Correcting non-linear lens distortion in cameras without using a model

Camera lens distortion calibration is the first step in resolving any metric application with a camera. To date, lens distortion was corrected using some existing lens distortion non-metric or self-calibration methods. Using a lens distortion model means defining a global rule to correct the entire image. This global rule does not take into account particular lens distortion effects not represented by the model. Moreover, to calibrate the model, only some features of the scene such as straight lines, circles or vanishing points are used. Since only the feature of the scene used to calibrate the model is guaranteed by the distortion rectification, it is certain that the model will not be precise. The result is an approximation of the real image distortion.To improve the lens distortion rectification, a method without using a model is proposed. Using a set of control points distributed across the entire image, they are corrected to assure all the restrictions of the scene. With both sets of points, the points detected in the image and the undistorted ones, image local transformations are defined considering only nearby control points. Rather than calibrating a global model, local functions are characterized. The distortion correction is defined by a rectification surface composed of local surface patches each influenced by nearby control points. This method is more sensitive to local deformations and allows the image to be corrected in accordance with its distortion.     

Optical pumping of nuclear spin magnetization in GaAs/AlAs quantum wells of variable electron density

We report the use of time-resolved Faraday rotation to induce and probe the polarization of nuclear spins within a set of quantum wells with varying background electron density. The electron density was controlled over a broad range by making use of structures of mixed type-I/type-II GaAs/AlAs quantum wells that spatially separate photoexcited electron–hole pairs. We find that the optically detected nuclear magnetic field decreases quasi-monotonically with increasing electron density. The likely factors responsible for this behavior are increased electron spin-lattice relaxation, increased electron spin delocalization, and dilution of the electron spin polarization.     

Proximal Point Methods for Lipschitz Functions on Hadamard Manifolds: Scalar and Vectorial Cases

In the second part of our study, we introduce the concept of global extended exactness of penalty and augmented Lagrangian functions, and derive the localization principle in the extended form. The main idea behind the extended exactness consists in an extension of the original constrained optimization problem by adding some extra variables, and then construction of a penalty/augmented Lagrangian function for the extended problem. This approach allows one to design extended penalty/augmented Lagrangian functions having some useful properties (such as smoothness), which their counterparts for the original problem might not possess. In turn, the global exactness of such extended merit functions can be easily proved with the use of the localization principle presented in this paper, which reduces the study of global exactness to a local analysis of a merit function based on sufficient optimality conditions and constraint qualifications. We utilize the localization principle in order to obtain simple necessary and sufficient conditions for the global exactness of the extended penalty function introduced by Huyer and Neumaier, and in order to construct a globally exact continuously differentiable augmented Lagrangian function for nonlinear semidefinite programming problems.     

Isoparametric submanifolds in two-dimensional complex space forms

We show that an isoparametric submanifold of a complex hyperbolic plane, according to the definition of Heintze, Liu and Olmos’, is an open part of a principal orbit of a polar action. We also show that there exists a non-isoparametric submanifold of the complex hyperbolic plane that is isoparametric according to the definition of Terng’s. Finally, we classify Terng-isoparametric submanifolds of two-dimensional complex space forms.     

Counting arithmetical structures on paths and cycles

Let $G$ be a finite, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(diag\left(\mathbf{d}\right)?A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices $(diag\left(\mathbf{d}\right)?A)$). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients $\left(\genfrac{}{}{0ex}{}{2n?1}{n?1}\right)$, and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles.     

Sterling stirling play

In this paper we analyze a recently proposed impartial combinatorial ruleset that is played on a permutation of the set \(\left[ n\right] \). We call this ruleset Stirling Shave. A procedure utilizing the ordinal sum operation is given to determine the nim value of a given normal play position. Additionally, we enumerate the number of permutations of \(\left[ n\right] \) which are \(\mathcal {P}\)-positions. The formula given involves the Stirling numbers of the first-kind. We also give a complete analysis of the Misère version of Stirling Shave using Conway’s genus theory. An interesting by-product of this analysis is insight into how the ordinal sum operation behaves in Misère Play.     

Exponential stability for laminated beams with a frictional damping

We study a laminated beam which consists of two identical layers of uniform thickness, taking into account that an adhesive of small thickness is bonding the two surfaces thereby producing an interfacial slip. We show that when the frictional damping acts on the effective rotation angle there is no need for any other kind of internal or boundary control to produce exponential stability for the system.     

Lattice points in bodies of revolution II

In [3] it was shown that when a three-dimensional smooth convex body has rotational symmetry around a coordinate axis one can find better bounds for the lattice point discrepancy than what is known for more general convex bodies. To accomplish this, however, it was necessary to assume a non-vanishing condition on the third derivative of the generatrix. In this article we drop this condition, showing that the aforementioned bound holds for a wider family of revolution bodies, which includes those with analytic boundary. A novelty in our approach is that, besides the usual analytic methods, it requires studying some Diophantine properties of the Taylor coefficients of the phase on the Fourier transform side.