Grahl, Jürgen

Mathematics

• Blow-up solutions of Liouville's equation and quasi-normality
  (with Daniela Kraus and Oliver Roth)
  Comput. Meth. Funct. Theory 20 (2020), 677-692

  ---

• Oscillating functions that disprove misconceptions on real-valued functions
  (with Shahar Nevo)
  Mathematics Magazine 92 (2019), 47-57

  ---

• On the growth of real functions and their derivatives
  (with Shahar Nevo)
  Real Anal. Exch. 43 (2018), 333-346

  ---

• Differential inequalities and a Marty-type criterion for quasi-normality
  (with Tomer Manket and Shahar Nevo)
  J. Austr. Math. Soc. 105 (2018), 34-45

  ---

• Quasi-normality induced by differential inequalities
  (with Shahar Nevo)
  Bull. Lond. Math. Soc. 50 (2018), 73-84

  ---

• Differential inequalities and quasi-normal families
  (with Roi Bar and Shahar Nevo)
  Anal. Math. Phys. 4 (2014), 63-71

  ---

• Exceptional functions wandering on the sphere and normal families
  (with Shahar Nevo)
  Isr. J. Math. 202 (2014), 21-34

  ---

• An extension of one direction in Marty's normality criterion
  (with Shahar Nevo)
  Monatsh. Math. 174 (2014), 205-217

  ---

• On Riemann's theorem about conditionally convergent series
  (with Shahar Nevo)
  N. Z. J. Math. 43 (2014), 85-93

  ---

• A non-explicit counterexample to a problem of quasi-normality
  (with Shahar Nevo and Xuecheng Pang)
  J. Math. Anal. Appl. 406 (2013), 386-391

  ---

• On a result of Bergweiler and Eremenko concerning derivatives bounded on preimages of unbounded sets
  Comput. Methods Funct. Theory 13 (2013), 181-187

  ---

• Spherical derivatives and normal families
  (with Shahar Nevo)
  J. d'Anal. Math. 117 (2012), 119-128

  ---

• A normality criterion involving rotations and dilations in the argument
  Arkiv Math. 50 (2012), 89-110

  ---

• Differential polynomials and shared values
  (with Shahar Nevo)
  Ann. Acad. Sci. Fenn. Math. 36 (2011), 47-70

  ---

• Differential polynomials with dilations in the argument and normal families,
  Monatsh. Math. 162 (2011), 429-452

  ---

• Uniqueness theorems for L-functions
  (with Ramunas Garunkštis and Jörn Steuding)
  Comment. Math. Univ. St. Pauli 60 (2011), 15-35

  ---

• Differential polynomials which share a value with their derivative and normal families
  Analysis 31 (2011), 67-80

  ---

• On a result of Singh and Singh concerning shared values and normality
  (with Shahar Nevo),
  Compl. Var. Elliptic Equ. 55 (2010), 347-356

  ---

• A modification of the Nevanlinna theory
  Comput. Methods Funct. Theory10 (2010), 97-109.

  ---

• An extension of Lewis's lemma, renormalization of harmonic and analytic functions and normal families
  (with Oliver Roth)
  Math. Nachr. 282 (2009), 540-551

  ---

• Some new results on the semiduality of small sets of analytic functions,
  Analysis 29 (2009), 71-80

  ---

• Entire functions sharing a polynomial with their derivatives and normal families
  (with Chao Meng)
  Analysis 28 (2008), 51-61

  ---

• An addition to the Tumura-Clunie theorem
  Result. Math. 52 (2008), 55-61

  ---

• A short proof of Miranda's theorem and some extensions using Zalcman's lemma,
  J. Anal. 11 (2003), 105-113

  ---

   

• On the construction of semidual gap structures,
  Analysis 23 (2003), 185-198

  ---

• Hayman's alternative and normal families of nonvanishing meromorphic functions
  Comput. Methods Funct. Theory 2 (2002), 481-508.

  ---

• Semiduality of small sets of analytic functions
  Comput. Methods Funct. Theory 2 (2002), 113-135.

  ---

• An extension of a normality result of D. Drasin and H. Chen & X. Hua for analytic functions
  Comput. Methods Funct. Theory1 (2001), 457-478.­

  ---

• Some applications of Cartan's theorem to normality and semiduality of gap power series,
  J. d'Anal. Math. 82 (2000), 207-220

  Economy and Ecology

• Physics, Welfare Optimization, Russian Gas, and Climate Change: Questions to Economics
  (with Reiner Kümmel and Dietmar Lindenberger),
  preprint (April 2023)

  ---

• Vom ökonomischen Gewicht der Energie. Anmerkungen zur aktuellen Energiekrise aus wirtschaftstheoretischer Sicht
  (with Reiner Kümmel and Dietmar Lindenberger),
  Zeitschrift für Energiewirtschaft 4/2022

  ---

• What if calculations of the economic effects for Germany of a stop of energy imports from Russia are misled by the neoclassical cost-share theorem?
  (with Reiner Kümmel and Dietmar Lindenberger),
  preprint (June 2022)

  ---

• Zehn fragwürdige Dogmen und Paradigmen der traditionellen Ökonomie (Ten disputable dogmata and paradigms of standard economy)
  Jahrbuch Nachhaltige Ökonomie 2013/2014, ed.: H. Rogall et al., Metropolis, Marburg 2013, 135-154

  ---

• Das Loch im Fass - Energiesklaven, Arbeitsplätze und die Milderung des Wachstumszwangs (The hole in the bucket - energy slaves, jobs and the mitigation of the need to grow)
  (with Reiner Kümmel),
  Nachhaltiges Wachstum: Wissenschaft und Umwelt Interdisziplinär 13 (2009), 195-212

  ---

• Von Wachstum und Wachstumszwang (About growth and the force to grow)
  (with Stefan Brunnhuber)
  GAIA 16/3 (2007), 176-177

  ---

• Jenseits des Wachstumszwangs. Zum Verhältnis von Energie, Kapital und Arbeit (Beyond the need to grow)
  (with Stefan Brunnhuber)
  GAIA 15/2 (2006), 96-101

  Preprints

• Estimates for probabilities of independent events and infinite series (with Shahar Nevo)