We define doubly graded Sn modules Rmu for which we conjecture that the multiplicities of irreducible representations in various bi-degrees are given by the Macdonald coefficients Klambdamu. Assuming one fundamental conjecture, the modules Rmu can be given several equivalent definitions, which we discuss. We prove the conjectures in various special cases.
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http://dx.doi.org/10.1073/pnas.90.8.3607 | DOI Listing |
J Vis Exp
July 2024
College of Mechanical and Electrical Engineering, Wenzhou University; Institute of Laser and Optoelectronic Intelligent Manufacturing, Wenzhou University; Wecome Intelligent Manufacturing Co., Ltd.; College of Mechanical Engineering, Nanjing University of Aeronautics and Astronautics;
The Ring Main Unit (RMU) is a critical device in power distribution systems used for connecting and distributing electricity. However, due to its compact internal structure and high current load, heat dissipation issues are particularly prominent. To address this problem, this study innovatively proposes a simplified RMU model, employing finite element simulation methods to accurately solve for the ohmic losses of conductors under actual operating conditions and obtain ohmic loss data for various components.
View Article and Find Full Text PDFInt J Ment Health Syst
May 2021
University of Liverpool, Liverpool, UK.
Background: Globally, there is a large documented gap between needs of families and children with developmental disorders and available services. We adapted the World Health Organization's mental health Gap-Intervention Guidelines (mhGAP-IG) developmental disorders module into a tablet-based android application to train caregivers of children with developmental disorders. We aimed to evaluate the effectiveness of this technology-assisted, family volunteers delivered, parents' skills training intervention to improve functioning in children with developmental disorders in a rural community of Rawalpindi, Pakistan.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
April 1993
Department of Mathematics, University of Calfornia, San Diego, La Jolla, CA 92093-0112, USA.
We define doubly graded Sn modules Rmu for which we conjecture that the multiplicities of irreducible representations in various bi-degrees are given by the Macdonald coefficients Klambdamu. Assuming one fundamental conjecture, the modules Rmu can be given several equivalent definitions, which we discuss. We prove the conjectures in various special cases.
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