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The primary objective of the present study was to develop an appropriate scale for evaluating LMX by investigating how individuals personally perceive and encounter distinct relationships (both high quality and low quality) with their supervisors, with a specific focus on the Indian context.

The scale was administered on a sample of 290 middle-level managers from two large manufacturing organizations located in North India.

The factors identified as important for the construct of leader-member exchange were affect, loyalty, and contribution.

The internal consistency reliability of the LMX contribution dimension is very low. Future researchers should add a few additional items to increase the reliability of the contribution scale of LMX scale so that it fulfills adequate criteria of reliability. Further, the supervisor–subordinate relationship from both supervisor and subordinate perspectives should also be examined.

This study has made significant advancements in the field of LMX. The findings will also be utilized by the authorities of the organization in focusing future training for its managers.

The findings of this research will help not only advancement in the field of LMX but will also help the manager using LMX to influence subordinates to have better knowledge on which factors to focus on to get better results.

Overall, the results of the current study provide evidence for the sound reliability and validity of the leader-member exchange scale with employees of Indian manufacturing organizations, supporting its use with these populations. Further, this scale is suitable not only in Indian culture but also in the Western cultural context, as the results corroborate the findings of Western scholars, indicating a fair level of cross-cultural validity. However, future research should also address the cross-validation of the factor structure of LMX on other samples and occupations.

This paper aims to study boundary and interior layer phenomena in coupled multiscale parabolic convection–diffusion interface problems and to present their efficient numerical resolution and analysis.

This study includes cases in which the diffusion parameters are small, distinct and can differ in order of magnitude. The source term is considered to be discontinuous. The asymptotic behavior of the solution is examined. The layer structure is analyzed, leading to the development of a variant of layer-resolving Shishkin mesh. For efficient numerical resolution, two methods are developed by combining additive schemes on a uniform mesh to discretize in time and an upwind difference scheme away from the line of discontinuity and a specific upwind difference scheme along the line of discontinuity, defined on a variant of layer resolving Shishkin mesh, to discretize in space. The analysis of the numerical resolution is discussed using the barrier function approach. Numerical simulations provide a verification of the theory and efficiency of the approach.

The discontinuity in the source term, along with the inclusion of small and distinct diffusion parameters, results in multiple overlapping and interacting boundary and interior layers. The work demonstrates that the present approach is robust in resolving boundary and interior layers. From a computational cost perspective, the numerical resolution presented in the paper is more efficient than conventional approaches.

Efficient numerical resolution and analysis of boundary and interior layer phenomena in coupled multiscale parabolic convection–diffusion interface problems are provided. The discretization of the coupled system in the approach incorporates a distinctive feature, wherein the components of the approximate solution are decoupled at each time level, resulting in tridiagonal linear systems to be solved, in contrast to large banded linear systems with conventional approaches.