The division algorithm for multivariate polynomials over fields has been introduced not very long ago, in connection with algorithmic and computational problems in the rings since the work of Buchberger. The well-known fact is a term order must be a well-ordering and the division procedure in the ring of multivariate polynomials over a field terminates even if the division term is not leading term, but is freely chosen. In this paper, we will show the original geometric approach to the classification of all possible orders on the ring of polynomials in two variables is given. The connection between this classification and the well-known classification of Robiano is exposed in details.

The United States (US) as the second leading economy in global ecological pollution has become a fertile ground for a rigorous analysis of the ecological neutrality using load capacity factor (LCF) and carbon-based consumption (CCO2). This is important for the global drive of achieving environmental sustainability by 2050. The LCF is one of the most comprehensive ecological proxies that incorporate the biocapacity and ecological footprint. In this context, this research examines the effect of natural resources, technological innovation, renewable energy and financial globalization on ecological neutrality in the US for the date spanning from 1990 to 2021. Using the novel augmented auto-regressive distributive lag (AARDL) model, the empirical findings of this study indicate that (i) natural resources, renewable energy, and technological innovation promote ecological neutrality by increasing LCF and decreasing CCO2 emissions; (ii) financial globalization and economic growth mitigate the LCF and increase CCO2 emissions; and (iii) a causal effect is observed among technological innovation, natural resources, renewable energy, CCO2 and LCF. In light of the findings, this study recommends several crucial measures for ecological neutrality targets set out in sustainable development goals (SDGs) 7 and 13, respectively.

The study aimed to present the first record of insect families in Farwa Island. Farwa Island is the largest and most important island in Libya; located in Northern west part of Libya in the Mediterranean, its insect fauna is poorly studied. Short time intensive collection of insect samples was conducted in four areas (mouth of the valley, bay of containers, center of the Island, and Ras-Attalgha) in February, March and April 2021. Different methods were used for insect collection, sorting, preservation and later identification to the lowest taxonomic level and verification. 9 orders, 31 families, 40 genera and 58 insect species were collected in the study; the center of the Island had the highest numerical density and diversity of insect fauna due to its diverse vegetation compared to other areas. Diverse suitable habitats and absent insect control measures provided suitable environmental conditions for insects breeding, feeding and hiding from enemies. This study constitutes the first comprehensive survey of insect fauna on Farwa Island and adds significant value to the ongoing assessment of insect diversity in Libya. A long-term study has to be conducted to investigate detailed information about the abundance and diversity of insects and other arthropods on Farwa Island.

The new era of distance education opens up a new problem space for researchers to redefine educational needs. The COVID-19 lockdown with its tremendous consequences has affected the way of thinking and acting and has highlighted the merits of distance education. One of the most important of these problems is the inability of the lecturer technically to manage and present remote lectures, which resulted in the student's dissatisfaction with distance education. In this research, we have studied how to facilitate the work of the lecturer, who suffers from many problems, including the technical issues that need technical competencies in the field of information technology and modern technologies used in distance education, including the simulation system and displaying the system via the Internet, studying how to help the student also, in receiving distance education techniques and dealing with the programs used by the lecturer in skillfully presenting educational curricula. For that, the research focused on studying how to use a team to facilitate this work called the E-Learning Facilitator Team. This team plays a vital role in developing and maintaining an online program that is effective, and smooth, and that will support the realization of the planned learning outcomes. Faculty delivering courses online must be more than transmitters of knowledge; they must become facilitators of learning. Some highly seasoned instructors from the traditional on-ground environment will quickly adapt to the online model, while others may find the transition challenging at first [10].