Strict Contraction Research Articles

Correction: Two existence results regarding strict contractions on metric spaces with graphs

Correction: Two existence results regarding strict contractions on metric spaces with graphs

Two existence results regarding strict contractions on metric spaces with graphs

Two existence results regarding strict contractions on metric spaces with graphs

A framework for assessing stakeholder interface health in complex capital projects

PurposeStakeholders in complex capital projects are characterized by complicated interactions, adversarial short-term relationships and cooperative demand for deliverables. Unhealthy interfaces between stakeholders often lead to significant interface conflicts, which gradually become apparent in the construction stage. However, stakeholder interface health (SIH) has not been well understood and measured in the construction industry by either scholars or practitioners. It is essential to identify unhealthy interface relationships between stakeholders by comprehensively assessing SIH for enhancing project performance.Design/methodology/approachThe study provided a comprehensive framework to assess SIH. The assessment was based on Wuli-Shili-Renli theory. Moreover, the CRITIC and Grey-TOPSIS methodologies were applied to precisely evaluate the SIH level. Besides, graph-based interface networks were developed to visualize SIH. At last, the framework was applied to a mass rapid transit project in China to test the validity of the study.FindingsThe result showed that stakeholder interfaces with strict contract constraints are healthier. On the other hand, IM behaviors make up for the soft coordination mechanism without contract constraints to a certain extent. The results of the case study were consistent with the actual project practices. The proposed framework provided a useful IM tool for assessing and visualizing SIH.Research limitations/implicationsThe limitation of this study is that only the mass rapid transit project was selected for empirical analysis to validate the effectiveness of the proposed framework. It is recommended that the proposed framework be applied to other types of complex capital projects to further discussions in IM.Practical implicationsTheoretically, this study introduces a comprehensive framework to measure the health of stakeholder interfaces in complex capital projects, which helps to provide a theoretical basis and methodological support for stakeholder interface management.Social implicationsPractically, applying SIH assessment to existing interface management procedures can help the project manager identify interface conflicts between stakeholders in time and eventually contribute to the improvement of PM performance. At the same time, the interface management team tracks the responsibilities of unhealthy interface stakeholders and requires them to take measures to improve the SIH level. Stakeholder interfaces with lower health scores should be given more attention. The proposed framework can serve as a novel IM approach to identify weaknesses in IM and take targeted management measures to alleviate unhealthy stakeholder interface relationships.Originality/valueThe study provides an innovative method for scientifically and accurately assessing SIH. This research can help scholars and practitioners in the project management field facilitate the diagnosis of unhealthy interface relationships and provide decision support for the project management theoretical foundation.

Existence of a fixed point and stability results for contractive mappings on metric spaces with graphs

It is known that a strict contraction on complete metric spaces with graphs possesses a fixed point. In the present paper we show that this property holds for mappings on complete metric spaces with graphs which are merely contractive. We also obtain some stability results.

Fixed Point and Convergence Results for Contractive-Type Self-Mappings of Metric Spaces with Graphs

It is known that a strict contraction on a complete metric space with a graph possesses a fixed point. In the present paper, we show that this property holds for single valued and set-valued self-mappings of metric spaces with graphs that are of the contractive type. We also show the convergence of iterates of these mappings to fixed points. In particular, our results are true for metric spaces with symmetric graphs.

Optimization‐based adaptive control for MIMO nonlinear systems: A data‐driven method

AbstractThis article concentrates on the challenging adaptive tracking problem of multi‐input and multi‐output (MIMO) nonlinear systems with unknown nonlinear dynamics, for which a novel optimization‐based data‐driven adaptive control (ODDAC) equipped with an extended dynamic linearization method is developed. Through considering MIMO nonlinear systems in the fully‐actuated case and over‐actuated case separately, the ODDAC is proposed consisting of a parameter updating algorithm and an adaptive control law. A new design of parameter updating algorithm is presented such that the estimation can be guaranteed to be bounded by a strict contraction process. By leveraging properties of the nonnegative matrix, a grouping‐based contraction mapping (GCM) analysis method is proposed for the convergence of tracking error. Notably, the GCM does not require the contraction mapping condition to hold at all time instants. The proposed ODDAC is data‐based, avoiding reliance on model information, and its validity is verified through simulations.

Study on the Multi-Point Boundary Value Problem for Second-Order Nonlinear Impulsive Integro-Differential Equation

In the field of biological control, there are a large number of systems that gradually evolve over a certain period of time. However, due to some natural or human intervention behavior, the system state will be subjected to some relatively short time interference, so that the system state changes in an instant. This sudden change of state makes the system not simply described by continuous or discrete dynamical systems, but by means of impulse dynamical systems. In this paper, the multi-point boundary value problem of a class of second-order nonlinear impulsive integral differential equations is studied on the basis of impulsive differential equation theory. The main results of this kind of equation are obtained by using the fixed point theorem of strict set contraction operator. Under certain assumptions, the existence of the solution of the equation is proved by constructing the operator on the special cone. Finally, combined with the practical application, the theory was applied to the stability prediction of biological ecosystem, and the correctness of the conclusion was verified.

The effect of contract- and network management on performance and innovation in infrastructure projects

IMPACT How should complex infrastructure projects be managed? A survey of practitioners in public–private partnership (PPP) projects and 35 interviews with these practitioners provided a detailed picture of the management of these projects. The survey research revealed that strict contract management (monitoring performance criteria and sticking to the contract) did not show a significant relationship to either the performance of, or innovation in, these projects. Network management (for example connecting involved parties and exploring new solutions), however, was significant—especially in terms of performance. In the interviews, practitioners highlighted that the complexity of these projects meant that a collaborative relationship between the public and private parties was essential to overcome unforeseen problems. It is therefore advisable to make process agreements at the start of contracts that provide for unexpected issues. The authors conclude that the contract is certainly important but will not generate good performance without active network management and making process rules about how parties can collaborate. ABSTRACT Based on economic and governance theories, this article uses survey and interview data to examine the relationship between contract management and network management on the one hand and collaboration, innovation and performance on the other. A positive relationship was found between network management and collaboration and performance. Contract management demonstrated no significant relationship with either collaboration or performance. Additionally, while there was a positive association between network management and innovation, it was not statistically significant. Qualitative data emphasized the complexity of projects and limitations of contracts as a possible explanation.

Lender individualism and monitoring: Evidence from syndicated loans

This paper addresses the question, “Does lenders’ culture affect their monitoring efforts and style?”, by exploring whether lender individualism affects the loan monitoring of U.S. borrowers for a sample of 27,164 syndicated loan facilities granted between 1998 and 2017. We proxy lender individualism based on the ancestral country of origin of the lead bank's CEO. We show that lender individualism leads to a less stringent monitoring style. We find that individualist lenders resort less to covenant monitoring, impose less strict contract terms, such as performance pricing and rely more on soft information. We also provide evidence that individualist lenders retain a larger loan share and deal with a larger number of lenders. Finally, we find that some governance characteristics (board size and percentage of female directors) and other CEO features (cash compensation, tenure, and non-duality) moderate the negative association between lender individualism and loan monitoring.

Wirtinger Flow for Nonconvex Blind Demixing With Optimal Step Size

The prospect of massive deployment of devices for Internet-of-Things (IoT) motivates grant-free access for simultaneously uplink transmission by multiple nodes. Blind demixing represents a promising technique for recovering multiple such source signals over unknown channels. Recent studies show Wirtinger Flow (WF) algorithm can be effective in blind demixing. However, existing theoretical results on WF step size selection tend to be conservative and slow down convergence rates. To overcome this limitation, we propose an improved WF (WF-OPT) by optimizing its step size in each iteration and expediting the convergence. We provide a theoretical guarantee on the strict contraction of WF-OPT and present the upper bounds of the contraction ratio. Simulation results demonstrate the expected convergence gains.

Subdifferential set of an operator

Let X, Y be complex Banach spaces. Let {mathcal L}(X,Y) be the space of bounded operators. An important aspect of understanding differentiability is to study the subdifferential of the norm at a point, say x in X, this is the set, {f in X^*:Vert fVert =1~,f(x)=Vert xVert }. See page 7 in Deville et al. (Pitman Monographs and Surveys in Pure and Applied Mathematics. 64. Harlow: Longman Scientific and Technical. New York: John Wiley and Sons, Inc. 1993). Motivated by recent results of Singla (Singla in Linear Alg. Appl. 629:208–218, 2021) in the context of Hilbert spaces, for T in {{mathcal {L}}}(X,Y), we determine the subdifferential of the operator norm at T, partial _T = {Lambda in {{mathcal {L}}}(X,Y)^*: Lambda (T) = Vert TVert ~,~Vert Lambda Vert =1}. Our approach is based on the ‘position’ of the space of compact operators and the Calkin norm of T. Our ideas give a unified approach and extend several results from Singla (Linear Alg. Appl. 629:208–218, 2021) to the case of ell ^p-spaces for 1<p<infty . We also investigate the converse, using the structure of the subdifferential set to decide when the Calkin norm is a strict contraction. As an application of these ideas, we partially solve the open problem of relating the subdifferential of the operator norm at a compact operator T to that of T(x_0), where x_0 is a unit vector where T attains its norm.

Strict Kantorovich contractions for Markov chains and Euler schemes with general noise

We study contractions of Markov chains on general metric spaces with respect to some carefully designed distance-like functions, which are comparable to the total variation and the standard Lp-Wasserstein distances for p≥1. We present explicit lower bounds of the corresponding contraction rates. By employing the refined basic coupling and the coupling by reflection, the results are applied to Markov chains whose transitions include additive stochastic noises that are not necessarily isotropic. This can be useful in the study of Euler schemes for SDEs driven by Lévy noises. In particular, motivated by recent works on the use of heavy tailed processes in Markov Chain Monte Carlo, we show that chains driven by the α-stable noise can have better contraction rates than corresponding chains driven by the Gaussian noise, due to the heavy tails of the α-stable distribution.

Persistence landscapes of affine fractals

Abstract We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes, which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations.

Growing inequality during the Great Recession: Labour market institutions and the education gap in unemployment across Europe and in the United States.

We study how the education gap in unemployment has evolved by gender and age groups across 28 European countries and the United States from 2000 to 2014, using the European Union's Labour Force Surveys and the US Current Population Surveys. During and after the Great Recession, the absolute education gap in unemployment expanded in almost all countries, which was mainly driven by a marked increase in the unemployment risk among low educated men. A two-step multilevel analysis confirmed the negative relationship between the education gap and both (lagged) GDP growth and GDP level. Further, institutional labour market features moderated the impact of the business cycle. A higher share of temporary employment boosted employment for less educated persons, thus flattening the education gradient in unemployment, while a larger public sector somewhat protected more highly educated individuals against unemployment. The gap for young workers was large in settings with strict regular contract regulations.

Utilization of Google Glassroom in Islamic Religious Education in Higher Education during the Covid 19 Pandemic

The Covid-19 pandemic condition requires teachers to use technology in online learning. This study analyses the planning, implementation and evaluation of Islamic religious education assisted by Google class media. This research was conducted using a qualitative descriptive method involving 87 students. Data was collected through surveys, interviews, documentation, and observations. Data analysis was carried out using qualitative descriptive techniques and triangulation. The results showed that the use of Google Classroom in learning Islamic Religious Education gradually improved the quality of learning. It is supported by good planning, competent teaching skills, systematic learning implementation, and measurable evaluation. The learning process is democratic, humanist and technological. Students are given initiative, innovation, and creative freedom to foster motivation, awareness, independence, and togetherness in learning. On the other hand, they were encouraging learning objectives by implementing strict lecture contracts and sanctions for students who ignore agreed learning. Online learning using Google classroom can improve the quality of teaching lecturers, interaction or student activities in learning, discipline, timeliness of assignments, several responsible students, student attendance in meetings through Google Meet, student interaction in learning, and student learning outcomes.

Dilations of linear maps on vector spaces

We continue the study dilation of linear maps on vector spaces introduced by Bhat, De, and Rakshit. This notion is a variant of vector space dilation introduced by Han, Larson, Liu, and Liu. We derive vector space versions of Wold decomposition, Halmos dilation, N-dilation, inter-twining lifting theorem and a variant of Ando dilation. It is noted further that unlike a kind of uniqueness of Halmos dilation of strict contractions on Hilbert spaces, vector space version of Halmos dilation can not be characterized.

Some common fixed point theorems for strict contractions

The extension of Aamri and El Moutawakil's property [1] to set-valued mappings arena is given. Also, some common fixed point theorems for strict contractions are established. these theorems extend results in [1,8].

Image restoration via Picard's and Mountain-pass Theorems

&lt;abstract&gt;&lt;p&gt;In this work, we present existence results for some problems which arise in image processing namely image restoration. Our essential tools are Picard's fixed point theorem for a strict contraction and Mountain-pass Theorem for critical point.&lt;/p&gt;&lt;/abstract&gt;

Convergence of inexact iterates of strict contractions in metric spaces with graphs

Convergence of inexact iterates of strict contractions in metric spaces with graphs

Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces

AbstractThis paper is mainly concerned with some new asymptotic properties on mild solutions to a nonlocal Cauchy problem of integrodifferential equation in Banach spaces. Under some well-imposed conditions on the nonlocal Cauchy, the neutral and forced terms, respectively, we establish some existence results for weighted pseudoS-asymptotically (ω,k)-Bloch periodic mild solutions to the referenced equation onR+${\mathbb{R}}_{+}$by suitable superposition theorems. The results show that the strict contraction of the nonlocal Cauchy and the neutral terms with the state variable has an appreciable effect on the existence and uniqueness of such a solution compared with the forced term. As an auxiliary result, the existence of weighted pseudoS-asymptotically (ω,k)-Bloch periodic mild solutions is deduced under the sublinear growth condition on the force term with its state variable. The existence of weighted pseudoS-asymptoticallyω-antiperiodic mild solution is also obtained as a special example.