Search results

This paper aims to present a meshless technique to find the Green’s functions for solutions of Laplacian boundary value problems on rectangular domains. This paper also investigates a theoretical basis for the Steklov series expansion methods to reduce and estimate the error of numerical approaches for the boundary correction kernel of the Laplace operator.

The main interest is how the Green's functions differ from the fundamental solution of the Laplace operator. Steklov expansion methods for finding the correction term are supported by the analysis that bases of the class of all finite harmonic functions can be formed using harmonic Steklov eigenfunctions. These functions construct a basis of the space of solutions of harmonic boundary value problems and their boundary traces generate an orthogonal basis of the trace space of solutions on the boundary.

The main conclusion is that the boundary correction term for the Green's functions is well-approximated by Steklov expansions with a few Steklov eigenfunctions. The error estimates for the Steklov approximations of the boundary correction term involved in Dirichlet or Robin boundary value problems are found. They appear to provide very good approximations in the interior of the region and become quite oscillatory close to the boundary.

This paper concentrates to document the first attempt to find the Green's function for various harmonic boundary value problems with the explicit Steklov eigenfunctions without concerns regarding discretizations when the region is a rectangle.

This study aims to explore the ways in which management scholars affiliated with Peruvian universities navigate the tensions between global expectations and local realities in their research practices, drawing on their capitals and habitus.

Drawing on Bourdieu’s field theory, the authors analyse 25 in-depth interviews and a unique database of academic publications in the business and management field from 2000 to 2022. The analysis identifies the positions scholars occupy within the Peruvian management field and examines the factors influencing their research practices.

The authors find that the Peruvian management field is complex and unequal, where actors have different positions and interests, but are all influenced by a logic of academic dependency on the Global North. The authors identify three main positions held by scholars: transnational dominators, who accumulate greater resources and ignore local debates; dominated adaptors, who unsuccessfully try to imitate the dominant logic; and isolated innovators, who critique the dominant model but lack institutional support to develop alternatives.

This research presents an analysis of the Peruvian management field, a site often overlooked in international business studies. By examining scholarly practices, the authors reveal how academic inequalities are reproduced by the forces of globalization. The study underscores the urgent need for greater acknowledgement of regionally informed research, advocating for a more inclusive and diverse understanding in the field of management research.