CURRICULUM VITAE M.Sc., University of Bucharest, Romania. Advisor: Martin Jurchescu. Thesis title: Analytic Mappings of Constant Norm.

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1 CURRICULUM VITAE Name Born Mailing Address Nicolae Anghel April 8, 1954 in Văleni de Munte, Romania Department of Mathematics University of North Texas 1155 Union Circle, # Denton, TX Education in Mathematics 1989 Ph.D., Ohio State University, Columbus, OH. Advisor: Henri Moscovici. Dissertation title: L 2 -Index Theorems for Perturbed Dirac Operators M.Sc., University of Bucharest, Romania. Advisor: Martin Jurchescu. Thesis title: Analytic Mappings of Constant Norm B.Sc., University of Bucharest. Employment History Associate Professor, Department of Mathematics, University of North Texas, Denton, TX Assistant Professor, Department of Mathematics, University of North Texas, Denton, TX Graduate Teaching Assistant/Lecturer, Department of Mathematics, Ohio State University, Columbus, OH High School Mathematics Teacher, Bucharest, Romania. Areas of Expertise and Interest Geometric Analysis, Differential Geometry, Mathematical Physics, Complex Analysis of One and Several Variables, Math Education. Publications [01] A Generalization of Problem O.59, (Romanian), Gaz. Mat. 85, No. 5 (1980), Typeset by AMS-TEX

2 [02] A Direct Proof of the Fact that L 1 (X, B, µ) Satisfies the Strong Maximum Modulus Principle, (Romanian), Bull. Inst. Politehn. Bucureşti, Ser. Electroteh. 42, No. 1 (1980), [03] Mixed Grassmann Manifolds, (Romanian), Stud. Cerc. Mat. 34, No. 5 (1982), [04] The Levi Problem on Mixed Manifolds, Rend. Mat. (7) 4, No. 2 (1984), [05] Remark on Callias Index Theorem, Rep. Math. Phys. 28, No 3 (1989), 1-6. [06] L 2 - Index Formulae for Perturbed Dirac Operators, Commun. Math. Phys. 128, No 1 (1990), [07] The Two-Dimensional Magnetic Field Problem Revisited, J. Math. Phys. 31, (9) (1990), [08] Extrinsic Upper Bounds for Eigenvalues of Dirac-Type Operators, Proc. Amer. Math. Soc. 117, No. 2 (1993), [09] An Abstract Index Theorem on Non-Compact Riemannian Manifolds, Houston J. Math. 19, No. 2 (1993), [10] On the Index of Callias-Type Operators, Geom. Funct. Anal. 3, No. 5 (1993), [11] Index Theory for Short-Ranged Fields in Higher Dimensions, J. Funct. Anal. 119 (1994), [12] A Note on a Local Chern Character on the Circle, Manuscripta Math. 85 (1994), [13] A Multiple Sum Proposed Problem No , Amer. Math. Monthly 103, No. 5 (1996), 426; An Iterated Sum Solution to Problem No , Amer. Math. Monthly 105, No. 7 (1998), 676. [14] Generic Vanishing for Harmonic Spinors of Twisted Dirac Operators, Proc. Amer. Math. Soc. 124, No. 11 (1996), [15] On the Constructibility with Ruler and Compass of a Minimum Chord in a Parabola, Libertas Math. XVII (1997), [16] SL 2 Polynomial Invariance, Rev. Roumaine Math. Pures Appl. 43, No. 1-2 (1998), [17] Geometric Loci Associated to Certain Minimal Chords in Convex Regions, J. Geom. 66 (1999), 1-16.

3 [18] Clifford Matrices and a Problem of Hurwitz, Linear and Multlinear Algebra 47 (2000), [19] On the First Vafa-Witten Bound for Two-Dimensional Tori, Séminaires et Congrès 4, SMF (2000), [20] On Bär s Conformal Lower Bound for the Spectrum of Generalized Dirac Operators, Analele Univ. Buc. XLIX (2000), [21] On a Geometric Locus Problem of A. Dafina, (Romanian), Gaz. Mat. CVII, No. 12, (2003), [22] On Morley s Miracle Theorem, Libertas Math., XXIV (2004), [23] Minimal Chords in Angular Regions, Forum Geom., 4 (2004), [24] On Power Series and Summation, (Romanian), Gaz. Mat. A, XXII (C1), Nr. 4 (2004), [25] On Newton s Sums of Like-Powers, (Romanian), Axioma, V, Nr. 13 (2005), 4-7. [26] The L 2 -Harmonic Forms on Rotationally Symmetric Riemannian Manifolds Revisited, Proc. Amer. Math. Soc. 133, No. 8 (2005), [27] The Essential Uniqueness of the Connes-Morley Theorem, Libertas Math., XXVI (2006), [28] Projecting on Polynomial Dirac Spinors, Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, Softex Sofia (2007), [29] On the Structure of Finite Abelian Groups, (Romanian), Gazeta Mat. A, XXV (CIV) No. 2 (2007), [30] Projecting on Polynomial Solutions of Second Order Partial Differential Operators, Proc. Conference RIGA 2007, Bull. Transilvania Univ. Brasov, No. 14(49)s (2007), [31] An Extremal Integral Proposed Problem No , Amer. Math. Monthly 115, No. 5 (2008), 462; Supremum of a Nonlinear Functional Solution to Problem No , Amer. Math. Monthly 117, No. 3 (2010), [32] A Maximal Parallelogram Characterization of Ovals Having Circles as Orthoptic Curves, Forum Geom. 10, (2010), [33] A Triangle Inequality with Fermat-Torricelli-Erdös-Mordell Flavor Proposed Problem No , Amer. Math. Monthly 117, No. 3 (2010), 278;

4 A Weighted Fermat Triangle Problem Solution to Problem No , Amer. Math. Monthly 119, No. 3 (2012), [34] The Stieltjes-Calogero-Gil Relations Associated to Entire Functions of Finite Order, J. Math. Phys. 51, No. 5 (2010), , 9 pp. [35] On a Question of Connes and Zagier Regarding Parallelograms Inscribed in a Pair of Confocal Ellipses, Amer. Math. Monthly 117, No. 9 (2010), [36] On the Exact Solution of Certain Generic Nonlinear Polynomial Systems with Cyclic Symmetry, Annals Univ. Bucharest, 2(LX), No. 2 (2011), [37] An Elementary Characterization of the Orders of Non-Abelian Groups, Gazeta Mat. A, XXVIV(CVIII), No. 3-4 (2011), [38] On a Class of Magnetic Schrödinger Operators with Discrete Spectrum, Proc. Amer. Math. Soc., 140, No. 5 (2012), [39] Entire Functions of Finite Order as Solutions to Certain Complex Linear Differential Equations, Proc. Amer. Math. Soc., 140, No. 7 (2012), [40] Realization of the Stieltjes Sums via the Elementary Symmetric Sums, (Romanian), Gazeta Mat. B, CXVII, No. 2 (2012), [41] Magnetic Schrödinger Operators with Discrete Spectra on Non-Compact Kähler Manifolds, Proc. 10th Int. Workshop Diff. Geom. Appl., An. St. Univ. Ovidius Constanta, XX, No. 2 (2012), [42] A Generalization of the Three-Circle Problem, (Romanian), Gazeta Mat. B, CXVII, No. 11 (2012), [43] On the Centrally Symmetric Ovals Circumscribing Invariant Maximal Quadrilaterals, Note di Matem., 32, No. 2 (2012), [44] Two Limits Proposed Problem No , Amer. Math. Monthly, 120, No. 7 (2013), 660; A Limit with Integrals Solution to Problem No , Amer. Math. Monthly 122, No. 5 (2015), [45] On a Class of Stieltjes Van Vleck Polynomials, Advances in Math., Romanian Academy (2013), [46] On a Family of Iterated Integrals, Gazeta Mat. B, CXVIII, No. 2 (2013), [47] On the Spectrum of Spherical Dirac-Type Operators, Rocky Mountain J. Math., 43, No. 6 (2013),

5 [48] Square Roots of Real 2 2 Matrices, Gazeta Mat. B, CXVIII, No. 11 (2013), [49] Maximum of a Function, Rec. Mat. Iasi, XVI, No. 1 (2014), [50] Determinant Identities and the Geometry of Lines and Circles, An. St. Univ. Ovidius Constanta, 22, No. 2 (2014), [51] An Inductive Proof of the Cayley-Hamilton Theorem, Rec. Mat. Iasi, XVI, No. 2 (2014), [52] On the Erdős-Mordell Center and Constant, Revue Roumaine Math. Pures Appl. LIX, No. 4 (2014), [53] A Multiple Sum and the Riemann Zeta Function, Gazeta Mat. A, XXXIII (CXII), No. 1-2 (2015), [54] Optimal Bounds for the Roots of Quadratic Equations, Gazeta Mat. B, CXX, No. 12 (2015), [55] Fredholmness vs. Spectral Discreteness for First-Order Differential Operators, Proc. Amer. Math. Soc. 144, (2016), [56] Curvature Bundle Morphisms for Hypersurface Generalized Dirac Operators, Houston J. Math. 42, (2016), [57] On a 2015 Putnam Problem, Gazeta Mat. B, CXXI, No. 3 (2016), [58] Food for Thought, Rec. Mat. Iasi XVIII, No. 1 (2016), [59] Optimal Bounds for the Roots of Polynomials, Amer. Math. Monthly, 123, No. 9, (2016), [60] Concurrency and Collinearity in Hexagons, J. Geom. Graphics, 20, No. 2, (2016), [61] On a 2015 Putnam Problem Related to a Double Recursion, Amer. Math. Monthly, 124, No. 1, (2017), [62] Polynomial Harmonic Decompositions, An. St. Univ. Ovidius Constanta (2017) (to appear). [63] Square Roots of 3X3 Real Matrices vs. Quartic Polynomials with Real Zeros, An. St. Univ. Ovidius Constanta (2017) (to appear). [64] Addendum to Concurrency and Collinearity in Hexagons, J. Geom. Graphics (2017) (to appear). [65] Foias Numbers, (submitted) (2016).

6 [66] Non-Compact Riemannian Manifolds with Pure-Point Spectrum, (in preparation) (2017). [67] Projecting on Polynomial Solutions of Homogeneous Elliptic Systems with Constant Coefficients, (in preparation) (2017). [68] Inverse Spectral Problems, (in preparation) (2017).