The status of the Gerasimov-Drell-Hearn sum rules for polarized inclusive photo-production on nucleons is reviewed. It is shown that results from currently available data compare favorably with an estimate based on an extended current algebra. Implications for integrals of spin-dependent structure functions are also briefly discussed.

Matrix elements of the form < 0|T r g 2 GG|G > are calculated using the lattice QCD Monte Carlo method. Here, |G > is a glueball state with quantum numbers 0 ++ , 2 ++ , 0 −+ and G is the gluon field strength operator. The matrix elements are obtained from the hybrid correlation functions of the fuzzy and plaquette operators performed on the 12 4 and 14 4 lattices at β = 5.9 and 5.96 respectively. These matrix elements are compared with those from the QCD sum rules and the tensor meson dominance model. They are the nonperturbative matrix elements needed in the calculation of the partial widths of J/Ψ radiative decays into glueballs.

We formulate the yield management problem as a continuous time, stochastic, dynamic programming model. We derive an expression for the expected revenue in terms of the stochastic booking processes and the control policies. The solution to the problem is found by maximizing the expected revenue over the possible control decisions. The solution is for an arbitrary number of fare classes and arbitrary booking curves. In particular, it requires no assumptions on the order of arrivals from different fare classes. The solution can be expressed in terms of a double recursion complex. At each node of the complex, the upper limit of a one-dimensional integral is solved to find a critical time for each fare class and for each value of remaining capacity. The critical times are the only values that need to be stored in the reservation control system to achieve optimal real-time control. This simple result is somewhat surprising given the complexity of even the static programming versions of the problem. We derive simple expressions of expected revenues and bid prices, which provide useful information to the user of a yield management system.

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The necessity for q-number Schwinger terms in the equal-time commutators between flavor charge densities for chiral fermions in 3 + 1 dimensions is shown. The charge densities here are not coupled to any gauge field. The number of quark species (colors) gives the central charge of an infinite-dimensional Lie algebra. The result is obtained by considering the analogue of the double spectral function in current-current correlation functions.