Related papers: Hyperfocused arcs in PG(2,32)
Let p be a puncture of a punctured sphere, and let Q be the set of all other punctures. We prove that the maximal cardinality of a set of arcs pairwise intersecting at most once, which start at p and end in Q, is |X|(|X| + 1). We deduce…
We present the results of a systematic search for gravitationally-lensed arcs in clusters of galaxies located in the Hubble Space Telescope Wide Field and Planetary Camera 2 data archive. By carefully examining the images of 128 clusters we…
We present the results of a search for gravitationally-lensed giant arcs conducted on a sample of 825 SDSS galaxy clusters. Both a visual inspection of the images and an automated search were performed and no arcs were found. This result is…
The statistics of strongly lensed arcs in samples of galaxy clusters provide information on cluster structure that is complementary to that from individual clusters. However, samples of clusters that have been analyzed to date have been…
We present constructions and bounds for additive codes over a finite field in terms of their geometric counterpart, i.e., projective systems. It is known that the maximum number of $(h-1)$-spaces in PG$(2,q)$, such that no hyperplane…
We consider the Keplerian arcs around a fixed Newtonian center joining two prescribed distinct positions in a prescribed flight time. We prove that, putting aside the "opposition case" where infinitely many planes of motion are possible,…
We classify maximal systems of arcs which intersect at most once on the 4-punctured sphere.
We apply verified numerics to the Nirenberg problem, proving that a genuine solution exists near two given computer-generated approximate solutions. This proves existence of a solution for a particular prescribed curvature that was…
In 1978, Anderson and White asked whether there is a decomposition of $K_{12}$ into two graphs, one planar and one toroidal. Using theoretical arguments and a computer search of all maximal planar graphs of order 12, we show that no such…
We resolve two problems of [Cameron, Praeger, and Wormald -- Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica 1993]. First, we construct a locally finite highly arc-transitive digraph with universal…
Superpixels group perceptually similar pixels to create visually meaningful entities while heavily reducing the number of primitives for subsequent processing steps. As of these properties, superpixel algorithms have received much attention…
The contraction method in different limits to obtain 22 different realizations of kinematical algebras is applied to study the supersymmetric extension of \AdS\ algebra and its contractions. It is shown that $\frak{p}_2$ $\frak{h}_-$,…
In a former paper the authors counted the number of non-isomorphic Mathon maximal arcs of degree 8 in PG(2,2^h), h not 7 and prime. In this paper we will show that in PG(2,2^7) a special class of Mathon maximal arcs of degree 8 arises which…
We report the follow-up spectroscopic confirmation of two lensed quasars, six dual quasars, and eleven projected quasars that were previously identified as lensed-quasar candidates in \cite{He2023}. The spectroscopic data were obtained from…
This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that…
The paper presents two edge grouping algorithms for finding a closed contour starting from a particular edge point and enclosing a fixation point. Both algorithms search a shortest simple cycle in \textit{an angularly ordered graph} derived…
We consider two families of hyperbolic polygons: ideal and ideal once-punctured, some of whose spikes are decorated with horoballs. We show that the arc complexes of these two families of surfaces, generated by edge-to-edge arcs and…
According to a computer search conducted by the author and described in [7], in $Q^+(6, 4)$ there are two types of hyperovals, having 72 and 96 points, respectively. Here we give geometric descriptions for these examples.
Because the problem of Apollonius is generally considered over the reals, it suffers from variance of number: there are at most eight circles simultaneously tangent to a given trio of circles, but some configurations have fewer than eight…
The computer calculations in arXiv:0808.0284 to classify sharp polynomials with nonegative coefficients constant on the line $x+y=1$ have been extended to degrees 19 and 21. In degree 19 a surprisingly large number of 13 sharp polynomials…