相关论文: Dynamics of quadratic polynomials: Complex bounds …

We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the…

We present a more general proof that cyclotomic polynomials are irreducible over Q and other number fields that meet certain conditions. The proof provides a new perspective that ties together well-known results, as well as some new…

We define iterated monodromy groups of more general structures than partial self-covering. This generalization makes it possible to define a natural notion of a combinatorial model of an expanding dynamical system. We prove that a naturally…

Let $f_1(x),\ldots,f_n(x)$ be some polynomials. The upper bound on the number of $x\in\mathbb F_p$ such that $f_1(x),\ldots,f_n(x)$ are roots of unit of order $t$ is obtained. This bound generalize the bound of the paper \cite{V-S} to the…

This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…

We establish new upper bounds about symmetric bilinear complexity in any extension of finite fields. Note that these bounds are not asymptotical but uniform. Moreover we give examples of Shimura curves that do not descend over their field…

Given any polynomial with real coefficients, the existence of a real quadratic polynomial factor is proven using only basic real analysis. The aim is to provide an approachable proof to anybody who is familiar with the least upper bound…

We use the stabilization functors to study the combinatorial aspects of the $F$-polynomial of a representation of any finite-dimensional basic algebra. We characterize the vertices of their Newton polytopes. We give an explicit formula for…

A model for the Mandelbrot set is due to Thurston and is stated in the language of geodesic laminations. The conjecture that the Mandelbrot set is actually homeomorphic to this model is equivalent to the celebrated MLC conjecture stating…

Spinor polynomials are polynomials with coefficients in the even sub-algebra of conformal geometric algebra whose norm polynomial is real. They describe rational conformal motions. Factorizations of spinor polynomial corresponds to the…

In this article we prove an upper bound for a Hilbert polynomial on quaternionic Kaehler manifolds of positive scalar curvature. As corollaries we obtain bounds on the quaternionic volume and the degree of the associated twistor space.…

We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents. One of these families is obtained by replacing…

We prove a linear upper bound for the number of singular points on the boundary of a quadrature domain, improving a previously known quadratic bound due to Gustafsson \cite{Gus88}. This linear upper bound on the number of boundary double…

A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.

A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…

We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…

We consider a tuple $\Phi = (\phi_1,\ldots,\phi_m)$ of commuting maps on a finitary matroid $X$. We show that if $\Phi$ satisfies certain conditions, then for any finite set $A\subseteq X$, the rank of $\{\phi_1^{r_1}\cdots\phi_m^{r_m}(a):a…

It is a classical result that the absolute value of any $k$-minor of an $r\times s$ real or complex matrix is bounded by the product of its first $k$ singular values. We generalize this statement to the context of real or complex simple…

We deform the real potential of Poeschl and Teller by a shift of its coordinate in imaginary direction. We show that the new model remains exactly solvable. Its bound states are constructed in closed form. Wave functions are complex and…

Some new bounds for the extreme zeroes of Jacobi polynomials are obtained with an elementary approach. A feature of these bounds is their simple forms, which make them easy to work with. Despite their simplicity, our lower bounds for the…