Uspenskii Aleksandr Aleksandrovich

Publications in Math-Net.Ru

1. Newton's method in constructing a singular set of a minimax solution in a class of boundary value problems for the Hamilton — Jacobi equations
   
   Chelyab. Fiz.-Mat. Zh., 9:1 (2024),  63–76
2. On smoothness conditions and selection of the edge of a scattering surface in one class of 3D time-optimal problems
   
   Izv. IMI UdGU, 63 (2024),  37–48
3. Numerical-analytical construction of a generalized solution of the eikonal equation in the plane case
   
   Mat. Sb., 215:9 (2024),  99–124
4. Alpha sets and their hulls: analytical relationships in the plane case
   
   Russian Universities Reports. Mathematics, 29:146 (2024),  204–217
5. Combined algorithms for constructing a solution to the time-optimal problem in three-dimensional space based on the selection of extreme points of the scattering surface
   
   Ural Math. J., 8:2 (2022),  115–126
6. Iterative algorithms for minimizing the Hausdorff distance between convex polyhedrons
   
   Izv. IMI UdGU, 57 (2021),  142–155
7. On the analytical construction of solutions for one class of time-optimal control problems with nonconvex target set
   
   Trudy Inst. Mat. i Mekh. UrO RAN, 27:3 (2021),  128–140
8. On singularity structure of minimax solution to Dirichlet problem for eikonal type equation with discontinuous curvature of boundary of boundary set
   
   Ufimsk. Mat. Zh., 13:3 (2021),  129–154
9. On the structure of the singular set of solutions in one class of 3D time-optimal control problems
   
   Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:3 (2021),  471–486
10. Algorithms of minimization of Hausdorff deviation of a convex compact from a set of movable convex polygons
    
    Chelyab. Fiz.-Mat. Zh., 5:2 (2020),  218–232
11. Numerical methods for constructing suboptimal packings of nonconvex domains with curved boundary
    
    Diskretn. Anal. Issled. Oper., 27:4 (2020),  58–79
12. Construction of scattering curves in one class of time-optimal control problems with leaps of a target set boundary curvature
    
    Izv. IMI UdGU, 55 (2020),  93–112
13. Properties of non stationer pseudo vertex with the break of smoothness of the target set boarder curvature in the Dirichlet problem to eikonal type equation
    
    Sib. Èlektron. Mat. Izv., 17 (2020),  2028–2044
14. Elements of analytical solutions constructor in a class of time-optimal control problems with the break of curvature of a target set
    
    Russian Universities Reports. Mathematics, 25:132 (2020),  370–386
15. Algorithms for solving the velocity problem with circular vectogram in inhomogeneous medium
    
    Chelyab. Fiz.-Mat. Zh., 4:4 (2019),  387–397
16. Construction of a solution to a velocity problem in the case of violation of the smoothness of the curvature of the target set boundary
    
    Izv. IMI UdGU, 53 (2019),  98–114
17. Construction of a nonsmooth solution in a time-optimal problem with a low order of smoothness of the boundary of the target set
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 25:1 (2019),  108–119
18. Alpha-sets in finite-dimensional Euclidean spaces and their applications in control theory
    
    Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 14:3 (2018),  261–272
19. Euclidean distance to a closed set as a minimax solution of the Dirichlet problem for the Hamilton-Jacobi equation
    
    Tambov University Reports. Series: Natural and Technical Sciences, 23:124 (2018),  797–804
20. Identification of the singularity of the generalized solution of the Dirichlet problem for an eikonal type equation under the conditions of minimal smoothness of a boundary set
    
    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018),  59–73
21. Weak invariance of a cylindrical set with smooth boundary with respect to a control system
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 23:1 (2017),  241–250
22. Theorems on the separability of $\alpha$-sets in Euclidean space
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  277–291
23. Construction of the optimal result function and dispersing lines in time-optimal problems with a nonconvex target set
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  188–198
24. The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 22:1 (2016),  282–293
25. $\alpha$-sets in finite dimensional Euclidean spaces and their properties
    
    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016),  95–120
26. Derivatives by virtue of diffeomorphisms and their applications in control theory and geometrical optics
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 21:2 (2015),  252–266
27. Necessary conditions for the existence of pseudovertices of the boundary set in the Dirichlet problem for the eikonal equation
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 21:1 (2015),  250–263
28. Calculation formulas for nonsmooth singularities of the optimal result function in a time-optimal problem
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 20:3 (2014),  276–290
29. Approximation of nonsmooth optimal result in one class of velocity problems
    
    Vestnik Chelyabinsk. Gos. Univ., 2013, no. 16,  71–77
30. Geometry of singular curves for one class of velocity
    
    Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2013, no. 3,  157–167
31. Algorithms of the best approximations of the flat sets by the union of circles
    
    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4,  88–99
32. Stability defect of maximal stable bridge in approaching game problem with closed target
    
    Izv. IMI UdGU, 2012, no. 1(39),  140
33. Estimate of the stability defect for a positional absorption set subjected to discriminant transformations
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 17:2 (2011),  209–224
34. Function defect in differential games with terminal pay
    
    Mat. Teor. Igr Pril., 2:2 (2010),  99–128
35. On the set of limit values of local diffeomorphisms in wavefront evolution
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 16:1 (2010),  171–185
36. On a supplement to the stability property in differential games
    
    Trudy Mat. Inst. Steklova, 271 (2010),  299–318
37. Singularities' of Optimal-Time Function in One Class of Optimal-Time Control Problems Construction Algorithms
    
    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 3,  30–41
38. Construction of the optimal outcome function for a time-optimal problem on the basis of a symmetry set
    
    Avtomat. i Telemekh., 2009, no. 7,  50–57
39. Procedures for calculating the nonconvexity measures of a plane set
    
    Zh. Vychisl. Mat. Mat. Fiz., 49:3 (2009),  431–440
40. Geometry and the asymptotics of wave forms
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 3,  27–37
41. Условия трансверсальности ветвей решения нелинейного уравнения в задаче быстродействия с круговой индикатрисой
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 14:4 (2008),  82–99
42. Construction of a minimax solution for an eikonal-type equation
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 14:2 (2008),  182–191
43. Construction of the function of the best result for the system with simple dynamic
    
    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 2,  152–154
44. On the geometry of wave fronts
    
    Izv. IMI UdGU, 2006, no. 3(37),  79–80
45. Construction of solutions in certain differential games with phase constraints
    
    Mat. Sb., 196:4 (2005),  51–78
46. Stable bridges in differential games in a finite time interval
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 10:2 (2004),  155–177
47. Constructions of the differential game theory for solving the Hamilton–Jacobi equations
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 6:2 (2000),  320–336