Related papers: Generalized Koch curves and Thue-Morse sequences

We consider positive solutions of a semilinear Dirichlet problem \[ \Delta u+\lambda f(u)=0, \;\; \mbox{for $|x|<1$}, \;\; u=0 , \;\; \mbox{when $|x|=1$} \] on a unit ball in $R^n$. For four classes of self-similar equations it is possible…

We prove that any geometrically connected curve $X$ over a field $k$ is an algebraic $K(\pi,1)$, as soon as its geometric irreducible components have nonzero genus. This means that the cohomology of any locally constant constructible…

We study the structure of collections of algebraic curves in three dimensions that have many curve-curve incidences. In particular, let $k$ be a field and let $\mathcal{L}$ be a collection of $n$ space curves in $k^3$, with…

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot…

For $n\leq 6$, we compute the integral Chow ring of every modular compactification of $\mathcal{M}_{1,n}$ parametrising only Gorenstein curves with smooth, distinct markings. These include the Deligne--Mumford, Schubert, and Smyth…

In the first part of this paper, we establish some results around generalized Borel's Theorem. As an application, in the second part, we construct example of smooth surface of degree $d\geq 19$ in $\mathbb{CP}^3$ whose complements is…

We continue the study of the $k$-cut complex $\Delta_k(G)$ of a graph $G$ initiated in the paper of Bayer, Denker, Jeli\'c Milutinovi\'c, Rowlands, Sundaram and Xue [Topology of cut complexes of graphs, SIAM J. on Discrete Math. 38(2):…

Let $\Theta_{k_1,\cdots,k_\ell}$ denote the generalized theta graph, which consists of $\ell$ internally disjoint paths with lengths $k_1,\cdots, k_{\ell}$, connecting two fixed vertices. We estimate the corresponding extremal number…

This paper presents the Tate pairing computation on generalized Huff curves proposed by Wu and Feng. In fact, we extend the results of the Tate pairing computation on the standard Huff elliptic curves done previously by Joye, Tibouchi and…

We prove a generalization of van der Corput's Difference Theorem in the theory of uniform distribution by establishing a connection with unitary operators that have Lebesgue spectrum. This allows us to show, for example, that if $(x_n)_{n =…

Consider a finite connected graph denoted as $G=(V, E)$. This study explores a generalized Chern-Simons Higgs model, characterized by the equation: $$ \Delta u = \lambda e^u (e^u - 1)^{2p+1} + f,$$ where $\Delta$ denotes the graph…

In this paper we obtain an explicit formula for the number of curves in two dimensional complex projective space, of degree d, passing through d(d+3)/2-(k+1) generic points and having one node and one codimension k singularity, where k is…

Let X be a non-singular algebraic curve of genus at least 3 and let M denote the moduli space of stable vector bundles of rank n and fixed determinant of degree d with n and d coprime. For any semistable bundle E over X, we can pull E back…

Generalized Kauer moves are local moves of multiple edges in a Brauer graph that yield derived equivalences between Brauer graph algebras of multiplicity identically 1. Moreover, these derived equivalences are given by a tilting mutation.…

We consider the moduli space of genus 4 curves endowed with a $g^1_3$ (which maps with degree 2 onto the moduli space of genus 4 curves). We prove that it defines a degree $\frac{1}{2}(3^{10}-1)$ cover of the 9-dimensional Deligne-Mostow…

Let $k$ be a perfect field and let $C_0:f=0$ be a smooth curve in the torus $\mathbb{G}_{m,k}^2$. Let $\mathbb{T}_\Delta$ be the toric variety associated to the Newton polygon of $f$. Extending the toric resolution of $C_0$ on…

Kirchhoff energy is a classical functional on the space of arclength-parameterized framed curves whose critical points approximate configurations of springy elastic rods. We introduce a generalized functional on the space of framed curves…

We generalize the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki-Calderbank-Moran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting number-theoretic results…

Given a generically smooth stable curve over a discrete valuation ring such that its special fibre is irreducible with one double point, we construct a moduli stack over that descrete valuation ring which is a model for the moduli stack of…

Using Serre's adelic interpretation of cohomology, we develop a `differential and integral calculus' on an algebraic curve X over an algebraically closed filed k of constants of characteristic zero, define algebraic analogs of additive…