On the Number of Positive Solutions to a Class of Integral Equations

By using the complete discrimination system for polynomials, we study the number of positive solutions in {\small $C[0,1]$} to the integral equation {\small $\phi (x)=\int_0^1k(x,y)\phi ^n(y)dy$}, where {\small $k(x,y)=\phi_1(x)\phi_1(y)+\phi_2(x)\phi_2(y), \phi_i(x)>0, \phi_i(y)>0, 0<x,y<1, i=1,2,$} are continuous functions on {\small $[0,1]$}, {\small $n$} is a positive integer. We prove the following results: when {\small $n= 1$}, either there does not exist, or there exist infinitely many positive solutions in {\small $C[0,1]$}; when {\small $n\geq 2$}, there exist at least {\small 1}, at most {\small $n+1$} positive solutions in {\small $C[0,1]$}. Necessary and sufficient conditions are derived for the cases: 1) {\small $n= 1$}, there exist positive solutions; 2) {\small $n\geq 2$}, there exist exactly {\small $m(m\in \{1,2,...,n+1\})$} positive solutions. Our results generalize the existing results in the literature, and their usefulness is shown by examples presented in this paper.Comment: 9 page

On University Teacher’s Non-wage Income and Higher Education Dissimilation

In the current era of knowledge economy, higher education plays an increasingly important role in promoting social development. University teachers’ non-wage income from the commercial lectures, training classes, off-campus part-time jobs and academic activities has grown rapidly. Popularization of university teachers’ profit-making has constantly eroded the essential attribute of higher education, and led to the higher education dissimilation embodied by phenomena such as “transactions between money and knowledge”, “part-time job tendency”, “becoming rich by scientific research” and “abuse of power”.Key words: University teacher; No-wage income; Higher education; DissimilationRésumé Dans le contexte actuel de l’économie du savoir, l’enseignement supérieur joue un rôle de plus en plus important dans la promotion du développement social. Les professeurs d’université ‘‘des conférences commerciales, les classes de formation, hors campus emplois à temps partiel et des activités académiques a connu une croissance rapide. Vulgarisation des professeurs d’universitéles revenus non salariaux ‘‘à but lucratif a constamment érodé l’attribut essentiel de l’enseignement supérieur, et a conduit à la dissimilation de l’enseignement supérieur incarné par des phénomènes tels que “les transactions entre l’argent et des connaissances”, “la tendance emploi à temps partiel’’, ‘‘de devenir riche par la recherche scientifique’’et ‘‘ l’abus de pouvoir ’’.Mots clés: Professeur d’université, Non salarié; L’enseignement supérieur; Dissimilatio

Model-as-a-Service (MaaS): A Survey

Due to the increased number of parameters and data in the pre-trained model exceeding a certain level, a foundation model (e.g., a large language model) can significantly improve downstream task performance and emerge with some novel special abilities (e.g., deep learning, complex reasoning, and human alignment) that were not present before. Foundation models are a form of generative artificial intelligence (GenAI), and Model-as-a-Service (MaaS) has emerged as a groundbreaking paradigm that revolutionizes the deployment and utilization of GenAI models. MaaS represents a paradigm shift in how we use AI technologies and provides a scalable and accessible solution for developers and users to leverage pre-trained AI models without the need for extensive infrastructure or expertise in model training. In this paper, the introduction aims to provide a comprehensive overview of MaaS, its significance, and its implications for various industries. We provide a brief review of the development history of "X-as-a-Service" based on cloud computing and present the key technologies involved in MaaS. The development of GenAI models will become more democratized and flourish. We also review recent application studies of MaaS. Finally, we highlight several challenges and future issues in this promising area. MaaS is a new deployment and service paradigm for different AI-based models. We hope this review will inspire future research in the field of MaaS.Comment: Preprint. 3 figures, 1 table

Blind separation of cyclostationary signals from instantaneous mixtures

This paper presents a new approach for blind separation of unknown cyclostationary signals from instantaneous mixtures. The proposed method can perfectly separate the mixed source signals so long as they have either different cyclic frequencies or clock phases. This is a weaker condition than those required by the algorithms. The separation criterion is to diagonalize a polynomial matrix whose coefficient matrices consist of the correlation and cyclic correlation matrices, at time delay &tau;=0, of multiple measurements. <br /