Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.Comment: 10 page

A new integrable spin chain of the Haldane-Shastry type is introduced. It is interpreted as the inverse-square interacting spin chain with a reflecting end. The lattice points of this model consist of the square roots of the zeros of the Laguerre polynomial. Using the "exchange operator formalism", the integrals of motion for the model are explicitly constructed.

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In order to understand the phase structure of d>1 strings we investigate the c=1 matrix model with g′(tr M(t)2)2 interaction which is the simplest approximation of the large-N reduced model of odd-dimensional matrix field theory. We find three distinct phases: (i) an ordinary c=1 gravity phase, (ii) a branched polymer phase and (iii) an intermediate phase, and compute the disk and cylinder amplitudes in the phases (i) and (iii). Further we also analyze the model with slightly generalized [Formula: see text][Formula: see text] interaction. As a result the multi-critical versions of the phase (ii) are found.

SynopsisThere exists a need to improve the high temperature reducibility and lower the softening rate of pellets in order to get high productivity in the blast furnace.This paper introduces the influence of the MgO/Si02 and the CaO/ Si02 ratios in pellets on the high temperature reduction and softening properties.The pellets whose MgO/Si02 ratio is held at above 0.6, and whose CaO/Si02 ratio is held at below 0.05, are proved to have better high temperature properties than those of acid or self-fluxed pellets. There was no deterioration in properties, even if the quantity of SiO2 is significant.