The recession cone and recession function are very important research objects in Convex Analysis. They have extensive applications in the optimization theory. Firstly, we study the properties of the recession cone and recession function. The positive homogeneity and subadditivity of recession function are mainly discussed. And the different methods are considered to prove these properties. Secondly, we discuss the unboundedness of the convex sets and convex functions by using recession cone and recession function.

The demography of Saudi Arabia has been discussed many times but its conflict with the theories of transition and associated structural changes is unexplained. This research explains the demographic differentials stated as lag - real from theoretical – separately for the native and total population. This research developed demographic indicators revealing trends and patterns by adopting a secondary data analysis method, utilizing the General Authority for Statistics census data and other online data. The demographic transition of Saudi Arabia is in line with the theoretical contentions of pretransition and transition (early, mid, and late) stages but at definite time intervals. The absolute size, percentage change, and annual growth rate are explanatory for natives and are considered separately. Moreover, the structural population changes reveal transition stages from expansive to near expansive and constricting and stabilizing. Furthermore, broad age groups indicate rapid declines in the percentage of children, rapid increases in young adults, slow increases in older adults, and no changes in older persons. Even the sex ratio of natives is at par with other populations in transition (slightly above 100). Thus, it could be concluded that a demographic transition with structural changes as per theories: flawless growth rates with an expanding demographic dividend. At this juncture, the integration of migrants into society by endorsing family life and enabling social and demographic balance appears as imperative to improving the labor sector, productivity, and the image of the country in the international spheres for comparisons and benchmarking.

The process management variable and the service quality variable date most prominently from the beginning of the last century, and therefore, in organizations from different parts of the world, whose search was to contribute effectively to administrative tasks, facing the challenges of constant changes and evaluations. In Peru, both variables were implemented since 2018, by technical standards, in order to contribute and improve public institutional work. Thus, the objective was to know the most outstanding characteristics of process management and service quality, using studies from different entities at the ecumenical level and revealing their main benefits of application and contribution. Furthermore, based on the systematic and methodical review of scientific articles from databases indexed to multiple journals, which are registered and organized in databases such as WOS and SCOPUS, thus theorizing their authors and perspectives. For this study, the documentary analysis technique and the data collection guide were considered as an instrument; in accordance with the PRISMA method. Finally, it is concluded that process management are methods available in an organization to provide effective results using resources efficiently, with dimensions of analysis, monitoring, and process improvements, contributing to organizational and strategic productivity; Likewise, the quality of the service is user satisfaction when judging the value of some service, dimensioning, analyzing needs, as well as evaluating, supervising and improving the service, fulfilling needs with knowledge of their expectations.

This study aims to examine the entrepreneurial activities of 240 women in the districts of Konaseema, East Godavari, and Kakinada during 2021–2022, focusing on the diverse range of 286 enterprises they managed across 69 business types. These enterprises were tailored to local resources and market demands, with coconut wholesale, cattle breeding, and provision shops being the most common. The study also analyzes income distribution, noting that one-third of the women earned between ₹50,000–1,00,000 annually, while only 0.70% earned over ₹5,00,000. More than half of the enterprises served as the primary income source for their families. The research highlights the significant role these women entrepreneurs play in their communities, their job satisfaction derived from financial independence and social empowerment, and the challenges they face, such as limited capital and market access. Finally, the study offers recommendations to empower these women to seize entrepreneurial opportunities and enhance their success.

Conspiracy theories during Covid-19 pandemic spread worldwide, including in Indonesia. What political and religious factors explain their spread in Indonesia with particular reference to the DKI Jakarta province, its surrounding municipalities, and West Sumatera province? This study aimed to answer the questions. It employed a qualitative approach with multi-data collection methods, including those from media, documents, and interviews. The spread of Conspiracy theories benefited from the democratic system that promotes the freedom of information in using social media. First, the government officials initially spread conspiracy theories to satisfy people’s anxiety about the obscured Pandemic. However, they resulted in the government’s ambiguous, controversial, and reckless policies leading to people’s distrust of the government. Jokowi-Makruf Amien, political opponents capitalized on the government’s poor policies to spread conspiracy theories which partly discredited the Jokowi-Amien administration. Both government officials and the opposition capitalized on politics and religious teaching or supra-natural pretexts to posit their conspiracy theories.