Theory and methods of idempotent algebra, modeling and performance evaluation of stochastic dyscrete event dynamical systems.
Main publications:
Nikolai Krivulin, “Unbiased estimates for gradients of stochastic network performance measures”, Acta Applicandae Mathematicae, 33 (1993), 21–43
N. K. Krivulin, “A recursive equations based representation for the G/G/m queue”, Applied Mathematics Letters, 7:3 (1994), 73–78
N. K. Krivulin, “A max-algebra approach to modeling and simulation of tandem queueing systems”, Mathematical and Computer Modelling, 22:3 (1995), 25–37
N. K. Krivulin, “Solution of generalized linear vector equations in idempotent algebra”, Vestnik St. Petersburg University: Mathematics, 39:1 (2006), 16–26
N. K. Krivulin, Idempotent algebra methods for problems in modelling and analysis of complex systems, St. Petersburg University, St. Petersburg, 2009 (in Russian)
N. Krivulin, “On solution of two-sided vector equation in tropical algebra”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10:2 (2023), 236–248; Vestn. St. Petersbg. Univ., Math., 10:2 (2023), 236–248
N. Krivulin, M. A. Briushinin, “Solving a two-facility location problem in a space with Chebyshev metric”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9:4 (2022), 625–635; Vestn. St. Petersbg. Univ., Math., 9:4 (2022), 406–413
2021
3.
N. К. Krivulin, S. A. Gubanov, “Algebraic solution of a problem of optimal project scheduling in project management”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:1 (2021), 73–87; Vestn. St. Petersbg. Univ., Math., 8:3 (2021), 58–68
N. K. Krivulin, E. Yu. Romanova, “Approximate factorization of positive matrices by using methods of tropical optimization”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 16:4 (2020), 357–374
2019
5.
N. Krivulin, V. A. Ageev, “Methods of tropical optimization in multicriteria problems of raiting alternatives from pairwise comparisons”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 15:4 (2019), 472–488
P. V. Plotnikov, N. K. Krivulin, “Direct solution of a minimax location problem on the plane
with rectilinear metric in a rectangular area”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 14:2 (2018), 116–130
N. K. Krivulin, S. A. Gubanov, “The use of tropical optimization methods in problems of project scheduling”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 13:4 (2017), 384–397
N. Krivulin, V. A. Ageev, I. V. Gladkikh, “Application of methods of tropical optimization for evaluating alternatives based on pairwise comparisons”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 13:1 (2017), 27–41
N. Krivulin, S. A. Gubanov, “Solution of a project scheduling problem by using methods of tropical optimization”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2016, no. 3, 62–72
N. Krivulin, D. N. Vasilyev, “Computation of the Lyapunov exponent of a generalized linear stochastic dynamical system with a second-order matrix”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2015, no. 1, 120–134
2007
11.
N. K. Krivulin, “The growth rate of state vector in a generalized linear stochastic system with symmetric matrix”, Zap. Nauchn. Sem. POMI, 341 (2007), 134–141; J. Math. Sci. (N. Y.), 147:4 (2007), 6924–6928
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