Journal de mathématiques appliquées et computationnelles

Today, 3D models are utilized during a good kind of fields. The medical industry uses detailed models of organs; these could even be created with multiple 2-D image slices from an MRI or CT scan. The movie industry uses them as characters and objects for animated and real-life motion pictures. the pc game industry uses them as assets for computer and video games. The science sector uses them as highly detailed models of chemical compounds. The architecture industry uses them to demonstrate proposed buildings and landscapes in lieu of traditional, physical architectural models. The engineering community utilizes them as designs of latest devices, vehicles and structures also as variety of other uses. In recent decades the planet science community has begun to construct 3D geological models as a typical practice. 3D models can also be the thought for physical devices that are built with 3D printers or CNC machines.

This paper comprises a smooth limiting curve having C9 continuity using a non-stationary binary six-point approximating subdivision technique. The proposed technique is more efficient and produces more smooth results having a very large domain as compared with its stationary counterpart.

We have created a formula to calculate the number of primes less than or equal to any given positive integer ‘n'. It is denoted by π (n). This is a fundamental concept in number theory and it is difficult to calculate. A prime number can be divided by 1 and itself . Therefore the set of primes (2,3,5,7,11,13,17.). The Prime Counting Function was conjectured the end of the 18th century by Gauss and by Legendre to be approximately x/Ln(x) But in this paper we are presenting the real formula, by applying the modern approach that is applying the basic concept of set theory.

In the seventeenth century Fermat defined a sequence of numbers Fn=22n +1 for n ≥ 0 known as Fermat’s number . If Fn happens to be prime then Fn is called Fermat prime. All the Fermat’s number are of the form n!k+ Σnk for some fixed value of k and n. Further we will prove that after F4 no other Fermat prime exist upto 1050 .

S. Bisht defined a class of sequences called multiple Factoriangular sequences of the form Ft (n,k) = (n!)k +∑nk in a recent paper, and we have a special set of multiple Factoriangular numbers corresponding to each sequence. We expand the concept in this paper to find all the multiple Factoriangular primes