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In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings.

Showed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping.

This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

Introducing technology at work presents a special challenge as learning is tightly integrated with workplace practices. Current design-based research (DBR) methods are focused on formal learning context and often questioned for a lack of yielding traceable research insights. This paper aims to propose a method that extends DBR by understanding tools as sociocultural artefacts, co-designing affordances and systematically studying their adoption in practice.

The iterative practice-centred method allows the co-design of cognitive tools in DBR, makes assumptions and design decisions traceable and builds convergent evidence by consistently analysing how affordances are appropriated. This is demonstrated in the context of health-care professionals’ informal learning, and how they make sense of their experiences. The authors report an 18-month DBR case study of using various prototypes and testing the designs with practitioners through various data collection means.

By considering the cognitive level in the analysis of appropriation, the authors came to an understanding of how professionals cope with pressure in the health-care domain (domain insight); a prototype with concrete design decisions (design insight); and an understanding of how memory and sensemaking processes interact when cognitive tools are used to elaborate representations of informal learning needs (theory insight).

The method is validated in one long-term and in-depth case study. While this was necessary to gain an understanding of stakeholder concerns, build trust and apply methods over several iterations, it also potentially limits this.

Besides generating traceable research insights, the proposed DBR method allows to design technology-enhanced learning support for working domains and practices. The method is applicable in other domains and in formal learning.

This paper aims to identify and evaluate resolutions to key learning and teaching challenges in very large courses that involve practical mathematics, such as foundational finance.

A design-based research approach is used across three semesters to iteratively identify practical problems within the course and then develop and evaluate resolutions to these problems. Data are collected from both students and teachers and analysed using a mixed-method approach.

The results indicate that key learning and teaching challenges in large foundational finance courses can be mitigated through appropriate consistency of learning materials; check-your-understanding interactive online content targeting foundational concepts in the early weeks; connection points between students and the coordinator to increase teacher presence; a sustained focus on supporting student achievement within assessments; and signposting relevance of content for the broader program and professional settings. Multiple design iterations using a co-design approach were beneficial to incrementally improve the course and consider multiple perspectives within the design process.

This paper develops a set of design principles to provide guidance to other practitioners who seek to improve their own courses.

The use of design-based research and mixed-method approaches that consider both student and teacher perspectives to examine the design of very large, foundational finance courses is novel.

Design-based research (DBR) involves multiple iterations, and innovations are needed in analytical methods for understanding how learners experience a learning experience in ways that both embrace the complexity of learning and allow for data-driven changes to the design of the learning experience between iterations. The purpose of this paper is to propose a method of crafting design moves in DBR using network analysis.

This paper introduces learning experience network analysis (LENA) to allow researchers to investigate the multiple interdependencies between aspects of learner experiences, and to craft design moves that leverage the relationships between struggles, what worked and experiences aligned with principles from theory.

The use of network analysis is a promising method of crafting data-driven design changes between iterations in DBR. The LENA process developed by the authors may serve as inspiration for other researchers to develop even more powerful methodological innovations.

LENA may provide design-based researchers with a new approach to analyzing learner experiences and crafting data-driven design moves in a way that honors the complexity of learning.

LENA may provide novice design-based researchers with a structured and easy-to-use method of crafting design moves informed by patterns emergent in the data.

To the best of the authors’ knowledge, this paper is the first to propose a method for using network analysis of qualitative learning experience data for DBR.

This study explored use of big data analytics (BDA) to analyse data of a large number of construction firms to develop a construction business failure prediction model (CB-FPM). Careful analysis of literature revealed financial ratios as the best form of variable for this problem. Because of MapReduce’s unsuitability for iteration problems involved in developing CB-FPMs, various BDA initiatives for iteration problems were identified. A BDA framework for developing CB-FPM was proposed. It was validated by using 150,000 datacells of 30,000 construction firms, artificial neural network, Amazon Elastic Compute Cloud, Apache Spark and the R software. The BDA CB-FPM was developed in eight seconds while the same process without BDA was aborted after nine hours without success. This shows the issue of not wanting to use large dataset to develop CB-FPM due to tedious duration is resolvable by applying BDA technique. The BDA CB-FPM largely outperformed an ordinary CB-FPM developed with a dataset of 200 construction firms, proving that use of larger sample size with the aid of BDA, leads to better performing CB-FPMs. The high financial and social cost associated with misclassifications (i.e. model error) thus makes adoption of BDA CB-FPMs very important for, among others, financiers, clients and policy makers.

Risk parity, also known as equal risk contribution, has recently gained increasing attention as a portfolio allocation method. However, solving portfolio weights must resort to numerical methods as the analytic solution is not available. This study improves two existing iterative methods: the cyclical coordinate descent (CCD) and Newton methods. The authors enhance the CCD method by simplifying the formulation using a correlation matrix and imposing an additional rescaling step. The authors also suggest an improved initial guess inspired by the CCD method for the Newton method. Numerical experiments show that the improved CCD method performs the best and is approximately three times faster than the original CCD method, saving more than 40% of the iterations.

This paper aims to present an iterative path-following method with joint limits to solve the problem of large computation cost, movement exceeding joint limits and poor path-following accuracy for the path planning of hyper-redundant snake-like manipulator.

When a desired path is given, new configuration of the snake-like manipulator is obtained through a geometrical approach, then the joints are repositioned through iterations until all the rotation angles satisfy the imposed joint limits. Finally, a new arrangement is obtained through the analytic solution of the inverse kinematics of hyper-redundant manipulator. Finally, simulations and experiments are carried out to analyze the performance of the proposed path-following method.

Simulation results show that the average computation time is 0.1 ms per step for a hyper-redundant manipulator with 12 degrees of freedom, and the deviation in tip position can be kept below 0.02 mm. Experiments show that all the rotation angles are within joint limits.

Currently , the manipulator is working in open-loop, the elasticity of the driving cable will cause positioning error. In future, close-loop control based on real-time attitude detection will be used in in combination with the path-following method to achieve high-precision trajectory tracking.

Through a series of iterative processes, the proposed method can make the manipulator approach the desired path as much as possible within the joint constraints with high precision and less computation time.

The purpose of this study is to develop an optimization method for charging plans with the implementation of time-of-day (TOD) electricity tariff, to reduce electricity bill.

Two optimization models for charging plans respectively with fixed and stochastic trip travel times are developed, to minimize the electricity costs of daily operation of an electric bus. The charging time is taken as the optimization variable. The TOD electricity tariff is considered, and the energy consumption model is developed based on real operation data. An optimal charging plan provides charging times at bus idle times in operation hours during the whole day (charging time is 0 if the bus is not get charged at idle time) which ensure the regular operation of every trip served by this bus.

The electricity costs of the bus route can be reduced by applying the optimal charging plans.

This paper produces a viable option for transit agencies to reduce their operation costs.

The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued ρ-quasi-contractive mappings in modular function spaces. We approximate fixed points of this class of nonlinear multivalued mappings in modular function spaces. Moreover, we extend the concepts of T-stability, almost T-stability and summably almost T-stability to modular function spaces and give some results.