Consider two critical Liouville quantum gravity surfaces (i.e., $\gamma$-LQG for $\gamma=2$), each with the topology of $\mathbb{H}$ and infinite boundary length. We prove that there a.s. exists a conformal welding surfaces, when boundaries are identified according to This results in LQG surface decorated by an independent SLE$_4$. Combined proof uniqueness such welding, recently established Mc...

This article proposes a method that combines linear quadratic Gaussian (LQG) control design and structure preserving model reduction for the reduced order of infinite dimensional port Hamiltonian systems (IDPHS).For purpose weighting operators used in LQG are chosen such resulting dynamic controller is passive closed-loop system equivalent to by interconnection. The Petrov-Galerkin then approxi...

The Sirri jacket offshore platform was designed and installed in Persian gulf of Iran in 1975 and has been in service since that time. The importance of offshore structure's stability and the failure of this kind of structure during an earthquake in different active zones revealed that earthquake loading has to be considered. In this paper, Magnetorheological (MR) fluid dampers have been propos...

In this paper, optimal design of hybrid low damping base isolation and magnetorheological (MR) damper has been studied. Optimal hybrid base isolation system has been designed to minimize the maximum base drift of low damping base isolation system where for solving the optimization problem, genetic algorithm (GA) has been used. In design procedure the maximum acceleration of the structure has ...

We prove that the SLE? loop measure arises naturally from conformal welding of two ?-Liouville quantum gravity (LQG) disks for ?2=??(0,4). The proof relies on our companion work LQG and uses as an essential tool concept uniform embedding surfaces. Combining result with Gwynne Miller, we get random quadrangulations decorated by a self-avoiding polygon converge in scaling limit to sphere SLE8?3 l...

Partially observed major-minor nonlinear and linear quadratic Gaussian (PO MM LQG) mean field game (MFG) systems where the major agent's state is partially by each minor agent, agent completely observes its own have been analyzed in literature. In this article, PO LQG MFG problems with general information patterns are studied has partial observations of state, state. The assumption all agents l...