The generalized projective synchronization GPS of chaotic systems with uncertain parameter noise and external disturbance is discussed. Based on the adaptive technique, a response system is constructed, and a novel adaptive controller is designed to guarantee the GPS between the driveresponse systems, and to eliminate the effect of external disturbance and parameters noise on GPS. The conclusio...

We study integrable lattice equations and their perturbations over finite fields. We write these equations in projective coordinates and assign boundary values along axes in the first quadrant. We propose some growth diagnostics over finite fields that can often distinguish between integrable equations and their non-integrable perturbations. We also discuss the limitations of the diagnostic. Fi...

This work is concerned with branes and differential equations for one–parameter Calabi–Yau hypersurfaces in weighted projective spaces. For a certain class of B–branes we derive the inhomogeneous Picard–Fuchs equations satisfied by brane superpotential. In this way we arrive at a prediction for the real BPS invariants for holomorphic maps of worldsheets with low Euler characteristics, ending on...

An overview of advanced dynamical algorithms capable of spanning the widely disparate time scales that govern the decay of metastable phases in discrete spin models is presented. The algorithms discussed include constrained transfer-matrix, Monte Carlo with Absorbing Markov Chains (MCAMC), and projective dynamics (PD) methods. The strengths and weaknesses of each of these algorithms are discuss...

This paper deals with the concept of auto-calibration, i.e. methods to calibrate a camera on-line. In particular, we deal with minimal conditions on the intrinsic parameters needed to make a Euclidean reconstruction, called flexible calibration. The main theoretical results are that it is only needed to know that one intrinsic parameter is constant. The method is based on an initial projective ...

Adaptive feedback controllers based on Lyapunov’s direct method for chaos control and hybrid projective synchronization HPS of a novel 3D chaotic system are proposed. Especially, the controller can be simplified ulteriorly into a single scalar one to achieve complete synchronization. The HPS between two nearly identical chaotic systems with unknown parameters is also studied, and adaptive param...

The main purpose of this paper is to show that ideas of deformation theory can be applied to “infinite dimensional geometry”. We develop the deformation theory of Brody curves. Brody curve is a kind of holomorphic map from the complex plane to the projective space. Since the complex plane is not compact, the parameter space of the deformation can be infinite dimensional. As an application we pr...

The equation also appears in investigation of geodesically equivalent metrics. Recall that two metrics on one manifold are geodesically equivalent, if every geodesic of one metric is a reparametrized geodesic of the second metric. Solodovnikov [9] has shown that Riemannian metrics on (n > 3)−dimensional manifolds admitting nontrivial 3-parameter family of geodesically equivalent metrics allow n...

Motivated by the study of hyperkähler structures in moduli problems and hyperkähler implosion, we initiate the study of non-reductive hyperkähler and algebraic symplectic quotients with an eye towards those naturally tied to projective geometry, like cotangent bundles of blow-ups of linear arrangements of projective space. In the absence of a Kempf-Ness theorem for non-reductive quotients, we f...

let $g$ be a finite group and $pi_{e}(g)$ be the set of element orders of $g $. let $k in pi_{e}(g)$ and $s_{k}$ be the number of elements of order $k $ in $g$. set nse($g$):=${ s_{k} | k in pi_{e}(g)}$. in this paper, it is proved if $|g|=|$ pgl$_{2}(q)|$, where $q$ is odd prime power and nse$(g)= $nse$($pgl$_{2}(q))$, then $g cong $pgl$_