scholarly journals Some Identities Involving Derangement Polynomials and Numbers and Moments of Gamma Random Variables

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Lee-Chae Jang ◽  
Dae San Kim ◽  
Taekyun Kim ◽  
Hyunseok Lee
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Random Variables ◽  
Natural Extensions ◽  
Element Set

The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708. A derangement is a permutation that has no fixed points, and the derangement number D n is the number of fixed point free permutations on an n element set. Furthermore, the derangement polynomials are natural extensions of the derangement numbers. In this paper, we study the derangement polynomials and numbers, their connections with cosine-derangement polynomials and sine-derangement polynomials, and their applications to moments of some variants of gamma random variables.

Density approximation and exact simulation of random variables that are solutions of fixed-point equations

2002 ◽  
Vol 34 (2) ◽  
pp. 441-468 ◽  
Author(s):  
Luc Devroye ◽  
Ralph Neininger
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Error Bounds ◽  
Probabilistic Analysis ◽  
Analysis Of Algorithms ◽  
Random Variables ◽  
Probability Measures ◽  
Density Approximation ◽  
Exact Simulation ◽  
Probabilistic Analysis Of Algorithms

An algorithm is developed for exact simulation from distributions that are defined as fixed points of maps between spaces of probability measures. The fixed points of the class of maps under consideration include examples of limit distributions of random variables studied in the probabilistic analysis of algorithms. Approximating sequences for the densities of the fixed points with explicit error bounds are constructed. The sampling algorithm relies on a modified rejection method.

Density approximation and exact simulation of random variables that are solutions of fixed-point equations

2002 ◽  
Vol 34 (02) ◽  
pp. 441-468 ◽  
Author(s):  
Luc Devroye ◽  
Ralph Neininger
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Error Bounds ◽  
Probabilistic Analysis ◽  
Analysis Of Algorithms ◽  
Random Variables ◽  
Probability Measures ◽  
Density Approximation ◽  
Exact Simulation ◽  
Probabilistic Analysis Of Algorithms

An algorithm is developed for exact simulation from distributions that are defined as fixed points of maps between spaces of probability measures. The fixed points of the class of maps under consideration include examples of limit distributions of random variables studied in the probabilistic analysis of algorithms. Approximating sequences for the densities of the fixed points with explicit error bounds are constructed. The sampling algorithm relies on a modified rejection method.

Fixed points of a generalized smoothing transformation and applications to the branching random walk

1998 ◽  
Vol 30 (01) ◽  
pp. 85-112 ◽  
Author(s):  
Quansheng Liu
Keyword(s):  
Fixed Point ◽  
Random Walk ◽  
Fixed Points ◽  
Branching Processes ◽  
Random Variables ◽  
Initial Distribution ◽  
Branching Random Walk ◽  
Independent Random Variables ◽  
Sorting Algorithm ◽  
Hausdorff Measures

Let {Ai:i≥ 1} be a sequence of non-negative random variables and letMbe the class of all probability measures on [0,∞]. Define a transformationTonMby lettingTμ be the distribution of ∑i=1∞AiZi, where theZiare independent random variables with distribution μ, which are also independent of {Ai}. Under first moment assumptions imposed on {Ai}, we determine exactly whenThas a non-trivial fixed point (of finite or infinite mean) and we prove that all fixed points have regular variation properties; under moment assumptions of order 1 + ε, ε > 0, we findallthe fixed points and we prove that all non-trivial fixed points have stable-like tails. Convergence theorems are given to ensure that each non-trivial fixed point can be obtained as a limit of iterations (byT) with an appropriate initial distribution; convergence to the trivial fixed points δ0and δ∞is also examined, and a result like the Kesten-Stigum theorem is established in the case where the initial distribution has the same tails as a stable law. The problem of convergence with an arbitrary initial distribution is also considered when there is no non-trivial fixed point. Our investigation has applications in the study of: (a) branching processes; (b) invariant measures of some infinite particle systems; (c) the model for turbulence of Yaglom and Mandelbrot; (d) flows in networks and Hausdorff measures in random constructions; and (e) the sorting algorithm Quicksort. In particular, it turns out that the basic functional equation in the branching random walk always has a non-trivial solution.

Fixed points of a generalized smoothing transformation and applications to the branching random walk

1998 ◽  
Vol 30 (1) ◽  
pp. 85-112 ◽  
Author(s):  
Quansheng Liu
Keyword(s):  
Fixed Point ◽  
Random Walk ◽  
Fixed Points ◽  
Branching Processes ◽  
Random Variables ◽  
Initial Distribution ◽  
Branching Random Walk ◽  
Independent Random Variables ◽  
Sorting Algorithm ◽  
Hausdorff Measures

Let {Ai : i ≥ 1} be a sequence of non-negative random variables and let M be the class of all probability measures on [0,∞]. Define a transformation T on M by letting Tμ be the distribution of ∑i=1∞AiZi, where the Zi are independent random variables with distribution μ, which are also independent of {Ai}. Under first moment assumptions imposed on {Ai}, we determine exactly when T has a non-trivial fixed point (of finite or infinite mean) and we prove that all fixed points have regular variation properties; under moment assumptions of order 1 + ε, ε > 0, we find all the fixed points and we prove that all non-trivial fixed points have stable-like tails. Convergence theorems are given to ensure that each non-trivial fixed point can be obtained as a limit of iterations (by T) with an appropriate initial distribution; convergence to the trivial fixed points δ0 and δ∞ is also examined, and a result like the Kesten-Stigum theorem is established in the case where the initial distribution has the same tails as a stable law. The problem of convergence with an arbitrary initial distribution is also considered when there is no non-trivial fixed point. Our investigation has applications in the study of: (a) branching processes; (b) invariant measures of some infinite particle systems; (c) the model for turbulence of Yaglom and Mandelbrot; (d) flows in networks and Hausdorff measures in random constructions; and (e) the sorting algorithm Quicksort. In particular, it turns out that the basic functional equation in the branching random walk always has a non-trivial solution.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Coincidence and fixed points for hybrid tangential maps

2010 ◽  
Vol 17 (2) ◽  
pp. 273-285
Author(s):  
Tayyab Kamran ◽  
Quanita Kiran
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Property ◽  
Fixed Point Theorems ◽  
Acta Math ◽  
Contractive Condition ◽  
The Common

Abstract In [Int. J. Math. Math. Sci. 2005: 3045–3055] by Liu et al. the common property (E.A) for two pairs of hybrid maps is defined. Recently, O'Regan and Shahzad [Acta Math. Sin. (Engl. Ser.) 23: 1601–1610, 2007] have introduced a very general contractive condition and obtained some fixed point results for hybrid maps. We introduce a new property for pairs of hybrid maps that contains the property (E.A) and obtain some coincidence and fixed point theorems that extend/generalize some results from the above-mentioned papers.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals CONFORMAL HOUSE

2010 ◽  
Vol 25 (24) ◽  
pp. 4603-4621 ◽  
Author(s):  
THOMAS A. RYTTOV ◽  
FRANCESCO SANNINO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Group ◽  
Gauge Theories ◽  
Simultaneous Presence ◽  
Consistency Check ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Mass Terms

We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

scholarly journals Common fixed points of single-valued and multivalued maps

2005 ◽  
Vol 2005 (19) ◽  
pp. 3045-3055 ◽  
Author(s):  
Yicheng Liu ◽  
Jun Wu ◽  
Zhixiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Partial Answer ◽  
Multivalued Maps ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems

We define a new property which contains the property (EA) for a hybrid pair of single- and multivalued maps and give some new common fixed point theorems under hybrid contractive conditions. Our results extend previous ones. As an application, we give a partial answer to the problem raised by Singh and Mishra.

scholarly journals Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dušan Ðukić ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces ◽  
Type Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

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