Related papers: Some new parameterizations for the Diophantine bi-…
We classify the local bifurcations of one dov quantum billiards, showing that only saddle-center bifurcations can occur. We analyze the resulting planar system when there is no coupling in the superposition state. In so doing, we also…
This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best…
This article shines new light on the classical problem of tiling rectangles with squares efficiently with a novel method. With a twist on the traditional approach of resistor networks, we provide new and improved results on the matter using…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Periodic solution parameters, in chaotic dynamical systems, form periodic windows with characteristic distribution in two-parameter spaces. Recently, general properties of this organization have been reported, but a theoretical explanation…
This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where the system exhibits multiple coexisting solutions for given…
For any given positive definite binary quadratic form $Q$ with integer coefficients, we establish two results on Diophantine approximation with integers represented by $Q$. Firstly, we show that for every irrational number $\alpha$, there…
There are parallelepipeds with edge lengths, face diagonal lengths and body diagonal lengths all positive integers. In particular, there is a parallelepiped with edge lengths 271, 106, 103, minor face diagonal lengths 101, 266, 255, major…
A set of lines in $\mathbb{R}^d$ passing through the origin is called equiangular if any two lines in the set form the same angle. We proved an alternative version of the three-point semidefinite constraints developed by Bachoc and…
We investigate approximation to a given real number by algebraic numbers and algebraic integers of prescribed degree. We deal with both best and uniform approximation, and highlight the similarities and differences compared with the…
A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. Its existence is equivalent to the existence of a perfect cuboid with all…
In this paper we introduce a new bifurcation in Hamiltonian systems, which we call the double flip bifurcation. The Hamiltonian depends on two parameters, one of which controls the double flip bifurcation. The result of the bifurcation is…
In this short communication we introduce a rather simple autonomous system of 2 nonlinearly-coupled first-order Ordinary Differential Equations (ODEs), whose initial-values problem is explicitly solvable by algebraic operations. Its ODEs…
This paper describes the demonstration of linearly polarized picosecond pulse shaping with variable profiles including symmetric and non-symmetric intensity distributions. Important characteristics such as stability and transmission were…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination a3b). Parallel to a complete classification by Cheung, Luk and Yan, the method implemented…
Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…
The inhomogeneous metric theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous Khintchine-Jarnik type theorems recently established in [Ann.…
In this paper, we study a two-parameter family of two-dimensional diffeomorphisms such that it has a cubic homoclinic tangency unfolding generically which is associated with a dissipative saddle point. Our first theorem presents an open set…
In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…