Home Page of Nikolai Krivulin

[photograph] Curriculum Vitae in pdf

 Personal information
 Education and degrees
 Work and academic experience
 Administration experience
 Courses taught
 Research areas
 Research support
 Scholarships and travel grants
 Conference presentations and research visits
 Ph.D. students supervised
 Other professional activities
 Selected list of publications
 
 
 
 

Personal information

Name:

NIKOLAI K. KRIVULIN

Present position:

Professor, Department of Statistical Modeling, Faculty of Mathematics and Mechanics, St. Petersburg State University

Office address:

Faculty of Mathematics and Mechanics, St. Petersburg State University,
28 Universitetsky Ave., St. Petersburg, 198504 Russia
Tel.: (+7 812) 363 6000 (ext. 9043)
Fax.: (+7 812) 428 6944
E-mail: nkk@math.spbu.ru
URL: http://www.math.spbu.ru/user/krivulin/

Date of birth:

November 29, 1958

Place of birth:

Ulyanovsk, Russia

Author identifiers and research profiles:

Scopus Author ID: 22980220800
Web of Science ResearcherID: C-6660-2012
ORCiD ID: 0000-0003-3070-9355
MathSciNet AuthorID: 345662
zbMATH Author ID: krivulin.nikolai-k
Google Scholar Profile: Nikolai Krivulin
arXiv.org ID: krivulin_n_1

Education and degrees

Work and academic experience

Administration experience

Courses taught

Research areas

Research support

Scholarships and travel grants

Conference presentations and research visits

Talks and conference presentations

Research visits

Ph.D. students supervised

Other professional activities

Conference organization

Refereeing and reviewing

Membership of editorial boards

Membership of professional societies

Selected list of publications

Refereed journal articles

[1]   N. Krivulin. Algebraic solution of tropical best approximation problems. Mathematics, 11(18):3949, Sep 2023.

[2]   N. K. Krivulin. On the solution of a two-sided vector equation in tropical algebra. Vestnik St. Petersburg Univ. Math., 56(2):172–181, Jun 2023. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 10(2):236-248.

[3]   N. K. Krivulin and M. A. Bryushinin. Solution of a two-facility location problem in a space with Chebyshev distance. Vestnik St. Petersburg Univ. Math., 55(4):406–413, Dec 2022. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 9(4):625-635.

[4]   N. Krivulin and S. Sergeev. Minimizing maximum lateness in two-stage projects by tropical optimization. Kybernetika, 58(5):816–841, Dec 2022.

[5]   N. Krivulin. Algebraic solution to box-constrained bi-criteria problem of rating alternatives through pairwise comparisons. Kybernetika, 58(5):665–690, Dec 2022.

[6]   N. Krivulin, A. Prinkov, and I. Gladkikh. Using pairwise comparisons to determine consumer preferences in hotel selection. Mathematics, 10(5):730, Mar 2022.

[7]   N. Krivulin. Algebraic solution of tropical polynomial optimization problems. Mathematics, 9(19):2472, Oct 2021.

[8]   N. Krivulin. Algebraic solution to constrained bi-criteria decision problem of rating alternatives through pairwise comparisons. Mathematics, 9(4):303, Feb 2021.

[9]   N. K. Krivulin and S. A. Gubanov. Algebraic solution of a problem of optimal project scheduling in project management. Vestnik St. Petersburg Univ. Math., 54(1):58–68, Jan 2021. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 8(1):73-87.

[10]   N. Krivulin. Using parameter elimination to solve discrete linear Chebyshev approximation problems. Mathematics, 8(12):2210, Dec 2020.

[11]   N. Krivulin. Complete solution of tropical vector inequalities using matrix sparsification. Appl. Math., 65(6):755–775, Dec 2020.

[12]   N. Krivulin. Algebraic solution of minimax single-facility constrained location problems with Chebyshev and rectilinear distances. J. Log. Algebr. Methods Program., 115:100578, Oct 2020.

[13]   N. Krivulin. Tropical optimization technique in bi-objective project scheduling under temporal constraints. Comput. Manag. Sci., 17(3):437–464, Jun 2020.

[14]   N. Krivulin. Using tropical optimization techniques in bi-criteria decision problems. Comput. Manag. Sci., 17(1):79–104, Jan 2020.

[15]   N. Krivulin and S. Sergeev. Tropical implementation of the Analytical Hierarchy Process decision method. Fuzzy Sets and Systems, 377:31–51, Dec 2019.

[16]   N. K. Krivulin and U. L. Basko. Solving a tropical optimization problem with application to optimal scheduling. Vestnik St. Petersburg Univ. Math., 52(3):293–300, Jul 2019. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 6(3):440-451.

[17]   N. K. Krivulin and E. Yu. Romanova. On the rank-one approximation of positive matrices using tropical optimization methods. Vestnik St. Petersburg Univ. Math., 52(2):145–153, Apr 2019. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 6(2):208-220.

[18]   N. Krivulin. Complete algebraic solution of multidimensional optimization problems in tropical semifield. J. Log. Algebr. Methods Program., 99:26–40, Oct 2018.

[19]   N. K. Krivulin and E. Yu. Romanova. Rank-one approximation of positive matrices based on methods of tropical mathematics. Vestnik St. Petersburg Univ. Math., 51(2):133–143, Apr 2018. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 5(2):256-269.

[20]   N. K. Krivulin and V. N. Sorokin. Solution of a multidimensional tropical optimization problem using matrix sparsification. Vestnik St. Petersburg Univ. Math., 51(1):66–76, Jan 2018. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 5(1):91-104.

[21]   N. Krivulin. Using tropical optimization to solve constrained minimax single-facility location problems with rectilinear distance. Comput. Manag. Sci., 14(4):493–518, Sep 2017.

[22]   N. Krivulin. Tropical optimization problems with application to project scheduling with minimum makespan. Ann. Oper. Res., 256(1):75–92, Sep 2017.

[23]   N. K. Krivulin and J. V. Romanovsky. Solution of mathematical programming problems using tropical optimization methods. Vestnik St. Petersburg Univ. Math., 50(3):274–281, Jul 2017. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 4(3):448-458.

[24]   N. Krivulin. Algebraic solution of tropical optimization problems via matrix sparsification with application to scheduling. J. Log. Algebr. Methods Program., 89:150–170, Jun 2017.

[25]   N. Krivulin. Tropical optimization problems in time-constrained project scheduling. Optimization, 66(2):205–224, Feb 2017.

[26]   N. Krivulin. Direct solution to constrained tropical optimization problems with application to project scheduling. Comput. Manag. Sci., 14(1):91–113, Jan 2017.

[27]   N. K. Krivulin and P. V. Plotnikov. Using tropical optimization to solve minimax location problems with a rectilinear metric on the line. Vestnik St. Petersburg Univ. Math., 49(4):340–349, Dec 2016. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 3(4):602-614.

[28]   N. Krivulin. A maximization problem in tropical mathematics: A complete solution and application examples. Informatica, 27(3):587–606, Sep 2016.

[29]   N. K. Krivulin and V. N. Sorokin. Solution of a tropical optimization problem with linear constraints. Vestnik St. Petersburg Univ. Math., 48(4):224–232, Dec 2015. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 2(4):541-552.

[30]   N. Krivulin. Algebraic solutions of tropical optimization problems. Lobachevskii J. Math., 36(4):363–374, Dec 2015.

[31]   N. K. Krivulin and P. V. Plotnikov. On an algebraic solution of the Rawls location problem in the plane with rectilinear metric. Vestnik St. Petersburg Univ. Math., 48(2):75–81, Jun 2015. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 2(2):194-202.

[32]   N. Krivulin. A multidimensional tropical optimization problem with a non-linear objective function and linear constraints. Optimization, 64(5):1107–1129, May 2015.

[33]   N. Krivulin. Extremal properties of tropical eigenvalues and solutions to tropical optimization problems. Linear Algebra Appl., 468:211–232, Mar 2015.

[34]   N. K. Krivulin and O. A. Nev. Calculation of the asymptotic characteristics of a stochastic synchronized dynamic system. Vestnik St. Petersburg Univ. Math., 47(4):145–153, Oct 2014. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Matematika, 1(4):533-543.

[35]   N. Krivulin. Solution of linear equations and inequalities in idempotent vector spaces. Int. J. Appl. Math. Inform., 7(1):14–23, 2013.

[36]   N. Krivulin. A new algebraic solution to multidimensional minimax location problems with Chebyshev distance. WSEAS Trans. Math., 11(7):605–614, Jul 2012.

[37]   N. Krivulin. An algebraic approach to project schedule development under precedence constraints. Int. J. Appl. Math. Inform., 6(2):92–100, 2012.

[38]   N. K. Krivulin. An extremal property of the eigenvalue for irreducible matrices in idempotent algebra and solution of the Rawls location problem. Vestnik St. Petersburg Univ. Math., 44(4):272–281, Dec 2011. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (4):42-51.

[39]   N. Krivulin. An algebraic approach to multidimensional minimax location problems with Chebyshev distance. WSEAS Trans. Math., 10(6):191–200, Jun 2011.

[40]   N. K. Krivulin. Calculating the mean growth rate of the vector of states of a stochastic system with synchronization of events. Vestnik St. Petersburg Univ. Math., 44(1):79–86, Mar 2011. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (1):107-114.

[41]   Y. C. Huei, P. H. Keng, and N. Krivulin. Calculating approximate blocking probabilities for TDM wavelength optical networks with OTSIs. J. High Speed Netw., 17(3):129–145, Jan 2010.

[42]   N. K. Krivulin. Calculating the Lyapunov exponent for generalized linear systems with exponentially distributed elements of the transition matrix. Vestnik St. Petersburg Univ. Math., 42(2):95–105, May 2009. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (2):37-47.

[43]   N. K. Krivulin. Evaluation of the growth rate of the state vector in a second-order generalized linear stochastic system. Vestnik St. Petersburg Univ. Math., 41(1):28–38, May 2008. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (1):38-48.

[44]   N. K. Krivulin. On evaluation of the blocking probability in multiwave time division multiplexing networks. Vestnik St. Petersburg Univ. Math., 40(4):279–286, Dec 2007. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (4):73-81.

[45]   N. K. Krivulin. Growth rate of the state vector in a generalized linear stochastic system with a symmetric matrix. J. Math. Sci., 147(4):6924–6928, Dec 2007. Transl. from the Russian original publ. in Zapisky Nauchnih Seminarov POMI, 341:134-141.

[46]   N. K. Krivulin. Evaluation of the growth rate of the state vector in a generalized linear stochastic system. Vestnik St. Petersburg Univ. Math., 40(3):224–232, Sep 2007. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (3):91-99.

[47]   N. K. Krivulin and I. V. Romanovskii. On the convergence of matrix powers of a generalized linear operator in idempotent algebra. J. Math. Sci., 142(1):1806–1816, Apr 2007. Transl. from the Russian original publ. in Problemy Matematicheskogo Analiza, 34:69-77, Dec 2006.

[48]   N. K. Krivulin. Eigenvalues and eigenvectors of matrices in idempotent algebra. Vestnik St. Petersburg Univ. Math., 39(2):72–83, Jun 2006. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (2):29-40.

[49]   N. K. Krivulin. Solution of generalized linear vector equations in idempotent algebra. Vestnik St. Petersburg Univ. Math., 39(1):16–26, Mar 2006. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (1):23-36.

[50]   N. K. Krivulin, D. Guster, and C. Hall. On parallel implementation of a discrete optimization random search algorithm. WSEAS Trans. Comput., 4(9):1122–1129, Sep 2005.

[51]   N. K. Krivulin. Evaluation of bounds on the mean rate of growth of the state vector of a linear dynamical stochastic system in idempotent algebra. Vestnik St. Petersburg Univ. Math., 38(2):42–51, Jun 2005. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (2):45-54.

[52]   N. K. Krivulin. The growth rate of state vector in a generalized linear dynamical system with random triangular matrix. Vestnik St. Petersburg Univ. Math., 38(1):25–28, Mar 2005. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (1):33-38.

[53]   N. K. Krivulin. A convergence theorem for matrix powers and evaluation of the eigenvalue in idempotent algebra. Vestnik St. Petersburg Univ. Math., 37(2):38–42, Jun 2004. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (2):49-55.

[54]   N. K. Krivulin. Estimation of the rate of growth of the state vector of a generalized linear dynamical system with random matrix. Vestnik St. Petersburg Univ. Math., 36(3):41–49, Sep 2003. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (3):47-55.

[55]   N. K. Krivulin. Evaluation of the mean cycle time in fork-join queueing networks. Vestnik St. Petersburg Univ. Math., 35(3):20–26, Sep 2002. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (3):27-35.

[56]   N. K. Krivulin and D. S. Milov. Evaluation of the mean in-process time for queueing networks with random topology. Vestnik St. Petersburg Univ. Math., 34(3):16–19, Sep 2001. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (3):27-31.

[57]   N. K. Krivulin and D. S. Milov. Estimates for a mean time of trouble-free work for one queueing network class. Vestnik St. Petersburg Univ. Math., 34(1):17–22, Jan 2001. Transl. from the Russian original publ. in Vestnik Sankt-Peterburgskogo Universiteta. Ser. 1, (1):23-30.

[58]   N. K. Krivulin. A max-algebra approach to modeling and simulation of tandem queueing systems. Math. Comput. Modelling, 22(3):25–37, Aug 1995.

[59]   S. M. Ermakov and N. K. Krivulin. Efficient algorithms for tandem queueing system simulation. Appl. Math. Lett., 7(6):45–49, Nov 1994.

[60]   N. K. Krivulin. A recursive equations based representation for the G/G/m queue. Appl. Math. Lett., 7(3):73–77, May 1994.

[61]   N. K. Krivulin. Unbiased estimates for gradients of stochastic network performance measures. Acta Appl. Math., 33(1):21–43, Oct 1993.

[62]   N. K. Krivulin. Optimization of complex systems for simulation modeling. Vestnik Leningrad Univ. Math., 23(2):64–67, June 1990. Transl. from the Russian original publ. in Vestnik Leningradskogo Universiteta. Ser. 1, (3):100-102.

Refereed conference papers and book chapters

[63]   N. Krivulin. Algebraic solution of weighted minimax single-facility constrained location problems. In J. Desharnais, W. Guttmann, and S. Joosten, eds, Relational and Algebraic Methods in Computer Science, vol. 11194 of LNCS, pp. 317–332. Springer, Cham, Oct 2018.

[64]   N. Krivulin. Methods of tropical optimization in rating alternatives based on pairwise comparisons. In A. Fink, A. Fügenschuh, and M. J. Geiger, eds, Operations Research Proceedings 2016, Operations Research Proceedings, pp. 85–91. Springer, Cham, 2018.

[65]   N. Krivulin and S. Sergeev. Tropical optimization techniques in multi-criteria decision making with Analytical Hierarchy Process. In D. Al-Dabass, Z. Xie, A. Orsoni, and A. Pantelous, eds, UKSim-AMSS 11th European Modelling Symposium on Computer Modelling and Simulation (EMS 2017), pp. 38–43. IEEE, Nov 2017.

[66]   N. Krivulin. Complete solution of an optimization problem in tropical semifield. In P. Höfner, D. Pous, and G. Struth, eds, Relational and Algebraic Methods in Computer Science, vol. 10226 of LNCS, pp. 226–241. Springer, Cham, May 2017.

[67]   N. Krivulin. Using tropical optimization techniques to evaluate alternatives via pairwise comparisons. In A. H. Gebremedhin, E. G. Boman, and B. Ucar, eds, 2016 Proc. 7th SIAM Workshop on Combinatorial Scientific Computing, pp. 62–72. SIAM, Philadelphia, PA, 2016.

[68]   N. Krivulin. Tropical optimization problems in project scheduling. In Z. Hanzálek, G. Kendall, B. McCollum, and P. Šůcha, eds, MISTA 2015 Proceedings, pp. 492–506. MISTA, 2015.

[69]   N. Krivulin. Solving a tropical optimization problem via matrix sparsification. In W. Kahl, M. Winter, and J. N. Oliveira, eds, Relational and Algebraic Methods in Computer Science, vol. 9348 of LNCS, pp. 326–343. Springer, Cham, Sep 2015.

[70]   N. Krivulin. Rating alternatives from pairwise comparisons by solving tropical optimization problems. In Z. Tang, J. Du, S. Yin, L. He, and R. Li, eds, 2015 12th Intern. Conf. on Fuzzy Systems and Knowledge Discovery (FSKD), pp. 162–167. IEEE, Aug 2015.

[71]   N. Krivulin. Tropical optimization problems. In L. A. Petrosyan, J. V. Romanovsky, and D. W.-K. Yeung, eds, Advances in Economics and Optimization: Collected Scientific Studies Dedicated to the Memory of L. V. Kantorovich, Economic Issues, Problems and Perspectives, pp. 195–214. Nova Sci. Publ., New York, Apr 2014.

[72]   N. Krivulin. Complete solution of a constrained tropical optimization problem with application to location analysis. In P. Höfner, P. Jipsen, W. Kahl, and M. E. Müller, eds, Relational and Algebraic Methods in Computer Science, vol. 8428 of LNCS, pp. 362–378. Springer, Cham, Apr 2014.

[73]   N. Krivulin and K. Zimmermann. Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints. In D. Biolek, H. Walter, I. Utu, and C. von Lucken, eds, Mathematical Methods and Optimization Techniques in Engineering, pp. 86–91. WSEAS Press, Athens, Oct 2013.

[74]   N. Krivulin. Explicit solution of a tropical optimization problem with application to project scheduling. In D. Biolek, H. Walter, I. Utu, and C. von Lucken, eds, Mathematical Methods and Optimization Techniques in Engineering, pp. 39–45. WSEAS Press, 2013.

[75]   N. Krivulin. Algebraic solutions to scheduling problems in project management. In I. J. Rudas, A. Zaharim, K. Sopian, and J. Strouhal, eds, Recent Researches in Communications, Electronics, Signal Processing and Automatic Control, pp. 161–166. WSEAS Press, Athens, Feb 2012.

[76]   N. Krivulin. Solution to an extremal problem in tropical mathematics. In G. L. Litvinov, V. P. Maslov, A. G. Kushner, and S. N. Sergeev, eds, Tropical and Idempotent Mathematics. International Workshop, pp. 132–139, Moscow, 2012.

[77]   N. Krivulin. A complete closed-form solution to a tropical extremal problem. In S. Yenuri, ed., Advances in Computer Science, vol. 5 of Recent Advances in Computer Engineering Series, pp. 146–151. WSEAS Press, Sep 2012.

[78]   N. Krivulin. A solution of a tropical linear vector equation. In S. Yenuri, ed., Advances in Computer Science, vol. 5 of Recent Advances in Computer Engineering Series, pp. 244–249. WSEAS Press, Sep 2012.

[79]   N. Krivulin. A tropical extremal problem with nonlinear objective function and linear inequality constraints. In S. Yenuri, ed., Advances in Computer Science, vol. 5 of Recent Advances in Computer Engineering Series, pp. 216–221. WSEAS Press, Sep 2012.

[80]   N. Krivulin. Algebraic solution to a constrained rectilinear minimax location problem on the plane. In 2011 Intern. Conf. on Multimedia Technology (ICMT), pp. 6212–6220. IEEE, Jul 2011.

[81]   N. Krivulin. Algebraic solutions to multidimensional minimax location problems with Chebyshev distance. In V. Vasek, Y. Shmaliy, D. Trcek, N. P. Kobayashi, R. S. Choras, and Z. Klos, eds, Recent Researches in Applied and Computational Mathematics, pp. 157–162. WSEAS Press, May 2011.

[82]   N. Krivulin. Evaluation of the mean cycle time in stochastic discrete event dynamic systems. In B. Kim, H. W. Lee, G. U. Hwang, and Y. W. Shin, eds, Proc. 6th Intern. Conf. on Queueing Theory and Network Applications (QTNA’11), pp. 93–100. ACM, New York, NY, Aug 2011.

[83]   N. K. Krivulin. Evaluation of Lyapunov exponent in generalized linear dynamical models of queueing networks. In I. Troch and F. Breitenecker, eds, Proceedings MATHMOD 2009 Vienna – Full Papers CD Volume, pp. 706–717, Vienna, Feb 2009. Vienna University of Technology, ARGESIM.

[84]   Y. C. Huei, P. H. Keng, and N. Krivulin. Average network blocking probabilities for TDM WDM optical networks with OTSIs and without WC. In 15th Intern. Symp. on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, pp. 424–431. IEEE, Oct 2007.

[85]   N. K. Krivulin and N. B. Nevzorov. On evaluation of the mean service cycle time in tandem queuing systems. In M. Ahsanullah, J. Kennyon, and S.K. Sarkar, eds, Applied Statistical Science V, pp. 145–155. Nova Sci. Publ., Huntington, NY, Oct 2001.

[86]   N. K. Krivulin and V. B. Nevzorov. Evaluation of the mean interdeparture time in tandem queueing systems. In S. M. Ermakov, Yu. N. Kashtanov, and V. B. Melas, eds, Simulation 2001. Proc. 4th St. Petersburg Workshop on Simulation, pp. 310–315, St. Petersburg, 2001. NII Chemistry St. Petersburg University Publishers.

[87]   N. K. Krivulin. Algebraic modelling and performance evaluation of acyclic fork-join queueing networks. In N. Balakrishnan, V. B. Melas, and S. Ermakov, eds, Advances in Stochastic Simulation Methods, pp. 63–81. Birkhäuser, Boston, MA, Jun 2000.

[88]   N. K. Krivulin. Monotonicity properties and simple bounds on the mean cycle time in acyclic fork-join queueing networks. In N. E. Mastorakis, ed., Recent Advances in Information Science and Technology, pp. 147–152. World Scientific, Singapore, Oct 1998.

[89]   N. K. Krivulin. Max-plus algebra models of queueing networks. In Intern. Workshop on Discrete Event Systems WODES’96, pp. 76–81. IEE, London, Aug 1996.

[90]   N. K. Krivulin. An algebraic approach in modelling and simulation of queueing networks. In Nikos E. Mastorakis, ed., Proc. Intern. Conf. on Circuits, Systems and Computers ’96., vol. 2, pp. 668–672. Hellenic Naval Academy, Jul 1996.

[91]   N. K. Krivulin. Unbiased gradient estimation in queueing networks with parameter-dependent routing. In W. S. Wong, ed., Proc. Intern. Conf. on Control and Information 1995, pp. 351–356, Hong Kong, Jun 1995. The Institute of Mathematical Sciences, The Chinese University of Hong Kong, The Chinese University Press.

[92]   N. K. Krivulin. Using max-algebra linear models in the representation of queueing systems. In J. G. Lewis, ed., Proc. 5th SIAM Conf. on Applied Linear Algebra, vol. 72 of SIAM Proceedings Series, pp. 155–160. SIAM, Philadelphia, PA, Jun 1994.

[93]   N. Krivulin. An analysis of gradient estimates in stochastic network optimization problems. In W. G. Müller, H. P. Wynn, and A. A. Zhigljavsky, eds, Model-Oriented Data Analysis, Contributions to Statistics, pp. 227–240, Heidelberg, 1993. Physica-Verlag.

[94]   N. Krivulin. An analysis of the least median of squares regression problem. In Y. Dodge and J. Whittaker, eds, Computational Statistics, pp. 471–476. Physica-Verlag, Heidelberg, Aug 1992.

Refereed journal articles in Russian

[95]   N. K. Krivulin and E. Yu. Romanova. Approximate factorization of positive matrices by using methods of tropical optimization. Vestnik Sankt-Peterburgskogo Universiteta. Prikladnaya Matematika, 16(4):357–374, Dec 2020. (in Russian).

[96]   N. K. Krivulin, T. Abildaev, V. D. Gorshechnikova, D. Kapatsa, E. A. Magdich, and A. A. Mandrikova. On solving multicriteria decision making problems based on pairwise comparisons. Computer Tools in Education, (2):27–58, Jun 2020. (in Russian).

[97]   N. K. Krivulin and V. A. Ageev. Methods of tropical optimization in multicriteria problems of raiting alternatives from pairwise comparisons. Vestnik Sankt-Peterburgskogo Universiteta. Prikladnaya Matematika, 15(4):472–488, Dec 2019. (in Russian).

[98]   P. V. Plotnikov and N. K. Krivulin. Solution of minimax location problem in three-dimensional space with rectilinear metric. Computer Tools in Education, (1):31–50, Feb 2018. (in Russian).

[99]   N. K. Krivulin and M. A. Tsobenko. Solution of the two-criteria problem of rating alternatives using tropical optimization. Computer Tools in Education, (4):15–32, Dec 2019. (in Russian).

[100]   P. V. Plotnikov and N. K. Krivulin. Direct solution of a minimax location problem on the plane with rectilinear metric in a rectangular area. Vestnik Sankt-Peterburgskogo Universiteta. Prikladnaya Matematika, 14(2):116–130, Jun 2018. (in Russian).

[101]   N. K. Krivulin, V. A. Ageev, and I. V. Gladkikh. Application of methods of tropical optimization for evaluating alternatives based on pairwise comparisons. Vestnik Sankt-Peterburgskogo Universiteta. Prikladnaya Matematika, 13(1):27–41, Mar 2017. (in Russian).

[102]   N. K. Krivulin and S. A. Gubanov. The use of tropical optimization methods in problems of project scheduling. Vestnik Sankt-Peterburgskogo Universiteta. Prikladnaya Matematika, 13(4):384–397, Dec 2017. (in Russian).

[103]   N. K. Krivulin and S. A. Gubanov. Solution of a project scheduling problem by using methods of tropical mathematics. Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10, 12(3):62–67, Sep 2016. (in Russian).

[104]   N. K. Krivulin and I. V. Gladkikh. Computation of the consistent pairwise comparison matrix in marketing research by using methods of tropical mathematics. Vestnik Sankt-Peterburgskogo Universiteta. Seriya 8, (1):3–43, Mar 2015. (in Russian).

[105]   N. K. Krivulin and D. N. Vasilyev. Computation of the Lyapunov exponent of a generalized linear stochastic dynamical system with a second-order matrix. Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10, (1):120–134, Mar 2015. (in Russian).

[106]   N. K. Krivulin. On solution of a multidimensional extremal problem in tropical mathematics. Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1, 47(4):145–153, Dec 2013. (in Russian).

[107]   N. K. Krivulin. On solution of a class of linear vector equations in idempotent algebra. Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10, (3):64–77, Sep 2009. (in Russian).

[108]   I. V. Gladkikh and N. K. Krivulin. Marketing research of price levels in differentiated product markets. Vestnik Sankt-Peterburgskogo Universiteta. Seriya 8, (1):129–156, Mar 2002. (in Russian).

Monographs

[109]   N. K. Krivulin. Methods of Idempotent Algebra for Problems in Modeling and Analysis of Complex Systems. Saint Petersburg Univ. Press, St. Petersburg, 2009. (in Russian).