Related papers: On the characteristic of integral point sets in $\…
A non-equilateral triangle in a Euclidean plane has exactly two isogonic and two isodynamic points. There are a number of different but equivalent characterizations of these triangle centers. The aim of this paper is to work out…
We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the…
Both the USA TST 2008 and the ELMO Shortlist 2013 suggested two issues that are connected to fixed points. These problems provide a strong linkage between the various attributes of specific points in a triangle. In this article, we will…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
The paper is devoted to discretization of integral norms of functions from a given collection of finite dimensional subspaces. For natural collections of subspaces of the multivariate trigonometric polynomials we construct sets of points,…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
In this paper, using Kronecker's theorem, we discuss the set of common fixed points of an n-parameter continuous semigroup of mappings. We also discuss convergence theorems to a common fixed point of an n-parameter nonexpansive semigroup.
For studying intrusion detection data we consider data points referring to individual IP addresses and their connections: We build networks associated with those data points, such that vertices in a graph are associated via the respective…
In analogy with the 290-Theorem of Bhargava-Hanke, a criterion set is a finite subset $C$ of the totally positive integers in a given totally real number field such that if a quadratic form represents all elements of $C$, then it…
In this note, we provide two characterizations of the set of integer points in an integral bisubmodular polyhedron. Our characterizations do not require the assumption that a given set satisfies the hole-freeness, i.e., the set of integer…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.
Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…
We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…
We introduce the notion of the symplectic characteristic polynomial of an endomorphism of a symplectic vector space. This is a polynomial in two variables and can be considered as a generalization of the characteristic polynomial of the…
Recently $C^m$-conforming finite elements on simplexes in arbitrary dimension are constructed by Hu, Lin and Wu. The key in the construction is a non-overlapping decomposition of the simplicial lattice in which each component will be used…
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…
Structural parameter identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. One of the standard approaches to assessing this…
The concept of a visible point of a convex set relative to a given point is introduced. A number of basic properties of such visible point sets is developed. In particular, it is shown that this concept is useful in the study of best…
Answering a question of Frank Calegari, we extend some of our earlier results on dimension of fixed point spaces of elements in irreducible linear groups. We consider characteristic polynomials rather than just fixed spaces.