Let H be a subgroup of the symmetric group of degree m and let χχ be an irreducible character of H . In this paper we give conditions that characterize the pairs of matrices that leave invariant the value of a generalized matrix function associated with H and χχ, on the set of the upper triangular matrices.
A procedure is described for comparing bacteria growint under aerobic and anaerobic conditions in identical small-scale, magnetically stirrable culture vessels. Cultures, 5–15 ml, can be sampled easily and the technique lends itself to radioactive tracer studies with any number of parallel incubations. The whole procedure uses equipment which is readily available in any laboratory.
The set of pattern graphs for which the fixed directed subgraph homeomorphism problem is NP-complete is characterized. A polynomial time algorithm is given for the remaining cases. The restricted problem where the input graph is a directed acyclic graph is in polynomial time Ghd Straighteners Amazon Uk
for all pattern graphs and an algorithm is given.
Transport equations for spin transistor action, appropriate for realistic models of materials and interfaces, are developed Babyliss Big Hair
from a detailed microscopic Babyliss Curl Secret
model. Experimental results from prototypes are summarized in the context of device applications. Using spin injection to study spin accumulation in superconducting films is discussed.