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TU Berlin

Inhalt des Dokuments

Dr. Philipp J. di Dio

Forschungsinteressen

  • Momentenproblem

    • abgeschnittenes und volles Momtenproblem
    • klassisch (über Polynomen) sowie messbaren Funktionen
    • Verbindungen zu anderen Gebieten (reelle algebraischen Geometrie, Optimierung, Wahrscheinlichkeitstheorie, etc.)

  • Molekulardynamik Simulationen und deren Analysen

    • Kraftfeld- und ab initio-Simulationen
    • temperaturabhängige Analysen (RDFs, SDFs, CDFs, etc.)

Paper

[10]  P. J. di Dio:
        The multidimensional truncated Moment Problem: Gaussian and
        Log-Normal Mixtures, their Carathéodory Numbers, and Set of Atoms
       
Proc. Am. Math. Soc. 147 (2019), 3021-3038   arXiv:1804.07058

[9]   P. J. di Dio, K. Schmüdgen:
       The multidimensional truncated Moment Problem: Atoms, Determinacy,
       and Core Variety
      
J. Funct. Anal. 2018, 274, 3124–3148   arXiv:1703.01497

[8]  P. J. di Dio, K. Schmüdgen:
      The multidimensional truncated Moment Problem: Carathéodory Numbers
     
J. Math. Anal. Appl. 2018, 461, 1606–1638   arXiv:1703.01494

[7]  K. Schmüdgen, P. J. di Dio:
      Truncated Moment Problem: Set of Atoms and Carathéodory Numbers
      Oberwolfach Reports 2017, 14, 847–849

[6]  P. J. di Dio:
      Thermal Stability of Water up to Super-Critical States: Application
     
of the Singular Value Decomposition and Grund Functions
      J. Mol. Liq. 2013, 187, 206–217

[5]  B. Kirchner, P. J. di Dio, J. Hutter:
      Real-World Predictions from Ab Initio Molecular Dynamics Simulations
     
Top. Curr. Chem. 2012, 307, 109–154

[4]  P. J. di Dio, M. Brüssel, K. Muñiz, R. S. Ray, S. Zahn, B. Kirchner:
      Pd-N to Pd-O Rearrangement for a Carbamate Synthesis from Carbon
      Dioxide and Methane: A Density Functional and Ab Initio Molecular
      Dynamics Metadynamics Study
     
Angew. Chemie (DFG-Spezialausgabe) 2011, 50(37), A40–A45

[3]  P. J. di Dio, M. Brehm, B. Kirchner:
      Singular Value Decomposition for Analyzing Temperature- and
      Pressure-Dependent Radial Distribution Functions: Decomposition
      into Grund RDFs (GRDFs)
     
J. Chem. Theory Comput. 2011, 7(10), 3035–3040

[2]  M. Brüssel, P. J. di Dio, K. Muñiz, B. Kirchner:
      Comparison of Free Energy Surfaces Calculations from Ab Initio
      Molecular Dynamic Simulations at the Example of Two Transition
      Metal Catalyzed Reactions
     
Int. J. Mol. Sci. 2011, 12(2), 1389–1409

[1]  P. J. di Dio, S. Zahn, C. B. W. Stark, B. Kirchner:
      Understanding Selectivities in Ligand-free Oxidative Cyclizations
      of 1,5- and 1,6-Dienes with RuO4 from Density Functional Theory
     
Z. Naturforsch. 2010, 65b, 367–375

Dissertation (PhD-Thesis)

Philipp J. di Dio: The Truncated Moment Problem (Abstract), Dissertation, Universität Leipzig, 2018

Preprints (arXiv)

[4]  P. J. di Dio:
      The multidimensional truncated Moment Problem: Shape and Gaussian Mixture
      Reconstruction from Derivatives of Moments (*)
      arXiv:1907.00790

[3]  P. J. di Dio, M. Kummer:
      The multidimensional truncated Moment Problem: Carathéodory Numbers from
      Hilbert Functions (*)
      arXiv:1903.00598

[2]  P. J. di Dio, K. Schmüdgen:
      The multidimensional truncated Moment Problem: The Moment Cone
      arXiv:1809.00584

[1]  P. J. di Dio:
      Weyl Circles for one-dimensional Moment Problems
      arXiv:1506.06589

(*) In the first version of [3] (arXiv:1903.00598v1: Carathéodory Numbers from Hilbert Functions and Shape Reconstruction from Derivatives of Moments) the papers [3] and [4] were combined. While working on the Gaussian Mixtures and Derivatives of Moments part it became so large and independent that we decided for a better reading and presentation of the results to split it into two papers.

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