相关论文: The Main Cubioid
The periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics. The corresponding partition is mapped to a topological well-ordered symbol plane. In the symbol plane the pruning front is…
There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean…
We study multiple orthogonal polynomials of type I and type II which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the…
We describe polynomial time algorithms for determining whether an undirected graph may be embedded in a distance-preserving way into the hexagonal tiling of the plane, the diamond structure in three dimensions, or analogous structures in…
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. Finding such a cuboid is equivalent to finding a perfect cuboid with all…
We classify the planar cubic Cayley graphs of connectivity 2, providing an explicit presentation and embedding for each of them. Combined with [9] this yields a complete description of all planar cubic Cayley graphs.
This report on axisymmetric ultraspherical/Gegenbauer polynomials and their use in Ambisonic directivity design in 2D and 3D presents an alternative mathematical formalism to what can be read in, e.g., my and Matthias Frank's book on…
The task of listing all triangles in an undirected graph is a fundamental graph primitive with numerous applications. It is trivially solvable in time cubic in the number of vertices. It has seen a significant body of work contributing to…
Combining a modular approach to the $abc$ conjecture developed by the second author with the classical method of linear forms in logarithms, we obtain improved unconditional bounds for two classical problems. First, for Szpiro's conjecture…
We exhibit products of Mandelbrot sets in the two-dimensional complex parameter space of cubic polynomials. These products were observed by J. Milnor in computer experiments which inspired Lavaurs' proof of non local-connectivity for the…
The quantum Frobenius map and it splitting are shown to descend to corresponding maps for generalized $q$-Schur algebras at a root of unity. We also define analogs of $q$-Schur algebras for any affine algebra, and prove the corresponding…
In a given hypercube, draw grid lines parallel to the edges, and consider all hypercuboids (or hypercubes) whose edges are lying on the grid lines or the boundary. We find the limit of the value of the ratio of the arithmetic mean of the…
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study the probabilistic central Bell polynomials associated with random variable Y, as probabilistic extension of the…
We discuss the construction of oscillator-like systems associated with orthogonal polynomials on the example of the Fibonacci oscillator. In addition, we consider the dimension of the corresponding lie algebras.
We study algebraic and arithmetic properties of submonoids (resp. subrings) of factorial monoids (resp. factorial domains) whose non-invertible elements all lie in the conductor. This continues earlier work of Baeth, Cisto, et al.. On our…
We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…
We introduce and study symmetric and exterior algebras in braided monoidal categories such as the category O for quantum groups. We relate our braided symmetric algebras and braided exterior algebas with their classical counterparts.
We discuss quantum analogues of minimal surfaces in Euclidean spaces and tori.
In this paper, we investigate some properties of q-Bernoulli polynomi- als arising from q-umbral calculus. Finally, we derive some interesting identities of q-Bernoulli polynomials from our investigation.
We study the dynamics of cubic polynomials restricted to their basins of infinity, and we enumerate topological conjugacy classes with given combinatorics.