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 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].

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 theory of operators is an important subject in analytic function theory, geometric function theory and univalent function theory. It also is an important subject in applied sciences. It is still an active field of research and various types of problems, which can be solved by generalising operators. Recently, many researchers have shown great interests in the study of differential operators in the theory of univalent functions and various subclasses of analytic functions defined in the open unit disc. In this paper a generalised derivative operator will be used to derive some results concerning the subordination and superordination of analytic function in the open unit disc.

Heavy metals can be released from cooking stewpots into food, causing food contamination and posing a risk to human health. This research study investigated the release of heavy metals into food from stewpot cookers used in Gharyan, Libya. As well as, investigating the effect of scratches, acidic food, and storage on the concentrations of those metals. Eight new and used cooking stewpots (with scratches) made of: (Tefal, stainless steel, copper and aluminum) were collected, and then fresh tomato juice was cooked in these stewpots and left in the refrigerator for six days, the samples were digested and analyzed by atomic absorption spectrophotometer (AAS) to measure the concentration of the heavy metals: (cadmium, lead, iron, copper and zinc). Results showed that cadmium and lead concentrations were less than the detection limit of the AAS instrument, except for one sample (old Tefal stewpot with scratches), in which the lead concentration was (0.046ppm). The concentration of iron, copper and zinc in the samples was less than the maximum limit allowed by WHO/FAO; except for one sample in which the iron concentration exceeded that value (old copper pot with scratches) and its value was (2.892ppm). The results of the descriptive statistical analysis showed that the average concentration of iron (0.493 ppm) was higher than that of zinc and copper (0.054 ppm), (0.016 ppm), respectively. In addition, the rate of leakage of those elements from old (scratched) cookware was higher than that from the new ones made from the same material, and the concentration of these elements increases significantly when these stewpots contain scratches, since that increases the rate of leakage of those metals, especially in acidic food such as tomatoes.