New York Club

Hope Photo

Country Club

postmark dated

Club bulletin.

Some numbers issued in revised editions.

Michigan state industries : catalogue A : Ionia, Jackson, Marquette, Saginaw.

"This Catalogue is printed by the State of Michigan and contains a list of products manufactured by the State at the Michigan Employment Institution for the Blind at Saginaw and the State Prisons at Jackson, Ionia and Marquette."--P. 3.

Water Flow Through the Gills of Port Jackson Sharks

Evidence is presented for the existence of a countercurrent flow between water and blood at the respiratory surfaces of the Port Jackson shark gill.

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.