Dr. Mihaela Vajiac
- Scholarly Works:
- Digital Commons
- Education:
- University of Bucharest, Bachelor of Science
Boston University, Ph.D.
Biography
Dr. Mihaeila Vajiac is the Director of the Center of Excellence in Complex and Hypercomplex Analysis (CHECHA). She is also the organizer of the Math/Physics/Computation Seminar at Chapman, and one of the organizers of the Special Session on Geometric Methods in Hypercomplex Analysis at the AMS Fall Western Sectional Meeting in late 2018.
Some of her research interests include:
Complex and Hypercomplex Analysis
Complex Analysis is a classical branch of mathematics, having its roots in late 18th
and early 19th centuries, which investigates functions of one and several complex
variables. It has applications in many branches of mathematics, including Number Theory
and Applied Mathematics, as well as in physics, including Hydrodynamics, Thermodynamics,
Electrical Engineering, and Quantum Physics. Clifford Analysis is the study of Dirac
and Dirac type operators in Analysis and Geometry, together with their applications.
In 3 and 4 dimensions Clifford Analysis is referred to as Quaternionic Analysis. Furthermore,
methods and tools of Clifford Analysis are extended to the field of Hypercomplex Analysis.
Algebraic Computational Methods in Geometric and Physics PDEs
In recent years, techniques from computational algebra have become important to render
effective general results in the theory of Partial Differential Equations. My research
is following the work of D.C. Struppa, I. Sabadini, F. Colombo, F. Sommen, etc., authors
which have shown how these tools can be used to discover and identify important properties
of several systems of interest, such as the Cauchy-Fueter, the Mosil-Theodorescu,
the Maxwell, the Proca system, as well as the systems which naturally arise from the
work of the Belgian school of Brackx, Delanghe and Sommen.
Differential Geometry, Symplectic Geometry, Integrable Sustems
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Recent Creative, Scholarly Work and Publications
- D.Alpay,A.De Martino, K. Diki, and M. Vajiac. The bicomplex tensor product and a bicomplex Choi theorem. Physica. Scripta, vol. 99 095245 (2024).
- D.Alpay,I.Cho and M. Vajiac. Scaled global operators and Fueter variables on non-zero scaled hypercomplex numbers. Advances in Applied Clifford Algebras. vol. 34 (2024), no. 5, Paper No. 53, 61pp
- D.Alpay, K. Diki, and M. Vajiac: New Fueter variables associated to the global operator in the quaternionic case. Publications of the Research Institute for Mathematical Sciences, Kyoto University, vol. 60 (2024), no. 4, 859–891.
- D. Alpay, I. Lewkowicz and M. Vajiac. Discrete Wiener algebra in the bicomplex setting, spectral factorization with symmetry, and superoscillations. Analysis and Mathematical Physics,13, No. 3, Paper No. 54, 32 p. (2023).
- D. Alpay, I. Lewkowicz and M. Vajiac. Interpolation with symmetry and a Herglotz Theorem in the bicomplex setting. Journal of Mathematical Analysis and Applications, vol. 524 (2023), no. 2, Paper No. 127201
- D. Alpay, K. Diki and M. Vajiac: A note on the complex and bicomplex neural networks. Applied Mathematics and Computation, vol. 445 (2023) Paper No. 127864, 12pp.
- D. Alpay, K. Diki and M. Vajiac: An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications. Mathematische Nachrichten