We characterize local Noetherian domains R with infinite residue field which admit only finitely many star (prime) operations. We further show that a positive integer n is equal to the number of star operations on such an R if and only if n=2,4n=2,4 or an odd positive integer.
We study the initial value problem for a hyperbolic–elliptic coupled system with arbitrary large discontinuous initial data. We prove existence and uniqueness for that model by means of L1-contraction and comparison properties. Moreover, after suitable scalings, we study both the hyperbolic–parabolic and the hyperbolic–hyperbolic relaxation limits for that system.
The uniform subset graph G(n, k, t) is defined to have all k-subsets of an n-set as vertices and edges joining k-subsets intersecting at t elements. We conjecture that G(n, k, t) is hamiltonian when it is different from the Petersen graph and does possess cycles. We verify this conjecture for k − t = 1, 2, Cheap Air Max
3 and for suitably large n when t = 0, 1.
Lorito, M., Woo, S.L., Fernandez, I.G., Colucci, G., Nike Air Max 2011 Harman, G.E., Pintor-Toro, J.A., Filippone, E., Muccifora, S., Lawrence, C.B., Zoina, A., Tuzun, S. and Scala, F. (1998) Genes from mycoparasitic fungi as a source for improving resistance to fungal pathogens, Proc. Natl. Acad. Sci. U. S. A. 95, 7860–7865