Related papers: Five Definitions of Critical Point at Infinity
We introduce a method based on the finite size scaling assumption which allows to determine numerically the critical point and critical exponents related to observables in an infinite system starting from the knowledge of the observables in…
A position $p$ in a word $w$ is critical if the minimal local period at $p$ is equal to the global period of $w$. According to the Critical Factorisation Theorem all words of length at least two have a critical point. We study the number…
We consider the space $P$ of generic complex 5-degree polynomials. Critical values of such polynomial, i.e. four points in the complex plane, either are vertices of a convex quadrangle $Q$, or vertices of a triangle $T$ with one point…
In this article we consider alternative definitions-descriptions of a set being Infinite within the primitive Axiomatic System of Zermelo.
At a critical point of a second order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can…
Let V $\subset$ C n be an equidimensional algebraic set and g be an n-variate polynomial with rational coefficients. Computing the critical points of the map that evaluates g at the points of V is a cornerstone of several algorithms in real…
In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…
We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the…
Answering a question posed by Adam Epstein, we show that the collection of conjugacy classes of polynomials admitting a parabolic fixed point and at most one infinite critical orbit is a set of bounded height in the relevant moduli space.…
Limit can be defined by two axioms: 1. Strict inequality between limits implies, ultimately, strict inequality between functions. 2. For constant functions limit is trivial. How can basic results on convergence be derived from these axioms?…
We investigate the existence and multiplicity of solutions for fourth order discrete boundary value problems via critical point theory.
Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This yields a classification statement on preperiodic points for quadratic polynomials over…
We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…
We consider an infinite-dimensional non-linear operator related to a hard core (HC) model with a countable set $\mathbb{N}$ of spin values. It is known that finding the fixed points of an infinite-dimensional operator is generally…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions.
A continuous selection of polynomial functions is a continuous function whose domain can be partitioned into finitely many pieces on which the function coincides with a polynomial. Given a set of finitely many polynomials, we show that…
Nonstandard analysis is very complex, so finding a simple description of infinitesimal points will be useful. In this paper, ultrafilters as infinitesimal points in a topological space will be proposed, and some topological concepts is…
We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
We give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2.