Let Γg be the fundamental group of a closed oriented Riemann surface Σg, g ≥ 2, and let G be a simple Lie group of Hermitian type. The Toledo invariant defines the subset of maximal representations Repmax(Γg , G) in the representation variety Rep(Γg , G). Repmax(Γg, G) is a union of connected components with similar properties as Teichmüller space T (Σg) = Repmax(Γg , PSL(2, R)). We prove that ...

Photometric invariance is used in many computer vision applications. The advantage of photometric invariance is the robustness against shadows, shading, and illumination conditions. However, the drawbacks of photometric invariance is the loss of discriminative power and the inherent instabilities caused by the non-linear transformations to compute the invariants. In this paper, we propose a new...

Given measured data we propose a model consisting of a linear, time-invariant system aaected by norm-bounded perturbation. In this paper we examine the special case of (real) parameter uncertainty. The plants belonging to the resulting uncertain family form a convex set. A robust control method based on strict-positive realness results can be applied. This method allows the computation of a con...

In mathematical chemistry, a particular attention is given to degree-based graph invariant. The Zagrebpolynomial is one of the degree based polynomials considered in chemical graph theory. A dendrimer isan artificially manufactured or synthesized molecule built up from branched units called monomers. Inthis note, the first, second and third Zagreb poly...

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

We argue that the second-order gauge-invariant Schwinger-Dyson operator of a gauge theory is the Wheeler-DeWitt operator in the dual string theory. Using this identification, we construct a set of operators in the gauge theory that correspond to excitations of gravity in the bulk. We show that these gauge theory operators have the expected properties for describing the semiclassical local gravi...

Given measured data we propose a model consisting of a linear, time-invariant system aaected by norm-bounded perturbation. The plants belonging to the resulting uncertain family form a convex set. It turns out that a robust control method based on strict-positive realness results can be applied. This method allows the computation of a controller which maximizes the stability margin. Lower and u...

We present a method for finding optimal controlled variables, which are polynomial combinations of measurements. Controlling these variables gives optimal steady state operation. Our work extends the concept of self-optimizing control; starting from the first-order necessary optimality conditions, any unknown variables are eliminated using elimination theory for polynomial systems to obtain inv...

The influence of large-scale advective cooling and/or moistening on the quasi-equilibrium behavior of simulated, tropical oceanic cumulus ensembles is examined in this study. Two sensitivity simulations are performed by imposing time varying/invariant large-scale advective cooling effects and time invariant/varying large-scale advective moistening effects. The results are compared with a contro...