scholarly journals COMMUTING POLYNOMIALS AND POLYNOMIALS WITH SAME JULIA SET

1996 ◽  
Vol 06 (12a) ◽  
pp. 2427-2432 ◽  
Author(s):  
PAU ATELA ◽  
JUN HU
Keyword(s):  
Julia Set ◽  
Exact Relation ◽  
Complete Answer ◽  
Commuting Pairs

It has been known since Julia that polynomials commuting under composition have the same Julia set. More recently in the works of Baker and Eremenko, Fernández, and Beardon, results were given on the converse question: When do two polynomials have the same Julia set? We give a complete answer to this question and show the exact relation between the two problems of polynomials with the same Julia set and commuting pairs.

scholarly journals Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials

2021 ◽  
Author(s):  
Alexander Mielke
Keyword(s):  
Gradient Flow ◽  
Careful Analysis ◽  
Flow Equation ◽  
Uniqueness Result ◽  
Gradient System ◽  
Independent System ◽  
Exact Relation ◽  
Flow Equations ◽  
Total Variation Flow ◽  
Energetic Solutions

AbstractWe consider a non-negative and one-homogeneous energy functional $${{\mathcal {J}}}$$ J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional $${{\mathcal {E}}}(t,u)= t {{\mathcal {J}}}(u)$$ E ( t , u ) = t J ( u ) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system.

scholarly journals Toughness, Forbidden Subgraphs and Pancyclicity

2021 ◽  
Vol 37 (3) ◽  
pp. 839-866
Author(s):  
Wei Zheng ◽  
Hajo Broersma ◽  
Ligong Wang
Keyword(s):  
Recent Article ◽  
Forbidden Subgraph ◽  
Forbidden Subgraphs ◽  
Free Graph ◽  
Induced Subgraph ◽  
Complete Answer ◽  
Open Case

AbstractMotivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$ K 1 ∪ P 4 can act as a forbidden subgraph to ensure that every 1-tough H-free graph is hamiltonian, and that there is no other forbidden subgraph with this property, except possibly for the graph $$K_1\cup P_4$$ K 1 ∪ P 4 itself. The hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs, as conjectured by Nikoghosyan, was left there as an open case. In this paper, we consider the stronger property of pancyclicity under the same condition. We find that the results are completely analogous to the hamiltonian case: every graph H such that any 1-tough H-free graph is hamiltonian also ensures that every 1-tough H-free graph is pancyclic, except for a few specific classes of graphs. Moreover, there is no other forbidden subgraph having this property. With respect to the open case for hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs we give infinite families of graphs that are not pancyclic.

EIGENVALUES OF FIBONACCI STOCHASTIC ADDING MACHINE

2010 ◽  
Vol 10 (02) ◽  
pp. 291-313 ◽  
Author(s):  
A. MESSAOUDI ◽  
D. SMANIA
Keyword(s):  
Julia Set ◽  
Transition Operator ◽  
Complex Numbers ◽  
Topological Properties

In this work, we compute the eigenvalues of the transition operator associated to the Fibonacci stochastic adding machine. In particular, we show that the eigenvalues are connected to the set [Formula: see text] of complex numbers z where (z2, z) belongs to the filled Julia set of a particular endomorphism of ℂ2. We also study some topological properties of the set [Formula: see text].

On the Julia set of the perturbed Mandelbrot map

2000 ◽  
Vol 11 (13) ◽  
pp. 2067-2073 ◽  
Author(s):  
John Argyris ◽  
Theodoros E Karakasidis ◽  
Ioannis Andreadis
Keyword(s):  
Julia Set

On uniformly perfect boundary of stable domains in iteration of meromorphic functions II

2002 ◽  
Vol 132 (3) ◽  
pp. 531-544 ◽  
Author(s):  
ZHENG JIAN-HUA
Keyword(s):  
Entire Function ◽  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Julia Set ◽  
Fatou Set ◽  
Deficient Value ◽  
Uniformly Perfect ◽  
Simply Connected ◽  
Stable Domains ◽  
Uniform Perfectness

We investigate uniform perfectness of the Julia set of a transcendental meromorphic function with finitely many poles and prove that the Julia set of such a meromorphic function is not uniformly perfect if it has only bounded components. The Julia set of an entire function is uniformly perfect if and only if the Julia set including infinity is connected and every component of the Fatou set is simply connected. Furthermore if an entire function has a finite deficient value in the sense of Nevanlinna, then it has no multiply connected stable domains. Finally, we give some examples of meromorphic functions with uniformly perfect Julia sets.

scholarly journals Singular perturbations of the unicritical polynomials with two parameters

2016 ◽  
Vol 37 (6) ◽  
pp. 1997-2016 ◽  
Author(s):  
YINGQING XIAO ◽  
FEI YANG
Keyword(s):  
Julia Set ◽  
Dynamical Behavior ◽  
Rational Maps ◽  
Topological Properties ◽  
Fatou Set ◽  
The Family ◽  
Image Position ◽  
Two Parameters ◽  
Unicritical Polynomials

In this paper, we study the dynamics of the family of rational maps with two parameters $$\begin{eqnarray}f_{a,b}(z)=z^{n}+\frac{a^{2}}{z^{n}-b}+\frac{a^{2}}{b},\end{eqnarray}$$ where $n\geq 2$ and $a,b\in \mathbb{C}^{\ast }$. We give a characterization of the topological properties of the Julia set and the Fatou set of $f_{a,b}$ according to the dynamical behavior of the orbits of the free critical points.

scholarly journals Exact relation between singular value and eigenvalue statistics

2016 ◽  
Vol 05 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Mario Kieburg ◽  
Holger Kösters
Keyword(s):  
Singular Values ◽  
Singular Value ◽  
Specific Class ◽  
Rotation Invariant ◽  
Exact Relation ◽  
Finite Matrix ◽  
Eigenvalue Statistics ◽  
Probability Densities ◽  
Analytical Relations ◽  
Matrix Spaces

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint densities of the singular values and the eigenvalues for complex random matrices which are bi-unitarily invariant (also known as isotropic or unitary rotation invariant). We prove that each of these joint densities determines the other one. Moreover, we construct an explicit formula relating both joint densities at finite matrix dimension. This relation covers probability densities as well as signed densities. With the help of this relation we derive general analytical relations among the corresponding kernels and biorthogonal functions for a specific class of polynomial ensembles. Furthermore, we show how to generalize the relation between the singular value and eigenvalue statistics to certain situations when the ensemble is deformed by a term which breaks the bi-unitary invariance.

FokI polymorphism of the vitamin D receptor (VDR) gene and susceptibility to tuberculosis: evidence through a meta-analysis

2021 ◽  
Author(s):  
Upendra Yadav ◽  
Pradeep Kumar ◽  
Vandana Rai
Keyword(s):  
Vitamin D ◽  
Vitamin D Receptor ◽  
Meta Analysis ◽  
Receptor Gene ◽  
Asian Population ◽  
Recessive Model ◽  
Dominant Model ◽  
Vdr Gene ◽  
Exact Relation ◽  
Significance Level

Abstract Background: Tuberculosis is one of the top ten causes of deaths worldwide. The deficiency of vitamin D was reported to be associated with the increased susceptibility of tuberculosis. Various previous reports were published to check the association of FokI polymorphism of the vitamin D receptor gene with tuberculosis risk. But their results were inconsistent so, we performed a meta-analysis to know the exact relation of the two.Methods: Different databases were screened up to November, 2020 with the keywords “Vitamin D receptor”, “VDR”, and “FokI”, along with “Tuberculosis” and “TB” to find the suitable articles. All the statistical analyses were performed by the Open Meta-Analyst program and all p-values were two-tailed with a significance level of 0.05.Results: No statistically significant association was observed in the allele contrast model (ORfvs.F= 1.11, 95%CI= 0.99-1.24, p= 0.05, I2= 73.46%), in the dominant model (ORff+Ffvs.FF= 1.11, 95%CI= 0.96-1.28, p= 0.14, I2= 71.39%), and in the co-dominant model (ORFfvs.FF= 1.05, 95%CI= 0.92-1.21, p= 0.41, I2= 65.97%). However, a significant association was found in the homozygote model (ORffvs.FF= 1.32, 95%CI= 1.03-1.69, p= 0.02, I2= 67.02%) and in the recessive model (ORFF+Ff vs.ff= 1.26, 95%CI= 1.03-1.54, p= 0.02, I2= 58.01%). Further analysis was performed on the bases of the ethnicity. In Asian population a significant association was found in the homozygote model (ORffvs.FF= 1.57, 95%CI= 1.12-2.21, p= 0.008, I2= 70.37%) and in the recessive model (ORFF+Ff vs.ff= 1.43, 95%CI= 1.08-1.89, p= 0.01, I2= 63.13%).Conclusion: In conclusion, a significant association of FokI with tuberculosis susceptibility was found in the overall analysis and in the Asian population.

Sign in / Sign up

Export Citation Format

Share Document