We consider linear port-Hamiltonian differential-algebraic equations. Inspired by the geometric approach of van der Schaft and Maschke [System Control Lett., 121 (2018), pp. 31--37] algebraic Mehl, Mehrmann, Wojtylak [SIAM J. Matrix Anal. Appl., 39 1489--1519], we present another view using theory relations. show that this allows us to elaborate differences mutualities views, introduce a class ...

This paper is the first in a series where we attempt to define defects critical lattice models that give rise conformal field theory topological continuum limit. We focus mostly on based Temperley-Lieb algebra, with future applications restricted solid-on-solid (also called anyonic chains) models, as well non-unitary like percolation or self-avoiding walks. Our approach essentially algebraic an...

Steepness is a generic geometric property which, together with complex-analyticity, needed in order to ensure stability of nearly-integrable hamiltonian system over exponentially long times. Following strategy developed by Nekhoroshev, we construct sufficient conditions for steepness given function that involve algebraic equations on its derivatives up five. This important view applications (e....

Valiant introduced some 25 years ago an algebraic model of computation along with the complexity classes VP and VNP, which can be viewed as analogues of the classical classes P and NP. They are defined using non-uniform sequences of arithmetic circuits and provides a framework to study the complexity for sequences of polynomials. Prominent examples of difficult (that is, VNP-complete) problems ...

in this paper energy bands and berry curvature of graphene was studied. desired hamiltonian regarding the next-nearest neighbors obtained by tight binding model. by using the second quantization approach, the transformation matrix is calculated and the hamiltonian of system is diagonalized. with this hamiltonian, the band structure and wave function can be calculated. by using calculated wave f...