scholarly journals Oscillating wandering domains for functions with escaping singular values

2021 ◽  
Author(s):  
Kirill Lazebnik
Keyword(s):  
Singular Values ◽  
Wandering Domains

scholarly journals Iteration of certain meromorphic functions with unbounded singular values

2009 ◽  
Vol 30 (3) ◽  
pp. 877-891 ◽  
Author(s):  
TARAKANTA NAYAK ◽  
M. GURU PREM PRASAD
Keyword(s):  
Real Line ◽  
Critical Parameter ◽  
Meromorphic Functions ◽  
Period Doubling ◽  
Inverse Function ◽  
Singular Values ◽  
Fatou Set ◽  
Unbounded Subset ◽  
Simply Connected ◽  
Wandering Domains

AbstractLet ℳ={f(z)=(zm/sinhm z) for z∈ℂ∣ either m or m/2 is an odd natural number}. For eachf∈ℳ, the set of singularities of the inverse function offis an unbounded subset of the real line ℝ. In this paper, the iteration of functions in one-parameter family 𝒮={fλ(z)=λf(z)∣λ∈ℝ∖{0}} is investigated for eachf∈ℳ. It is shown that, for eachf∈ℳ, there is a critical parameterλ*>0 depending onfsuch that a period-doubling bifurcation occurs in the dynamics of functionsfλin 𝒮 when the parameter |λ| passes throughλ*. The non-existence of Baker domains and wandering domains in the Fatou set offλis proved. Further, it is shown that the Fatou set offλis infinitely connected for 0<∣λ∣≤λ*whereas for ∣λ∣≥λ*, the Fatou set offλconsists of infinitely many components and each component is simply connected.

scholarly journals Fatou components and singularities of meromorphic functions

2019 ◽  
Vol 150 (2) ◽  
pp. 633-654 ◽  
Author(s):  
Krzysztof Barański ◽  
Núria Fagella ◽  
Xavier Jarque ◽  
Bogusława Karpińska
Keyword(s):  
Relative Position ◽  
Meromorphic Functions ◽  
Julia Set ◽  
Singular Values ◽  
Wandering Domain ◽  
Meromorphic Maps ◽  
Fatou Components ◽  
Meromorphic Map ◽  
Wandering Domains ◽  
Uniformly Bounded

AbstractWe prove several results concerning the relative position of points in the postsingular set P(f) of a meromorphic map f and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer a question of Mihaljević-Brandt and Rempe-Gillen. For wandering domains we show that if the iterates Un of such a domain have uniformly bounded diameter, then there exists a sequence of postsingular values pn such that ${\rm dist} (p_n, U_n)\to 0$ as $n\to \infty $. We also prove that if $U_n \cap P(f)=\emptyset $ and the postsingular set of f lies at a positive distance from the Julia set (in ℂ), then the sequence of iterates of any wandering domain must contain arbitrarily large disks. This allows to exclude the existence of wandering domains for some meromorphic maps with infinitely many poles and unbounded set of singular values.

A SVD and Modified Firefly Optimization Based Robust Digital Image Watermarking Technique

2017 ◽  
Vol 7 (7) ◽  
pp. 268
Author(s):  
Chauhan Usha ◽  
Singh Rajeev Kumar
Keyword(s):  
Digital Media ◽  
Firefly Algorithm ◽  
Image Watermarking ◽  
Singular Values ◽  
Robust Watermarking ◽  
Scaling Factors ◽  
Geometric Attacks ◽  
Host Image ◽  
Firefly Optimization ◽  
Value Decomposition

Digital Watermarking is a technology, to facilitate the authentication, copyright protection and Security of digital media. The objective of developing a robust watermarking technique is to incorporate the maximum possible robustness without compromising with the transparency. Singular Value Decomposition (SVD) using Firefly Algorithm provides this objective of an optimal robust watermarking technique. Multiple scaling factors are used to embed the watermark image into the host by multiplying these scaling factors with the Singular Values (SV) of the host image. Firefly Algorithm is used to optimize the modified host image to achieve the highest possible robustness and transparency. This approach can significantly increase the quality of watermarked image and provide more robustness to the embedded watermark against various attacks such as noise, geometric attacks, filtering attacks etc.

Estimation of the Number of Signal Components Based on Singular Values of Noise Subspace

2011 ◽  
Vol 33 (9) ◽  
pp. 2039-2044 ◽  
Author(s):  
Xin-peng Zhou ◽  
Feng Han ◽  
Guo-hua Wei ◽  
Si-liang Wu
Keyword(s):  
Singular Values ◽  
Noise Subspace

Analysis of multiplicity of Hankel singular values of control systems

2015 ◽  
Vol 76 (2) ◽  
pp. 205-218 ◽  
Author(s):  
L. A. Mironovskii ◽  
T. N. Solov’eva
Keyword(s):  
Control Systems ◽  
Singular Values ◽  
Hankel Singular Values

scholarly journals Ramanujan’s function k(τ)=r(τ)r 2(2τ) and its modularity

2020 ◽  
Vol 18 (1) ◽  
pp. 1727-1741
Author(s):  
Yoonjin Lee ◽  
Yoon Kyung Park
Keyword(s):  
Continued Fraction ◽  
Quadratic Field ◽  
Singular Values ◽  
Modular Function ◽  
Imaginary Quadratic Field ◽  
Modular Equations ◽  
Positive Rational Number ◽  
Congruence Relations ◽  
Symmetry Relations ◽  
Ray Class Field

Abstract We study the modularity of Ramanujan’s function k ( τ ) = r ( τ ) r 2 ( 2 τ ) k(\tau )=r(\tau ){r}^{2}(2\tau ) , where r ( τ ) r(\tau ) is the Rogers-Ramanujan continued fraction. We first find the modular equation of k ( τ ) k(\tau ) of “an” level, and we obtain some symmetry relations and some congruence relations which are satisfied by the modular equations; these relations are quite useful for reduction of the computation cost for finding the modular equations. We also show that for some τ \tau in an imaginary quadratic field, the value k ( τ ) k(\tau ) generates the ray class field over an imaginary quadratic field modulo 10; this is because the function k is a generator of the field of the modular function on Γ 1 ( 10 ) {{\mathrm{\Gamma}}}_{1}(10) . Furthermore, we suggest a rather optimal way of evaluating the singular values of k ( τ ) k(\tau ) using the modular equations in the following two ways: one is that if j ( τ ) j(\tau ) is the elliptic modular function, then one can explicitly evaluate the value k ( τ ) k(\tau ) , and the other is that once the value k ( τ ) k(\tau ) is given, we can obtain the value k ( r τ ) k(r\tau ) for any positive rational number r immediately.

Stable Calibrations of Six-DOF Serial Robots by Using Identification Models with Equalized Singular Values

Robotica ◽  
2021 ◽  
pp. 1-22
Author(s):  
Zhouxiang Jiang ◽  
Min Huang
Keyword(s):  
Industrial Robot ◽  
Singular Values ◽  
Calibration Method ◽  
Identification Accuracy ◽  
Condition Numbers ◽  
Measurement Instruments ◽  
Unknown Parameters ◽  
Calibration Methods ◽  
Six Dof ◽  
The Stability

SUMMARY In typical calibration methods (kinematic or non-kinematic) for serial industrial robot, though measurement instruments with high resolutions are adopted, measurement configurations are optimized, and redundant parameters are eliminated from identification model, calibration accuracy is still limited under measurement noise. This might be because huge gaps still exist among the singular values of typical identification Jacobians, thereby causing the identification models ill conditioned. This paper addresses such problem by using new identification models established in two steps. First, the typical models are divided into the submodels with truncated singular values. In this way, the unknown parameters corresponding to the abnormal singular values are removed, thereby reducing the condition numbers of the new submodels. However, these models might still be ill conditioned. Therefore, the second step is to further centralize the singular values of each submodel by using a matrix balance method. Afterward, all submodels are well conditioned and obtain much higher observability indices compared with those of typical models. Simulation results indicate that significant improvements in the stability of identification results and the identifiability of unknown parameters are acquired by using the new identification submodels. Experimental results indicate that the proposed calibration method increases the identification accuracy without incurring additional hardware setup costs to the typical calibration method.

scholarly journals $$L_2$$-norm sampling discretization and recovery of functions from RKHS with finite trace

2021 ◽  
Vol 19 (2) ◽  
Author(s):  
Moritz Moeller ◽  
Tino Ullrich
Keyword(s):  
Random Function ◽  
Additional Assumption ◽  
Main Tool ◽  
Singular Values ◽  
Rates Of Convergence ◽  
Concentration Inequality ◽  
Worst Case ◽  
Mercer Kernels ◽  
Finite Trace ◽  
Complex Valued

AbstractIn this paper we study $$L_2$$ L 2 -norm sampling discretization and sampling recovery of complex-valued functions in RKHS on $$D \subset \mathbb {R}^d$$ D ⊂ R d based on random function samples. We only assume the finite trace of the kernel (Hilbert–Schmidt embedding into $$L_2$$ L 2 ) and provide several concrete estimates with precise constants for the corresponding worst-case errors. In general, our analysis does not need any additional assumptions and also includes the case of non-Mercer kernels and also non-separable RKHS. The fail probability is controlled and decays polynomially in n, the number of samples. Under the mild additional assumption of separability we observe improved rates of convergence related to the decay of the singular values. Our main tool is a spectral norm concentration inequality for infinite complex random matrices with independent rows complementing earlier results by Rudelson, Mendelson, Pajor, Oliveira and Rauhut.

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