Research

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., Generalized holomorphic functions: sketches of a new theory. To appear in the volume “Women is Analysis and PDE”, series “Research Perspectives Ghent Analysis and PDE Center”, Birkhäuser, 2023.

• 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.

Preprints:

• Nugraheni, S.,  Giordano, P., Dirac delta as a generalized holomorphic function.  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:

1. 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”

2. Participant at the 2023 Generalized Functions Online Workshop; May 2023; title: ”Natural Definition of Generalized Holomorphic Functions”

3. Participant at the International Conference on Generalized Functions; September 2022; Vienna, Austria; title: “Generalized Holomorphic Functions”

4. 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”

5. 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”

6. 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”