Periodic strong ergodicity in non-homogeneous Markov systems

1991 ◽  
Vol 28 (1) ◽  
pp. 58-73 ◽  
Author(s):  
Ioannis I. Gerontidis
Keyword(s):  
State Space ◽  
Manpower Planning ◽  
Practical Aspect ◽  
Periodic Case ◽  
Convergence Properties ◽  
Markov Systems ◽  
Numerical Examples ◽  
The Individual ◽  
Special Case ◽  
Theoretical Results

This paper presents a unified treatment of the convergence properties of nonhomogeneous Markov systems under different sets of assumptions. First the periodic case is studied and the limiting evolution of the individual cyclically moving subclasses of the state space of the associated Markov replacement chain is completely determined. A special case of the above result is the aperiodic or strongly ergodic convergence. Two numerical examples from the literature on manpower planning highlight the practical aspect of the theoretical results.

Periodic strong ergodicity in non-homogeneous Markov systems

1991 ◽  
Vol 28 (01) ◽  
pp. 58-73
Author(s):  
Ioannis I. Gerontidis
Keyword(s):  
State Space ◽  
Manpower Planning ◽  
Practical Aspect ◽  
Periodic Case ◽  
Convergence Properties ◽  
Markov Systems ◽  
Numerical Examples ◽  
The Individual ◽  
Special Case ◽  
Theoretical Results

This paper presents a unified treatment of the convergence properties of nonhomogeneous Markov systems under different sets of assumptions. First the periodic case is studied and the limiting evolution of the individual cyclically moving subclasses of the state space of the associated Markov replacement chain is completely determined. A special case of the above result is the aperiodic or strongly ergodic convergence. Two numerical examples from the literature on manpower planning highlight the practical aspect of the theoretical results.

On certain aspects of non-homogeneous Markov systems in continuous time

1990 ◽  
Vol 27 (3) ◽  
pp. 530-544 ◽  
Author(s):  
Ioannis I. Gerontidis
Keyword(s):  
Continuous Time ◽  
Initial Distribution ◽  
Markov Systems ◽  
Numerical Examples ◽  
Stationary Structure ◽  
Periodic Environment ◽  
Time Formulation ◽  
Relative Structure ◽  
The Relationship ◽  
Theoretical Results

In the present paper we study three aspects in the theory of non-homogeneous Markov systems under the continuous-time formulation. Firstly, the relationship between stability and quasi-stationarity is investigated and conditions are provided for a quasi-stationary structure to be stable. Secondly, the concept of asymptotic attainability is studied and the possible regions of asymptotically attainable structures are determined. Finally, the cyclic case is considered, where it is shown that for a system in a periodic environment, the relative structure converges to a periodic vector, independently of the initial distribution. Two numerical examples illustrate the above theoretical results.

scholarly journals Coordination Contracts for Hotels and Online Travel Agents

2020 ◽  
Vol 12 (8) ◽  
pp. 3355
Author(s):  
Qiang Guo ◽  
Chris K. Anderson ◽  
Junfeng Dong ◽  
Pengfei Zhao ◽  
Qingkai Ji
Keyword(s):  
Supply Chain ◽  
Third Party ◽  
Numerical Examples ◽  
Travel Agents ◽  
New Type ◽  
The Individual ◽  
Online Travel ◽  
Theoretical Results ◽  
Online Travel Agents

Herein, we address a common problem of hotels in the current world of online selling, namely the management of relationships with third party resellers (also known as online travel agents (OTAs)). We highlight the role of OTAs in the current travel landscape, and we discuss the popular contracting forms between OTAs and hotels, which are the so-called merchant and retail (commission) models. We illustrate how these contracts fail to coordinate the hotel–OTA relationship, and then, we develop a new type of contract that can efficiently coordinate a supply chain consisting of the OTA and the individual hotels. We provide theoretical results and numerical examples for a one-to-one model with one OTA and one supplier and a more realistic setting with an OTA selling to consumers on behalf of numerous hotel partners.

Research on the model of a multistate aggregated Markov repairable system

2019 ◽  
pp. 1748006X1988765
Author(s):  
Quan Zhang ◽  
Shihang Yu ◽  
Yang Han ◽  
Yanjun Li
Keyword(s):  
System Performance ◽  
The State ◽  
Theory And Practice ◽  
Process Theory ◽  
Repairable System ◽  
Repairable Systems ◽  
Numerical Examples ◽  
Markov Repairable System ◽  
Special Case ◽  
Theoretical Results

In theory and practice, system performance is one of the most important issues. Therefore, a series of indexes has been proposed for evaluating the system performance, such as availability. However, these indexes still cannot meet the variant requirements in the reliability and other fields. The purpose of the article is to develop some theoretical results that may be used in modeling the evolution of system performance. So, based on the aggregated stochastic process theory, some new indexes are introduced and established in Markov repairable systems. In this model, the state space is partitioned into working subset W and failure subset F. The system is regarded as stable if the state of system enters one subset, either W or F, at any instance and sojourns within the subset exceeding a given non-negative threshold [Formula: see text]. Otherwise, the system is regarded as unstable. Under these assumptions, the concepts of point-wise and interval-wise are proposed, and the computation formulae of two types of indexes are derived in the theory. Finally, a special case and a few of numerical examples are given to illustrate the results obtained in the paper.

On certain aspects of non-homogeneous Markov systems in continuous time

1990 ◽  
Vol 27 (03) ◽  
pp. 530-544 ◽  
Author(s):  
Ioannis I. Gerontidis
Keyword(s):  
Continuous Time ◽  
Initial Distribution ◽  
Markov Systems ◽  
Numerical Examples ◽  
Stationary Structure ◽  
Periodic Environment ◽  
Time Formulation ◽  
Relative Structure ◽  
The Relationship ◽  
Theoretical Results

In the present paper we study three aspects in the theory of non-homogeneous Markov systems under the continuous-time formulation. Firstly, the relationship between stability and quasi-stationarity is investigated and conditions are provided for a quasi-stationary structure to be stable. Secondly, the concept of asymptotic attainability is studied and the possible regions of asymptotically attainable structures are determined. Finally, the cyclic case is considered, where it is shown that for a system in a periodic environment, the relative structure converges to a periodic vector, independently of the initial distribution. Two numerical examples illustrate the above theoretical results.

scholarly journals Convergence properties of the Broyden-like method for mixed linear–nonlinear systems of equations

2021 ◽  
Author(s):  
Florian Mannel
Keyword(s):  
Linear Independence ◽  
Affine Subspace ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Convergence Properties ◽  
Initial Matrix ◽  
First Time ◽  
Special Case ◽  
Dimensional Mapping ◽  
Finite Number Of Iterations

AbstractWe consider the Broyden-like method for a nonlinear mapping $F:\mathbb {R}^{n}\rightarrow \mathbb {R}^{n}$ F : ℝ n → ℝ n that has some affine component functions, using an initial matrix B0 that agrees with the Jacobian of F in the rows that correspond to affine components of F. We show that in this setting, the iterates belong to an affine subspace and can be viewed as outcome of the Broyden-like method applied to a lower-dimensional mapping $G:\mathbb {R}^{d}\rightarrow \mathbb {R}^{d}$ G : ℝ d → ℝ d , where d is the dimension of the affine subspace. We use this subspace property to make some small contributions to the decades-old question of whether the Broyden-like matrices converge: First, we observe that the only available result concerning this question cannot be applied if the iterates belong to a subspace because the required uniform linear independence does not hold. By generalizing the notion of uniform linear independence to subspaces, we can extend the available result to this setting. Second, we infer from the extended result that if at most one component of F is nonlinear while the others are affine and the associated n − 1 rows of the Jacobian of F agree with those of B0, then the Broyden-like matrices converge if the iterates converge; this holds whether the Jacobian at the root is invertible or not. In particular, this is the first time that convergence of the Broyden-like matrices is proven for n > 1, albeit for a special case only. Third, under the additional assumption that the Broyden-like method turns into Broyden’s method after a finite number of iterations, we prove that the convergence order of iterates and matrix updates is bounded from below by $\frac {\sqrt {5}+1}{2}$ 5 + 1 2 if the Jacobian at the root is invertible. If the nonlinear component of F is actually affine, we show finite convergence. We provide high-precision numerical experiments to confirm the results.

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

The Uniform Distribution of a Fluid Flowing Through a Perforated Pipe

1950 ◽  
Vol 17 (4) ◽  
pp. 431-438
Author(s):  
Willard M. Dow
Keyword(s):  
Fluid Flow ◽  
High Capacity ◽  
Practical Significance ◽  
Linear Rate ◽  
Gaseous Fuels ◽  
Extended Range ◽  
Flow Through ◽  
Perforated Pipe ◽  
Special Case ◽  
Theoretical Results

Abstract A theoretical analysis is made of the flow through a perforated pipe with a closed end for the special case of a constant linear rate of discharge along the length of the pipe. The results of the fluid-flow considerations are applicable to many practical manifold systems. The practical significance of the results with respect to pipe burners for gaseous fuels is emphasized as the results make possible the design of simple high-capacity and extended-range pipe burners of industrial importance. The capacity of commercially available pipe burners may be increased several hundred per cent. The validity of the theoretical results was verified by experiment.

Acceleration Analysis of Platform-Type Manipulators

1996 ◽  
Author(s):  
Maher G. Mohamed
Keyword(s):  
Stewart Platform ◽  
Algebraic Manipulation ◽  
Analysis Procedure ◽  
Compact Form ◽  
Numerical Examples ◽  
Acceleration Field ◽  
Center Point ◽  
Planar Manipulators ◽  
Acceleration Analysis ◽  
Special Case

Abstract The screw algebra is used to efficiently derive expressions in compact form for both the angular accelerations of the moving links and the linear accelerations of points on the links of platform-type manipulators. The analysis employs the property that the acceleration state of the manipulator platform can be determined by considering the acceleration states of the links of only one — any one — of the manipulator legs. The obtained expressions provide an ease in symbolic and algebraic manipulation. The analysis is then extended to specify the acceleration center point of ithe nstantaneous motion of the manipulator platform. The acceleration center point is then used in expressing the distribution of the acceleration field of the platform instant motion which is important in manipulator synthesis. The special case of planar manipulators is studied and simpler expressions are derived. Numerical examples are presented for the analysis of a 3-DOF planar platform-type and of a 6-DOF spatial “Stewart Platform” manipulators to illustrate the analysis procedure.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document