Publications of Michael Oberguggenberger

Books, Articles, Contributions to Proceedings, Preprints

Books

    Monographs

  1. Der Graphensatz in lokalkonvexen topologischen Vektorräumen. Teubner-Texte Math. Bd. 44, Teubner, Leipzig 1982.
  2. Multiplication of Distributions and Applications to Partial Differential Equations. Pitman Research Notes Math. Vol. 259, Longman, Harlow 1992.
  3. with E. E. Rosinger. Solution of Continuous Nonlinear PDEs through Order Completion. North-Holland Math. Studies Vol. 181, North-Holland, Amsterdam 1994.
  4. with M. Grosser, M. Kunzinger, R. Steinbauer. Geometric Theory of Generalized Functions with Applications to General Relativity. Mathematics and its Applications Vol. 537, KluwerAcad. Publ., Dordrecht 2001.
  5. with A. Ostermann. Analysis für Informatiker. Springer-Verlag, Berlin  2005. 2nd Ed. 2009.
  6. with A. Ostermann. Analysis für Informatiker. 2nd Ed., Springer-Verlag, Berlin 2009.
  7. with A. Ostermann. Analysis for Computer Scientists. Foundations, Methods, and Algorithms. Springer-Verlag, London 2011.
  8. with A. Ostermann. Analysis for Computer Scientists. Foundations, Methods, and Algorithms. 2nd Ed., Springer Nature Switzerland 2018.

    Edited Books/Proceedings

  1. with M. Grosser, G. Hörmann, M. Kunzinger (Eds.). Nonlinear Theory of Generalized Functions. Chapman & Hall/CRC Research Notes Math. Vol. 401, Boca Raton 1999.
  2. with W. Fellin, H. Lessmann and R. Vieider (Eds.). Analyzing Uncertainty in Civil Engineering. Springer-Verlag, Berlin 2005.
  3. with A. Kamiński and S. Pilipović (Eds.). Linear and Non-Linear Theory of Generalized Functions and its Applications. Banach Center Publications, Vol. 88, Warszawa 2010.
  4. with F. Coolen, G. de Cooman and T. Fetz (Eds.). Proceedings of the Seventh International Symposium on Imprecise Probability: Theories and Applications. SIPTA, Studia Verlag, Innsbruck 2011.
  5. with J. Toft, J. Vindas, P. Wahlberg (Eds.). Generalized Functions and Fourier Analysis. Operator Theory: Advances and Applications Vol. 260. Birkhäuser, Cham 2017

    Edited Special Issues

  1. with G. I. Schuëller and K. Marti (Eds.). Special Issue on  Fuzzy Sets, Imprecise Probability and Stochastics in Engineering. ZAMM  84, No. 10-11, 2004.
  2. with A. Kamiński and S. Pilipović (Eds). Special Issue, Proceedings of the Conference: Linear and Non-Linear Theory of Generalized Functions and its Applications, held in Bedlewo, Poland, 2-8 September 2007. Inegral Transforms and Special Functions 20, No. 3-4, 2009.
  3. with F. Coolen and M. Troffaes (Eds.). Special Issue on Uncertainty in Engineering Risk and Reliability. Proceedings of the Institute of Mechanical Engineers Part O: Journal of Risk and Reliability 224, No. 4, 2010.
  4. with G. Hörmann and M. W. Wong, Special Issue on Generalized Functions and Applications. Applicable Analysis 90, No. 11, 2011.
  5. with F. Coolen, Th. Fetz, S. Moral, Special Issue "Imprecise Probability: Theories and Applications (ISIPTA'11)", International Journal of Approximate Reasoning 53, No. 8, 1107-1302, 2012.
  6. with W. A. Lodwick. Special Issue "Differential Equations Over Fuzzy Spaces - Theory, Applications, and Algorithms", Fuzzy Sets and Systems 230, 1-162, 2013.

Articles

  1. A note on surjections of locally convex spaces. Math. Ann. 267 (1984), 549 - 554.
  2. Über Folgenkonvergenz in lokalkonvexen Räumen. Math. Nachr. 129 (1986), 219 - 234.
  3. Products of distributions. J. reine angew. Math. 365 (1986), 1 - 11.
  4. Multiplication of distributions in the Colombeau algebra G(W). Boll. Un. Mat. Ital. (6) 5-A (1986), 423 - 429.
  5. Weak limits of solutions to semilinear hyperbolic systems. Math. Ann. 274 (1986), 599 - 607.
  6. Propagation of singularities for semilinear hyperbolic initial-boundary value problems in one space dimension. J. Diff. Eqs. 61 (1986), 1 - 39.
  7. Propagation and reflection of regularity for semilinear hyperbolic (2x2) systems in one space dimension. Nonlinear Anal. 10 (1986), 965 - 981.
  8. Generalized solutions to semilinear hyperbolic systems. Monatshefte Math. 103 (1987), 133 - 144.
  9. Solutions généralisées de systèmes hyperboliques semilinéaires. C. R. Acad. Sci. Paris, Sér. I, 305 (1987), 17 - 18.
  10. Products of distributions: Nonstandard methods. Zeitschr. Anal. Anw. 7 (1988), 347 - 365. Correction: Zeitschr. Anal. Anw. 10 (1992), 263 - 264.
  11. Systèmes hyperboliques à coefficients discontinus: solutions généralisées et une application à l'acoustique linéaire. C. R. Math. Rep. Acad. Sci. Canada 10 (1988), 143 - 148.
  12. Hyperbolic systems with discontinuous coefficients: Generalized solutions and a transmission problem in acoustics. J. Math. Anal. Appl. 142 (1989), 452 - 467.
  13. with J. F. Colombeau. On a hyperbolic system with a compatible quadratic term: Generalized solutions, delta waves, and multiplication of distributions. Comm. Part. Diff. Eqs. 15 (1990), 905 - 938.
  14. with F. Lafon. Generalized solutions to symmetric hyperbolic systems with discontinuous coefficients: the multidimensional case. J. Math. Anal. Appl. 160 (1991), 93 - 106.
  15. The Carleman system with positive measures as initial data. Transport Theory Statist. Phys. 20 (1991), 177 - 197.
  16. with H.G. Embacher and G. Grübl. Products of distributions in several variables and applications to zero-mass QED2. Zeitschr. Anal. Anw. 11 (1992), 437 - 454.
  17. with H. A. Biagioni. Generalized solutions to Burgers' equation. J. Diff. Eqs. 97 (1992), 263 - 287.
  18. with H. A. Biagioni. Generalized solutions to the Korteweg - de Vries and the regularized long-wave equations. SIAM J. Math. Anal. 23 (1992), 923 - 940.
  19. Case study of a nonlinear, nonconservative, non-strictly hyperbolic system. Nonlinear Anal. 19 (1992), 53 - 79.
  20. with J. F. Colombeau and A. Heibig. Le problème de Cauchy dans un espace de fonctions généralisées I. C. R. Acad. Sci. Paris, Sér. I, 317 (1993), 851 - 855.
  21. with W. Netzer and O. Pregl. The horizontal bedding of flexible buried pipelines in variable bedding areas. 3R international 32 (1993), 101 - 106.
  22. with Y.-G. Wang. Generalized solutions to conservation laws. Zeitschr. Anal. Anw. 13 (1994), 7 - 18.
  23. with Y.-G. Wang. Reflection of delta-waves for nonlinear wave equations in one space variable. Nonlinear Anal. 22 (1994), 983 - 992.
  24. with Y.-G. Wang. Delta-waves for semilinear hyperbolic Cauchy problems. Math. Nachr. 166 (1994), 317 - 327.
  25. with H. Lessmann and J. Mühlögger. Netzplantechnik mit unscharfen Methoden. Der Bauingenieur 69 (1994), 469 - 478.
  26. with J. F. Colombeau and A. Heibig. Le problème de Cauchy dans un espace de fonctions généralisées II. C. R. Acad. Sci. Paris, Sér.I, 319 (1994), 1179 - 1183.
  27. with J. F. Colombeau and A. Heibig. Generalized solutions to partial differential equations of evolution type. Acta Appl. Math. 45 (1996), 115 - 142.
  28. with Th. Fetz, M. Hofmeister, G. Hunger, J. Jäger, H. Lessmann, A. Rieser, R.F. Stark. Tunnelberechnung - Fuzzy? Der Bauingenieur 72 (1997), 33 - 40.
  29. with T. Todorov. An embedding of Schwartz distributions in the algebra of asymptotic functions. Int. J. Math. Math. Sci. 21 (1998), 417 - 428.
  30. with F. Russo. Nonlinear stochastic wave equations. Integral Transforms and Special Functions 6 (1998), 71 - 83.
  31. with Th. Fetz, J. Jäger, D. Köll, G. Krenn, H. Lessmann, R.F. Stark. Fuzzy models in geotechnical engineering and construction management. Computer-Aided Civil and Infrastructure Engineering 14 (1999), 93 - 106.
  32. with Y.-G. Wang. Regularized conservation laws and nonlinear geometric optics. Monatshefte Math. 127(1999), 55 - 66.
  33. with Y.-G. Wang. Nonlinear parabolic equations with regularized derivatives. J. Math. Anal. Appl. 233(1999), 644 - 658.
  34. with M. Kunzinger. Characterization of Colombeau generalized functions by their pointvalues. Math. Nachr 203 (1999), 147 - 157.
  35. with S. Pittschmann. Differential equations with fuzzy parameters. Math. and Computer Modelling of Dynamical Systems 5(1999), 181 - 202.
  36. with M. Kunzinger. Group analysis of differential equations and generalized functions. SIAM J. Math. Anal. 31(2000), 1192 - 1213.
  37. with Th. Fetz, S. Pittschmann. Applications of possibility and evidence theory in civil engineering. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8(2000), 295 - 309.
  38. with H. Grosse, I.T. Todorov. Generalized functions for quantum fields obeying quadratic exchange relations. Proc. Steklov Inst. Math. 228(2000), 81 - 91.
  39. with Y.-G. Wang. Semilinear geometric optics for generalized solutions. Zeitschr. Anal. Anw. 19(2000), 913 - 926.
  40. Generalized functions in nonlinear models - a survey. Nonlinear Analysis 47/8(2001), 5029 - 5040.
  41. with S. Pilipovic and D. Scarpalézos. Local properties of Colombeau generalized functions. Math. Nachrichten 256(2003), 88 - 99.
  42. with M. Kunzinger, R. Steinbauer and J. A. Vickers. Generalized flows and singular ODEs on differentiable manifolds. Acta Appl. Math., 80(2004), 221 - 241.
  43. with G. Hörmann. Elliptic regularity and solvability for partial differential equations with Colombeau coefficients. Electron. J. Diff. Eqns., 2004(2004), No. 14, pp. 1 - 30.
  44. with Th. Fetz. Propagation of uncertainty through multivariate functions in the framework of sets of probability measures. Reliability Engineering and Systems Safety 85(2004), 73 - 87.
  45. Generalized solutions to nonlinear wave equations. Matemática Contemporânea 27(2004), 169 - 187.
  46. with M. Nedeljkov and S. Pilipović. Generalized solutions to a semilinear wave equation. Nonlinear Analysis 61(2005), 461 - 475.
  47. with G. Hörmann and S. Pilipović. Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients. Trans. Am. Math. Soc. 358(2006), 3363 - 3383.
  48. with D. Rajter. Stochastic differential equations driven by generalized positive noise. Publ. Inst. Math. Beograd 77(91) (2005), 7 - 19.
  49. with C. Garetto and T. Gramchev. Pseudodifferential operators with generalized symbols and regularity theory. Electron. J. Diff. Eqns. 2005(2005), No. 116, pp. 1 - 43.
  50. Regularity theory in Colombeau algebras.  Bull. T. CXXXIII Acad. Serbe Sci. Arts, Cl. Sci. Math. Nat., Sci. Math. 31(2006), 147 - 162.
  51. Notes on regularity results in Colombeau algebras. Integral Transforms and Special Functions 17(2006), 101 - 107.
  52. with S. Pilipović and D. Scarpalézos. Positivity and positive definiteness in generalized function algebras. J. Math. Anal. Appl. 328(2007), 1321 - 1335.
  53. with S. Pilipović and V. Valmorin. Global Representatives of Colombeau Holomorphic Generalized Functions. Monatshefte Math. 151(2007), 67 - 74.
  54. with W. Fellin. Reliability bounds through random sets: nonparametric methods and geotechnical applications. Computers & Structures 86(2008), 1093 - 1101.
  55. with H. Vernaeve. Internal sets and internal functions in Colombeau theory. J. Math. Anal. Appl. 341(2008), 649 - 659.
  56. with H. Schumacher. Die Determinierung der "überwiegenden Wahrscheinlichkeit" in der Fortbestehensprognose. Recht der Wirtschaft 3/2008, 187 - 191.
  57. with S. Konjik and M. Kunzinger. Foundations of the calculus of variations in generalized function algebras. Acta Appl. Math. 103(2008), 169 - 199. 
  58. with J.-A. Marti and A. Delcroix. Microlocal asymptotic analysis in algebras of generalized functions. Asymptotic Analysis 59(2008), 83 - 107.
  59. with C. Garetto and G. Hörmann. Generalized Oscillatory Integrals and Fourier Integral Operators. Proc. Edinburgh Math. Soc. 52(2009), 351 - 386.
  60. with M. De Hoop and G. Hörmann. Evolution systems for paraxial wave equations of Schrödinger-type with non-smooth coefficients. J. Diff. Eqs. 245(2008), 1413 - 1432.
  61. with M. Nedeljkov. Interactions of delta shock waves in a strictly hyperbolic system of conservation laws. J. Math. Anal. Appl. 344(2008), 1143 - 1157.
  62. with J. King and B. Schmelzer. Classical and imprecise probability methods for sensitivity analysis in engineering: A case study. International Journal of Approximate Reasoning 50(2009), 680 - 693.
  63. with J. Aleksić, J.-F. Colombeau and S. Pilipović. Approximate generalized solutions and measure-valued solutions to conservation laws. Integral Transforms and Special Functions 20(3-4)(2009), 161 - 170.
  64. with W. Fellin, J. King and A. Kirsch, Uncertainty modelling and sensitivity analysis of tunnel face stability. Structural Safety 32(2010), 402 - 410.
  65. with Th. Fetz, Multivariate Models of Uncertainty: A Local Random Set Approach. Structural Safety 32(2010), 417 - 424.
  66. with. B. Schmelzer and C. Adam, Efficiency of Tuned Mass Dampers with Uncertain Parameters on the Performance of Structures under Stochastic Excitation. Journal of Risk and Reliability 224(4)(2010), 297 - 308.  
  67. with M. Husty, G. Netzer, A. Ostermann, F. Pauer, Mathematik in Innsbruck. Internationale Mathematische Nachrichten 213(2010), 7 - 18.
  68. with J. Aragona, S.O. Juriaans, R. Fernandez, Differential calculus and integration of generalized functions over membranes. Monatshefte für Mathematik 166(2012), 1 - 18.
  69. with W. Fellin, Robust assessment of shear parameters from direct shear tests. Int. J. Reliability and Safety 6(2012), 49 - 64.
  70. with V. Kreinovich and G. Xiang, How to define a confidence set for functions: a new justification of the area method. Int. J. General Systems, 40(7)(2011), 727 - 739.
  71. with M. Nedeljkov, Ordinary differential equations with delta function terms. Publ. Inst. Math. Beograd 91(105)(2012), 125 - 135.
  72. with C. Garetto, Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients. Math. Nachrichten 288(2015), 185 - 205. DOI 10.1002/mana.201400192.
  73. with C. Garetto. Generalised Fourier integral operator methods for hyperbolic equations with singularities, Proc. Edinburgh Math. Soc. 57(2014), 423 - 463. 
  74. Analysis and computation with hybrid random set stochastic models. Structural Safety 52(2015), 233 - 243.
  75. with V. De Groof. Assessing random field models in finite element analysis: a case study. International Journal of Reliability and Safety 8(2/3/4) (2014), 117 - 134. 
  76. with S. Tsantaki, L. Wurzer, C. Jäger and C. Adam. Refined analytical collapse capacity spectra. Iranian Journal of Science & Technology, Transactions of Civil Engineering 39, C2(2015), 253 - 270.
  77. with H. Deguchi. Propagation of singularities for generalized solutions to wave equations with discontinuous coefficients. SIAM J. Math. Analysis 48(2016), 397 - 442.
  78. with S. Gamse. Assessment of long-term coordinate time series using hydrostatic-season-time model for rock-fill embankment dam, Structural Control and Health Monitoring 24:e1859(2017), DOI: 10.1002/stc.1859.
  79. with T. Fetz. Imprecise random variables, random sets, and Monte Carlo simulation. International Journal of Approximate Reasoning Reasoning 78(2016) 252 - 264.
  80. with R. Eberle, and D. Heinrich, P. Kaps and W. Nachbauer. Effect of ski boot rear stiffness (SBRS) on maximal ACL force during injury prone landing movements in alpine ski racing: A study with a musculoskeletal simulation model. Journal of Sports Sciences 35:12(2017), 1125 - 1133, DOI: 10.1080/02640414.2016.1211309.
  81. with M. Nedeljkov, L. Neumann, M. R. Sahoo. Radially symmetric shadow wave solutions to the system of pressureless gas dynamics in arbitrary dimensions. Nonlinear Analysis 163(2017) 104 - 126, doi.org/10.1016/j.na.2017.07.006.
  82. with S. Gamse, W.-H. Zhou, F. Tan, K.-V. Yuen. Hydrostatic-season-time model updating using Bayesian model class selection. Reliability Engineering and System Safety 169(2018) 40 - 50, doi.org/10.1016/j.ress.2017.07.018.
  83. with S. Gordić, S. Pilipović D. Seleši. Probabilistic properties of generalized stochastic processes in algebras of generalized functions. Monatshefte Math. 186(2018), 609 - 633, DOI 10.1007/s00605-017-1109-z, Postprint
  84. with R. Eberle, D. Heinrich, A.J. van den Bogert, W. Nachbauer. An approach to generate noncontact ACL-injury prone situations on a computer using kinematic data of non-injury situations and Monte Carlo simulation. Computer Methods in Biomechanics and Biomedical Engineering (2018), doi.org/10.1080/10255842.2018.1522534.
  85. with C. Adam, B. Hirzinger, P. Salcher. On computational interdisciplinary modeling for reliability assessment of high-speed train – bridge interaction. PAMM 18(2018), DOI 10.1002/pamm.201800047.
  86. with C. Ableitinger, H. Humenberger. Kurze Replik auf einen Aufsatz von R. Winkler: Zentralmatura in der Sackgasse? Internationale Mathematische Nachrichten 238 (2018), 23 - 31.
  87. with R. Eberle, P. Kaps. A multibody simulation study of alpine ski vibrations caused by random slope roughness. Journal of Sound and Vibration 446 (2019), 225-237, doi.org/10.1016/j.jsv.2019.01.035.
  88. with B. Hirzinger, C. Adam, P. Salcher. On the optimal strategy of stochastic-based reliability assessment of railway bridges for high-speed trains. Meccanica 54(2019), 1385 - 1402, doi.org/10.1007/s11012-019-00999-0.
  89. with B. Caillaud, R. Winkler,  M. Luger, J. Gerstmayr. Static model of a snowboard undergoing a carved turn: validation by full-scale test. Sports Engineering 22:15(2019), doi.org/10.1007/s12283-019-0307-4.
  90. Gilbert Helmberg 1928-2019. Internationale Mathematische Nachrichten 241(2019), 21 - 28.
  91. with L. Wurzer. Random Set Solutions to Stochastic Wave Equations. Proceedings of Machine Learning Research 103 (2019), 314–323, arXiv:1903.06543
  92. with R. Eberle. Vibrations of an alpine ski under structural randomness. PAMM 2019;19:e201900345, doi.org/10.1002/pamm.201900345.
  93. with S. Gordić, S. Pilipović D. Seleši. Generalized stochastic processes in algebras of generalized functions: Independence, stationarity and SPDEs. J. Math. Anal. Appl. 475(2019), 1196–1214 Postprint
  94. with S. Gamse, M. J. Henriques, J. T. Mata. Analysis of periodicities in long-term displacement time series in concrete dams. Struct. Control Health Monit. 2020;27:e2477, doi.org/10.1002/stc.2477.
  95. with B. Hirzinger, C. Adam, P. Salcher. Approaches for predicting the probability of failure of bridges subjected to high-speed trains. Probabilistic Engineering Mechanics 59 (2020), 103021.
  96. with J.-T. Fischer, A. Kofler, A. Huber, W. Fellin, M. Mergili. Bayesian Inference in Snow Avalanche Simulation with r.avaflow. Geosciences 2020, 10(5), 191, doi.org/10.3390/geosciences10050191.
  97. with H. Deguchi. Propagation of singularities for generalized solutions to nonlinear wave equations. Journal of Fixed Point Theory and Applications (2020) 22:67, https://doi.org/10.1007/s11784-020-00802-8
  98. with M. Schwarz. Deterministic and stochastic damage detection via dynamic response analysis. International Journal of Approximate Reasoning 126(2020), 70–83. https://doi.org/10.1016/j.ijar.2020.08.008
  99. with H. Dabhi, M. Rotach, M. Dubrovský. Evaluation of a stochastic weather generator in simulating univariate and multivariate climate extremes in different climate zones across Europe. Meteorologische Zeitschrift 30 (2021),127–151. DOI: 10.1127/metz/2020/1021
  100. with H. Deguchi, Regular generalized solutions to semilinear wave equations. Monatshefte für Mathematik 194 (2021), 67-84. https://doi.org/10.1007/s00605-020-01470-z
  101. with M. Schwarz, Wave propagation in random media, parameter estimation and damage detection via stochastic Fourier integral operators. Journal of Sound and Vibration, 513(2021), 116409. https://doi.org/10.1016/j.jsv.2021.116409
  102. with R. Eberle, A new method for estimating the bending stiffness curve of non-uniform Euler-Bernoulli beams using static deflection data. Applied Mathematical Modelling 105(2022), 514-533. https://doi.org/10.1016/j.apm.2021.12.042
  103. with L. Neumann, M. R. Sahoo, A. Sen, Initial-boundary value problem for 1D pressureless gas dynamics. Journal of Differential Equations 316(2022), 687-725. https://doi.org/10.1016/j.jde.2022.01.05
  104. Was ist und was soll Wahrscheinlichkeit? Schriftenreihe zur Didaktik der Mathematik der Österreichischen Mathematischen Gesellschaft (ÖMG), 53(2021), 89-106.
    https://www.oemg.ac.at//DK/Didaktikhefte/2021%20Band%2053/VortragOberguggenberger.pdf
  105. with J. Karakašević, Random set solutions to elliptic and hyperbolic partial differential equations. Probabilirtic Engineering Mechanics 69(2022), 103289. https://doi.org/10.1016/j.probengmech.2022.103289 
  106. with R. Eberle. Vibrations of a Bridge with Random Structural Irregularities Under Random Traffic Load and a Probabilistic Structural Degradation Assessment Approach. Journal of Vibration Engineering & Technologies (2022). https://doi.org/10.1007/s42417-022-00675-w

Contributions to Books and Proceedings

  1. Weak limits of solutions to semilinear hyperbolic systems. In: F. Colombini, M. K. V. Murthy (Eds.), Hyperbolic Equations. Pitman Research Notes Math. Vol. 158, Longman, Harlow 1987, 278 - 281.
  2. Hyperbolic systems with discontinuous coefficients: examples. In: B. Stankovic, E. Pap, S. Pilipovic, V. S. Vladimirov (Eds.), Generalized Functions, Convergence Structures, and Their Applications. Plenum Press, New York 1988, 257 - 266.
  3. Semilinear wave equations with rough initial data: generalized solutions. In: P. Antosik, A. Kaminski (Eds.), Generalized Functions and Convergence. World Sci. Publ., London 1990, 181 - 203.
  4. Nonlinear theories of generalized functions. In: S. Albeverio, W. A. J. Luxemburg, M. P. H. Wolff (Eds.), Advances in Analysis, Probability, and Mathematical Physics - Contributions from Nonstandard Analysis. Kluwer, Dordrecht 1994, 56 - 74.
  5. Generalized functions and stochastic processes. In: E. Bolthausen, M. Dozzi, F. Russo (Eds.), Seminar on Stochastic Analysis, Random Fields and Applications. Birkhäuser-Verlag, Basel 1995, 215 - 229.
  6. Contributions of Nonstandard Analysis to partial differential equations. In: N.J. Cutland, V. Neves, F. Oliveira, J. Sousa Pinto (Eds.), Developments in Nonstandard Mathematics. Pitman Research Notes Math. Vol. 336, Longman, Harlow 1995, 130 - 150.
  7. with M. Kunzinger. Symmetries of differential equations in Colombeau algebras. In: N.H. Ibragimov, F.M. Mahomed (Eds.), Modern Group Analysis VI. New Age Int. Publ., New Delhi 1997, 9 - 20.
  8. Fuzzy differential equations. In: I. Troch, F. Breitenecker (Eds.), Proceedings IMACS Symposium on Mathematical Modelling, Vienna 1997, ARGESIM Report 11 (1997), 75 - 80.
  9. with F. Russo. Nonlinear SPDEs: Colombeau solutions and pathwise limits. In: L. Decreusefond, J. Gjerde, B. Øksendal, A.S. Üstünel (Eds.), Stochastic Analysis and Related Topics VI.Birkhäuser, Boston 1998, 319 - 332.
  10. with R. Hermann. Ordinary differential equations and generalized functions. In: M. Grosser, G. Hörmann, M. Kunzinger, M. Oberguggenberger (Eds.), Nonlinear Theory of Generalized Functions. Chapman & Hall/CRC Research Notes Math. Vol. 401, Boca Raton 1999, 85 - 99.
  11. with F. Russo. White noise driven stochastic partial differential equations: triviality and non-triviality. In: M. Grosser, G. Hörmann, M. Kunzinger, M. Oberguggenberger (Eds.), Nonlinear Theory of Generalized Functions. Chapman & Hall/CRC Research Notes Math. Vol. 401, Boca Raton 1999, 315 - 333.
  12. with F. Russo. Singular limiting behavior in nonlinear stochastic wave equations. In: A. B. Cruzeiro, J.-C. Zambrini (Eds.), Stochastic Analysis and Mathematical Physics, Birkhäuser-Verlag, Basel 2001, 87 - 99.
  13. Generalized functions, nonlinear partial differential equations, and Lie groups. In: R. S. Pathak (Ed.), Geometry, Analysis and Applications. World Sci. Publ., Singapore 2001, 271 - 281.
  14. Symmetry Groups, Nonlinear Partial Differential Equations, and Generalized Functions. In: J. A. Leslie, T. P. Robart (Eds.), Geometrical Study of Differential Equations, AMS Contemp.Math. Vol. 285, Providence, Rhode Island 2001, 101 - 110.
  15. with F. Russo. Fuzzy, probabilistic and stochastic modelling of an elastically bedded beam. In: G. de Cooman, T. Fine, T. Seidenfeld (Eds.), ISIPTA '01, Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications. Shaker Publishing BV, Maastricht 2001, 293 - 300.
  16. Multiplication of distributions and generalized function algebras. Five items: Multiplication of distributions, Generalized function algebras, Colombeau generalized function algebras, Egorovgeneralized function algebra, Rosinger nowhere dense generalized function algebra. In: M. Hazewinkel (Ed.), Encyclopedia of Mathematics, Supplement III. Kluwer Acad. Publ., Dordrecht, 2001, pp. 106, 138, 173 - 174, 270 - 271, 337.
  17. with W. Fellin. From probability to fuzzy sets: the struggle for meaning in geotechnical risk assessment. In: R. Pöttler, H. Klapperich, H. F. Schweiger (Eds.), Probabilistics inGeoTechnics: Technical and Economic Risk Estimation. United Engineering Foundation, Verlag Glückauf GmbH, Essen, 2002, 29 - 38.
  18. Fuzzy data in geotechnical models. In: D. Kolymbas (Ed.), Advanced Mathematical and Computational Geomechanics. Springer, Berlin 2003, 301 - 315.
  19. with W. Fellin. Das Problem der Unsicherheit der Versagenswahrscheinlichkeit und mögliche Alternativen. In: M. Ziegler (Ed.), Beiträge zum Workshop Stochastische Prozesse in der Geotechnik. Schriftenreihe Geotechnik im Bauwesen, RWTH Aachen, Heft 1, 2003, 15 - 28.
  20. Rotationally invariant Colombeau generalized functions. In: A. Delcroix, M. Hasler, J.-A. Marti, V. Valmorin (Eds.), Nonlinear Algebraic Analysis and Applications, Proceedings of the International Conference on Generalized Functions (ICGF 2000). Cambridge Scientific Publ., Cottenham 2004, 227 - 236.
  21. Introductory remarks: mathematical models of uncertainty. In: Fuzzy Sets, Imprecise Probability and Stochastics in Engineering. ZAMM 84(2004), 661 - 665.
  22. with W. Fellin. The fuzziness and sensitivity of failure probabilities. In: W. Fellin, H. Lessmann, M. Oberguggenberger, R. Vieider (Eds.), Analyzing Uncertainty in Civil Engineering.Springer-Verlag, Berlin 2004, 33 - 49.
  23. The mathematics of uncertainty: models, methods and interpretations. In: W. Fellin, H. Lessmann, M. Oberguggenberger, R. Vieider (Eds.), Analyzing Uncertainty in Civil Engineering.Springer-Verlag, Berlin 2004, 51 - 72.
  24. Queueing models with fuzzy data in construction management. In: W. Fellin, H. Lessmann, M. Oberguggenberger, R. Vieider (Eds.), Analyzing Uncertainty in Civil Engineering. Springer-Verlag, Berlin 2004, 197 - 210.
  25. Fuzzy and weak solutions to differential equations. Proceedings of the Tenth International Conference IPMU 2004, Perugia. Editrice Università La Sapienza, Italy 2004, 517 - 524.
  26. with A. Tautschnig, R. Feik, M. Leitner and G. Dittrich. Systematik eines praxisgerechten Chancen-Gefahren-Managements. In: H. Lechner, C. Hofstadler, R. Nöstlthaller (Eds.), Baubetrieb- und Bauwirtschaft - Festschrift Prof. Gert Stadler. Verlag der Technischen Universität Graz, Graz 2004, 319 - 335.
  27. with W. Fellin. Assessing the sensitivity of failure probabilities: a random set approach. In: G. Augusti, G.I. Schuëller, M. Ciampoli (Eds.), Safety and Reliability of Engineering Systems and Structures. ICOSSAR 2005 - Rome. Millpress, Rotterdam 2005, 1755 - 1760.
  28. Mathematische Methoden im Risikomanagement. In: R. Feik, W. Gächter (Eds.), Neue Aspekte im projektbezogenen Risikomanagement aus der Sicht von Bauherren, Planern und Ausführenden. Schriftenreihe: Bauwirtschaft und Projektmanagement Nr. 13, Universität Innsbruck, Innsbruck 2006, 33 - 44.
  29. with J. King and B. Schmelzer. Imprecise probability methods for sensitivity analysis in engineering. In: G. de Cooman, J. Vejnarova, M. Zaffalon (Eds.), ISIPTA'07, Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications. Action M Agency, SIPTA, Prague 2007, 317 - 326.
  30. with A. Ostermann and C. Pfeifer. Damage detection of structures by analysing embedded time series of vibration signals. In: J. del Castillo, A. Espinal, P. Puig (Eds.), Proceedings of the 22nd International Workshop on Statistical Modelling. IDESCAT, Barcelona 2007, 504 - 507.
  31. with J. King and B. Schmelzer. Reliability of shell structures through sensitivity analysis. 1st CEAS European Air and Space Conference, Berlin 2007, CD ISSN 0700-408, 1823 - 1832.
  32. with B. Schmelzer and W. Fellin. Sensitivity analysis through random and fuzzy sets. 2008 NAFIPS Conference Proceedings, IEEE Catalog Number CFP08750-CDR, paper number 60606, 2008.
  33. Hyperbolic systems with discontinuous coefficients: generalized wavefront sets. In: L. Rodino, M. W. Wong (Eds.), New Developments in Pseudo-Differential Operators. Birkhäuser, Basel 2008, 117 - 136.
  34. Analyzing Uncertainty in Civil Engineering. In: A. Grmanova, M. Minarik (Eds.), 70 vears of FCE STU, Proceedings of the International Scientific Conference. Slovak University ofTechnology, Bratislava 2008, CD ISBN 978-80-227-2979-6.
  35. with J. King. Buckling and collapse of shell structures: sensitivity analysis. 2nd International Conference on Buckling and Postbuckling Behaviour of Composite Laminated Shell Structures.Braunschweig 2008. Conference Proceedings (CD), Abstract No. 45, COCOMAT Partners, DLR Braunschweig.
  36. with A. Ostermann. Damage Detection in Engineering Structures. In: A. Kendl, S. Schindler (Eds.), Introduction to Computer Science & Applied Computing. Innsbruck University Press, Innsbruck 2008, 55 - 56.
  37. with W. Fellin, J. King, A. Kirsch. Uncertainty modelling and sensitivity analysis of tunnel face stability. In: H. Furuta, D.M. Frangopol, M. Shinozuka (Eds.), Safety, Reliability and Risk of Structures, Infrastructures and Engineering Systems. Proceedings of ICOSSAR2009, CRC Press/Balkema, Leiden 2010, 1299 - 1306.
  38. with T. Fetz. Multivariate Models for Random Sets Generated by Non-parametric Methods. In: H. Furuta, D.M. Frangopol, M. Shinozuka (Eds.), Safety, Reliability and Risk of Structures, Infrastructures and Engineering Systems. Proceedings of ICOSSAR2009, CRC Press/Balkema, Leiden 2010, 1246 - 1253.
  39. with C. Aichinger, B. Caillaud, H. Haller, H. Roth. Simulation tools for assessing the reliability and the design of shell structures. CD-ROM. In: Conference Proceedings, 4th International Conference "Supply on the Wings", Frankfurt 2009. AIRTEC Frankfurt, Paper No. D13.
  40. with W. Fellin. Robust assessment of shear parameters in geotechnics. In: M. Beer, R.L. Muhanna, R.L. Mullen (Eds.), REC2010 - Proceedings of the 4th International Workshop on Reliable Engineering Computing. Research Publishing Services, Singapore 2010, 229 - 240.
  41. with B. Schmelzer and C. Adam, Set-valued processes induced by parametrised stochastic differential equations with an application to Tuned Mass Dampers. Proc. Appl. Math. Mech.11(2011), 705 - 706.
  42. Combined methods in nondeterministic mechanics. In: I. Elishakoff, C. Soize (Eds.), Nondeterministic Mechanics. CISM International Centre for Mechanical Sciences, Vol. 539. Springer, Wien 2012, 263 - 356.
  43. with V. De Groof, H. Haller, R. Degenhardt and A. Kling. Quantitative assessment of random field models in finite element buckling analyses of composite cylinders. In: J. Eberhardsteiner, H.J. Böhm, F.G. Rammerstorfer (Eds.), CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna University of Technology, Wien 2012, 14 pp.
  44. with B. Schmelzer and C. Adam. Seismic performance of Tuned Mass Dampers with uncertain parameters. In: J. Eberhardsteiner, H.J. Böhm, F.G. Rammerstorfer (Eds.), CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna University of Technology, Wien 2012, 19 pp.
  45. with S. Tsantaki, L. Wurzer, C. Jäger, and C. Adam. Refined collapse capacity spectra for predicting seismic collapse of structures vulnerable to the P-delta effect. In: J. Eberhardsteiner, H.J. Böhm, F.G. Rammerstorfer (Eds.), CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna University of Technology, Wien 2012, 17 pp.
  46. with H. Deguchi and Günther Hörmann. The wave equation with a discontinuous coefficient depending on time only: generalized solutions and propagation of singularities. In: S. Molahajlo, S. Pilipović, J. Toft, M.W. Wong (Eds.), Pseudo-Differential Operators, Generalized Functions and Asymptotics. Birkhäuser, Basel 2013, 323 - 340.
  47. with V. De Groof, M. Prackwieser and M. Schwarz. Reliability analysis of shell structures. In: M. Barden, A. Ostermann (Eds.), Scientific Computing @ uibk. Innsbruck University Press, Innsbruck 2013, 39 - 42.
  48. Analysis and computation with hybrid random set stochastic models. In: G. Deodatis, B. Ellingwood,D. Frangopol (Eds.), Safety, Reliability, Risk and Life-Cycle Performance of Structures & Infrastructures CRC Press, 2014, 383 - 390.
  49. with V. De Groof, H. Haller, R. Degenhardt and A. Kling. A case study of random field models applied to thinwalled composite cylinders in finite element analysis. In: G. Deodatis, B. Ellingwood, D. Frangopol (Eds.), Safety, Reliability, Risk and Life-Cycle Performance of Structures & Infrastructures, CRC Press, 2014, 2137 - 2144.
  50. Engineering. In: T. Augustin, F. Coolen, G. de Cooman, M. Troffaes (Eds.), Introduction to Imprecise Probabilities. John Wiley & Sons Ltd, Chichester 2014, 291 - 304.
  51. with C. Adam and B. Schmelzer. Seismic performance of Tuned Mass Dampers with uncertain parameters. In: Computational Engineering (G. Hofstetter, ed.), Springer 2014, 57 - 84.
  52. Sensitivity and reliability analysis of engineering structures: sampling based methods. In: Computational Engineering (G. Hofstetter, ed.), Springer 2014, 85 - 112.
  53. Stochastic Response Surfaces, Interval Analysis, and the Reliability of Structures. In: M. Beer, S.-K. Au, J.W. Hall (Eds.), Vulnerability, Uncertainty, and Risk Quantification: Mitigation and Management. CD-ROM Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, and 6th International Symposium on Uncertainty Modelling and Analysis. American Society of Civil Engineers, Reston VA 2014, pp. 864 - 875.
  54. with M. Schwarz. Fourier Integral Operators in Stochastic Structural Analysis. In: F. Werner, M. Huber,  T. Lahmer, T. Most, D. Proske (Eds.), Proceedings of the 12th International Probabilistic Workshop. Schriftenreihe des DFG Graduiertenkollegs 1462 Modellqualitäten, Heft 11. Bauhaus-Universitätsverlag Weimar 2014, pp. 250 - 257.
  55. with S. Gamse. Assessment of long term geodetic observations on embankment dam, In: Pina, C.; Portela, E.; Caldeira, L.; Batista, A.; Dias, I.; Santos R. (Eds.), Proceedings of the Second International Dam World  Conference, Laboratório Nacional de Enghenaria Civil, Lisboa 2015, pp. 817 – 826.
  56. with T. Fetz. Imprecise Random Variables, Random Sets, and Monte Carlo Simulation. In: T. Augustin, S. Doria, E. Miranda, E. Quaeghebeur (Eds.), ISIPTA ’15. Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications. Aracne Editrice, Roma 2015, pp. 137 – 146.
  57. Analyzing Uncertainty in Civil Engineering. In: Freitag, R. L. Muhanna, R. L. Mullen (Eds.), REC2016, Proceedings of the 7th International Workshop on Reliable Engineering Computing. Ruhr Universität Bochum 2016, pp. 41 – 64.
  58. with V. Hellweger, J.-T. Fischer, A. Kofler, A. Huber, W. Fellin. Stochastic methods in operational avalanche simulation - from back calculation to prediction. In: Proceedings, International Snow Science Workshop, Breckenridge, Colorado, 2016, pp. 1375 – 1381.
  59. with S. Gamse, M. J. Henriques, Assessment of long term pendulum and geodetic observations on a concrete arch dam. In: International Federation of Surveyors, Conference and Seminar Proceedings, 3rd Joint International Symposium on Deformation Monitoring (JISDM 2016), Weblink
  60. with F. Baumgartner, M. Schwarz. Transport in a stochastic Goupillaud medium. In: M. Oberguggenberger, J. Toft, J. Vindas, P. Wahlberg (Eds.), Generalized Functions and Fourier Analysis. Birkhäuser, Cham 2017, pp. 19 – 30, arXiv:1604.05104
  61. with L. Lamplmayr, M. Schwarz. Stochastic Fourier integral operators for damage detection. In: M. Voigt, D. Proske, W.Graf, M. Beer, U. Häußler-Combe, P. Voigt (Eds.), Proceedings of the 15th International Probabilistic Workshop & 10th Dresdner Probablistik Workshop. TUDpress, Dresden, 2017, 73 - 84, Postprint
  62. with M. Schwarz. Stochastic methods in damage detection. In: M. De Angelis (Ed.), REC2018 - Proceedings of the 8th International Workshop on Reliable Engineering Computing. University of Liverpool, 2018, 1 – 11, Weblink
  63. with A. Kofler, J.-T. Fischer, A. Huber, M. Mergili, W. Fellin.  A Bayesian approach to consider uncertainties in avalanche Simulation. In: Proceedings ISSW 2018, International Snow Science Workshop, Innsbruck, Austria 2018. Montana State University Library, 797 - 801.
  64. with T. Fetz, M. Troffaes.  Iterative importance sampling for estimating expectation bounds under partial probability specifations. In: M. De Angelis, Marco (Ed.), REC 2018 - Proceedings of the 8th International Workshop on Reliable Engineering Computing. : Liverpool University Press, 147 - 154.
  65. with J. Sadeghi, M. De Angelis, E. Patelli, T. Fetz. Probability box propagation: benchmarking challenge problems. In.: B. Sudret, S. Marelli (Eds.), Reliability and Optimization of Structural Systems. Institute of Structural Engineering, ETH Zürich 2018, 41 – 47, doi.org/10.3929/ethz-b-000335938.
  66. with B. Hirzinger, C. Adam, P. Salcher, Reliability of bridges for high-speed trains: assessment of different stochastic approaches. In: George Deodatis and Pol D Spanos (Eds.), Proceedings of the 8th International Conference on Computational Stochastic Mechanics (CSM 8). Research Publishing (S) Pte. Ltd. (2018), 265 - 278, Weblink
  67. with M. Schwarz, On the Measurability of Stochastic Fourier Integral Operators (2019). In: Boggiatto, P., Cappiello, M., Cordero, E., Coriasco, S., Garello, G., Oliaro, A., Seiler, J. (Eds.), Advances in Microlocal and Time-Frequency Analysis. Birkhäuser Basel 2020, 383 - 401. arXiv:1903.06546v1
  68. with M. Nedeljkov, L. Neumann, Spherically symmetric shadow wave solutions to the compressible Euler system at the origin. In: A. Bressan, M. Lewicka, D. Wang, Y. Zheng, Hyperbolic Problems: Theory, Numerics, Applications. AIMS Series on Applied Mathematics, Vol. 10. American Institute of Mathematics, Springfield 2020, 577 - 585. https://www.aimsciences.org/book/AM/volume/Volume%2010
  69. Anomalous solutions to nonlinear hyperbolic equations. In: M. Cicognani, D. Del Santo, A. Parmeggiani, M. Reissig (Eds.), Anomalies in Partial Differential Equations, Springer INdAM Series, Cham 2021, 347 - 367.
  70. with J. Karakašević, Random set solutions to partial differential equations. In: A. Sofi, G. Muscolino, R.L. Muhanna (Eds.), Proceedings of the 9th International Workshop on Reliable Engineering Computing 2021, 279 - 294. http://ww2new.unime.it/REC2021/proceedings/REC2021_Proceedings.pdf

Preprints

  1. with J. F. Colombeau. Approximate generalized solutions and measure valued solutions to conservation laws. École Normale Supérieure de Lyon, Prépublication 37(1990).
  2. Fuzzy Logik, Statistik, Risiko und Unschärfe. Kurzreferat zum Workshop Alpine Sicherheit - Naturgefahrenmanagement, Universität Innsbruck, Juni 2000. Preprint Series 6-2000, Institut für Technische Mathematik, Geometrie und Bauinformatik.
  3. Beschreibende Statistik - Beispiele für den Unterricht. Preprint Series 4-2003, Institut für Technische Mathematik, Geometrie und Bauinformatik.
  4. Fuzzy-Logik - Was ist das? Preprint Series 5-2003, Institut für Technische Mathematik, Geometrie und Bauinformatik.
  5. On the algebraic dual of D(Ω). 2004, arXiv:1304.2512v2.
  6. Colombeau solutions to nonlinear wave equations. 2006, arXiv.math/0612445.
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