We consider the partition function Z(N ;x1, . . . , xN , y1, . . . , yN ) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set to the special value a = exp(iπ/3). Our proof does not use any determinantal interpretation of Z and can be adapted to other situations (for examp...

Geometric Representation Theory for semi-simple Lie groups has two main sheaf theoretic models. Namely, through Beilinson-Bernstein localization theory, Harish-Chandra modules are related to holonomic sheaves of D modules on the flag variety. Then the (algebraic) Riemann-Hilbert correspondence relates these sheaves to constructible sheaves of complex vector spaces. On the other hand, there is a...

In this paper, global uniform exponential stability of perturbed dynamical systems is studied by using Lyapunov techniques. The system presents a perturbation term which is bounded by an integrable function with the assumption that the nominal system is globally uniformly exponentially stable. Some examples in dimensional two are given to illustrate the applicability of the main results.

This paper presents a practical and efficient method to solve large-scale nonlinear equations. The global convergence of this new trust region algorithm is verified. The algorithm is then used to solve the nonlinear equations arising in an Expanded Lagrangian Function (ELF). Numerical results for the implementation of some large-scale problems indicate that the algorithm is efficient for these ...

conclusions silent ventricular systolic dysfunction was more common in the patients with sle than in the control group. newer echocardiographic techniques such as two-dimensional ste provide an earlier chance for the detection of subclinical lv systolic dysfunction. our findings were independent of the traditional risk factors. results the mean duration of sle was 5.5 ± 3.4 years in our patient...