Currently, during my doctoral studies, my focus is on generalized smooth functions (GSF) theory which is a branch of Colombeau theory where generalized functions share a number of fundamental properties with smooth functions, in particular with respect to composition and nonlinear operations. At the present, I am studying generalized holomorphic functions under the supervision of Dr. Paolo Giordano, Privatdoz.
Publications:
Nugraheni, S., Giordano, P., 2024. Generalized Holomorphic Functions: Sketches of a New Theory. In: Chatzakou, M., Ruzhansky, M., Stoeva, D. (eds) Women in Analysis and PDE. Trends in Mathematics vol. 5. pp 283–292. Birkhäuser, Cham. DOI
Nugraheni, S., and Indrati, C.R., 2018, Solusi Lemah Masalah Dirichlet Persamaan Diferensial Parsial Linear Eliptik Order Dua, Journal of Fundamental Mathematics and Application, Vol. 1, pp. 1-11. DOI
Preprints:
Nugraheni, S., Giordano, P., Dirac delta as a generalized holomorphic function. The actual paper has been submitted. GHF1
Nugraheni, S., Giordano, P., Path integration of generalized holomorphic functions. GHF2
Nugraheni, S., Giordano, P., Hyper power series for generalized holomorphic functions. GHF3
Conference and Seminar Talks:
Participant at the 9th Southeast Mathematical Society-Universitas Gadjah Mada (SEAMS-UGM) 2023 International Conference on Mathematics and Its Applications; July 2023; Yogyakarta, Indonesia; title: “Natural Definition of Generalized Holomorphic Functions”
Participant at the 2023 Generalized Functions Online Workshop; May 2023; title: ”Natural Definition of Generalized Holomorphic Functions”
Participant at the International Conference on Generalized Functions; September 2022; Vienna, Austria; title: “Generalized Holomorphic Functions”
Participant at the 4th IndoMS Conference on Mathematics and Its Applications (IICMA) 2019 (http://iicma.untan.ac.id); September 2019; Pontianak, Indonesia; title: “Properties of Orlicz-Sobolev Space on Domain with Cone Condition”
Participant at the 2nd International Conference on Mathematics Education Theory and Application (ICMETA) (http://icmeta.uns.ac.id); October 2018; Surakarta, Indonesia; title: “The Embedding of Sobolev Spaces into Orlicz Spaces on the Euclidean Domains”
Participant at the Konverensi Nasional Matematika ke-18 (The 18th National Conference on Mathematics) that held by Indonesian Mathematical Society (IndoMS); November 2016; Pekanbaru, Indonesia; title: “Weak Solutions of Dirichlet Problems for Second Order Linear Elliptic Partial Differential Equations”