scholarly journals TARGET SPACE DUALITY AND MODULI STABILIZATION IN STRING GAS COSMOLOGY

2007 ◽  
Vol 22 (01) ◽  
pp. 165-179 ◽  
Author(s):  
AUTTAKIT CHATRABHUTI
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Moduli Space ◽  
Target Space ◽  
Moduli Stabilization ◽  
String Gas Cosmology ◽  
The Stability

Motivated by string gas cosmology, we investigate the stability of moduli fields coming from compactifications of string gas on torus with background flux. It was previously claimed that moduli are stabilized only at a single fixed-point in moduli space, a self-dual point of T-duality with vanishing flux. Here, we show that there exist other stable fixed-points on moduli space with nonvanishing flux. We also discuss the more general target space dualities associated with these fixed-points.

scholarly journals Invariant curves around a parabolic fixed point at infinity

1990 ◽  
Vol 10 (2) ◽  
pp. 209-229 ◽  
Author(s):  
Dov Aharonov ◽  
Uri Elias
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Invariant Curves ◽  
The Stability ◽  
Area Preserving ◽  
Parabolic Fixed Point

AbstractThe stability of a fixed point of an area-preserving transformation in the plane is characterized by the invariant curves which surround it. The existence of invariant curves had been extensively studied for elliptic fixed points. Here we study the similar problem for parabolic fixed points. In particular we are interested in the case where the fixed point is at infinity.

New fixed point of on-orbit calibration scale based on the In-Bi eutectic alloy for application in novel high-stable space-borne standard sources

2021 ◽  
pp. 32-37
Author(s):  
Andrei A. Burdakin ◽  
Valerii R. Gavrilov ◽  
Ekaterina A. Us ◽  
Vitalii S. Bormashov
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Fixed Points ◽  
Eutectic Alloy ◽  
Earth Observation ◽  
Melt Temperature ◽  
Phase Transition Temperatures ◽  
Set Up ◽  
The Stability ◽  
Observation Space

The problem of ensuring stability of Earth observation space-borne instruments undertaking long-term temperature measurements within thermal IR spectral range is described. For in-flight reliable control of the space-borne IR instruments characteristics the stability of onboard reference sources should be improved. The function of these high-stable sources will be executed by novel onboard blackbodies, incorporating the melt↔freeze phase transition phenomenon, currently being developed. As a part of these works the task of realizing an on-orbit calibration scale within the dynamic temperature range of Earth observation systems 210−350 K based on fixed-point phase transition temperatures of a number of potentially suitable substances is advanced. The corresponding series of the onboard reference blackbodies will be set up on the basis of the on-orbit calibration scale fixed points. It is shown that the achievement of the target lies in carrying out a number of in-flight experiments with the selected fixed points and the prospective onboard fixed-point blackbodies prototypes. The new In-Bi eutectic alloy melt temperature fixed point (~345 K) is proposed as the significant fixed points of the future on-orbit calibration scale. The results of the new fixed point preliminary laboratory studies have been analyzed. The results allowed to start preparation of the in-flight experiments investigating the In-Bi alloy for the purpose of its application in the novel onboard reference sources.

scholarly journals Fixed-Point Theorems for Multivalued Mappings in Modular Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Parin Chaipunya ◽  
Chirasak Mongkolkeha ◽  
Wutiphol Sintunavarat ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Modular Metric Spaces ◽  
Contraction Type ◽  
The Stability

We give some initial properties of a subset of modular metric spaces and introduce some fixed-point theorems for multivalued mappings under the setting of contraction type. An appropriate example is as well provided. The stability of fixed points in our main theorems is also studied.

scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

scholarly journals On D-brane dynamics and moduli stabilization

2017 ◽  
Vol 32 (29) ◽  
pp. 1750150
Author(s):  
Noriaki Kitazawa
Keyword(s):  
String Theory ◽  
Fixed Points ◽  
Supersymmetry Breaking ◽  
Compact Space ◽  
Complex Structure ◽  
Simultaneous Presence ◽  
Moduli Stabilization ◽  
Type Iib String Theory ◽  
The Stability ◽  
Repulsive Forces

We discuss the effect of the dynamics of D-branes on moduli stabilization in type IIB string theory compactifications, with reference to a concrete toy model of [Formula: see text] orientifold compactification with fractional D3-branes and anti-D3-branes at orbifold fixed points. The resulting attractive forces between anti-D3-branes and D3-branes, together with the repulsive forces between anti-D3-branes and O3-planes, can affect the stability of the compact space. There are no complex structure moduli in [Formula: see text] orientifold, which should thus capture some generic features of more general settings where all complex structure moduli are stabilized by three-form fluxes. The simultaneous presence of branes and anti-branes brings along the breaking of supersymmetry. Non-BPS combinations of this type are typical of “brane supersymmetry breaking” and are a necessary ingredient in the KKLT scenario for stabilizing the remaining Kähler moduli. The conclusion of our analysis is that, while mutual D-brane interactions sometimes help Kähler moduli stabilization, this is not always the case.

scholarly journals Stability to a Kind of Functional Differential Equations of Second Order with Multiple Delays by Fixed Points

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Cemil Tunç ◽  
Emel Biçer
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Differential Equations ◽  
Multiple Delays ◽  
Stability Of Solutions ◽  
Variable Delays ◽  
Multiple Variable ◽  
Fixed Point Technique ◽  
Functional Differential ◽  
The Stability

We discuss the stability of solutions to a kind of scalar Liénard type equations with multiple variable delays by means of the fixed point technique under an exponentially weighted metric. By this work, we improve some related results from one delay to multiple variable delays.

scholarly journals On Stability of Fixed Points for Multi-Valued Mappings with an Application

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Qi-Qing Song
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Stable Fixed Point ◽  
Inclusion Problems ◽  
Point Mapping ◽  
Lower Semi ◽  
The Stability ◽  
Essential Sets ◽  
Almost All ◽  
Stable Result

This paper studies the stability of fixed points for multi-valued mappings in relation to selections. For multi-valued mappings admitting Michael selections, some examples are given to show that the fixed point mapping of these mappings are neither upper semi-continuous nor almost lower semi-continuous. Though the set of fixed points may be not compact for multi-valued mappings admitting Lipschitz selections, by finding sub-mappings of such mappings, the existence of minimal essential sets of fixed points is proved, and we show that there exists at least an essentially stable fixed point for almost all these mappings. As an application, we deduce an essentially stable result for differential inclusion problems.

scholarly journals Stability of the Discrete Stage–Structure Prey–Predator Model

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Rehab Noori Shalan ◽  
Shireen R. Jawad ◽  
Alaa Hussien Lafta
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Three Dimensional ◽  
Stage Structure ◽  
Prey Population ◽  
Topological Properties ◽  
Proposed Model ◽  
Predator Model ◽  
The Stability ◽  
Theoretical Results

This paper discusses the discrete stage–structure prey-predator model involved in the Beddington–DeAngelis type of functional response described by differential equation systems proposed as three-dimensional systems. Furthermore, the predators are divided into two types of populations, namely, mature and immature, along with the prey population. The stability of all possible fixed points is demonstrated by solving our proposed model analytically using the standard lemma and topological properties, which give all possible properties to each fixed point. In the same manner, we identify three fixed points, which are as follows: the origin fixed point, which means there are no species; the axial fixed point, which means the prey population increases logistically with the absence of a predator one (mature and immature populations); and the positive fixed point, which signifies the coexistence of all species. We show that the numerical simulations part is used not only to plot the time series of fixed values, but also, to find and illustrate the theoretical results.

scholarly journals Fixed Points and Stability for Integral-Type Multivalued Contractive Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhefu An ◽  
Mengyao Li ◽  
Liangshi Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Integral Type ◽  
Point Sets ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
The Stability ◽  
Fixed Point Sets

The existence and iterative approximations of fixed points concerning two classes of integral-type multivalued contractive mappings in complete metric spaces are proved, and the stability of fixed point sets relative to these multivalued contractive mappings is established. The results obtained in this article generalize and improve some known results in the literature. An illustrative example is given.

scholarly journals Stability of Real Parametric Polynomial Discrete Dynamical Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Fermin Franco-Medrano ◽  
Francisco J. Solis
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Special Function ◽  
Real Polynomial ◽  
Polynomial Maps ◽  
Polynomial Map ◽  
Exact Boundary ◽  
The Stability ◽  
Real Polynomial Maps

We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameterλand generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to realmth degree real polynomial maps. In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this, we have introduced the concept ofcanonical polynomial mapswhich are topologically conjugate to any polynomial map of the same degree with real fixed points. The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termedProduct Position Functionfor a given fixed point. The values of this product position determine the stability of the fixed point in question, when it bifurcates and even when chaos arises, as it passes through what we have termedstability bands. The exact boundary values of these stability bands are yet to be calculated for regions of type greater than one for polynomials of degree higher than three.

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