We study bundles on rank 4 maximal orders on P ramified on a smooth plane quartic. We compute the possible Chern classes for line bundles. Our main result is that the moduli space of line bundles with minimal second Chern class is either a point or a smooth genus two curve. Throughout, all objects and maps are assumed to be defined over some algebraically closed base field k of characteristic 0...

‎Let $G $ be a finite group and $X$ be a conjugacy class of $G.$ The‎ ‎rank of $X$ in $G,$ denoted by $rank(G{:}X),$ is defined to‎ ‎be the minimal number of elements of $X$ generating $G.$ In this‎ ‎paper we establish the ranks of all the conjugacy classes of‎ ‎elements for simple alternating group $A_{10}$ using the structure‎ ‎constants method and other results established in‎ ‎[A.B.M‎. ‎Bas...

In this article, we investigate sufficient conditions for existence of maximal and minimal solutions to a coupled system of highly nonlinear differential equations of fractional order with mixed type boundary conditions. To achieve this goal, we apply monotone iterative technique together with the method of upper and lower solutions. Also an error estimation is given to check the accuracy of th...

Let X be the blowup of P 2 at six general points p 1 ; : : :; p 6 and let L X be the total transform of a line on P 2. We show that the natural multiplication map ? L)) has maximal rank for any numerically eeective divisor F on X. This fact implicitly allows determination of minimal free resolutions for ideals deening fat point subschemes Z = m 1 p 1 + + m 6 p 6 of P 2 .

We study bundles on rank 4 maximal orders on P ramified on a smooth plane quartic. We compute the possible Chern classes for line bundles. Our main result is that the moduli space of line bundles with minimal second Chern class is either a point or a smooth genus two curve. Throughout, all objects and maps are assumed to be defined over some algebraically closed base field k of characteristic 0...

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...

the triple factorization of a group $g$ has been studied recently showing that $g=aba$ for some proper subgroups $a$ and $b$ of $g$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. in this paper we study two infinite classes of non-abelian finite groups $d_{2n}$ and $psl(2,2^{n})$...