scholarly journals Structural Stability of a Family of Exponential Polynomial Maps

2020 ◽  
Vol 25 (2) ◽  
pp. 20
Author(s):  
Francisco Solis ◽  
Silvia Jerez ◽  
Roberto Ku-Carrillo ◽  
Sandra Delgadillo
Keyword(s):  
Structural Stability ◽  
Analytical Form ◽  
Exponential Polynomial ◽  
Polynomial Maps ◽  
Iteration Functions ◽  
The Family

We perturbed a family of exponential polynomial maps in order to show both analytically and numerically their unpredictable orbit behavior. Due to the analytical form of the iteration functions the family has numerically different behavior than its correspondent analytical one, which is a topic of paramount importance in computer mathematics. We discover an unexpected oscillatory parametrical behavior of the perturbed family.

Conducting and Superhydrophobic Hybrid 2D Material from Coronene and Pyrene

2021 ◽  
Author(s):  
Jyothibabu Sajila Arya ◽  
Malay Krishna Mahato ◽  
Sethuraman Sankararaman ◽  
Prasad Edamana
Keyword(s):  
Structural Stability ◽  
2D Material ◽  
The Family ◽  
Potential Applications ◽  
Recent Addition

Graphdiyne, a recent addition to the family of 2D covalent organic nanosheet structure, is known for its structural stability and potential applications in catalysis, sensors, electronics and optoelectronics. Design and...

scholarly journals Reduction of dynatomic curves

2018 ◽  
Vol 39 (10) ◽  
pp. 2717-2768 ◽  
Author(s):  
JOHN R. DOYLE ◽  
HOLLY KRIEGER ◽  
ANDREW OBUS ◽  
RACHEL PRIES ◽  
SIMON RUBINSTEIN-SALZEDO ◽  
...  
Keyword(s):  
Complex Dynamics ◽  
Uniform Boundedness ◽  
Mandelbrot Set ◽  
Modular Curves ◽  
Good Reduction ◽  
One Dimensional ◽  
Formula One ◽  
Polynomial Maps ◽  
Ramification Theory ◽  
The Family

In this paper, we make partial progress on a function field version of the dynamical uniform boundedness conjecture for certain one-dimensional families ${\mathcal{F}}$ of polynomial maps, such as the family $f_{c}(x)=x^{m}+c$, where $m\geq 2$. We do this by making use of the dynatomic modular curves $Y_{1}(n)$ (respectively $Y_{0}(n)$) which parametrize maps $f$ in ${\mathcal{F}}$ together with a point (respectively orbit) of period $n$ for $f$. The key point in our strategy is to study the set of primes $p$ for which the reduction of $Y_{1}(n)$ modulo $p$ fails to be smooth or irreducible. Morton gave an algorithm to construct, for each $n$, a discriminant $D_{n}$ whose list of prime factors contains all the primes of bad reduction for $Y_{1}(n)$. In this paper, we refine and strengthen Morton’s results. Specifically, we exhibit two criteria on a prime $p$ dividing $D_{n}$: one guarantees that $p$ is in fact a prime of bad reduction for $Y_{1}(n)$, yet this same criterion implies that $Y_{0}(n)$ is geometrically irreducible. The other guarantees that the reduction of $Y_{1}(n)$ modulo $p$ is actually smooth. As an application of the second criterion, we extend results of Morton, Flynn, Poonen, Schaefer, and Stoll by giving new examples of good reduction of $Y_{1}(n)$ for several primes dividing $D_{n}$ when $n=7,8,11$, and $f_{c}(x)=x^{2}+c$. The proofs involve a blend of arithmetic and complex dynamics, reduction theory for curves, ramification theory, and the combinatorics of the Mandelbrot set.

THE PARAMETER SPACE OF A QUADRATIC FAMILY OF POLYNOMIAL MAPS OF ℂ2

2008 ◽  
Vol 19 (05) ◽  
pp. 541-556
Author(s):  
ALINA ANDREI
Keyword(s):  
Lyapunov Exponents ◽  
Parameter Space ◽  
Mandelbrot Set ◽  
General Context ◽  
One Dimensional ◽  
Polynomial Maps ◽  
Regular Maps ◽  
The Family ◽  
The One ◽  
Polynomial Family

In this paper, we study the parameter space of the quadratic polynomial family fλ,μ(z, w) = (λz + w2, μw + z2), which exhibits interesting dynamics. Two distinct subsets of the parameter space are studied as appropriate analogs of the one-dimensional Mandelbrot set and some of their properties are proved by using Lyapunov exponents. In the more general context of holomorphic families of regular maps, we show that the sum of the Lyapunov exponents is a plurisubharmonic function of the parameter, and pluriharmonic on the set of expanding maps. Moreover, for the family fλ,μ, we prove that the sum of the Lyapunov exponents is continuous.

BIFURCATION CURVES OF A FAMILY OF ONE-DIMENSIONAL BIQUADRATIC POLYNOMIAL MAPS, DEPENDING ON THE COMPLEX VARIABLE, AND TWO REAL PARAMETERS

2010 ◽  
Vol 20 (12) ◽  
pp. 4119-4125
Author(s):  
HISASHI ISHIDA ◽  
TSUYOSHI ITOH
Keyword(s):  
Fixed Points ◽  
Complex Variable ◽  
Elementary Proof ◽  
Precise Description ◽  
One Dimensional ◽  
Polynomial Maps ◽  
The Family ◽  
Connectedness Locus

Sun and Yin [2007] had presented a precise description of the connectedness locus of the family of real biquadratic polynomials {pa,b(z) = (z2 + a)2 + b}. We shall first give an elementary proof of their result. Second, we shall give a precise description of the sets of parameters (a, b) such that the family {pa,b} has attracting fixed points.

Triassic sponges (Sphinctozoa) from Hells Canyon, Oregon

1988 ◽  
Vol 62 (03) ◽  
pp. 419-423 ◽  
Author(s):  
Baba Senowbari-Daryan ◽  
George D. Stanley
Keyword(s):  
Endemic Species ◽  
Upper Triassic ◽  
Island Arc ◽  
Tropical Island ◽  
The Family ◽  
Wallowa Terrane ◽  
Unique Condition ◽  
Hells Canyon

Two Upper Triassic sphinctozoan sponges of the family Sebargasiidae were recovered from silicified residues collected in Hells Canyon, Oregon. These sponges areAmblysiphonellacf.A. steinmanni(Haas), known from the Tethys region, andColospongia whalenin. sp., an endemic species. The latter sponge was placed in the superfamily Porata by Seilacher (1962). The presence of well-preserved cribrate plates in this sponge, in addition to pores of the chamber walls, is a unique condition never before reported in any porate sphinctozoans. Aporate counterparts known primarily from the Triassic Alps have similar cribrate plates but lack the pores in the chamber walls. The sponges from Hells Canyon are associated with abundant bivalves and corals of marked Tethyan affinities and come from a displaced terrane known as the Wallowa Terrane. It was a tropical island arc, suspected to have paleogeographic relationships with Wrangellia; however, these sponges have not yet been found in any other Cordilleran terrane.

Electron Microscopy of Mycoplasma Pneumoniae

1971 ◽  
Vol 29 ◽  
pp. 258-259 ◽  
Author(s):  
E. S. Boatman ◽  
G. E. Kenny
Keyword(s):  
Electron Microscopy ◽  
Light Microscopy ◽  
Growth Phase ◽  
Hela Cells ◽  
Sulfonic Acid ◽  
Gamma Globulin ◽  
Horse Serum ◽  
Morphological Aspects ◽  
The Family

Information concerning the morphology and replication of organism of the family Mycoplasmataceae remains, despite over 70 years of study, highly controversial. Due to their small size observations by light microscopy have not been rewarding. Furthermore, not only are these organisms extremely pleomorphic but their morphology also changes according to growth phase. This study deals with the morphological aspects of M. pneumoniae strain 3546 in relation to growth, interaction with HeLa cells and possible mechanisms of replication.The organisms were grown aerobically at 37°C in a soy peptone yeast dialysate medium supplemented with 12% gamma-globulin free horse serum. The medium was buffered at pH 7.3 with TES [N-tris (hyroxymethyl) methyl-2-aminoethane sulfonic acid] at 10mM concentration. The inoculum, an actively growing culture, was filtered through a 0.5 μm polycarbonate “nuclepore” filter to prevent transfer of all but the smallest aggregates. Growth was assessed at specific periods by colony counts and 800 ml samples of organisms were fixed in situ with 2.5% glutaraldehyde for 3 hrs. at 4°C. Washed cells for sectioning were post-fixed in 0.8% OSO4 in veronal-acetate buffer pH 6.1 for 1 hr. at 21°C. HeLa cells were infected with a filtered inoculum of M. pneumoniae and incubated for 9 days in Leighton tubes with coverslips. The cells were then removed and processed for electron microscopy.

Time-resolved high-resolution electron microscopy of structural stability in mgo clusters

1996 ◽  
Vol 54 ◽  
pp. 672-673
Author(s):  
T. Kizuka ◽  
N. Tanaka
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Magnesium Oxide ◽  
Structural Stability ◽  
High Resolution Electron Microscopy ◽  
Video Tape ◽  
Solid State Physics ◽  
Time Resolved ◽  
Resolution Electron ◽  
Structural And Functional Properties

Structure and stability of atomic clusters have been studied by time-resolved high-resolution electron microscopy (TRHREM). Typical examples are observations of structural fluctuation in gold (Au) clusters supported on silicon oxide films, graphtized carbon films and magnesium oxide (MgO) films. All the observations have been performed on the clusters consisted of single metal element. Structural stability of ceramics clusters, such as metal-oxide, metal-nitride and metal-carbide clusters, has not been observed by TRHREM although the clusters show anomalous structural and functional properties concerning to solid state physics and materials science.In the present study, the behavior of ceramic, magnesium oxide (MgO) clusters is for the first time observed by TRHREM at 1/60 s time resolution and at atomic resolution down to 0.2 nm.MgO and gold were subsequently deposited on sodium chloride (001) substrates. The specimens, single crystalline MgO films on which Au particles were dispersed were separated in distilled water and observed by using a 200-kV high-resolution electron microscope (JEOL, JEM2010) equipped with a high sensitive TV camera and a video tape recorder system.

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