Related papers: Pole placement for overdetermined 2D systems
A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.
We analyze the transition into the most favorable ordered state for a system of 2D fermions with spin and valley degrees of freedom. We show that for a range of rotationally invariant dispersions, the ordering transition is highly…
Out-of-plane gap solitons in 2D photonic crystals are optical beams localized in the plane of periodicity of the medium and delocalized in the orthogonal direction, in which they propagate with a nonzero velocity. We study such gap solitons…
We give a canonical description of the formal moduli space of a vector bundle on a variety; as an application, we prove the closedness of certain differential forms on moduli corresponding to the trace form on the endomorphism algebra of…
In this note we consider the moduli space of stable bundles of rank two on a very general quintic surface. We study the potentially obstructed points of the moduli space via the spectral covering of a twisted endomorphism. This analysis…
Reorienting objects by using supports is a practical yet challenging manipulation task. Owing to the intricate geometry of objects and the constrained feasible motions of the robot, multiple manipulation steps are required for object…
The two-matrix model can be solved by introducing bi-orthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of bi-orthogonal polynomials (called "windows") satisfy polynomial ODEs as well as…
In this paper, we study a geometric counterpart of the cyclic vector which allow us to put a rank 2 meromorphic connection on a curve into a ``companion'' normal form. This allow us to naturally identify an open set of the moduli space of…
We are interested in studying moduli spaces of rank 2 logarithmic connections on elliptic curves having two poles. To do so, we investigate certain logarithmic rank 2 connections defined on the Riemann sphere and a transformation rule to…
This paper derives new formulations for designing dominant pole placement based proportional-integral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for…
Let ${\mathcal M}$ be a moduli space of stable vector bundles of rank $r$ and determinant $\xi$ on a compact Riemann surface $X$. Fix a semistable holomorphic vector bundle $F$ on $X$ such that $\chi(E\otimes F)= 0$ for $E \in \mathcal M$.…
Position representation is crucial for building position-aware representations in Transformers. Existing position representations suffer from a lack of generalization to test data with unseen lengths or high computational cost. We…
We analyze the local structure of the moduli space of semi-stable bundles on a curve. In particular, a complete description of the local structure is given in the rank 2 case. We obtain as a corollary of this analysis new results about the…
Let $(X,\,D)$ be an $m$-pointed compact Riemann surface of genus at least $2$. For each $x \,\in\, D$, fix full flag and concentrated weight system $\alpha$. Let $P \mathcal{M}_{\xi}$ denote the moduli space of semi-stable parabolic vector…
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in $\mathbb{R}^n$, we may obtain a global representation as a cell complex with vertices given by a representative subset of the point cloud. The vertex…
This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.
This work is a direct continuation of the authors work arXiv:0812.3779v1. A special case of conservative overdetermined time invariant 2D systems is developed and studied. Defining transfer function of such a systems we obtain a class CI of…
Let $ \mathcal{D} = \{D_{1}, \ldots, D_{\ell}\} $ be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space $ \mathbb{P}^{n} $ and let $ \Omega^{1}_{\mathbb{P}^{n}}(log \mathcal{D}) $ be the logarithmic…
We study two different actions on the moduli spaces of logarithmic connections over smooth complex projective curves. Firstly, we establish a dictionary between logarithmic orbifold connections and parabolic logarithmic connections over the…
In this paper we give a multiresolution construction in Bergman space. The successful application of rational orthogonal bases needs a priori knowledge of the poles of the transfer function that may cause a drawback of the method. We give a…