The semifields of order q which are two-dimensional over their left nucleus and six-dimensional over their center have been geometrically partitioned into six classes by using the associated linear sets in PG(3, q). One of these classes has been partitioned further (again geometrically) into three subclasses. In this paper the generic multiplication is determined for each of these three subclas...

One finds several q-differential equations of a higher order for q-Euler polynomials and q-Genocchi polynomials. Additionally, we have few order, which are mixed with numbers Moreover, investigate some symmetric by applying properties

<p style='text-indent:20px;'>Ramanujan introduced sixth order mock theta functions <inline-formula><tex-math id="M3">$ \lambda(q) $</tex-math></inline-formula> and id="M4">$ \rho(q) defined as:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> $ \begin{align*} & = \sum\limits_{n 0}^{\infty}\frac{(-1...

the prime graph $gamma(g)$ of a group $g$ is a graph with vertex set $pi(g)$, the set of primes dividing the order of $g$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $g$ of order $pq$. let $pi(g)={p_{1},p_{2},...,p_{k}}$. for $pinpi(g)$, set $deg(p):=|{q inpi(g)| psim q}|$, which is called the degree of $p$. we also set $d(g):...