We characterize Beauville surfaces of unmixed type with group either PSL(2, p) or PGL(2, p), thus extending previous results of Bauer, Catanese and Grunewald, Fuertes and Jones, and Penegini and the author.

A smooth algebraic surface S is said to be isogenous to a product of unmixed type if there exist two smooth curves C, F and a finite group G, acting faithfully on both C and F and freely on their product, so that S = (C × F )/G. In this paper we classify the surfaces of general type with pg = q = 1 which are isogenous to an unmixed product, assuming that the group G is abelian. It turns out tha...

‎In this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of Villarreal on bipartite graphs‎. ‎For bipartite graphs two‎ ‎different characterizations were given by Ravindra and Villarreal‎. ‎We show that these two characterizations imply each other‎.

Six laboratory scale biogas mixed anaerobic digesters were operated to study the effect of biogas recycling rates and draft tube height on their performance. The digesters produced methane at 0.40-0.45 L per liter of digester volume per day. A higher methane production rate was observed in unmixed digesters, while increased biogas circulation rate reduced methane production. However, different ...

Let $$(R,\mathfrak {m})$$ be a Noetherian local ring of prime characteristic p and Q an $$\mathfrak {m}$$ -primary parameter ideal. We give criteria for F-rationality R using the tight Hilbert function $$H^*_Q(n)=\ell (R/(Q^n)^*)$$ coefficient $$e_1^*(Q)$$ polynomial $$P^*_Q(n)=\sum _{i=0}^d(-1)^ie_i^*(Q)\left( {\begin{array}{c}n+d-1-i\\ d-i\end{array}}\right) .$$ obtain lower bound equidimensi...

Let $I$ be a square-free monomial ideal in polynomial ring $R=K[x_1,\ldots, x_n]$ over field $K$, $\mathfrak{m}=(x_1, \ldots, x_n)$ the graded maximal of $R$, and $\{u_1, u_{\beta_1(I)}\}$ independent set minimal generators such that $\mathfrak{m}\setminus x_i \notin \mathrm{Ass}(R/(I\setminus x_i)^t)$ for all $x_i\mid \prod_{i=1}^{\beta_1(I)}u_i$ some positive integer $t$, where $I\setminus x_...