Mathematics and Statistics Faculty Scholarship
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Cyclic curves over the reals
(eprint arXiv:1501.01559, 20141115)In this paper we study the automorphism groups of real curves admitting a regular meromorphic function f of degree p, so called real cyclic pgonal curves. When p = 2 the automorphism groups of real hyperelliptic curves ... 
Special issue on algebra and computational algebraic geometry
(Albanian J. Math., 200712)Algebraic geometry is one of the main branches of modern mathematics with roots from classical Italian geometers. Its modern flavor started with Grothendieck and continued with many illustrious algebraic geometers of the ... 
Thetanulls of cyclic curves of small genus
(Albanian J. Math., 20071215)We study relations among the classical thetanulls of cyclic curves, namely curves $\X$ (of genus $g(\X )>1$ ) with an automorphism $\s$ such that $\s$ generates a normal subgroup of the group $G$ of automorphisms, and $g ... 
Kalkulus I
(AulonaPress, 20171203) 
Rational points in the moduli space of genus two
(Contemporary Mathematics, 2018)We build a database of genus 2 curves defined over the field of rationals. 
Some open problems in computational algebraic geometry.
(Albanian J. Math., 20071215)The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry from a computational viewpoint. In this survey, we briefly describe some open ... 
Curves of genus 2 with (n, n)decomposable Jacobians
(Journal of Symbolic Computation, 200105)Let C be a curve of genus 2 and ψ1: C − → E 1 a map of degree n, from C to an elliptic curveE1 , both curves defined over C. This map induces a degree n map φ1:P1 − → P 1 which we call a Frey–Kani covering. We determine ... 
On generalized superelliptic Riemann surfaces
(eprint arXiv:1609.09576, 20161101)A closed Riemann surface X, of genus g ≥ 2, is called a generalized superelliptic curve of level n ≥ 2 if it admits an order n conformal automorphism τ so that X/hτihas genus zero and τ is central in Aut(X); the cyclic ... 
On the automorphism groups of some AGcodes based on C_{a,b} curves
(20060115)We study Ca,b curves and their applications to coding theory. Recently, Joyner and Ksir have suggested a decoding algorithm based on the automorphisms of the code. We show how Ca,b curves can be used to construct MDS ... 
Isogenous elliptic subcovers of genus two curves
(20171102)We prove that for $N=2,3, 5, 7$ there are only finitely many genus two curves $\X$ (up to isomorphism) defined over $\Q$ with $(2, 2)$split Jacobian and $\Aut (\X)\iso V_4$, such that their elliptic subcovers are ... 
Selfinversive polynomials, curves, and codes
(American Mathematical Society, 20160305)We study connections between selfinversive and selfreciprocal polynomials, reduction theory of binary forms, minimal models of curves, and formally selfdual codes 
Mësimdhënia e matematikës nëpërmjet problemeve klasike
(Albanian J. Math., 20161203)In this paper we discuss how teaching of mathematics for middle school and high school students can be improved dramatically when motivation of concepts and ideas is done through the classical problems and the history of ... 
Combinatorial Algorithm for Quadratic Programs with Laplacian Structure
(Utilitas Mathematica, 2016)An algorithm is presented that uses a mostly combinatorial approach to solve a family of convex quadratic programs over box constraints. It is proved that for convex programs with the required structure, the ... 
Applications of Subset Selection Procedures and Bayesian Ranking Methods in Analysis of Traffic Fatality Data
(WIREs Computational Statistics, 201611)Nonparametric and parametric subset selection procedures are used in the analysis of state motor vehicle traffic fatality rates (MVTFRs), for the years 1994 through 2012, to identify subsets of states that contain the ... 
Product measurability with applications to a stochastic contact problem with friction
(201412)A new product measurability result for evolution equations with random inputs, when there is no uniqueness of the ωwise problem, is established using results on measurable selection theorems for measurable multi functions. ... 
A Model for Chagas Disease with Oral and Congenital Transmission
(201306)This work presents a new mathematical model for the domestic transmission of Chagas disease, a parasitic disease affecting humans and other mammals throughout Central and South America. The model takes into account congenital ... 
Dynamic contact of two GAO beams
(201211)The dynamic contact of two nonlinear Gao beams that are connected with a joint is modeled, analyzed, and numerically simulated. Contact is modeled with either (i) the normal compliance condition, or (ii) the unilateral ... 
Regularity result for the problem of vibrations of a nonlinear beam
(200802)A model for the dynamics of the Gaonon linear beam, which allows for buckling, is studied. Existence and uniqueness of the local weak solution was established in Andrews et al. (2008). In this work the further regularity ... 
Dynamic contact with normal compliance wear and discontinuous friction coefficient
(200208)We apply the recent theory of evolution inclusions forsetvalued pseudomonotone maps, developed in Kuttler and Shillor[Commun.Contemp.Math.,1(1999),pp.87–123]to the problem of dynamic frictional contact with normal compliance ... 
Mathematical model for outgassing and contamination
(199110)A model for the mathematical description of the processes of outgassing and contamination in a vacuum system is proposed. The underlying assumptions are diffusion in the source, convection and diffusion in the cavity, mass ...