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 Head of laboratory, Professor, Dr.  Gennadii V. Demidenko Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, prospect Koptyuga, 4, 630090 Novosibirsk, Russia Phone: (+7-383)329-75-78 Fax: (+7-383)333-25-98 E-mail: demidenk@math.nsc.ru

 Personal data Education and degrees Experience in scientific institutes Teaching experience Other academic activities Research interests Participation in scientific projects, grants and awards Selected publications

Last name: Demidenko
First name: Gennadii
Middle name: Vladimirovich
Data of birth: September 7, 1955 (Novosibirsk region, Russia)
Languages: Russian (native), English

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1973-1977 - Department of Mathematics, Novosibirsk State University (Novosibirsk).

1977 - Diploma (M. Sc.), Novosibirsk State University (Novosibirsk).

1977-1978 - Probationer-researcher, Novosibirsk State University (Novosibirsk).

1978-1981 - Postgraduate, Novosibirsk State University (Novosibirsk).

1981 - Candidate of Physical and Mathematical Sciences (Ph. D.), Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences (Novosibirsk), Ph. D. Thesis "General Mixed Problems for Equations not Solved with respect to the Highest Derivative with Variable Coefficients", Ph. D. Advisor: Professor Stanislav V. Uspenskii.

1993 - Doctor of Physical and Mathematical Sciences (D. Sc.), Steklov Institute of Mathematics (Moscow), D. Sc. Thesis "Integral Operators Defined by Quasielliptic Equations and Equations of Composite Type".

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1982-1986 - Junior Scientific Researcher, Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences (Novosibirsk).

1986-1988 - Scientific Researcher, Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences (Novosibirsk).

1988-1993 - Senior Scientific Researcher, Institute of Mathematics of the Siberian Branch of the USSR Academy of Sciences (Novosibirsk).

1993-2000 - Leading Scientific Researcher, Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk).

2000-2005 - Leading Scientific Researcher, Head of the scientific collective "Boundary value problems for differential equations", Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk).

2005-present - Head of the Laboratory of Differential and Difference Equations, Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk).

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1983-1984 - Assistant Lecturer, Novosibirsk State University (Novosibirsk). ("Ordinary Differential Equations")

1984-1987 - Assistant Professor, Novosibirsk State University (Novosibirsk). ("Ordinary Differential Equations", "Embedding Theorems and Applications to Problems of Mathematical Physics")

1987-1994 - Associate Professor, Novosibirsk State University (Novosibirsk). ("Ordinary Differential Equations", "Partial Differential Equations and Equations of Mathematical Physics", "Cauchy Problem for Parabolic and Hyperbolic Equations", "Equations of Mathematical Physics - II", "Boundary Value Problems for Partial Differential Equations")

1994-present - Full Professor, Novosibirsk State University (Novosibirsk). ("Ordinary Differential Equations", "Partial Differential Equations and Equations of Mathematical Physics", "Embedding Theorems and Applications to Equations of Mathematical Physics")

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2000-2004 - Member, Editorial Board, Selcuk Journal of Applied Mathematics

2004-present - Member, Editorial Board, Siberian Mathematical Journal

2005-present - Member, Editorial Board, Journal of Analysis and Applications

2007-present - Member, Editorial Board, International Journal of Dynamical Systems and Differential Equations

2014-present - Member, Editorial Board, Siberian Advances in Mathematics

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Partial differential equations, ordinary differential equations, difference equations, delay differential equations, mathematical analysis, computational mathematics

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Project "Elaboration of New Statements of Applied Problems of  Linear Algebra that Admit Unconditional Possibility for Application of Algorithms with Guaranteed Accuracy of Result", supported by the Russian Foundation for Basic Research (RFBR),  no. 93-01-01515 (1993-1995)

Project "The Theory of Mixed Boundary Value Problems for Linear Equations not Solved with respect to the Highest Derivative, and Qualitative Research of Solutions in Bounded and Unbounded  Domains", supported by RFBR,  no. 95-01-01176 (1995-1997)

Project "Mathematics in Applications (Problems of Differential Equations and Numerical Linear Algebra)" in the framework of the program "Leading Scientific Schools in Russia", supported by RFBR, no. 96-15-96290 (1996-1998)

State Scientific Scholarship (1997-2000)

Project "The Embeddings Theory of Functional Sobolev-Wiener Spaces, Correct Statements and Qualitative Research of General Mixed Boundary Value Problems for Linear Equations and Systems of Sobolev Type", supported by RFBR, no. 98-01-00553 (1998-2000)

Project "Boundary Value Problems for Systems not of Cauchy-Kovalevskaya Type", supported by the Ministry of Education of the Russian Federation (1998-2000; head)

Project "Weighted Sobolev Spaces and Quasielliptic Operators", supported by RFBR, no. 99-01-00533 (1999-2001; head)

Soros Professor (2000)

Project "The Embedding Theory of  Generalized Functional Sobolev-Wiener Spaces, Qualitative Research of Functions in Unbounded domains, Correct Statements of General Mixed Boundary Value Problems for Equations and Systems not Solved with respect to the Highest Derivative", supported by RFBR, no. 01-01-00609 (2001-2003)

Project "Weighted Spaces of Summable Functions, Quasi-Elliptic Operators and Applications to Differential Equations", supported by RFBR, no. 03-01-00095 (2003-2005; head)

Complex integration project no. 1 "Elaboration of a Treelike Catalogue of Mathematical Internet Resources",  supported by the Siberian Branch of the Russian Academy of Sciences (2003-2005)

Interdisciplinary integration project no. 119 "Gene Networks: Theoretical Analysis, Computer Modelling and Experimental Designing", supported by the Siberian Branch of the Russian Academy of Sciences (2003-2005)

Project  "The Embedding Theory of Generalized Functional Sobolev Spaces. Qualitative Research of Correct Statements of Initial-Boundary Value Problems for Differential Equations and Systems not Solved with Respect to the Highest Derivative", supported by RFBR, no. 04-01-00750 (2004-2006)

Project "Limit Theorems in the Gene Networks Theory", supported by RFBR, no. 04-01-00458 (2004-2006)

Project "Algorithms for Research of Stability of Solutions and Solvability of Boundary Value Problems for Quasilinear Systems of Differential Equations with Periodic Coefficients", supported by the Ministry of Education and Science of the Russian Federation, Program "Development of Scientific Potential of the Higher School", no. 8273 (2005; head)

Complex integration project no. 2.2 "Deformation and Failure of Composite Materials and Structures",  supported by the Siberian Branch of the Russian Academy of Sciences (2006-2008)

Project  "The Embedding Theory of Generalized Functional Sobolev Spaces. Applications to Differential Equations", supported by RFBR, no. 07-01-00289 (2007-2009)

Project no. 85 "Qualitative and Numerical Analysis of Evolution Equations and Controllable Systems", supported by the Siberian Branch of the Russian Academy of Sciences (2009-2011)

Interdisciplinary integration project no. 107 "Methods of Research of Differential-Difference Equations and Applications to Problems of Biology and Chemistry", supported by the Siberian Branch of the Russian Academy of Sciences (2009-2011; head)

Project "Fundamental Problems of Contemporary Mathematics", supported by the Ministry of Education and Science of the Russian Federation, Federal Target Program "Scientific and Educational Personnel of Innovative Russia'' for 2009-2013, government contract no. 02.740.11.0429 (2009-2011)

Project  "Numerical Methods for Solving Direct and Inverse Problems for Differential, Difference and Delay Equations", supported by RFBR, no. 10-01-00035 (2010-2012; head)

Project "Direct and Inverse Problems for Differential Equations", supported by the Ministry of Education and Science of the Russian Federation, Federal Target Program "Scientific and Educational Personnel of Innovative Russia'' for 2009-2013, government contract no. 16.740.11.0127 (2010-2012; head)

Interdisciplinary integration project no. 80 "Differential-Difference and Integro-Differential Equations. Applications to Problems of the Natural Sciences", supported by the Siberian Branch of the Russian Academy of Sciences (2012-2014; head)

Project  "Algorithms and Numerical Methods for Solving Direct and Inverse Problems for Differential-Difference Equations", supported by RFBR, no. 13-01-00329 (2013-2015; head)

Project  "Theoretical and Numerical Methods for Study of Stability, Optimal Control and Identification for Some Classes of Differential-Difference Equations", supported by RFBR, no. 16-01-00592 (2016-2018; head)

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Books:

1. Embedding Theorems and Applications to Differential Equations. Nauka, Novosibirsk, 1984, 223 p. (jointly with S.V. Uspenskii, V.G. Perepelkin; Russian)

2. Introduction to the Theory of Sobolev Spaces. Textbook. Publishing office of the Novosibirsk State University, Novosibirsk, 1995, 111 p. (Russian)

3. Partial Differential Equations and Systems not Solvable with Respect to the Highest-Order Derivative. Nauchnaya Kniga, Novosibirsk, 1998, 456 p. (Russian); Marcel Dekker, New York, Basel, 2003, 490 p. (English). (jointly with S.V. Uspenskii)

4. Matrix Equations. Textbook. Publishing office of the Novosibirsk State University, Novosibirsk, 2009, 203 p. (Russian)

5. Ordinary Differential Equations in Problems. Textbook. Publishing office of the Novosibirsk State University, Novosibirsk, 2014, 192 p. (jointly with I.I. Matveeva; Russian)

6. Sobolev Spaces and Generalized Solutions. Publishing office of the Novosibirsk State University, Novosibirsk, 2015, 270 p. (Russian)

Articles:

1. Differential properties of the solutions of general boundary value problems for equations of Sobolev type. In: Mathematical Analysis and Related Mathematical Questions, Nauka, Sibirsk. Otdel., Novosibirsk, 1978, pp. 276-296. (jointly with S.V. Uspenskii; Russian)

2. On mixed boundary value problems for equations of Sobolev type with variable coefficients. In: Partial Differential Equations, Trudy Sem. S.L.Soboleva, no. 2, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1979, pp. 52-91. (Russian)

3. Mixed boundary value problems for equations of Sobolev type. In: Partial Differential Equations, Proc. Conf., Nauka,  Sibirsk. Otdel., Novosibirsk, 1980, pp. 32-34. (Russian)

4. Mixed boundary value problems for one class of equations not solved with respect to highest derivative. Dokl. Akad. Nauk SSSR, 252 (1980), no. 3, pp. 560-562; English transl. in Sov. Math. Dokl., 21 (1980), pp. 801-804. (jointly with S.V. Uspenskii)

5. On mixed boundary value problems for a class of equations not solved with respect to highest derivative. Trudy Sem. S.L.Soboleva, no. 2, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1980, pp. 92-115. (jointly with S.V. Uspenskii; Russian)

6. On mixed boundary-value problems for Sobolev equations. Sib. Mat. Zh., 22 (1981), no. 3, pp. 53-66; English transl. in Sib. Math. J., 22 (1982), pp. 370-380.

7. Mixed problems for a class of equations of Sobolev type. Trudy Sem. S.L.Soboleva, no.1, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1982, pp. 44-74.

8. Behavior as $t \to \infty$ of solutions of a problem of S.L. Sobolev. In: Application of Methods of the Theory of Functions and Functional Analysis to Problems of Mathematical Physics, Erevan State University Publishers, 1982, 5 p. (jointly with S.V. Uspenskii; Russian)

9. Behavior of solutions of a problem of S.L. Sobolev at infinity. Sib. Mat. Zh., 24 (1983), no. 5, pp. 199-210; English transl. in Sib. Math. J., 24 (1983), no. 5, pp. 809-818. (jointly with S.V. Uspenskii)

10. Mixed problems for generalized Sobolev equations. Uspekhi Mat. Nauk, 38 (1983), iss. 5, pp. 147-148. (Russian)

11. Estimates for $t \to \infty$ of the solution to a problem of Sobolev. Sib. Mat. Zh., 25 (1984), no. 2, pp.112-120; English transl. in Sib. Math. J., 25 (1984), no. 2, pp. 257-264.

12. Lp-estimates of solutions of boundary value problems for Sobolev type equations. Uspekhi Mat. Nauk, 39 (1984), iss. 4, p. 125. (Russian)

13. On conditions for the solvability of mixed problems for a class of equations of Sobolev type. In: Boundary Value Problems for Partial Differential Equations, Trudy Sem. S.L.Soboleva, no. 1, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1984, pp. 23-54. (Russian)

14. The Cauchy problem for generalized S.L.Sobolev equations. In: Functional Analysis and Mathematical Physics, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1985, pp. 88-105. (Russian)

15. The behavior as $t \to \infty$ of solutions of certain problems of hydrodynamics. Dokl. Akad. Nauk SSSR, 280 (1985), no. 5, pp. 1072-1074; English transl. in Sov. Math. Dokl., 31 (1985), pp. 218-220. (jointly with S.V. Uspenskii)

16. Boundary value problems for equations and systems of Sobolev type. In: Partial Differential Equations, Proc. Conf., Nauka, Sibirsk. Otdel., Novosibirsk, 1986, pp. 72-84. (jointly with  S.V. Uspenskii, V.G. Perepelkin, S.I. Yanov; Russian)

17. The Cauchy problem for equations and systems of Sobolev type. In: Boundary Value Problems for Partial Differential Equations, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1986, pp. 69-84. (Russian)

18. Necessary conditions for well-posedness of a Cauchy problem for the linearized Navier-Stokes system of equations. Sib. Mat. Zh., 29 (1988), no. 3, pp.186-189; English transl. in Sib. Math. J., 29 (1988), no. 3, pp. 485-488.

19. Correct solvability of boundary value problems in a halfspace for quasielliptic equations. Sib. Mat. Zh., 29 (1988), no. 4, pp. 54-67; English transl. in Sib. Math. J., 29 (1988), no. 4, pp. 555-567.

20. Conditions for the correct solvability of boundary value problems for equations and systems of Sobolev type. In: Some Applications of Functional Analysis to Problems of Mathematical Physics, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1988, pp. 64-71. (Russian)

21. A certain class of boundary value problems for the Sobolev system. In: Partial Differential Equations, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1989, pp. 54-78. (jointly with I.I. Matveeva; Russian)

22. Boundary value problems for a class of pseudodifferential equations. In: Embedding Theorems and Their Applications to Problems of Mathematical Physics, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1989, pp. 60-69. (Russian)

23. The Cauchy problem for a hyperbolic system of the dynamics of a stratified fluid. In: Boundary Value Problems for Partial Differential Equations, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1990, pp. 56-76. (Russian)

24. Lp-theory of boundary value problems for equations of Sobolev type. Preprint, Inst. of Math. Russian Acad. Sci., Siberian Branch, Novosibirsk, 1991, no. 16, 38 p. (Russian)

25. Lp-estimates of solutions of quasielliptic equations in Rn. Preprint, Inst. of Math. Russian Acad. Sci., Siberian Branch, Novosibirsk, 1992, no. 4, 30 p. (Russian)

26. Integral operators defined by boundary value problems for quasielliptic equations. Dokl. Akad. Nauk, 326 (1992),  no. 5, pp. 765-769; English transl. in Russian Acad. Sci. Dokl. Math., 46 (1993), no. 2, pp. 343-348.

27. Lp-theory of boundary value problems for Sobolev type equations. In: Partial Differential Equations, Banach Center Publications, Polish Academy of Sciences, Warsaw, 27 (1992), part I, pp. 101-109.

28 To question about determination of matrices whose spectrums lie on the imaginary axis. Preprint, Inst. of Math. Russian Acad. Sci., Siberian Branch, Novosibirsk, 1993, no. 12, 34 p. (Russian)

29. Integral operators determined by quasielliptic equations. I. Sib. Mat. Zh., 34 (1993), no. 6, pp. 52-67; English transl. in Sib. Math. J., 34 (1993), no. 6, pp. 1044-1058.

30. Integral operators determined by quasielliptic equations. II. Sib. Mat. Zh., 35 (1994), no. 1, pp. 41-65; English transl. in Sib. Math. J., 35 (1994), no. 1, pp. 37-61.

31. Weighted Sobolev spaces and integral operators defined by quasielliptic equations. Dokl. Acad. Nauk, 1994, v. 334, no. 4, pp. 420-423; English transl. in Russian Acad. Sci. Dokl. Math., 49 (1994), no. 1, pp. 113-118.

32. On a class of integral operators and applications to quasielliptic equations. I. Differ. Uravn., 30 (1994), no. 5, pp. 889-898; English transl. in Differ. Equations, 30 (1994), no. 5, pp. 821-830.

33. On a class of integral operators and applications to quasielliptic equations. II. Differ. Uravn., 30 (1994), no.10, pp. 1731-1737; English transl. in Differ. Equations, 30 (1994), no. 10, pp. 1599-1605.

34. On a certain class of spectral characteristics of matrices. Sib. Mat. Zh., 35 (1994), no. 5, pp. 1032-1051; English transl. in Sib. Math. J., 35 (1994), no. 5, pp. 917-935.

35. On properties of a class of spectral characteristics of matrices and applications to ordinary differential equations. INRIA report, France, 1994, no. 2270, 43 p. (jointly with I.I. Matveeva)

36. Lp-theory of boundary value problems for equations of Sobolev type. Sib. J. Diff. Equations, 1 (1995), no. 1, pp. 15-52.

37. On quasielliptic equations in unbounded domains. Sib. J. Diff. Equations, 1 (1995), no. 4, pp. 21-81.

38. Boundary value problems for non-Cauchy-Kovalevskaya-type systems in a quarter-space. Sib. Adv. Math., 5 (1995), no. 3, pp. 5-39. (jointly with I.I. Matveeva)

39. Integral criteria for the matrix spectrum to belong to convex sets. Preprint, Inst. of Math. Russian Acad. Sci., Siberian Branch, Novosibirsk, 1995, no. 17, 23 p. (jointly with I.I. Matveeva)

40. Integral representations for solutions of a class of systems not of Cauchy-Kovalevskaya type. Preprint, Inst. of Math. Russian Acad. Sci., Siberian Branch, Novosibirsk, 1996, no. 30, 19 p. (Russian)

41. On regularity of solutions to boundary value problems for quasielliptic equations. Sib. Adv. Math., 6 (1996), no. 2, pp. 10-34. (jointly with I.Yu. Nekhaev)

42. The Cauchy problem for pseudoparabolic systems. Sib. Mat. Zh., 38 (1997), no. 6, pp. 1251-1266; English transl. in Sib. Math. J., 38 (1997), no. 6, pp. 1084-1098.

43. Approximate constructing projections onto invariant subspaces of matrices. Computing Technologies, 2 (1997), no. 6, pp. 24-30. (jointly with I.I. Matveeva; Russian)

44. On a method of constructing projections onto invariant subspaces of matrices. Sib. Zh. Ind. Mat., 1 (1998), no. 1, pp. 104-113. (Russian)

45. On mixed boundary value problems for a class of systems not of Cauchy-Kovalevskaya type. Differ. Uravn., 34 (1998), no. 3, pp. 348-358; English transl. in Differ. Equations, 34 (1998), no. 3, pp. 347-357. (jointly with S.I. Yanov)

46. On a functional approach to constructing projections onto invariant subspaces of matrices. Sib. Mat. Zh., 39 (1998), no. 4, pp. 796-813; English transl. in Sib. Math. J., 39 (1998), no. 4, pp. 683-699.

47. On quasielliptic operators in Rn. Sib. Mat. Zh., 39 (1998), no. 5, pp. 1028-1037; English transl. in Sib. Math. J., 39 (1998), no. 5, pp. 884-893.

48. Isomorphic properties of quasielliptic operators. Dokl. Akad. Nauk, 364 (1999), no. 6, pp. 730-734; English transl. in Russ. Acad. Sci., Dokl. Math., 59 (1999), no. 1, pp. 102-106.

49. Numeric characteristics for asymptotic stability of solutions to linear difference equations with periodic coefficients. Sib. Mat. Zh., 41 (2000), no. 6, pp. 1227-1237; English transl. in Sib. Math. J., 41 (2000), no. 6, pp. 1005-1014. (jointly with K. Aydin, H. Bugak)

50. A new criterion of the inclusion of a matrix spectrum into the closed unit circle and applications to the stability theory. Sib. Zh. Ind. Mat., 3 (2000), no. 1, pp. 47-56. (jointly with A.Ya. Bulgakov; Russian)

51. The Cauchy problem for pseudohyperbolic equations. Selcuk J. Appl. Math., 1 (2000), no. 1, pp. 47-62.

52. On solvability of Cauchy problem for pseudohyperbolic equations. Proc. on Analysis and Geometry. Inst. of Math. Russian Acad. Sci., Siberian Branch, Novosibirsk, 2000, pp. 156-172. (Russian)

53. On stability of solutions to linear systems with periodic coefficients. Sib. Mat. Zh., 42 (2001), no. 2, pp. 332-348; English transl. in Sib. Math. J. 42 (2001), no. 2, pp. 282-296. (jointly with I.I. Matveeva)

54. A modification of the matrix sign function method. Selcuk J. Appl. Math., 2 (2001), no. 1, pp. 47-58. (jointly with Yu.Yu. Klevtsova)

55. On constructing approximate projections onto invariant subspaces of linear operators. Int. J. Differ. Equations Appl., 3 (2001), no. 2, pp. 135-146.

56. Isomorphic properties of one class of differential operators and their applications. Sib. Mat. Zh., 42 (2001), no. 5, pp. 1036-1056; English transl. in Sib. Math. J. 42 (2001), no. 5, pp. 865-883.

57. Continuity of numeric characteristics for asymptotic stability of solutions to linear difference equations with periodic coefficients. Selcuk J. Appl. Math., 2 (2001), no. 2, pp. 5-10. (jointly with K. Aydin, H. Bulgak)

58. On a fuctional approach to spectral problems of linear algebra. Selcuk J. Appl. Math., 2 (2001), no. 2, pp. 39-52.

59. Asymptotic stability of solutions to perturbed linear difference equations with periodic coefficients. Sib. Mat. Zh., 43 (2002), no. 3, pp. 493-507; English transl. in Sib. Math. J., 43 (2002), no. 3, pp. 389-401. (jointly with K. Aydin, H. Bulgak)

60. Estimation for the region of attraction of nonlinear difference equations. Numerische Mathematik, 92 (2002), no. 3, pp. 421-431. (jointly with H. Bulgak)

61. On properties of a class of matrix differential operators in Rn. Selcuk J. Appl. Math., 3 (2002), no. 2, pp. 23-36.

62. On asymptotic stability of solutions to nonlinear systems of differential equations with periodic coefficients. Selcuk J. Appl. Math., 3 (2002), no. 2, pp. 37-48. (jointly with I.I. Matveeva)

63. Isomorphic properties of one class of matrix differential operators. Dokl. Akad. Nauk, 391 (2003), no. 1, pp. 10-13; English transl. in Dokl. Math., 68 (2003), no. 1, pp. 4-7.

64. On location of the matrix spectrum inside an ellipse. Selcuk J. Appl. Math., 4 (2003), no. 1, pp. 25-41. (jointly with A. Bulgak, I.I. Matveeva)

65. On one class of matrix differential operators. Sib. Mat. Zh., 45 (2004), no. 1, pp. 103-118; English transl. in Sib. Math. J., 45 (2004), no. 1, pp. 86-99.

66. Modelling of multi-stage synthesis without branching by an equation with delay. Sib. Zh. Ind. Mat., 7 (2004), no. 1, pp. 73-94. (jointly with V.A. Likhoshvai, S.I. Fadeev, Yu.G. Matushkin; Russian)

67. Modelling of substance synthesis process without branching by the delay equation. Proceedings of the Fourth International Conference on Bioinformatics of Genome Regulation and Structure (July 25-30, 2004, Novosibirsk, Russia). Novosibirsk: Institute of Cytology and Genetics, 2004, vol. 2, pp. 97-100. (jointly with V.A. Likhoshvai, S.I. Fadeev)

68. An estimate for the attraction domains of difference equations with periodic linear terms. Sib. Mat. Zh., 45 (2004), no. 6, pp. 1199-1208; English transl. in Sib. Math. J., 45 (2004), no. 6, pp. 983-991. (jointly with K. Aydin, H. Bulgak)

69. On stability of solutions to quasilinear periodic systems of differential equations. Sib. Mat. Zh., 45 (2004), no. 6, pp. 1271-1284; English transl. in Sib. Math. J., 45 (2004), no. 6, pp. 1041-1052. (jointly with I.I. Matveeva)

70. Mathematical simulation of regulatory circuits of gene networks. Zh. Vychisl. Mat. Mat. Fiz.,44 (2004), no. 12, pp. 2276-2295; English translat. in Comput. Math. Math. Phys., 44 (2004), no. 12, pp. 2166-2183. (jointly with N.A.Kolchanov, V.A.Likhoshvai, Yu.G.Matushkin, S.I.Fadeev)

71. On differential equations with retarded argument. Sib. Mat. Zh., 46 (2005), no. 3, pp. 538-552; English transl. in Sib. Math. J., 46 (2005), no. 3, pp. 417-430. (jointly with V.A. Likhoshvai)

72. On mixed boundary value problems for pseudoparabolic systems. Sib. Zh. Ind. Mat., 8 (2005), no. 4, pp. 34-50; English transl. in J. Appl. Ind. Math., 1 (2007), no. 1, pp. 18-32. (jointly with I.I. Matveeva)

73. Asymptotic properties of solutions to delay differential equations. Vestnik NGU. Ser.: matematika, mekhanika, informatika, 5 (2005), iss. 3, pp. 20-28. (jointly with I.I. Matveeva; Russian)

74. Asymptotic properties of solutions of the nonhomogeneous Sobolev equation. In: Nonclassical Equations of Mathematical Physics, Russian Akad. Nauk Sibirsk. Otdel., Inst. Mat., Novosibirsk, 2005, pp. 50-59. (jointly with L.N. Buldygerova; Russian)

75. On solvability of boundary value problems for quasi-elliptic systems in $R^n_+$. J. Anal. Appl., 4 (2006), no. 1, pp. 1-11.

76. On one class of systems of differential equations and on retarded equations. Sib. Mat. Zh., 47 (2006), no. 1, pp. 58-68; English transl. in Sib. Math. J., 47 (2006), no. 1, pp. 45-54. (jointly with V.A. Likhoshvai, T.V. Kotova, Yu.E. Khropova)

77. Modeling of gene expression by the delay equation. In: Bioinformatics of Genome Regulation and Structure II (Eds. N. Kolchanov and R. Hofestaedt) Springer Science + Business Media, Inc. 2006, pp. 421-431. (jointly with V.A. Likhoshvai, S.I. Fadeev)

78. On one class of infinite-order systems of differential equations and on delay differential equations. Proceedings of the Fifth International Conference on Bioinformatics of Genome Regulation and Structure (July 16-22, 2006, Novosibirsk, Russia). Novosibirsk: Institute of Cytology and Genetics, 2006, vol. 3, pp. 29-32. (jointly with Yu.E. Khropova, T.V. Kotova)

79. On a new method of approximation of solutions of delay differential equations. Proceedings of the Fifth International Conference on Bioinformatics of Genome Regulation and Structure (July 16-22, 2006, Novosibirsk, Russia). Novosibirsk: Institute of Cytology and Genetics, 2006, vol. 3, pp. 33-37. (jointly with A.V. Mudrov)

80. On properties of solutions of one delay differential equations. Proceedings of the Fifth International Conference on Bioinformatics of Genome Regulation and Structure (July 16-22, 2006, Novosibirsk, Russia). Novosibirsk: Institute of Cytology and Genetics, 2006, vol. 3, pp. 38-42. (jointly with Yu.E. Khropova)

81. Asymptotic properties of solutions of differential-difference equations with periodic coefficients in linear terms. Proceedings of the Fifth International Conference on Bioinformatics of Genome Regulation and Structure (July 16-22, 2006, Novosibirsk, Russia). Novosibirsk: Institute of Cytology and Genetics, 2006, vol. 3, pp. 43-46. (jointly with I.I. Matveeva)

82. Mapping properties of quasielliptic operators and applications. Int. J. Dynamical Systems and Differential Equations, 1 (2007), no. 1, pp. 58-67.

83. Stability of solutions to delay differential equations with periodic coefficients of linear terms. Sib. Mat. Zh., 48 (2007), no. 5, pp. 1025-1040; English transl. in Sib. Math. J., 48 (2007), no. 5, pp. 824-836. (jointly with I.I. Matveeva)

84. Quasielliptic operators and Sobolev type equations. Sib. Mat. Zh., 49 (2008), no. 5, pp. 1065-1076; English transl. in Sib. Math. J., 49 (2008), no. 5, pp. 842-851.

85. Boundary value problems for quasielliptic systems. Sib. Mat. Zh., 49 (2008), no. 2, pp. 256-273; English transl. in Sib. Math. J., 49 (2008), no. 2, pp. 202-217. (jointly with L.N. Bondar)

86. Exponential dichotomy of linear systems of differential equations with periodic coefficients. Vestnik NGU. Ser.: matematika, mekhanika, informatika, 8 (2008), iss. 4, pp. 40-48. (jointly with Yu.Yu. Klevtsova; Russian)

87. Quasielliptic operators and Sobolev type equations. II. Sib. Mat. Zh., 50 (2009), no. 5, pp. 1060-1069; English transl. in Sib. Math. J., 50 (2009), no. 5, pp. 838-845.

88. Stability of solutions to linear differential equations of neutral type. J. Anal. Appl., 7 (2009), no. 3, pp. 119-130.

89. On the relationship between solutions of delay differential equations and infinite-dimensional systems of differential equations. Differ. Uravn., 45 (2009), no. 1, pp. 34-46; English transl. in Differ. Equations, 45 (2009), no. 1, pp. 33-45. (jointly with V.A. Likhoshvai, A.V. Mudrov)

90. On numerical study of asymptotic stability of solutions to linear periodic differential equations with a parameter. J. Comput. Math. Optim., 5 (2009), no. 3, pp. 163-173.  (jointly with I.I. Matveeva)

91. Delay differential equations in problems of multi-stage substance synthesis. Preprint, Inst. of Math. Russian Acad. Sci., Siberian Branch, Novosibirsk, 2009, no. 233, 26 p. (jointly with I.A. Mel'nik, Yu.E. Khropova; Russian)

92. Matrix quasi-elliptic operators in Rn. Dokl. Akad. Nauk, 431 (2010), no. 4, pp. 443-446; English transl. in Dokl. Math., 81 (2010), no. 2, pp. 244-247.

93. Stability of solutions to difference equations with periodic coefficients in linear terms. J. Comput. Math. Optim., 6 (2010), no. 1, pp. 1-12.

94. Stability of solutions to differential equations of neutral type. Vestnik NGU. Ser.: matematika, mekhanika, informatika, 10 (2010), iss. 3, pp. 17-29; English transl. in J. Math. Sci., 186 (2012), no. 3, pp. 394-406. (jointly with T.V. Kotova, M.A. Skvortsova)

95. On properties of solutions to equations modeling multi-stage substance synthesis. J. Anal. Appl., 8 (2010), no. 1, pp. 47-61. (jointly with V.A. Likhoshvai, I.A. Mel'nik)

96. Limit properties of solutions to one class of systems of differential equations with parameters. J. Anal. Appl., 8 (2010), no. 2, pp. 63-74. (jointly with T.V. Kotova)

97. On a method of approximation of solutions to delay differential equations. Sib. Mat. Zh., 51 (2010), no. 3, pp. 528-546; English transl. in Sib. Math. J., 51 (2010), no. 3, pp. 421-436. (jointly with I.A. Mel'nik)

98. On classes of systems of differential equations of large dimensions and delay equations. In: Itogi Nauki. Yug Rossii. Ser. Mat. Forum. YuMI VNTs RAN i RSO-A, Vladikavkaz, 2011, vol. 5, pp. 45-56. (Russian)

99. Systems of differential equations of higher dimension and delay equations. Sib. Mat. Zh., 53 (2012), no. 6, pp. 1274-1282; English transl. in Sib. Math. J., 53 (2012), no. 6, pp. 1021–1028.

100. Asymptotic stability of solutions to one class of nonlinear second-order differential equations with parameters. Vestnik YuUrGU. Ser.: matem. model. program., 40 (2012), no. 14, pp. 39-52. (jointly with K.M. Dulina, I.I. Matveeva; Russian)

101. Self-sustained oscillations in CO oxidation reaction on PdO/Al2O3 catalyst. Chem. Eng. Sci., 83 (2012), pp. 149-158. (jointly with E.A. Lashina, E.M. Slavinskaya, N.A. Chumakova, O.A. Stonkus, R.V. Gulyaev, A.I. Stadnichenko, G.A. Chumakov, A.I. Boronin)

102. Estimates of solutions to the linear differential equations of neutral type with several delays of the argument. Sib. Zh. Ind. Mat., 16 (2013), no. 3, pp. 53-60; English transl. in J. Appl. Ind. Math., 7 (2013), no. 4, pp. 472-479. (jointly with E.S. Vodop'yanov, M.A. Skvortsova)

103. Systems of differential equations with periodic coefficients. Sib. Zh. Ind. Mat., 16 (2013), no. 4, pp. 38-46; English transl. in J. Appl. Ind. Math., 8 (2014), no. 1, pp. 20-27.

104. On boundary value problems for a system of elasticity theory in a multilayered cylinder. J. Anal. Appl., 12 (2014), no. 1 & 2, pp. 13-23.

105. On exponential stability of solutions to one class of systems of differential equations of neutral type. Sib. Zh. Ind. Mat., 17 (2014), no. 3, pp. 59-70; English transl. in J. Appl. Ind. Math., 8 (2014), no. 4, pp. 510-520. (jointly with I.I. Matveeva)

106. On estimates of solutions to systems of differential equations of neutral type with periodic coefficients. Sib. Mat. Zh., 55 (2014), no. 5, pp. 1059-1077; English transl. in Sib. Math. J., 55 (2014), no. 5, pp.  866-881. (jointly with I.I. Matveeva)

107. Estimates for solutions to linear systems of neutral type with several delays. J. Anal. Appl., 12 (2014), no. 1 & 2, pp. 37-52. (jointly with I.I.Matveeva)

108. Estimates for solutions of one class of nonlinear neutral type systems with several delays. Vestnik NGU. Ser.: matematika, mekhanika, informatika, 14 (2014), iss. 4, pp. 32-43; English transl. in J. Math. Sci., 213 (2016), no. 6, pp. 811-822. (jointly with I.I. Matveeva)

109. Solvability conditions of the Cauchy problem for pseudohyperbolic equations. Sib. Mat. Zh., 56 (2015), no. 6, pp. 1289-1303; English transl. in Sib. Math. J., 56 (2015), no. 6, pp. 1028-1041.

110. On asymptotic stability of solutions to delay difference equations. Vestnik NGU. Ser.: matematika, mekhanika, informatika, 15 (2015), iss. 4, pp. 32-45. (jointly with D.Sh. Baldanov; Russian)

111. On the robust stability of solutions to linear differential equations of neutral type with periodic coefficients. Sib. Zh. Ind. Mat., 18 (2015), no. 4, pp. 18–29. (jointly with I.I. Matveeva; Russian)

112. Estimates for solutions to a class of nonlinear time-delay systems of neutral type. Electron. J. Diff. Equ., 2015 (2015), no. 34, pp. 1-14. (jointly with I.I. Matveeva)

113. Asymptotic stability of solutions to a class of linear time-delay systems with periodic coefficients and a large parameter. Journal of Inequalities and Applications, 2015 (2015), no. 331, pp. 1-10. (jointly with I.I. Matveeva)

114. Estimates for solutions to a class of time-delay systems of neutral type with periodic coefficients and several delays. Electron. J. Qual. Theory Differ. Equ., 2015 (2015), no. 83, pp. 1-22. (jointly with I.I. Matveeva)

115. On a class of systems of ordinary differential equations of large dimension. Sib. Zh. Ind. Mat., 19 (2016), no. 2, pp. 47-60. (jointly with I.A. Uvarova; Russian)

116. On conditions for exponential dichotomy of systems of linear differential equations with periodic coefficients. Int. J. Dynamical Systems and Differential Equations, 6 (2016), no. 1, pp. 63-74.

117. Exponential stability of solutions to nonlinear time-delay systems of neutral type. Electron. J. Diff. Equ., 2016 (2016), no. 19. pp. 1-20. (jointly with I.I. Matveeva)

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# Book sales news item: Beyond the Big Bang

Gold Member
Dearly Missed
https://www.amazon.com/dp/3540714227/?tag=pfamazon01-20

This book goes on sale 1 July. If it is widely sold and widely read it will mark an historic watershed. It will indicate that we have gotten away from the idea of the big bang as a BEGINNING. I expect to watch the sales figures and I think it is relevant to understanding the broad field of Beyond the Standard Model physics---and having a perspective on it.

The book has about 20 authors, experts in quantum cosmology and related fields. The editor is R. Vaas. Here is the Amazon review:

Beyond the Big Bang: Prospects for an Eternal Universe

by Rüdiger Vaas (Editor)
List Price: $89.95 The Big Bang model is now both theoretically and empirically well established. However, the very beginning of our universe still remains mysterious. General Relativity breaks down at very small spatio-temporal scales and at high energy densities. That is why Quantum Cosmology is needed. Recent developments open up the exciting new prospect of going "beyond" the Big Bang and even finding a physical explanation for it. Surprisingly, the ancient idea of a past-eternal universe is being revived, and fascinating new approaches are also being developed. This book provides an up-to-date overview of the competing scenarios in cosmology and discusses their foundations, implications, and philosophical aspects. It gathers original contributions from the world's leading researchers in Quantum Cosmology, who describe their own work and results in a manner understandable even to non-specialists. If this book goes over big (in the academic book market---it is not for general audience)---it will help put Quantum Cosmology on the map and challenge the notion of the big bang as an unexplained instant of creation. The Amazon sales rank of this book, two months ahead of its publication date, is currently around 2 million. Is mentioning this sort of information appropriate and welcome in this subforum? ## Answers and Replies nrqed Science Advisor Homework Helper Gold Member https://www.amazon.com/dp/3540714227/?tag=pfamazon01-20 This book goes on sale 1 July. If it is widely sold and widely read it will mark an historic watershed. It will indicate that we have gotten away from the idea of the big bang as a BEGINNING. I expect to watch the sales figures and I think it is relevant to understanding the broad field of Beyond the Standard Model physics---and having a perspective on it. The book has about 20 authors, experts in quantum cosmology and related fields. The editor is R. Vaas. Here is the Amazon review: Beyond the Big Bang: Prospects for an Eternal Universe by Rüdiger Vaas (Editor) List Price:$89.95

The Big Bang model is now both theoretically and empirically well established. However, the very beginning of our universe still remains mysterious. General Relativity breaks down at very small spatio-temporal scales and at high energy densities. That is why Quantum Cosmology is needed. Recent developments open up the exciting new prospect of going "beyond" the Big Bang and even finding a physical explanation for it. Surprisingly, the ancient idea of a past-eternal universe is being revived, and fascinating new approaches are also being developed. This book provides an up-to-date overview of the competing scenarios in cosmology and discusses their foundations, implications, and philosophical aspects. It gathers original contributions from the world's leading researchers in Quantum Cosmology, who describe their own work and results in a manner understandable even to non-specialists.

If this book goes over big (in the academic book market---it is not for general audience)---it will help put Quantum Cosmology on the map and challenge the notion of the big bang as an unexplained instant of creation.

The Amazon sales rank of this book, two months ahead of its publication date, is currently around 2 million.

Is mentioning this sort of information appropriate and welcome in this subforum?

It's interesting to know, yes.
I posted some comments about books in the Particle Physics subforum a while ago (without talking about sales figures but just commenting on some books) and my thread was moved to the Advanced Physics Learning Material subforum. So maybe it belongs there.

What is likely to be the required background level for a reader of this book?

cristo
Staff Emeritus

format: plain


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# Contents

## Definition

Let $k$ be a commutative ring.

A derived Deligne-Mumford stack (over $k$) is a generalized scheme in the sense of locally affine $\mathcal{G}$-structured (infinity,1)-topos for $\mathcal{G} = \mathcal{G}_{et}(k)$ the étale geometry (for structured (infinity,1)-toposes).

## Special cases

A 1-localic derived Deligne-Mumford stack is an ordinary Deligne-Mumford stack. See there for more details.

## Properties

### Relation to derived algebraic spaces

spectral Deligne-Mumford stack is quasi-compact, quasi-separated E-∞ algebraic space? precisely if it admits a scallop decomposition.

### Characterization as $(\infty,1)$-presheaves on $E_\infty$-rings

The (∞,1)-presheaves on E-∞ rings which are represented by spectral Deligne-Mumford stacks are described by the Artin-Lurie representability theorem.

Notice that for generalized schemes the étale geometry (for structured (infinity,1)-toposes) $\mathcal{G}_{et}(k)$ is not interchangeable with the Zariski geometry $\mathcal{G}_{et}(k)$. Instead $\mathcal{G}_{Zar}(k)$-generalized schemes are derived schemes.

## References

In the context of E-infinity geometry (spectral Deligne-Mumford stacks):

Revised on May 22, 2014 09:38:20 by Urs Schreiber (88.128.80.84)


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# Revision history [back]

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Timezone: »

Poster
Zhan Shi · Xinhua Zhang · Yaoliang Yu

Tue Dec 05 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #10

Adversarial machines, where a learner competes against an adversary, have regained much recent interest in machine learning. They are naturally in the form of saddle-point optimization, often with separable structure but sometimes also with unmanageably large dimension. In this work we show that adversarial prediction under multivariate losses can be solved much faster than they used to be. We first reduce the problem size exponentially by using appropriate sufficient statistics, and then we adapt the new stochastic variance-reduced algorithm of Balamurugan & Bach (2016) to allow any Bregman divergence. We prove that the same linear rate of convergence is retained and we show that for adversarial prediction using KL-divergence we can further achieve a speedup of #example times compared with the Euclidean alternative. We verify the theoretical findings through extensive experiments on two example applications: adversarial prediction and LPboosting.


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# Minimum cover of partitions of a set

Given $n,k\in\mathbb{N}$ where $k\leq n$, I want to compute the minimum subset of the set of partitions of $N$={$1,\ldots,n$}, satisfying these properties:

1. Each block of every partition has at most $k$ elements.
2. Every pair of elements of $N$ is in the same block in exactly one partition.

Anyone has a clue?

-

(Edit: Sorry, my original restatement was incorrect.)

This problem is equivalent to decomposition a complete graph $K_n$ into a collection of cliques $C:=\{K_s\}$ where each $s \leq k$, such that $C$ can be resolved (i.e. partitioned) into a set of resolution classes $\mathcal{P}$ (the vertices of the graphs within a resolution class partition $\{1,2,\ldots,n\}$).

If each $s=k$, then $C$ is a Steiner system S(2,k,n), a special type of block design, and we say $K_k$ divides $K_n$. In this case $|\mathcal{P}|=\frac{k}{n}|C|=\frac{k}{n}\frac{n \choose 2}{k \choose 2}$ and in fact, this is always a lower bound on $|\mathcal{P}|$. Although, it's not always known when a Steiner system exists (or does not exist). The case $k=3$ (and each $s=k$) gives rise to the well-known Steiner triple system which exist if and only if $n \equiv 1$ or $3 \pmod 6$. For the resolution classes to exist, we must have $n \equiv 3 \pmod 6$, whence we have a Kirkman triple system.

You could find an upper bound by a greedy algorithm (starting with $K_n$, pick the largest clique $K_s$ with $s \leq k$ from the unused vertices, delete those edges and continue until you run out of edges, starting a new part when necessary).

-

If $n=\frac{p^t-1}{p-1}$ and $k=p+1$ then we can consider the set $N$ as a finite projective space and our sets be lines in this space.

I think that in other cases problem is hard.

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A similar construction when $n = q^t$ and $k = q$ for some prime power $q$ is to identify the elements of $N$ with $(\mathbb{F}_q)^t$ and decompose the space into collections of parallel lines. –  JBL Apr 20 '10 at 13:16

If $k=2$, the answer is $2[(n+1)/2]-1$.

If $k=2$, then there are $n\choose2$ pairs, and each partition gets at most $[n/2]$ of them, so you can't do better than ${n\choose2}/[n/2]$, which is $2[(n+1)/2]-1$. So we have to show that we can achieve $2[(n+1)/2]-1$.

First let $n=2m-1$ be odd. Let the first partition be 1-with-$n$, 2-with-$(n-1)$, ..., $(m-1)$-with-$(m+1)$,$m$-by-itself. Get the other partitions by repeatedly adding 1 to each number in the previous partition, working modulo $n$.

E.g., for $n=7$, the first partition is 1-7, 2-6, 3-5, 4, and the others are 2-1, 3-7, 4-6, 5; 3-2, 4-1, 5-7, 6; 4-3, 5-2, 6-1, 7; 5-4, 6-3, 7-2, 1; 6-5, 7-4, 1-3, 2; and 7-6, 1-5, 2-4, 3.

Now if $n=2m$ is even, just take the solution for $n=2m-1$ and in each partition pair $n$ up with the singleton. E.g., when $n=8$, the solution starts 1-7, 2-6, 3-5, 4-8; 2-1, 3-7, 4-6, 5-8; etc.

As Douglas notes, this is a problem of factoring the symmetric graph. For $k=2$ we're factoring it into 1-factors, and undoubtedly what I've written above is well-known.

-
Indeed, the construction I give can be found at en.wikipedia.org/wiki/Graph_factorization –  Gerry Myerson Apr 20 '10 at 4:07


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Since finishing my first class on classical mechanics I have been interested in deriving the equations of motion for strings. Before I begin it should be noted that I do not have formal training in continuum mechanics, so the methods and definitions that I use may be nonstandard.

## Definitions

First lets define the coordinates $\ell$ and $t$, where $\ell$ is a unitless coordinate in the range [0, 1] denoting the location of a point along the string and $t$ is the time coordinate. To parameterize the string we will use the functions $\eta(\ell, t)$ and $\theta(\ell, t)$. The function $\theta(\ell, t)$ denotes the angle of an infinitesimal line segment of the string. The function $\eta(\ell, t)$ denotes the length of an infinitesimal line segment. Given these definitions the total length of the string is

and the spatial coordinates of the points along the string are given by

$$X(\ell, t) = \int_0^{\ell}\eta(\ell^{\prime}, t)sin(\theta(\ell^{\prime}, t))d\ell^{\prime}\label{def_x}$$

$$Y(\ell, t) = \int_0^{\ell}\eta(\ell^{\prime}, t)cos(\theta(\ell^{\prime}, t))d\ell^{\prime}\label{def_y}$$

In addition lets define the constants $\eta_0$, $m$, $\vec{g}$ and $k$, where $\eta_0$ is the length of an infinitesimal line segment in the absence of tension, $m$ is the linear mass density defined such that the total mass is $M=\int_0^1md\ell$, $\vec{g}$ is the gravitational acceleration vector and $k$ is the elasticity defined such that the linear potential energy density is $\frac{1}{2}k(\eta(\ell, t) - \eta_0)^2$.

Before we can construct the Lagrangian we need to be able to determine the parameter $\eta(\ell, t)$ in terms of the coordinates $X$ and $Y$. Taking the partial derivative of equation \eqref{def_x} and equation \eqref{def_y} with respect to $\ell$ results in the equations $\partial_{\ell}X=\eta(\ell, t)sin(\theta(\ell, t))$ and $\partial_{\ell}Y = \eta(\ell, t)cos(\theta(\ell, t))$. Defining $\vec{x}$ as $\vec{x} = X(\ell, t)\hat{x} + Y(\ell, t)\hat{y}$, then $\partial_{\ell}\vec{x} \cdot \partial_{\ell}\vec{x} = (\partial_{\ell}X)^2 + (\partial_{\ell}Y)^2=\eta(\ell, t)^2$, which results in the definition $\eta(\ell, t) = \pm \|\partial_{\ell}\vec{x}\|$. There is an ambiguity in the parameterization of $X(\ell, t)$ and $Y(\ell, t)$ in terms of $\eta(\ell, t)$ and $\theta(\ell, t)$. Given some $X(\ell, t)$ and $Y(\ell, t)$ a sign change in $\eta$ with a $\pm\pi$ radian shift in $\theta$ at some point $\ell_0$ will have no effect on the functions $X(\ell, t)$ and $Y(\ell, t)$. To resolve this $\eta$ is constrained to be positive such that $\eta(\ell, t) = \lvert\partial_{\ell}\vec{x}\rvert$. Now that we can unambiguously define $\eta(\ell, t)$, it is possible to write all of the energy components in terms of the coordinates of the individual elements of the string.

The string will have two energy components, the kinetic energy and potential energy. Using the definition of $\vec{x}$ given in the preceding paragraph these energy terms can be written as

## Lagrangian Mechanics

The Lagrangian of the string is $\mathscr{L}=E_k-E_p=\int_0^{1}\mathcal{L}d\ell^{\prime}$, where $\mathcal{L}$ is the Lagrangian density $\mathcal{L}=\frac{1}{2}m(\partial_t\vec{x})^2 - \left(m\vec{x}\cdot\vec{g} + \frac{1}{2}k(\lvert\partial_{\ell}\vec{x}\rvert - \eta_0)^2\right)$. The action $\mathcal{S}$ is then given by the equation $\mathcal{S} = \int_0^t\int_0^1\mathcal{L(\vec{x}, \partial_t\vec{x}, \partial_{\ell^{\prime}}\vec{x})}dtd\ell^{\prime}$. Using the form of the Euler-Lagrange equation as used in classical field theory with the coordinates $t$ and $\ell$,

Substituting the Lagrangian density into the Euler-Lagrange equation,

Evaluating the partial derivatives produces the equation,

While this equation was derived in two dimensional space it is generalizable to three dimensions given that the equation $\eta(\ell, t)^2=(\partial_{\ell}\vec{x})^2$ remains valid given the definition $\vec{x} = X(\ell, t)\hat{x} + Y(\ell, t)\hat{y} + Z(\ell, t)\hat{z}$. So the equation of motion for a string in three dimensional space is given by,

$$\partial_t^2\vec{x} = \frac{k}{m}\left(\partial_{\ell}^2\vec{x}-\eta_0\frac{\partial_{\ell}^2\vec{x}}{\lvert\partial_{\ell}\vec{x}\rvert}+\eta_0\frac{\partial_{\ell}\vec{x}(\partial_{\ell}\vec{x}\cdot\partial_{\ell}^2\vec{x})}{(\partial_{\ell}\vec{x})^2\lvert\partial_{\ell}\vec{x}\rvert}\right)-\vec{g}\label{string}$$

This equation should describe the dynamics of a string with a uniform elasticity and density in a uniform gravitational field assuming a simple linear model of elasticity. The energy component due to the stiffness of the string was not added to this derivation since it would require spatial derivatives higher than first order.

## Simplifying Cases

In the next three sections we will investigate simplified cases and solutions of equation \eqref{string}.

#### Case 1: String Under Tension

The elastic potential energy is defined as $\frac{1}{2}k(\lvert\partial_{\ell}\vec{x}\rvert - \eta_0)^2$. Assuming the string is stretched such that $\frac{\eta_0}{\lvert\partial_{\ell}\vec{x}\rvert}\ll 1$ then equation \eqref{string} reduces to the equation,

The general solution to this equation is,

where $\vec{F}(x)$ and $\vec{G}(x)$ are both arbitrary functions, $v$ satisfies $v^2=\frac{k}{m}$ and where $\vec{a}\_1$, $\vec{a}\_2$, $\vec{a}\_3$, $\vec{a}\_4$ and $\vec{a}\_5$ are arbitrary constant vectors. The actual velocity of a wave in the string is $c(\ell)=v\lvert\partial_{\ell}\vec{x}\rvert$. From the standard derivation of the equations for a vibrating string the wave velocity is $c=\sqrt{\frac{T}{\mu}}$, where $T$ is the magnitude of the tension and $\mu$ is the linear mass density. In terms of the quantities defined in this derivation the tension $T$ is $T=k\lvert\partial_{\ell}\vec{x}\rvert$ and the linear mass density $\mu$ is $\mu=\frac{m}{\lvert\partial_{\ell}\vec{x}\rvert}$, which leads to the equation for the velocity $c=\sqrt{\frac{k\eta^2(\ell)}{m}}=v\eta(\ell)$. So the assumption that $\eta_0$ is small relative to $\eta(\ell)$ leads to the expected result, that the string under tension is described by a vector form of the one dimensional wave equation and that the velocity of waves depends on the local tension and linear density of the string.

#### Case 2: Near Vertical String

Given $\vec{g}=g\hat{z}$ the necessary assumptions for a near vertical string are that $\frac{\left|\partial_\ell X\right|}{\left|\partial_\ell Z\right|}\ll 1$ and $\frac{\left|\partial_\ell Y\right|}{\left|\partial_\ell Z\right|}\ll 1$. Using these assumptions equation \eqref{string} simplifies to the equation,

This equation can be further simplified when written in expanded form,

In this approximation the equation for the vertical component of the wave is just the one dimensional wave equation. The equations for the horizontal components are a modified wave equation which behaves in one way if the string is under tension and behaves differently if it is under compression. If the string is locally under tension $\lvert\partial_{\ell}Z\rvert\gt\eta_0$ then the horizontal components behave like a form of wave equations. If the string is locally under compression then the sign of the equation is flipped and rather than oscillatory behavior any perturbations from vertical grow exponentially.

#### Case 3: Inelastic String

For the case of an inelastic string assume that the elastic potential energy is small relative to the other sources of energy, that is $\frac{1}{2}k(\lvert\partial_{\ell}\vec{x}\rvert - \eta_0)^2\ll E_\text{total}$ and that the coefficient $k$ is large such that $\frac{1}{2}k\eta_0^2\gg E_\text{total}$. These assumptions lead to the condition that $\lvert\frac{\lvert\partial_{\ell}\vec{x}\rvert}{\eta_0}-1\rvert\ll 1$, given these assumptions equation \eqref{string} reduces to the equation,

In the case of a near vertical inelastic string the equations become,

When this equation is expanded it has the form,

In this approximation again the equation for the vertical component assuming the string is nearly vertical is the one dimensional wave equation. In the horizontal components the equations will exhibit exponential growth or oscillatory behavior depending on the overall sign of $\frac{\partial_{\ell}^2Z}{\partial_{\ell}Z}$.


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# 13.2 Active circuit elements  (Page 7/7)

 Page 7 / 7

## The operational amplifier

The operational amplifier is a special kind of voltage amplifier which is made from a handful of bipolar or field effect transistors. Operational amplifiers are usually called op-amps for short. They are used extensively in all kinds of audio equipment (amplifiers, mixers and so on) and in instrumentation. They also have many other uses in other circuits - for example comparing voltages from sensors.

Operational amplifiers are supplied on Integrated Circuits (I.C.s). The most famous operational amplifier I.C. is numbered 741 and contains a single operational amplifier on an integrated circuit (chip') with eight terminals. Other varieties can be bought, and you can get a single integrated circuit with two or four 741'-type operational amplifiers on it.

The symbol for an op-amp is shown in [link] . The operational amplifier has two input terminals and one output terminal. The voltage of the output terminal is proportional to the difference in voltage between the two input terminals. The output terminal is on the right (at the sharp point of the triangle). The two input terminals are drawn on the left. One input terminal (labelled with a $+$ on diagrams) is called the non-inverting input . The other input terminal (labelled $-$ ) is called the inverting input . The labels $+$ and $-$ have nothing to do with the way in which the operational amplifier is connected to the power supply. Operational amplifiers must be connected to the power supply, but this is taken for granted when circuit diagrams are drawn, and these connections are not shown on circuit diagrams. Usually, when drawing electronic circuits, 0V' is taken to mean the negative terminal of the power supply. This is not the case with op-amps. For an op-amp, 0V' refers to the voltage midway between the $+$ and $-$ of the supply.

The output voltage of the amplifier ${V}_{out}$ is given by the formula ${V}_{out}=A\left({V}_{+},-,{V}_{-}\right)$ where $A$ is a constant called the open loop gain , and ${V}_{+}$ and ${V}_{-}$ are the voltages of the two input terminals. That said, the output voltage can not be less than the voltage of the negative terminal of the battery supplying it or higher than the positive terminal of the battery supplying it. You will notice that ${V}_{out}$ is positive if ${V}_{+}>{V}_{-}$ and negative if ${V}_{+}<{V}_{-}$ . This is why the $-$ input is called the inverting input: raising its voltage causes the output voltage to drop .

The input resistance of an operational amplifier is very high. This means that very little current flows into the input terminals during operation.

If all of the transistors in the operational amplifier were identical then the output voltage would be zero if the two inputs were at equal voltages. In practice this is not quite the case, and for sensitive work a trimming potentiometer is connected. This is adjusted until the op-amp is zeroed correctly.

Simple operational amplifiers require the trimming potentiometer to be built into the circuit containing them, and an example is shown in [link] . Other operational amplifier designs incorporate separate terminals for the trimming potentiometer. These special terminals are labelled offset on the manufacturer's diagram. The exact method of connecting the potentiometer to the offset terminals can depend on the design of the operational amplifier, and you need to refer to the manufacturer's data sheet for details of which potentiometer to use and how to connect it.

For most commercially produced operational amplifiers (known as op-amps for short), the open loop gain $A$ is very large and does not stay constant. Values of 100 000 are typical. Usually a designer would want an amplifier with a stable gain of smaller value, and builds the operational amplifier into a circuit like the one in [link] .

## Calculating the gain of the amplifier in [link] .

1. The input resistance of the operational amplifier is very high. This means that very little current flows into the inverting input of the op-amp. Accordingly, the current through resistor ${R}_{1}$ must be almost the same as the current through resistor ${R}_{2}$ . This means that the ratio of the voltage across ${R}_{1}$ to the voltage across ${R}_{2}$ is the same as the ratio of the two resistances.
2. The open loop gain $A$ of the op-amp is very high. Assuming that the output voltage is less than a few volts, this means that the two input terminals must be at very similar voltages. We shall assume that they are at the same voltage.
3. We want the output voltage to be zero if the input voltage is zero. Assuming that the transistors within the op-amp are very similar, the output voltage will only be zero for zero input voltage if ${V}_{+}$ is very close to zero. We shall assume that ${V}_{+}=0$ when the trimming potentiometer is correctly adjusted.
4. It follows from the last two statements that ${V}_{-}\approx 0$ , and we shall assume that it is zero.
5. With these assumptions, the voltage across ${R}_{2}$ is the same as ${V}_{out}$ , and the voltage across ${R}_{1}$ is the same as ${V}_{in}$ . Since both resistors carry the same current (as noted in point 1), we may say that the magnitude of ${V}_{out}/{V}_{in}={R}_{2}/{R}_{1}$ . However, if ${V}_{in}$ is negative, then ${V}_{out}$ will be positive. Therefore it is customary to write the gain of this circuit as ${V}_{out}/{V}_{in}=-{R}_{2}/{R}_{1}$ .

## Operational amplifiers

1. What are operational amplifiers used for?
2. Draw a simple diagram of an operational amplifier and label its terminals.
3. Why is a trimming potentiometer needed when using an op-amp?

#### Questions & Answers

how is ester formed
how is n ester formed
Aubrey
Alcohol reacts with a carboxylic acid
Texas
an athlete with a mass of 70kg runs at a velocity of 45km . determine the athlete's momentum
Is that a velocity or something else
msawenkosi
45km/h i guess
Texas
Change to m/s
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45km/h = 12.5 m/s p=mv =70×12.5 =875 kg.m/s
Thato
what are the measures of the rates of reaction
Volume Concentration Temperature Pressure Surface Area
Thato
the principle of superposition of waves
what is work
is this a group chat
Hey can y'all define newton's 2nd law
mthebzification
If a resultant force act on an object...the object will accelerate in the direction of a resultant force,the acceleration of the object is directly proportional to the net force and inversely proportional to the mass of the object
mosa
how do you calculate tension force
Bulumko
use the formula Fnet=ma if there is tension connecting two objects
Sboniso
to calculate Tension, usually calculate acceleration first Draw separate free body diagrams for each body. Apply Fnet = ma to calculate Tension
Kevin
Hi people
Paul
how does temperature affect the equilibrium position
an increased temperature increases the average kinetic energy thus in turn increases the number of effective collisions........
Lwando
so...which reaction is favored between endothermic and exothermic .when temperature is increased..?
Blessing
exothermic reaction because energy is realised to the surroundings as heat and light energy ....graphical so much energy is realised as reactants to form product and because temperature is high rate of reaction is fast which means there is a successful collision
Code
INTEMENDO - INCREASE IN TEMPERATURE FAVOURS ENDOTHERMIC DETEMEXO - DECREASE IN TEMPERATURE FAVOURS EXOTHERMIC
Thato
an object will continue in a state of rest unless it is acted upon an unbalanced force
Newton's Law 1
Code
First Newton's Law
Azola
Newton's first law
Surprise
newton first law
Thinavhuyo
Newton's first law
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when pressure is increased what happen to volume
decreases
Code
care to explain?
Mpati
if pressure is applied to a pistol , the volume will decrease and particles will collide more frequently with the wall of a container .Each time they collide with the wall they exert a force on them .More collision means more force and the pressure will increase , that Boyle's Law
Code
Because the volume has decreased , the particle will collide more frequently with the wall of a container and each time they collide with the wall of a container they exert a force on them.More collision means more force so the pressure will increase , that Boyle's Law
Code
what is the difference between momentum and a change in momentum?
How to name a branched molecule from right or left?
What's Free Fall
Free Fall means there is no acting force on that object.
Dingaletu
only gravitational force
Dingaletu
no external force acting on an object
Sphiwe
by only force of gravite
Sello
but gravitational force
Sphiwe
true
Lucky
a motion in which the only force acting is gravitational force
Blessing
and an object experiencing free fall is referred as a projectile
Blessing
Do polymers form restrictedly only if compound is saturated, only?
what is a free fall?
is when The Only Force acting On an Object is Gravitational Force
Thats right
Beyanca
then Why ask when you Know the answer?
She's just helping those who forgot it...bro
Thato
guys I need help on Getting ready for a last minute test
Neil
we'll I'm in grade 12 so we doing this topic about upac thing
Kenelioe
on What?
the organic molecule section
Kenelioe
IUPAC NAMING WHICH FUNCTIONAL GROUP YOU CANNOT NAME?SO I COULD HELP YOU
ester
Sboniso
you should also look at structural isomers. Its crucial that they might add that one. also try and write down the structural formula of all the given compounds on the table
milani


text:
# #finaltrashtination. An art-based intervention to collaboratively generate conversations about climate change

### Abstract:

In this practice insight, an art-based, participatory intervention (#finaltrashtination) is presented as higher education assignment in environmental and climate change communication. The project #finaltrashtination made dominant environmentally destructive ways of wasting visible and stimulated students to take responsibility, advocacy and authorship for transformation. Beyond the one-day eco-culture jam, the project engaged the wider public through conversations about a specific environmental problem. Thus, the project shows how conversational problematization and sensemaking around scientific facts can be initiated by using eco-culture jams promoting very unsettling moments of reflection.

Keywords:

2 October 2021

17 December 2021

28 March 2022

### 1 Introduction & background

At the beginning of the “Roaring 20ies” of our century, communication about scientific facts, about the climate crisis, and about technology to solve our most urgent societal problems (i.e. a global pandemic, natural hazards, CO2 emissions) is equally important as communication for transformation, for cultural change. Next to rather established pragmatic or instrumental approaches to communicate about scientific facts regarding the changing climate or related risks, communication for social change and sustainable development seems to require new, innovative, and rather critical, co-creational ways of communication. Here, recent work from science communication scholarship offers a new understanding of communication as conversations, more precisely: science communication as a social conversation around science [Bucchi and Trench, 2021]. Accordingly, new ways to inspire, stimulate, drive and facilitate these conversations are explored and further conceptualized in science communication. Also in practice, storytelling, art-based approaches, digital and design technologies are increasingly used and discussed regarding their potential to engage people not only intellectually, but as well emotionally [Metcalfe, 2019; Joubert, Davis and Metcalfe, 2019; Lesen, Rogan and Blum, 2016; Nature, 2021]. Alongside, rooted in the growing field of (higher) education for sustainability and transformation [Pedersen, 2017; Sterling and Huckle, 2014], critical pedagogical approaches in science and environmental communication [Weder, Lemke and Tungarat, 2019] have developed using similar conversational approaches. These concepts describe the conversational role of communication as carrying potential to crack existing norms, to challenge common sense and common beliefs. Consequently, they include the idea that transformation and cultural change happens in conversations [Weder and Milstein, 2021; Milstein and Pulos, 2015, p. 395; Dery, 2017].

In this situation, Universities as pivotal organizations in modern societies are particularly challenged [Schäfer and Fähnrich, 2020]. There seems to be a lack in engagement and acknowledgement of innovative, conversational approaches [Entradas et al., 2020; VanDyke and Lee, 2020]. Universities are accused to not (always) use their immense transformative potential [Soini et al., 2018; Burns, 2015; Adomßent, 2013; Leal Filho, 2009], except individual teachers who feel responsible for influencing students to take authorship and agency for their future [Henderson and Tilbury, 2004; Lozano et al., 2013; Mezirow, 2000]. Or those who create deeper “transformative learning” processes [Mezirow, 2000; O’Sullivan, Morrell and O’Connor, 2002]. These processes include problematization and critique on the one hand, and processes of collective sense-making processes via conversations on the other hand [Weder and Milstein, 2021].

The pedagogical understanding of conversations as negotiations of meaning and sense-making process meets the abovementioned innovative approaches to science communication as social conversations around science [Bucchi and Trench, 2021]. Bridging these two backgrounds, the paper at hand offers insights in the project #finaltrashtination that engaged scientists, teachers, students, and the audience [Bultitude and Sardo, 2012] by stimulating conversations about and for the (in)visibility of waste [Sunassee, Bokhoree and Patrizio, 2021; Weder and Milstein, 2021]. In the following, the genesis of the project and the intervention itself will be described, before the most important learnings in a science and environmental communication context will be discussed and an outlook is given on future perspectives for eco-culture jamming.

### 2 The intervention

In this section, a science communication project conceptualized as student activism [Halpern and O’Rourke, 2020] will be presented. It started with engagement on an individual level [Pauwels, 2019] and was embedded in a seminar on environmental communication. The intervention had the character of an “eco-culture jam”, which provided students ways to generate a situation that helped to bring in emotions [Davies, 2019] and to instigate journeys of conversations and reflection beyond the lecture hall [Milstein and Pulos, 2015]. In the following, the eco-culture jam and the conversations the students stimulated will be described. But before, the idea of an eco-culture jam with problematization as core process of the “jamming” will be briefly introduced.

#### 2.1 Eco-culture jamming

As mentioned above, the intervention itself was conceptualized as “eco-culture jam” [Weder and Milstein, 2021]. The concept of an eco-culture jam goes back to performances described as “culture jams” [Lasn, 2000]. As a simple act of creative resistance, the often art-based intervention raises awareness, reframes debates and, most importantly, reclaims and maintains individuals’ sovereignty [Milstein and Pulos, 2015]. An eco-culture jam in particular describes interventions and simple acts of resistance which “crack” patterns of environmental behavior or a specific representation of our current human-nature relationship, for example the concept of waste.

In a higher education setting, this sort of collaborative nonconformity and students co-expressively working together allows new, alternative ways of communication and learning. With an eco-culture jam, students create a situation where they are forced to question pervasive hegemonies that not only inform the institution of higher education and thus the University itself, but much more their very own everyday experiences like wasting and plastic waste and wider social structures like the lack of information and facts on where the waste goes. The process of questioning is here theoretically captured as problematization through conversations [Weder, 2021a]. Thus, an eco-culture jam is not only about one action or intervention only but also about the stories that are told around it, the conversations that happen alongside the intervention. In these conversations, an environmental problem like wasting or plastic waste are defined as problem by talking about it. Problematization sits at the core of the conversations about and for change, it works as driver and stimulus of conversations about certain facts, for example how much waste we produce, where it goes after we put it in the bin, potential for and techniques of recycling etc.

Problematization also includes the process of creating “cracks in underlying systems of power, and to promote unsettling moments of reflection and debate” [Milstein and Pulos, 2015, p. 397]. It includes the emotions, cognitive dissonances and morality that comes in as soon as people reflect on the sheer amount of waste or the fact that waste does not disappear just because it is put in the bin. Problematization is the process of permanent contestation; thus, in eco-culture jams and related conversations dissent is stimulated and hegemonic arguments are challenged [Weder, 2021a; Roberson and Orthia, 2021]. An eco-culture jam creates confusion over an issue like plastic waste [Weder, Lemke and Tungarat, 2019; Krainer, Lerchster and Goldmann, 2012; Karmasin et al., 2021] and allows new viewpoints and increased awareness, consciousness, and action to emerge from it [Crotty, 1998]. It invites the transformation of a specific situation and increases the level of involvement and action by communication [Crable and Vibbert, 1985]. How this has been put into practice in the eco-culture jam #finaltrahstination will be further described in the next section.

#### 2.2 Developing an intervention

The art-based intervention this paper talks about was part of a university-course specifically focusing on environmental activism, sustainability, and social movements. It started with a design thinking process [Dell’Era et al., 2020] to identify sustainability and its scope as a normative (westernized) framework [Hahn et al., 2017; Weder, 2021b], that has the potential to be reflected on and “cracked”. The design thinking process includes five stages; the first stage is to empathize and research, followed by a definition phase. In the third phase, the creative process starts, called “ideation”. A prototype or a specific intervention is then created and operationalized and evaluated, guided by the principle of challenging existing social representations and assumptions, which was described as “cracking” exiting patterns of thinking and behavior above.

For the intervention at hand, several sustainability issues were identified from an individual perspective (stage 1 of the design thinking process), with the most attention on waste and recycling. The students discovered that sustainability is not only divided in a social, environmental, and economic dimension [Pristl, Kilian and Mann, 2020], much more they deconstructed the Sustainable Development Goals [United Nations, 2021] as stimulating not only individuals but mainly organizations and even Universities to “take action” in very different thematic fields.

The second step (stage 2) of the design thinking process were expert interviews and individual research that helped to “empathize”, to further understand the problems and challenges around the chosen issue in a non-judgemental way [Buhl et al., 2019]. After identifying waste as one of the core problems and challenges related to the principle of sustainability meaning resource awareness, the students confirmed cultural patterns of waste and wasting, dominant narratives and existing knowledge with narrative interviews on campus. One of the identified waste-narratives was “out of sight, out of mind”. The interviews helped the students to not only identify the culture of wasting as part of an imbalanced human-nature relationship and example for unsustainable behavior, but as well possible moments of disruption. This part of the research was complemented by workshops with waste-experts and responsible internal staff members to understand the amount and sort of waste at the University of Klagenfurt as well as learn about facts around recycling and further processing of waste in this particular locality.

From there, the students started to share their ideas for an intervention in class, which was above described as ideating; this is a core process of design thinking, where the thinking process should diverge and converge as long as needed, before then a few ideas get prioritized. The existing culture of wasting and related patterns of behavior, specifically the concept of “out of sight, out of mind” was the one that got prioritized by the students. This is, what they decided to challenge and “crack”, to stimulate conversations around it.

Consequently, the students developed prototypes (stage 3) of wall elements for a wall of waste, which was meant to be built and co-created during the day of action: a wall, designed as a visual barrier for people to not “look away”, to no longer ignore and to not simply “pass on” the waste they are creating.

For the actual realization of the “wall of waste” (stage 4), the students co-operated with a local startup (pixapo / the thinking) to build the actual elements (1.50 meter $×$ 2 m each) with wood and plastic wrap, which was chosen on purpose to visualize the waste that you often don’t notice, as the “unseen” wrapping (see Figure ??a and ??b).

While building the “wall of waste”, the students further problematized the concept of waste by not only using the plastic wrap, but even more by producing waste themselves, like the water bottles they used during the process themselves. Here, the students negotiated the responsibility which is given away with each piece of waste that is thrown in the bin, responsibility that is allocated to “whoever is taking care of that” (Interview 6, April 2019). This led to the title of the planned intervention: “finaltrashtination”, a “wall of waste” which “hinders people to look away” (Student A., May 2019).

#### 2.3 Art-based intervention: the eco-culture jam #finalthrashtination

In the early morning of June 5${}^{\mathrm{th}}$, 2019, the students transported the transparent elements of the wall of waste and built it up in the entrance hall of the University (Alpen-Adria University of Klagenfurt, Austria; see Figure ??).

After this, they collected the University’s 2-week-plastic waste which was held back for this period of time for us and unfurled it in front of the University’s main entrance (see Figure ??a and ??b).

The difference between an eco-culture jam and an art piece is, that the jam itself, the process of creation is the intervention itself, rather than a pre-build or pre-created art piece which then acts as trigger for reflection or conversations [Lesen, Rogan and Blum, 2016; Davies et al., 2019]. An eco-culture jam is the “doing”, the ongoing problematization, by creating interrelatedness, connectedness, and involvement. Therefore, the students invited everyone who wanted to enter the University via the main entrance, to pick one piece of waste, enter the main entrance hall and throw the waste in one of the transparent parts of the wall, which were open on the top.

Thus, in a participatory process during the whole day, the transparent wall elements in the front hall of the University of Klagenfurt filled up with waste, piece by piece (see Figure ??).

As mentioned above, during the day of action and due to the fact that the intervention took place at the most crowded spot of the University (entrance hall), conversations and live storytelling were stimulated, again, with problematization happening automatically triggered by the action of throwing a piece of plastic waste in the “bin” again, rather than the art piece as a whole. Thus, in the following summary of the learnings of the project, these problematizing conversations and the potential of this concept for science communication in the future will be highlighted.

### 3 Discussion

Related to Bucchi and Trench’s [2021] work on social conversations around science, eco-culture jams are a participatory form of conversation, informal and open [Bucchi and Trench, 2021, p. 8] As described above, while stacking and building the “wall of waste”, the students not only invited people passing by to join in (direct communication), additionally, they stimulated a discourse via social media during the jam (indirect communication). This is what we defined as conversations about certain waste related facts (about the amount, quality, problems and challenges with recycling, comparisons with other contexts etc.), see Figure ??, first phase.

But furthermore, there was a second phase of problematization and resonance, a public discourse that was stimulated by the news coverage and the shared youtube-video of the intervention via individual social media and local newspaper’s websites. This discourse represents what we define as communication for change, for transformation, because the jam itself was discussed and problematized as sustainability related action in the media beyond the day of action. Thus, the art-based intervention #finaltrashtination left an impressive footprint in the local, regional and definitely the wider social media environment.

Finally, the intervention was discussed in the classroom (stage 5); this feedback and “back-coupling” of the jam itself closes the loop, is what we conceptualized as education for transformation and educating to take responsibility and authorship in the first section of the paper. Eco-culture jams are participatory, they engage not only every day and individual ways of communicating and constructing culture, here: a culture of wasting. Beyond this, a culture jam engages institutional ways of communicating. Science and environmental educators can use this participatory communication strategy to bring the act of jamming back into the realm of questioning, of creatively engage with the locality (here: University) and shifting or even repositioning culture.

Overall, the art-based intervention #finaltrashtination is not only an example of innovative pathways in learning and teaching science and environmental communication in a university setting. It also shows the potential of re-thinking science communication as social conversations around science and of bringing in new principles like sustainability into existing environmental discourses.

### 4 Outlook

The project #finaltrashtination was conceptualized as ecoculture jam and therefore as pedagogical tool which is particularly relevant for science, sustainability and environmental communication scholars, pedagogues, and practitioners, most of whom adhere to an “ethical duty” [Cox, 2018] that drives their work, and who are interested in transformative communication and ways and tactics to engage consciousness, reflexivity, and critical awareness [Darts and Tavin, 2010]. In introducing this specific ecoculture jam as valid mode of learning in on and off-campus teaching spaces, this insights paper shows how science and environmental communication students can be supported and motivated to take action, mobilize, and actively engage with scientific facts, technological solutions and concepts like sustainability by creating moments of disequilibration where real change can happen.

Contact: f.weder@uq.edu.au

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Sunassee, A., Bokhoree, C. and Patrizio, A. (2021). ‘Students’ Empathy for the Environment through Eco-Art Place-Based Education: A Review’. Ecologies 2 (2), pp. 214–247. https://doi.org/10.3390/ecologies2020013.

United Nations (September 2021). Take action for the sustainable development goals. URL: https://www.un.org/sustainabledevelopment/sustainable-development-goals/.

VanDyke, M. S. and Lee, N. M. (2020). ‘Science public relations: The parallel, interwoven, and contrasting trajectories of public relations and science communication theory and practice’. Public Relations Review 46 (4), p. 101953. https://doi.org/10.1016/j.pubrev.2020.101953.

Weder, F. (2021a). ‘Strategic problematization of sustainability reframing dissent in strategic communication for transformation’. Public Relations Inquiry, p. 2046147X2110268. https://doi.org/10.1177/2046147x211026857.

— (2021b). ‘Sustainability as Master Frame of the Future? Potency and Limits of Sustainability as Normative Framework in Corporate, Political and NGO Communication’. In: The Sustainability Communication Reader. Ed. by F. Weder, L. Krainer and M. Karmasin. Springer Fachmedien Wiesbaden, pp. 103–119. https://doi.org/10.1007/978-3-658-31883-3_7.

Weder, F., Lemke, S. and Tungarat, A. (2019). ‘(Re)storying Sustainability: The Use of Story Cubes in Narrative Inquiries to Understand Individual Perceptions of Sustainability’. Sustainability 11 (19), p. 5264. https://doi.org/10.3390/su11195264.

Weder, F. and Milstein, T. (2021). ‘Revolutionaries Needed! Environmental Communication as a Transformative Discipline’. In: The Handbook of International Trends in Environmental Communication. Routledge, pp. 407–419. https://doi.org/10.4324/9780367275204-30.

### Author

Assoc. Prof. Dr. Habil Franzisca Weder, Senior Lecturer at the University of Queensland, Brisbane (Australia), is researching, writing, and teaching in the areas of Organizational Communication and Public Relations with a specific focus on Sustainability Communication, Corporate Social Responsibility and Cultures of Sustainability. She mainly works with framing and storytelling concepts to study communication about and for sustainability.
Before her commencement at UQ, Franzisca worked as Guest Professor at University of Alabama (U.S.A.), University of Eichstätt-Ingolstadt (GER), University of Waikato (NZ), RMIT (Melbourne, AUS) and University of Ilmenau (GER) and she is currently the Chair of the International Environmental Communication Association (IECA).
E-mail: franzisca.weder@gmail.com.
UQ researchers’ profile: http://researchers.uq.edu.au/researcher/25707.
ORCID: https://orcid.org/0000-0003-1502-207X.
Current publication (“The Sustainability Communication Reader”): https://www.springer.com/gp/book/9783658318826.
Most recent paper on Framing, Storytelling & Sustainability: https://www.frontiersin.org/articles/10.3389/fcomm.2020.00008/full.

### How to cite

Weder, F. (2022). ‘#finaltrashtination. An art-based intervention to collaboratively generate conversations about climate change’. JCOM 21 (02), N05. https://doi.org/10.22323/2.21020805.


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# Numbers in congruence classes are regular languages

In this post we will consider natural Radix-b numbers in positional number systems. The congruence class of any such arbitrary natural number can be determined by a finite automata, and thus, intuitively speaking, the language of all Radix-b numbers that satisfy some fixed properties modulo b is regular.

## Radix-b numbers divisible by m

The key idea behind the automation construction is that after reading a digit, the new congruence class depends only on the current read digit and on the previous congruence class. There are only $m < \infty$ congruence classes so we can construct a finite automata that accepts all numbers divisible by m: \begin{aligned} A &= (Z,\Sigma,\delta, z_0, E) \\ Z &:= \{0,\dots, m-1\} \\ \Sigma &:= \{0,\dots, b-1\} \\ E &:= \{0\} \\ z_0 &:= 0 \\ \delta(r,d) &:= r \cdot b + d \bmod{m} \end{aligned}

The correctness of the transition function can be seen as follows: when the automation is in state $r$, the number that has been read is in the congruence class $r$ modulo $m$. So we can write it as $mk+r$. By multiplying with $b$ (i.e. shift the number by 1 digit to the left) and adding $d$ we get the new congruence class: \begin{aligned} \delta(r,d) &= (mk + r)\cdot b + d \bmod{m} \\ &= mkb + rb + d \bmod{m} \\ &= rb + d \bmod{m} \end{aligned}

Of course, by altering the set of final states $E$ we can accept not only multiples of $m$, but any such number $n$ with $n \bmod{m} \in E$ for any $E \subseteq Z$.

## Binary numbers modulo 4

For example, we can construct a finite automation that accepts all binary ($b = 2$) numbers divisible by 4 ($m = 4$):

The transitions are obtained as follows: \begin{aligned} 0 \cdot 2 \bmod{4} = 0 &\implies \delta(0, 0) = 0, \delta(0, 1) = 1 \\ 1 \cdot 2 \bmod{4} = 2 &\implies \delta(1, 0) = 2, \delta(1, 1) = 3 \\ 2 \cdot 2 \bmod{4} = 0 &\implies \delta(2, 0) = 0, \delta(2, 1) = 1 \\ 3 \cdot 2 \bmod{4} = 2 &\implies \delta(3, 0) = 2, \delta(3, 1) = 3 \end{aligned}

In this particular case the constructed automation is not minimal. States s1 and s3 are equivalent (this can be formally proven with the Myhill-Nerode theorem) and can be replaced by one state:

As languages accepted by DFA’s are exactly the regular languages, we can transform any DFA in a regular expression to see the exact structure of numbers divisible, for example, by 4. Unfortunately such regular expressions are very long when constructed with the Kleene or with the Arden method by a computer. These regular expressions must be massively simplified in order to be readable. With the Kleene construction I’ve implemented in this project we get the following regular expression:

ε|0|(ε|0)0*(ε|0)|(1|(ε|0)0*1)(1|0*1)*0*(ε|0)|(1|(ε|0)0*1)(1|0*1)*0((1|00*1)(1|0*1)*0)*(0|00*(ε|0)|(1|00*1)(1|0*1)*0*(ε|0))

It can be simplified by computer heuristics down to:

ε|0|1(1|01)*00|(0|ε|1(1|01)*00)(0|1(1|01)*00)*(0|ε|1(1|01)*00)

Still, the regular expression is not so readable. By transforming it further by hand, we can prove that it is equivalent to:

ε|0|1(1|01)*00|(0|ε|1(1|01)*00)(0|1(1|01)*00)*(0|ε|1(1|01)*00) =
ε|0|1(1|01)*00|(ε|0|1(1|01)*00)(0|1(1|01)*00)*(ε|0|1(1|01)*00) =
ε|0|1(1|01)*00|(0|1(1|01)*00)*(ε|0|1(1|01)*00) =
ε|0|1(1|01)*00|(0|1(1|01)*00)* =
ε|0|(0|1(1|01)*00)* =
ε|0|(0|1(1|0)*00)* =
ε|0|0*(1(1|0)*000*)* =
ε|0|0*(1(1|0)*0*00)* =
ε|0|0*(1(1|0)*00)* =
ε|0|0*(1(0|1)*00)* =
ε|0|0*(1(0|1)*00|ε) =
ε|0|0*|0*1(0|1)*00 =
ε|0|0*|0*(0|1)*00 =
ε|0|0*(0|1)*00 =
ε|0|(0|1)*00

So, any binary number divisible by 4 must be zero or end with 00.

## Other examples

### Hexadecimal numbers divisible by 24

Copyright © 2020 Alexander Mayorov. All rights reserved.


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# The Power of Programs over Monoids in J

1 VALDA - Value from Data
DI-ENS - Département d'informatique de l'École normale supérieure, Inria de Paris
Abstract : The model of programs over (finite) monoids, introduced by Barrington and Thérien, gives an interesting way to characterise the circuit complexity class $\mathsf{NC^1}$ and its subclasses and showcases deep connections with algebraic automata theory. In this article, we investigate the computational power of programs over monoids in $\mathbf{J}$, a small variety of finite aperiodic monoids. First, we give a fine hierarchy within the class of languages recognised by programs over monoids from $\mathbf{J}$, based on the length of programs but also some parametrisation of $\mathbf{J}$. Second, and most importantly, we make progress in understanding what regular languages can be recognised by programs over monoids in $\mathbf{J}$. We show that those programs actually can recognise all languages from a class of restricted dot-depth one languages, using a non-trivial trick, and conjecture that this class suffices to characterise the regular languages recognised by programs over monoids in $\mathbf{J}$.
Document type :
Conference papers
Domain :

Cited literature [28 references]

https://hal.archives-ouvertes.fr/hal-02414771
Contributor : Nathan Grosshans <>
Submitted on : Tuesday, December 17, 2019 - 12:34:22 PM
Last modification on : Tuesday, May 4, 2021 - 2:06:03 PM
Long-term archiving on: : Wednesday, March 18, 2020 - 1:08:11 PM

### Files

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### Citation

Nathan Grosshans. The Power of Programs over Monoids in J. LATA 2020 - 14th International Conference on Language and Automata Theory and Applications, Mar 2020, Milan, Italy. ⟨10.1007/978-3-030-40608-0_22⟩. ⟨hal-02414771⟩

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NumericalSgps

A package for numerical semigroups

Version 1.2.1
Released 2019-08-22

This project is maintained by Manuel Delgado, Pedro A. Garcia-Sanchez

NumericalSgps

NumericalSgps is a GAP package for computing with Numerical Semigroups.

Introduction

The features of the package NumericalSgps include

• defining numerical semigroups;
• computing several properties of numerical semigroups, namely: multiplicity, Frobenius number, (minimal) system of generators, Apéry set, gaps, fundamental gaps, etc.;
• perform several operations on numerical semigroups and ideals, namely: intersection, quotient by an integer, decompose into irreducible semigroups, add a special gap, …; -computing and testing membership to relevant families of numerical semigroups.

There is a manual in the sub-directory doc written using the GAP package gapdoc which describes the available functions in detail. The pdf, html versions of the manual are also available there.

If you have used this package, please let us know by sending us an email. If you have found important features missing or if there is a bug, we would appreciate it very much if you send us an email.

The current maintainers of the package are: