相关论文: Counting Hyperbolic Components in the Main Molecul…

We consider a system of two kinetic equations modelling a multicellular system : The first equation governs the dynamics of cells, whereas the second kinetic equation governs the dynamics of the chemoattractant. For this system, we first…

We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.

In this article, we study the hyperbolic components of McMullen maps. We show that the boundaries of all hyperbolic components are Jordan curves. This settles a problem posed by Devaney. As a consequence, we show that cusps are dense on the…

The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…

In this paper an explicit formula for a lower bound on the volume of a hyperbolic orbifold, dependent on dimension and the maximal order of torsion in the orbifolds' fundamental group, is constructed.

Loosely speaking, the Volume Conjecture states that the limit of the n-th colored Jones polynomial of a hyperbolic knot, evaluated at the primitive complex n-th root of unity is a sequence of complex numbers that grows exponentially.…

Mandelbrot set arose from the pioneering work of French mathematician Gaston Julia in the field of complex dynamics at the beginning of the 20th century. French-American mathematician Benoit Mandelbrot used computers to calculate iterations…

A calculation method for higher-order moments of physical quantities, including magnetization and energy, based on the higher-order tensor renormalization group is proposed. The physical observables are represented by impurity tensors. A…

We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a…

We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…

We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial complex, for a group to be hierarchically hyperbolic. We apply this to show that quotients of mapping class groups by large powers of Dehn twists are…

In this paper, we prove restriction estimates for hyperbolic paraboloids in dimensions $n>=5$ by the polynomial partitioning method.

A real univariate polynomial of degree $n$ is called hyperbolic if all of its $n$ roots are on the real line. Such polynomials appear quite naturally in different applications, for example, in combinatorics and optimization. The focus of…

Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic…

We consider a simple but infinite class of staked links known as bongles. We provide necessary and sufficient conditions for these bongles to be hyperbolic. Then, we prove that all balanced hyperbolic $n$-bongles have the same volume and…

We show that the Julia set of quadratic maps with parameters in hyperbolic components of the Mandelbrot set is given by a transseries formula, rapidly convergent at any repelling periodic point. Up to conformal transformations, we obtain…

Let G be a word-hyperbolic group with given finite generating set, for which various standard structures and constants have been pre-computed. A (non-practical) algorithm is described that, given as input two lists A and B, each composed of…

For the quadratic family $f_{c}(z) = z^2+c$ with $c$ in a hyperbolic component of the Mandelbrot set, it is known that every point in the Julia set moves holomorphically. In this paper we give a uniform derivative estimate of such a motion…

We show that the complex hyperbolic metrics defined by Deligne-Mostow and Thurston on ${\mathcal{M}}_{0,n}$ are singular K\"ahler-Einstein metrics when ${\mathcal{M}}_{0,n}$ is embedded in the Deligne-Mumford-Knudsen compactification…

We study Kostant's partial order on the elements of a semisimple Lie group in relations with the finite dimensional representations. In particular, we prove the converse statement of [3, Theorem 6.1] on hyperbolic elements.