On a product of universal hyperalgebras
Abstract We introduce and study a new operation of product of universal hyperalgebras which lies, with respect to set inclusion, between the cartesian product of the hyperalgebras and the cartesian product of their idempotent hulls. We give sufficient conditions for the validity of the first exponential law and a weak form of the second exponential law for the direct power of universal hyperalgebras with respect to the product introduced.
On a product of universal relational systems
In this paper, arities of relations are considered to be arbitrary sets. We introduce and study a new operation of product of universal relational systems, which lies between their direct product and the direct product of their reflexive hulls. For the new operation of product and the direct sum of universal relational systems, the validity of the distributive law is shown. Moreover, we define a new power of universal relational systems by combining their direct power and structural power. Then, all the three powers are discussed. It is shown that the introduced power of universal relational systems satisfies the first exponential law with respect to the combined product. Further, we show that the weak forms of the second and third exponential laws for each of the three powers of universal relational systems with respect to the new operation of product are satisfied. AMS Mathematics Subject Classification (2010): 08A02; 08A05; 08A99
Global attractivity in time-delayed predator-prey systems
Abstract For a predator-prey model with time-delay due to gestation, criteria are obtained for persistence and global attractivity. The global attractivity criteria apply only to models with a decreasing prey isocline.