Mathematical modeling of optimal allocation of remote workforce: an interdisciplinary investigation with Hofstede's cultural factors and managerial ability

PurposeAs the pandemic begins to ease, many companies are figuring out that working remotely is the future of work and "a new normal”. This research focuses on strategic planning and practices inherent in remote work, and aims to identify the optimal balance between virtual and on-site working. Specifically, the authors investigate the moderating effects of managerial ability and Hofstede's cultural factors.Design/methodology/approachThe authors build a mathematical model to locate the optimal balance between virtual and on-site working. A numerical study is presented, and additional sensitivity analysis is conducted to validate the proposed model.FindingsThis model provides organizations with a general guideline with recommended optimal percentages of remote workforce based on specific Hofstede's national scores. The authors also find that organizations with varying levels of managerial ability exhibit different adoption rates of remote working.Research limitations/implicationsBecause of the chosen research approach, the proposed model may lack empirical verification and require further adjustment of parameters. Therefore, researchers are encouraged to empirically and statistically test the proposed model further.Practical implicationsThis model equips organizations and practitioners with a general guideline to identify their desired portion of remote workforce. The incorporation of managerial ability and cultural factors makes our model applicable to various business structures across different sectors.Originality/valueThis proposed model addresses this optimization problem from a mathematical perspective with an interdisciplinary approach. The model also considers the moderating effects of managerial ability and Hofstede's cultural factors.HighlightsThe main contribution of this study is the theoretical development of our mathematical model that identifies the optimal balance between remote and on-site workforce in the context of managerial ability and Hofstede's cultural factors.A numerical study is presented, and additional sensitivity analysis is conducted to validate the proposed model and highlight the moderating effect of managerial ability and cultural influence on the adopted percentages of remote working.Our study suggests that organizational capabilities, managerial skills, and culturally suitable work arrangement are vital in successful development and implementation of remote working policy.Practical managerial implications and general guidelines are offered to organizations and practitioners.

Analysis of e-content of Khuzestan Province teachers during the COVID-19 period based on Mayer's principles

The current study investigates the e-content prepared by teachers during the COVID-19 period in terms of observing the principles of e-content design. Meyer's theory with 12 principles has been used for design principles. To this end, a checklist with 12 components with face validity and reliability of 0.78 from Cronbach's alpha test, and 275 educational videos produced by teachers in Khuzestan province based on available sampling method and based on 12 components of Mayer theory were reviewed by three educational technologist. The results revealed that the contents prepared in only three components ‘spatial contiguity', ‘segmentation' and ‘multimedia' at the level of 1% were significantly above average and the rest of the components were all significantly below average that include 8 components. The ‘pre-training' component was not significantly different from the mean. Generally, the results indicated that the e-content design principles were not significantly observed in the prepared e-content at the level of 1%. © 2023 Inderscience Enterprises Ltd.. All rights reserved.

Analysis of e-content of Khuzestan Province teachers during the COVID-19 period based on Mayer's principles

The current study investigates the e-content prepared by teachers during the COVID-19 period in terms of observing the principles of e-content design. Meyer's theory with 12 principles has been used for design principles. To this end, a checklist with 12 components with face validity and reliability of 0.78 from Cronbach's alpha test, and 275 educational videos produced by teachers in Khuzestan province based on available sampling method and based on 12 components of Mayer theory were reviewed by three educational technologist. The results revealed that the contents prepared in only three components 'spatial contiguity', 'segmentation' and 'multimedia' at the level of 1% were significantly above average and the rest of the components were all significantly below average that include 8 components. The 'pre-training' component was not significantly different from the mean. Generally, the results indicated that the e-content design principles were not significantly observed in the prepared e-content at the level of 1%.

The Relative (Co)homology Theory through Operator Algebras

This paper introduces a new idea in the unital involutive Banach algebras and its closed subset. This paper aims to study the cohomology theory of operator algebra. We will study the Banach algebra as an applied example of operator algebra, and the Banach algebra will be denoted by A. The definitions of cyclic, simplicial, and dihedral cohomology group of A will be introduced. We presented the definition of ℬ-relative dihedral cohomology group that is given by: HDn[(A,B),X]=Zn[(A,B),X]/Bn[(A,B),X], and we willshow that the relation between dihedral and B-relative dihedral cohomology group 0 →HD0[(A,B),X]→HD0(A,X)→HD0(A/B. X) →HD1[(A,B),X]→HD1(A,X)→ ⋯ →HDn[(A,B),X] →HDn(A,X)→HDn(A/B,X)→HDn+1[(A,B),X) →⋯ can be obtained from the sequence 0→CDn[(A,B),X] →CDn(A,X) →CDn(A/B,X) →0. Among the principal results that we will explain is the study of some theorems in the relative dihedral cohomology of Banach algebra as a Connes-Tsygan exact sequence, since the relation between the relative Banach dihedral and cyclic cohomology group (HDn[(A,B),X] and HCn[(A,B),X] of A will be proved as the sequence →−HDn[(A,B),X]i* →HCn[(A,B),X]j*→HDn[(A,B),X]→-HDn+1[(A,B),X] →⋯. Also, we studied and proved some basic notations in the relative cohomology of Banach algebra with unity and defined its properties. So, we showed the Morita invariance theorem in a relative case with maps tr∗:HD*(Mr(B),Mr(M)) →HD*(B,M) and inc∗: HD*(B,M→HD* HD*(Mr(B),Mr(M)), and proved the Connes-Tsygan exact sequence that relates the relative cyclic and dihedral (co)homology of A. We proved the Mayer-Vietoris sequence of HDn[(A,B),X] in a new form in the Banach B-relative dihedral cohomology: (Formula Presented). It should be borne in mind that the study of the cohomology theory of operator algebra is concerned with studying the spread of Covid 19. © 2022 by authors, all rights reserved.

Impact of Different Styles of Online Course Videos on Students' Attention During the COVID-19 Pandemic.

Background: The COVID-19 pandemic interfered with normal campus life, resulting in the need for the course to be conducted in an ideal online format. The purpose of this study is to analyze the impact of different styles of online political course videos on students' attention during the COVID-19 pandemic. Methods: Four college students participated in this small sample study. They were required to conduct two sessions of the experiment, in which they were required to watch three different styles of course videos in each session. While watching the videos, their EEG signals were acquired. For the acquired EEG signals, the sample entropy (SampEn) features were extracted. On the other hand, Mayer's theories of multimedia technology provide guidance for teachers' online courses to enhance students' attention levels. The results of EEG signals analysis and Mayer's theories of multimedia technology were combined to compare and analyze the effects of three styles of instructional videos. Results: Based on comparisons of the SampEn and Mayer's theories of multimedia technology analysis, the results suggest that online instruction in a style where the instructor and content appear on the screen at the same time and the instructor points out the location of the content as it is explained is more likely to elicit higher levels of students' attention. Conclusions: During the COVID-19 pandemic, online instructional methods have an impact on students' classroom attention. It is essential for teachers to design online instructional methods based on students' classroom attention levels and some multimedia instructional techniques to improve students' learning efficiency.