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Volume 74, Nº 6 (2019)
- Ano: 2019
- Artigos: 11
- URL: https://journals.rcsi.science/0042-1316/issue/view/7513
Another view of the maximum principle for infinite-horizon optimal control problems in economics
Resumo
The authors present their recently developed complete version of the Pontryagin maximum principle for a class of infinite-horizon optimal control problems arising in economics. The main distinguishing feature of the result is that the adjoint variable is explicitly specified by a formula analogous to the Cauchy formula for solutions of linear differential systems. In certain situations this formula implies the ‘standard’ transversality conditions at infinity. Moreover, it can serve as an alternative to them. Examples demonstrate the advantages of the proposed version of the maximum principle. In particular, its applications are considered to Halkin's example, to Ramsey's optimal economic growth model, and to a basic model for optimal extraction of a non-renewable resource. Also presented is an economic interpretation of the characterization obtained for the adjoint variable.Bibliography: 62 titles.
Uspekhi Matematicheskikh Nauk. 2019;74(6):3-54
3-54
Cubillages of cyclic zonotopes
Resumo
A survey is given of recent results on fine zonotopal tilings by cubes (briefly, cubillages) of cyclic zonotopes. The main interest of this theory is that it is interrelated with the theory of higher Bruhat orders, as well as with the parallel theory of triangulations of cyclic polytopes and Tamari–Stasheff posets, used in investigations of the Kadomtsev–Petviashvili equations and higher Auslander–Reiten algebras.
Uspekhi Matematicheskikh Nauk. 2019;74(6):55-118
55-118
Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line
Resumo
A brief survey of results on the characterization of the spaces associated with given classes of function spaces is presented. It is shown that the situation differs in general for ideal and non-ideal spaces. In the second case the notion of associated space splits into two. In the main body of the text a complete description is given of the function spaces associated with weighted Sobolev spaces of the first order on the real line.Bibliography: 54 titles.
Uspekhi Matematicheskikh Nauk. 2019;74(6):119-158
119-158
Variational principle for multidimensional conservation laws and pressureless media
Uspekhi Matematicheskikh Nauk. 2019;74(6):159-160
159-160
An explicit local combinatorial formula for the first Pontryagin class
Uspekhi Matematicheskikh Nauk. 2019;74(6):161-162
161-162
On a local holomorphic version of the fundamental theorem of projective geometry
Uspekhi Matematicheskikh Nauk. 2019;74(6):163-164
163-164
Moments of the numbers of particles in a heavy-tailed branching random walk
Uspekhi Matematicheskikh Nauk. 2019;74(6):165-166
165-166
Recovery of sparse integer vectors from linear measurements
Uspekhi Matematicheskikh Nauk. 2019;74(6):167-168
167-168
Pogorelov's problem on isometric transformations of a cylindrical surface
Uspekhi Matematicheskikh Nauk. 2019;74(6):169-170
169-170
On the 100th anniversary of the birth of Aleksei Vasil'evich Pogorelov
Uspekhi Matematicheskikh Nauk. 2019;74(6):171-193
171-193
Mikhail Ivanovich Shtogrin (on his 80th birthday)
Uspekhi Matematicheskikh Nauk. 2019;74(6):194-197
194-197