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The purpose of this paper was to analyse the research trends on the Indian Open and Distance Education (ODE) system as reflected in the articles published in the prominent journals of distance education across the world.

A study was undertaken to review the research articles on ODE in India published in 11 prominent peer-reviewed journals of distance education during the period 2010–2019. Content analysis was done to find out areas of research undertaken in the ODE of India based on a validated classification of research areas; types of research studies conducted; and authorship and publication patterns.

Out of a total of 2,571 articles published in 11 selected journals, only 191 (7.42%) pertained to ODE in India. The majority of these 191 articles (68.42%) were published in Indian journals. The Indian and Asian journals together accounted for 93.55% of total articles. Globally, the share of articles on the Indian ODE system was significantly low ranging between 4.27 and a maximum of 10.77%, which was much below expectations from a country having the maximum number of ODE learners in the world. Results further revealed that 63% of the contributors to research on ODE in India were affiliated to Indira Gandhi National Open University.

The limitation of this study was only analysing the research articles published in journals of distance education and other types of articles, namely, book reviews, editorials, field notes and workshop reports were excluded from the analysis.

The study is intended to help researchers, policymakers, and open and distance education institutions to draw a roadmap for the promotion and conduct of system-based research, which would be vital for strengthening the system.

The quantum of research is not proportionate to the number of faculty members working in the ODE system of India and the large number of learners that it serves, which is a matter of concern. For any system to grow its periodic systemic review is essential. The research outcomes need to be ploughed back into the system for its betterment.

The study is original. There is no such study undertaken till date. This study will be extremely useful to researchers, as the gaps in distance education research which are yet to be addressed, have been identified by the authors.

This paper seeks to develop, propose and validate, through a series of presentable examples, a comprehensive high‐precision and ultra‐fast computing concept for solving stiff ordinary differential equations (ODEs) and partial differential equations (PDEs) with cellular neural networks (CNN).

The core of the concept developed in this paper is a straight‐forward scheme that we call “nonlinear adaptive optimization (NAOP)”, which is used for a precise template calculation for solving any (stiff) nonlinear ODEs through CNN processors.

One of the key contributions of this work (this is a real breakthrough) is to demonstrate the possibility of mapping/transforming different types of nonlinearities displayed by various classical and well‐known oscillators (e.g. van der Pol‐, Rayleigh‐, Duffing‐, Rössler‐, Lorenz‐, and Jerk‐ oscillators, just to name a few) unto first‐order CNN elementary cells, and thereby enabling the easy derivation of corresponding CNN‐templates. Furthermore, in case of PDEs solving, the same concept also allows a mapping unto first‐order CNN cells while considering one or even more nonlinear terms of the Taylor's series expansion generally used in the transformation of a PDEs in a set of coupled nonlinear ODEs. Therefore, the concept of this paper does significantly contribute to the consolidation of CNN as a universal and ultra‐fast solver of stiff differential equations (both ODEs and PDEs). This clearly enables a CNN‐based, real‐time, ultra‐precise, and low‐cost Computational Engineering. As proof of concept a well‐known prototype of stiff equations (van der Pol) has been considered; the corresponding precise CNN‐templates are derived to obtain precise solutions of this equation.

This paper contributes to the enrichment of the literature as the relevant state‐of‐the‐art does not provide a systematic and robust method to solve nonlinear ODEs and/or nonlinear PDEs using the CNN‐paradigm. Further, the “NAOP” concept developed in this paper has been proven to perform accurate and robust calculations. This concept is not based on trial‐and‐error processes as it is the case for various classes of optimization methods/tools (e.g. genetic algorithm, particle swarm, neural networks, etc.). The “NAOP” concept developed in this frame does significantly contribute to the consolidation of CNN as a universal and ultra‐fast solver of nonlinear differential equations (both ODEs and PDEs). An implantation of the concept developed is possible even on embedded digital platforms (e.g. field‐programmable gate array (FPGA), digital signal processing (DSP), graphics processing unit (GPU), etc.); this opens a broad range of applications. On‐going works (as outlook) are using NAOP for deriving precise templates for a selected set of practically interesting PDE models such as Navier Stokes, Schrödinger, Maxwell, etc.

In this study, a new neural differential grey model is proposed for the purpose of accurately excavating the evolution of real systems.

For this, the proposed model introduces a new image equation that is solved by the Runge-Kutta fourth order method, which makes it possible to optimize the sequence prediction function. The novel model can then capture the characteristics of the input data and completely excavate the system's evolution law through a learning procedure.

The new model has a broader applicability range as a result of this technique, as opposed to grey models, which have fixed structures and are sometimes over specified by too strong assumptions. For experimental purposes, the neural differential grey model is implemented on two real samples, namely: production of crude and consumption of Cameroonian petroleum products. For validation of the new model, results are compared with those obtained by competing models. It appears that the precisions of the new neural differential grey model for prediction of petroleum products consumption and production of Cameroonian crude are respectively 16 and 25% higher than competing models, both for simulation and validation samples.

This article also takes an in-depth look at the mechanics of the new model, thereby shedding light on the intrinsic differences between the new model and grey competing models.

Institutional environment plays a crucial role in determining the nature of entrepreneurship that prevails in an economy. In this paper, the authors address how business, labour and credit regulations contribute differently to both the overall prevalence of opportunity-driven entrepreneurship (ODE) and its gender gap in high-income and emerging economies.

On the basis of an unbalanced panel of 41 countries over the period 2005–2016, the authors estimate system generalised method of moment models. The authors also perform an ordinary least square analysis to address gender differences in ODE.

The authors find that higher credit market liberalisation is especially associated with more entrepreneurship by opportunity. Nevertheless, while credit market regulation stands out as a key element to promote opportunity-based entrepreneurship in both high-income and emerging countries, in the emerging world business regulation is also largely related to the prevalence of opportunity entrepreneurship. In terms of gender gap, business and labour market freedom seem to exert an equalising effect on the divide in entrepreneurship by opportunity, specifically in emerging economies.

Findings allow the identification of regulatory policy reform priorities to enhance the prevalence of ODE depending on the level of a country's development. They also identify which specific areas of economic regulation would speed up closing the gender gap in opportunity entrepreneurship.

This paper aims to introduce a novel algorithm to solve initial/boundary value problems of high-order ordinary differential equations (ODEs) and high-order system of ordinary differential equations (SODEs).

The proposed method is based on Hermite polynomials and extreme learning machine (ELM) algorithm. The Hermite polynomials are chosen as basis function of hidden neurons. The approximate solution and its derivatives are expressed by utilizing Hermite network. The model function is designed to automatically meet the initial or boundary conditions. The network parameters are obtained by solving a system of linear equations using the ELM algorithm.

To demonstrate the effectiveness of the proposed method, a variety of differential equations are selected and their numerical solutions are obtained by utilizing the Hermite extreme learning machine (H-ELM) algorithm. Experiments on the common and random data sets indicate that the H-ELM model achieves much higher accuracy, lower complexity but stronger generalization ability than existed methods. The proposed H-ELM algorithm could be a good tool to solve higher order linear ODEs and higher order linear SODEs.

The H-ELM algorithm is developed for solving higher order linear ODEs and higher order linear SODEs; this method has higher numerical accuracy and stronger superiority compared with other existing methods.

Ordinary differential equations (ODEs) are widely used in the engineering curriculum. They model a spectrum of interesting physical problems that arise in engineering disciplines. Studies of different types of ODEs are determined by engineering applications. Various techniques are used to solve practical differential equations problems. This paper aims to present a computational tool or a computer-assisted technique aimed at tackling ODEs. This method is usually not taught and/or not accessible to undergraduate students. The aim of this strategy is to help the readers to develop an effective and relatively novel problem-solving skill. Because of the drudgery of hand computations involved, the method requires the need to use computers packages. In this work, the successive differentiation method (SDM) for solving linear and nonlinear and homogeneous or non-homogeneous ODEs is presented. The algorithm uses the successive differentiation of any given ODE to determine the values of the function’s derivatives at a single point, mostly x = 0. The obtained values are used to construct the Taylor series of the solution of the examined ODE. The algorithm does not require any new assumption, hence handles the problem in a direct manner. The power of the method is emphasized by testing a variety of models with distinct orders, with constant and variable coefficients. Most of the symbolic and numerical computations can be carried out using computer algebra systems.

This study presents a computational tool or a computer-assisted technique aimed at tackling ODEs. This method is usually not taught and/or not accessible to undergraduate students. The aim of this strategy is to help the readers to develop an effective and relatively novel problem-solving skill. Because of the drudgery of hand computations involved, the method requires the need to use computers packages.

This method is applied to a variety of well-known equations, such as the Bernoulli equation, the Riccati equation, the Abel equation and the second-order Euler equation, some with constant and variable coefficients. SDM handles linear and nonlinear and homogeneous or nonhomogeneous ODEs in a direct manner without any need to restrictive conditions. The method works effectively to the Volterra integral equations, as will be discussed in a coming work.

The method can be extended to a wide range of engineering problems that are modeled by differential equations. The method is simple and novel and highly accurate.

The simplified modeling of many physical processes results in a second-order ordinary differential equation (ODE) system. Often the damping of these resonating systems cannot be defined in the same simplified way as the other parameters due to the complexity of the physical effects. The purpose of this paper is to develop a mathematically stable approach for damping resonances in nonlinear ODE systems.

Modifying the original ODE using the eigenvalues and eigenvectors of a linearized state leads to satisfying results.

An iterative approach is presented, how to modify the original ODE, to achieve a well-damped solution.

The method can be applied for every physical resonating system, where the model complexity prevents the determination of the damping.

The iterative algorithm to modify the original ODE is novel. It can be used on different fields of the physics, where a second-order ODE is describing the problem, which has only measured or empirical damping.

The purpose of this report is to demonstrate open and distance education (ODE) can support poverty alleviation. Taking the practices of the Open University of China (the OUC) as an example, this paper aims to reveal how open universities make contributions to local residents in rural and remote areas.

Focusing on 25 poverty-stricken counties, the OUC had invested 58 million RMB to its learning centers in these counties from 2017 to 2020. The first one is to improve ICT and educational facilities in these learning centers. The second approach is to cultivate local residents with degree programs through ODE so as to promote local economic development. The third one is to design and develop training programs according to local context to meet the specific needs of local villagers.

After 3 years working, cloud-based classrooms and computer rooms have been set up. Bookstores have been founded and printed books have been donated. Hundreds of thousands of digital micro lectures have been supplied to these learning centers which have been improved and fully played their functions. Nearly 50,000 local residents have been directly benefited. Village leaders have helped lift local residents out of poverty. Poverty-stricken villagers have been financed to study on either undergraduate or diploma programs. Local residents have improved their skills by learning with the training programs offered by the OUC.

ODE is proved to be an effective way to eradicate poverty. Open universities are proved to be able to make contributions to social justice. By fulfilling its commitments to eliminate poverty within the national strategy framework, the OUC has built its brand nationwide.

The purpose of this paper is to investigate toxic behaviour (TB) that significantly harms individuals’ gameplay experience in multiplayer online video games. Multiplayer online video games allow to simultaneously interact with others in real time. They can be considered as digital communities unifying a group of players within a video game. TB is characterized by spreading a bad mood (e.g. upsetting and insulting) leading to unsatisfying outcomes in team-based multiplayer environments.

Using mixed methods, the authors show that handling TB should be addressed more firmly on a level of game design. First, the authors test the explanatory power of the online disinhibition effect (ODE) and its antecedents on TB using a quantitative survey (N = 320) and structural equation modelling. Specifically, the authors show that dissociative anonymity, asynchronicity, solipsistic introjection, dissociative imagination and minimization of authority have a mediated effect through toxic disinhibition as predictors of TB. Second, the authors conduct a focus group workshop (N = 10) with experts from diverse disciplines to derive design principles on a level of game design.

The results indicate that transparency and imminent feedback are still underutilized elements in game design that can significantly buffer several forms of TB. By developing a heuristic prototype and exemplary design principles in subsequent categories, the authors address all relevant in-game scenarios. With this study, the authors provide researchers and practitioners helpful insights on how to increase the well-being and safety of gaming communities.

ODE already showed its explanatory potential in the neighbouring context of cyberbullying. Embedded in theories of negative behaviour on the internet, the authors propose a holistic and theory-driven approach to handle TB on a level of game design. The authors’ insights allow for a better understanding of an innovative entity of the dark side of technology diffusion and adverse side effects linked to it.

This study aims to overcome the involved challenging issues and provide high-precision eigensolutions. General eigenproblems in the system of ordinary differential equations (ODEs) serve as mathematical models for vector Sturm-Liouville (SL) and free vibration problems. High-precision eigenvalue and eigenfunction solutions are crucial bases for the reliable dynamic analysis of structures. However, solutions that meet the error tolerances specified are difficult to obtain for issues such as coefficients of variable matrices, coincident and adjacent approximate eigenvalues, continuous orders of eigenpairs and varying boundary conditions.

This study presents an h-version adaptive finite element method based on the superconvergent patch recovery displacement method for eigenproblems in system of second-order ODEs. The high-order shape function interpolation technique is further introduced to acquire superconvergent solution of eigenfunction, and superconvergent solution of eigenvalue is obtained by computing the Rayleigh quotient. Superconvergent solution of eigenfunction is used to estimate the error of finite element solution in the energy norm. The mesh is then, subdivided to generate an improved mesh, based on the error.

Representative eigenproblems examples, containing typical vector SL and free vibration of beams problems involved the aforementioned challenging issues, are selected to evaluate the accuracy and reliability of the proposed method. Non-uniform refined meshes are established to suit eigenfunctions change, and numerical solutions satisfy the pre-specified error tolerance.

The proposed combination of methodologies described in the paper, leads to a powerful h-version mesh refinement algorithm for eigenproblems in system of second-order ODEs, that can be extended to other classes of applications in damage detection of multiple cracks in structures based on the high-precision eigensolutions.