposive sampling was used, and so the desktop review focused purposively on articles published on issues of illicit financial flows and their effects on the economic performance of Ghana and Sub-Saharan Africa as a whole. The review found a high propensity of trade mis-invoicing and thus high illicit financial flows, transactions across boarders from developing countries and for that matter Sub-Saharan Africa to the developed economies. Therefore, the research recommends that customs divisions in sub-Saharan Africa should have up-to-date commodity-level world pricing information to make relatively better comparisons to detect mis-pricing and avoid such falsification and manipulation in trade. Given the high propensity of trade mis-invoicing resulting in high illicit financial flows, we recommend that cross-border transactions from developing sub-Saharan African countries be subjected to heightened scrutiny to curtail any potential traces of falsification in trade for tax evasion.

The last three decades have witnessed in Europe an increasing interest from institutions, and creative communities in independent research connected to crafting, DIY, maker culture, and design activism. A new generation of designers has focused on the experimentation of processes, materials, and technologies used as a vehicle for socio-political and environmental messages and as the starting point of solid narrative projects. This paper aims to analyse this phenomenon inside the niche of Collectible Design, a field in recent years of great interest by galleries and institutions for its ability to embrace material and technological research as well as craftsmanship and art. We investigate the phenomenon, through a series of interviews with designers such as Shahar Livne, Eugenia Morpurgo, Pleun van Dijk, Tellurico, and Standard 404, selected for their ability to use experimental materials and technologies, as communicative media for reflections on systemic issues.