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In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the f...
We show that by Miura-type transformation the Itoh-Narita- Bogoyavlenskii lattice, for any n ≥ 1, is related with some differential-difference (modified) equation. We present corresponding integrabl...
Define a chi-square random field on a multi-dimensional lattice points index set with a direct-product covariance structure, and consider the distribution of the maximum of this random field. We provi...
We explore a simple lattice field model intended to describe statistical properties of high frequency financial markets. The model is relevant in the cross-disciplinary area of econophysics. Its signa...
A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara[Phys. Rev. ...
A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible Euler equations is proposed (D2V19-LBM). The fifth-order Weighted Essentially Non-Oscillatory (5th-WENO) finite d...
We wish to explore a link between the Lax integrability of the q-Painleve equations and the symmetries of the q-Painleve equations. To do this, we consider the set of associated linear problems for th...

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