Abstract:In this present study, the leaf extracts of Litsea liyuyingi, were subjected to evaluate the phytochemical screenings, thrombolytic, membrane stabilizing, antioxidant, antimicrobial, cytotoxic, antinociceptive, anti-diarrheal

In this short paper we have presented an interesting method of trisecting 45 degree angle by only using unmarked straightedge and a compass. This process can also be used as a unique way of drawing 15 degree angle.

In 1922 Hardy and Littlewood proposed a conjecture on the asymptotic density of admissible prime k-tuples. Here we have used a sieve method and shown an elementary process to calculate the approximate number of admissible prime k-tuples and compared with Hardy-Littlewood conjecture and real values. Then we have combined our elementary formula with the results obtained from numerical data of real values and generated a new formula which gives almost same results as Hardy-Littlewood conjecture. We have also proposed an easy form of this conjecture which gives us a new perspective to think about it.

In this article we have expressed Euler’s number (e) in some different ways. These expressions help us to observe ‘e’ from a new perspective. In the main part of this article we have developed a formula to calculate the sum of infinitely many infinite series. Then we have shown thirteen important summations where we have added infinitely many convergent infinite series.

In this paper we have proposed a new theory about geometric shape conversion. Through a particular process where the number of steps of the process tends to infinity, keeping one or more shapes of two or more shapes the same throughout the whole process and by gradually changing its size, shifting another shape toward another specific new size or new shape is the main topic of discussion of the theory. Again, if the shape that changes its size does not shift toward another specific new size or new shape then it is considered as error and this theory also discussed the properties of that error.