Dr. 米卡尔Vajiac
Program Director for Mathematics
- 教育:
- University of Bucharest, Bachelor of Science
波士顿大学博士.D.
传记
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 :ied Mathematics, 在物理上也是一样, 包括流体力学, 热力学, 电气工程, 和量子物理. Clifford Analysis is the study of Dirac and Dirac type operators in Analysis and Geometry, 连同它们的应用. In 3 and 4 dimensions Clifford Analysis is referred to as Quaternionic Analysis. 此外, methods and tools of Clifford Analysis are extended to the field of Hypercomplex Analysis.
Algebraic Computational Methods in Geometric and Physics PDEs
近年来, 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,我. Sabadini F. 科伦坡,F. Sommen等., authors which have shown how these tools can be used to discover and identify important properties of several systems of interest, 比如Cauchy-Fueter, 的Mosil-Theodorescu, 麦克斯韦, Proca系统, as well as the systems which naturally arise from the work of the Belgian school of Brackx, 德朗赫和索曼.
Differential Geometry, Symplectic Geometry, Integrable Sustems
Learn more about each of these on 她的网站.
Recent Creative, Scholarly Work and Publications
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D. Alpay,我. Lewkowicz和M. Vajiac. Discrete Wiener algebra in the bicomplex setting, spectral factorization with symmetry, 和superoscillations. Analysis and Mathematical Physics,13, No. 3、论文编号. 54, 32 p. (2023).
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D. Alpay,我. Lewkowicz和M. Vajiac. Interpolation with symmetry and a Herglotz Theorem in the bicomplex setting. Journal of Mathematical Analysis and :ications, vol. 524 (2023), no. 2、论文编号. 127201
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D. Alpay K. Diki和M. Vajiac: A note on the complex and bicomplex neural networks. :ied Mathematics and Computation, vol. 445(2023)号文件. 127864, 12pp.
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D. Alpay K. Diki和M. Vajiac: An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications. Mathematische后
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A note on the complex and bicomplex valued neural networks with D. 支付宝和K.Diki in :ied Mathematics and Computation 445, 127864
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Ternary Complex Analysis and :ications瓦加克，M.B., in "New 方向 in Function Theory: From Complex to Hypercomplex to Non-Commutative", Birkhauser 2021
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The infinity is the chasm in which our thoughts are lost: Reflections on Sophie Germain's Essay, A. Glesser,.B.瓦加克，M.B., in Memoirs of the Scientific Sections of the Romanian Academy AND in The Best Writing on Mathematics 2021
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"Differential Geometry and Global Analysis: in honor of Tadashi Nagano" Publisher: Contemporary Mathematics, volume 777, American Mathematical Society ISBN: 978-147-04-6015-0 编辑:陈，B.Y.纽约州布鲁贝克(Brubaker.酒井，T.B.D.田中，M.S.Tamaru, H.瓦加克，M.B.
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"New 方向 in Function Theory: From Complex to Hypercomplex to Non-Commutative", Birkhauser 2021. 编辑:D. Alpay R. ,维. Shoikhet和M.B. Vajiac
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Ternary Clifford Algebras, Cerejeiras, P.瓦加克，M.B., Advances in :ied Clifford Algebras 31(1) , 1-18
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Birkhauser: Linear Systems and Operator Theory: Linear Systems, Signal Processing and Hypercomplex Analysis, 编辑:Alpay, D.瓦加克，M.B.
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B的估计.-Y. Chen's \delta^\hat-Invariant in Terms of Casorati Curvature and Mean Curvature for Convex Euclidean HypersurfacesB.瓦加克，M., in International Electronic Journal of Geometry, vol.12, No. 1 (2019)
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A primer on Script Geometry, Cerejeiras, P.卡勒，美国.莫滕斯，T.索曼，F.瓦加克，A.，刘建平，刘建平.org/abs/1911.07102.
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Gleason's Problem Associated to a Real Ternary Algebra and :ications, D. Alpay,. Vajiac, M.B. 公元瓦家. :. Clifford代数(2018)28:43
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Norms and Moduli on Multicomplex Spaces, M.B. Vajiac, in Clifford Analysis and Related Topics, In Honor of Paul A. M. Dirac, CART 2014, Tallahassee, Florida, Springer, 2018