Related papers: Existence of Two View Chiral Reconstructions
We describe computer searches that prove the graph reconstruction conjecture for graphs with up to 13 vertices and some limited classes on larger sizes. We also investigate the reconstructibility of tournaments up to 13 vertices, digraphs…
Vanishing points and vanishing lines are classical geometrical concepts in perspective cameras that have a lineage dating back to 3 centuries. A vanishing point is a point on the image plane where parallel lines in 3D space appear to…
This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist wavelet frames $\{a^{j/2}\psi( a^j\cdot -kb)\}_{j,k\in \mathbb Z}$ in $L^2(\mathbb R)$ for which no dual frame has wavelet…
According to [1] an $n$-dimensional $\mathcal{N}$--set is a compact subset $A$ of $\mathbb{R}^n$ such that for every $x$ in $\mathbb{R}^n$ there is $y$ in $A$ with $y-x$ in $\mathbb{Z}^n$. We prove that every two dimensional…
In the second, fourth and fifth authors' previous work, a duality on generic real analytic cuspidal edges in the Euclidean 3-space $\boldsymbol R^3$ preserving their singular set images and first fundamental forms, was given. Here, we call…
We investigate whether a three-mirror system, having secondary and the tertiary mirrors with surfaces warped by Zernike polynomials generated by active vase mirrors, is suitable to do the corrections of a fixed parabolic mirror observing at…
We construct the chiral algebra associated with the $A_{1}$-type class $\mathcal{S}$ theory for genus two Riemann surface without punctures. By solving the BRST cohomology problem corresponding to a marginal gauging in four dimensions, we…
We study the congruence of bitangent lines of an irreducible surface in the 3-dimensional projective space in arbitrary characteristic, with special attention to quartic surfaces with rational double points and, in particular, Kummer…
In this paper, we continue the study of the relation between rational points of rational elliptic surfaces and plane curves. As an application, we give first examples of Zariski pairs of cubic-line arrangements that do not involve…
We discuss the pseudodual chiral model to illustrate a class of two-dimensional theories which have an infinite number of conservation laws but allow particle production, at variance with naive expectations. We describe the symmetries of…
Reflective and textureless surfaces remain a challenge in multi-view 3D reconstruction. Both camera pose calibration and shape reconstruction often fail due to insufficient or unreliable cross-view visual features. To address these issues,…
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…
Modern theories of physics tell that the vacuum is not an empty space. Hidden in the vacuum is a structure of anti-quarks $\bar{q}$ and quarks $q$. The $\bar{q}$ and $q$ pair has the same quantum number as the vacuum and condensates in it…
Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…
We present a series of examples of pairs of singular semialgebraic surfaces (real semialgebraic sets of dimension two) in ${\mathbb R}^3$ and ${\mathbb R}^4$ which are bi-Lipschitz equivalent with respect to the outer metric, ambient…
We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite number of pieces whose graphs are solutions of a linear…
We perform a theoretical and numerical study of the optical properties of both direct and inverse three-dimensional (3D) chiral woodpile structures, and a corresponding chiral Bragg stack. We compute transmission spectra in the helical…
We study the symplectic reparametrizations that are possible for theories of N=2 supersymmetric vector multiplets in the presence of a chiral background and discuss some of their consequences. One of them concerns an anomaly arising from a…
Optical (or Robinson) structures are one generalisation of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the…
We prove that the Hilbert scheme of points on a normal quasi-projective surface with at worst rational double point singularities is irreducible.