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In characteristic $p>0$ and for $q$ a power of $p$, we compute the number of nonplanar rational curves of arbitrary degrees on a smooth Hermitian surface of degree $q+1$ under the assumption that the curves have a parametrization given by…
We give a geometrical characterization of the ideal of quadrics containing a canonical curve with an involution. This implies to study involutions of rational normal scrolls and Veronese surfaces.
An algorithm to generate the locus of a circle using the intersection points of straight lines is proposed. The pixels on the circle are plotted independent of one another and the operations involved in finding the locus of the circle from…
It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance $\epsilon>0$ and an $\epsilon$-irreducible algebraic affine plane curve $\mathcal C$ of…
Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…
Inverse optimization describes a process that is the "reverse" of traditional mathematical optimization. Unlike traditional optimization, which seeks to compute optimal decisions given an objective and constraints, inverse optimization…
In this paper we construct parameterizations of elliptic curves over the rationals which have many consecutive integral multiples. Using these parameterizations, we perform searches in GMP and Magma to find curves with points of small…
We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.
We can associate with any irreducible curve singularity (ics) a numerical semigroup. Two ics are said to be equisingular if they have the same semigroup. Two equisingular ics have the same Milnor number. Conversely, The set of ics with a…
We prove that a general planar NURBS curve parametrization $\phi: [u_0,u_m] \xrightarrow{} C \subset \mathbb{R}^2$ admits an inverse map $\phi^{-1}: C \xrightarrow{} [u_0,u_m]$ defined by rational splines. More specifically, we construct a…
We present an algorithm for detecting basepoints of linear series of curves in the plane. Moreover, we give an algorithm for constructing a linear series of curves in the plane for given basepoints. The underlying method of these algorithms…
In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature…
Any smooth projective curve embeds into $\mathbb{P}^3$. More generally, any curve embeds into a rationally connected variety of dimension at least three. We prove conversely that if every curve embeds in a threefold $X$, then $X$ is…
We give several constructions of bicuspidal rational complex projective plane curves, and list the Newton pairs and the multiplicity sequences of the singularities on the resulting curves. Although the existence of some of the listed cusp…
Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…
We present the general theory of curves in conformal geometry using tractor calculus. This primarily involves a tractorial determination of distinguished parametrizations and relative and absolute conformal invariants of generic curves. The…
This paper, motivated by problems in Diophantine analysis which can be formulated as problems of finding rational points on the intersection of two quadrics, presents an explicit construction of a rationally defined isomorphism (biregular…
For a compact convex set F in R^n, with the origin in its interior, we present a formula to compute the curvature at a fixed point on its boundary, in the direction of any tangent vector. This formula is equivalent to the existing ones, but…
A rational triangle is a triangle with rational side lengths. We consider three different families of rational triangles having a fixed side and whose vertices are rational points in the plane. We display a one-to-one correspondence between…
Rotation curves of spiral galaxies are known with reasonable precision for a large number of galaxies with similar morphologies. The data implies that non-Keplerian fall--off is seen. This implies that (i) large amounts of dark matter must…