Webmail
MathScinet
OMS
vi en
Tin tức nổi bật
Xem tất cả
THÔNG BÁO Triệu tập thí sinh tham dự thi vấn đáp tại vòng 2
THÔNG BÁO Tuyển viên chức năm 2024
Kế hoạch tuyển viên chức năm 2024
Hội thảo sắp diễn ra
Xem tất cả
18/09/24, Hội nghị, hội thảo:
THE 3RD VIETNAM - KOREA JOINT WORKSHOP ON SELECTED TOPICS IN MATHEMATICS
02/01/25, Hội nghị, hội thảo:
Hội nghị toàn quốc lần thứ VII “Xác suất - Thống kê: Nghiên cứu, ứng dụng và giảng dạy”
18/12/24, Hội nghị, hội thảo:
International conference on commutative algebra to the memory of Jürgen Herzog
Xuất bản mới
Xem tất cả
Phạm Hữu Sách, Lê Anh Tuấn, Nguyễn Thế Vinh, Vector Quasi-Equilibria for the Sum of Two Multivalued Trifunctions, Journal of Optimization Theory and Applications, Volume 204, article number 44, (2025) (SCI-E, Scopus) .
Nguyễn Đình Công, Lưu Hoàng Đức, Phan Thanh Hồng, umerical Attractors via Discrete Rough Paths, Journal of Dynamics and Differential Equations, Volume 37, pages 727–748, (2025) (SCI-E, Scopus) .
Tan H. Cao, Nilson Chapagain, Haejoon Lee, Thi Phung, Nguyễn Năng Thiều, Optimal Control of Several Motion Models, Journal of Optimization Theory and Applications, Volume 205, article number 3, (2025) (SCI-E, Scopus) .

Bellman's equation and the value function

Người báo cáo: Nguyễn Quốc Tuấn

Time: 9Am-10Am, April 11th 2023 (Tuesday)

Location: Room 617, building A6, Institute of Mathematics (18 Hoang Quoc Viet, Cau Giay, Hanoi)

Abstract: In this seminar, we derive the dynamic programming equation called Bellman's equations. Their solutions are used to find optimal strategies in the form of closed loop control. We also show that, if the value function of optimal control problems is smooth, then it is a solution of the Bellman equation.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
Lịch hoạt động chung Lịch sử dụng phòng, hội trường, hội thảo Ảnh hoạt động
Giới thiệu Đăng nhập Đăng ký tài khoản Quên mật khẩu Chính sách bảo mật
MessagesTimelineExceptionsViews7RouteQueries36Models149MailsGateSessionRequest
8.1.30PHP Version154msRequest Duration4MBMemory UsageGET xemina-chi-tiet/{alias}Route
    • Booting (34.88ms)
    • Application (119ms)
    • 1 x Application (77.28%)
      119ms
      1 x Booting (22.72%)
      34.88ms
      7 templates were rendered
      • client.pages.seminar.seminar_detail (resources/views/client/pages/seminar/seminar_detail.blade.php)1blade
        Params
        0
        serminar
      • client.layout.app (resources/views/client/layout/app.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.head (resources/views/client/layouts/head.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.header (resources/views/client/layouts/header.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.navbar (resources/views/client/layouts/navbar.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.column_left (resources/views/client/layouts/column_left.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      • client.layouts.footer (resources/views/client/layouts/footer.blade.php)5blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        serminar
        4
        date_start
      uri
      GET xemina-chi-tiet/{alias}
      middleware
      web, locale
      controller
      App\Http\Controllers\SeminarController@view_seminar_detail
      namespace
      prefix
      where
      as
      seminar.detail
      file
      app/Http/Controllers/SeminarController.php:38-61
      36 statements were executed, 14 of which were duplicated, 22 unique43.15ms
      beta_math_vn
      • select * from `serminars` where `ser_alias` = 'bellmans-equation-and-the-value-function' limit 1
        2.86ms/app/Http/Controllers/SeminarController.php:40beta_math_vn
        Metadata
        Bindings
        • 0. bellmans-equation-and-the-value-function
        Backtrace
        • 15. /app/Http/Controllers/SeminarController.php:40
        • 16. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:262
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `members` where `members`.`id` in (299)
        800μs/app/Http/Controllers/SeminarController.php:40beta_math_vn
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/SeminarController.php:40
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:262
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `serminar_rooms` where `serminar_rooms`.`id` in (33)
        600μs/app/Http/Controllers/SeminarController.php:40beta_math_vn
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/SeminarController.php:40
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:262
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `pages`
        1.57ms/app/Repositories/Pages/PagesRepository.php:30beta_math_vn
        Metadata
        Backtrace
        • 17. /app/Repositories/Pages/PagesRepository.php:30
        • 18. view::41329013d802ceb5f40c0b002e8af12e76ed34df:33
        • 20. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 21. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `pages`
        1.15ms/app/Repositories/Pages/PagesRepository.php:30beta_math_vn
        Metadata
        Backtrace
        • 17. /app/Repositories/Pages/PagesRepository.php:30
        • 18. view::41329013d802ceb5f40c0b002e8af12e76ed34df:73
        • 20. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 21. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `departments` where `parent_id` = 0 order by `order` asc
        1.18ms/app/Repositories/Department/DepartmentRepository.php:17beta_math_vn
        Metadata
        Bindings
        • 0. 0
        Backtrace
        • 14. /app/Repositories/Department/DepartmentRepository.php:17
        • 15. view::41329013d802ceb5f40c0b002e8af12e76ed34df:91
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `departments` where `departments`.`parent_id` in (12, 13, 14, 15, 16) order by `order` asc
        900μs/app/Repositories/Department/DepartmentRepository.php:17beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Department/DepartmentRepository.php:17
        • 20. view::41329013d802ceb5f40c0b002e8af12e76ed34df:91
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `departments` where `departments`.`parent_id` = 1 and `departments`.`parent_id` is not null order by `order` asc
        710μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 2 and `departments`.`parent_id` is not null order by `order` asc
        670μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 2
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 3 and `departments`.`parent_id` is not null order by `order` asc
        640μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 3
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 4 and `departments`.`parent_id` is not null order by `order` asc
        650μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 4
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 5 and `departments`.`parent_id` is not null order by `order` asc
        640μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 5
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 6 and `departments`.`parent_id` is not null order by `order` asc
        720μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 6
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 7 and `departments`.`parent_id` is not null order by `order` asc
        570μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 7
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 8 and `departments`.`parent_id` is not null order by `order` asc
        590μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 8
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 9 and `departments`.`parent_id` is not null order by `order` asc
        700μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 9
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 17 and `departments`.`parent_id` is not null order by `order` asc
        750μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 17
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `departments` where `departments`.`parent_id` = 10 and `departments`.`parent_id` is not null order by `order` asc
        620μsview::41329013d802ceb5f40c0b002e8af12e76ed34df:109beta_math_vn
        Metadata
        Bindings
        • 0. 10
        Backtrace
        • 19. view::41329013d802ceb5f40c0b002e8af12e76ed34df:109
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
        • 24. /vendor/facade/ignition/src/Views/Engines/CompilerEngine.php:37
      • select * from `cadres`
        680μs/app/Repositories/Department/DepartmentRepository.php:37beta_math_vn
        Metadata
        Backtrace
        • 17. /app/Repositories/Department/DepartmentRepository.php:37
        • 18. view::41329013d802ceb5f40c0b002e8af12e76ed34df:144
        • 20. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 21. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `posts_category`
        770μs/app/Repositories/Posts/PostsRepository.php:48beta_math_vn
        Metadata
        Backtrace
        • 15. /app/Repositories/Posts/PostsRepository.php:48
        • 16. view::41329013d802ceb5f40c0b002e8af12e76ed34df:186
        • 18. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 20. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `posts` where `hot` = 1 and `posts`.`deleted_at` is null order by `date_create` desc limit 3
        3.9ms/app/Repositories/Posts/PostsRepository.php:19beta_math_vn
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 14. /app/Repositories/Posts/PostsRepository.php:19
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:15
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `conferences` where date(`date_show`) <= '2025-12-31' and ((date(`date_create`) >= '2025-01-01' and date(`date_create`) <= '2025-12-31') or (date(`date_end`) >= '2025-01-01' and date(`date_end`) <= '2025-12-31') or (date(`date_create`) <= '2025-01-01' and date(`date_end`) >= '2025-12-31')) limit 3
        2.81ms/app/Repositories/Conferences/ConferencesRepository.php:39beta_math_vn
        Metadata
        Bindings
        • 0. 2025-12-31
        • 1. 2025-01-01
        • 2. 2025-12-31
        • 3. 2025-01-01
        • 4. 2025-12-31
        • 5. 2025-01-01
        • 6. 2025-12-31
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:39
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:43
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `prints` where `pr_hot` = '1' order by `created_at` desc limit 3
        2.99ms/app/Repositories/Pages/PagesRepository.php:156beta_math_vn
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 14. /app/Repositories/Pages/PagesRepository.php:156
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:74
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select `members`.*, `same_authorsables`.`same_authors_id` as `pivot_same_authors_id`, `same_authorsables`.`members_id` as `pivot_members_id`, `same_authorsables`.`same_authors_type` as `pivot_same_authors_type` from `members` inner join `same_authorsables` on `members`.`id` = `same_authorsables`.`members_id` where `same_authorsables`.`same_authors_id` in (1134, 1135, 1137) and `same_authorsables`.`same_authors_type` = 'App\Models\Prints'
        1.98ms/app/Repositories/Pages/PagesRepository.php:156beta_math_vn
        Metadata
        Bindings
        • 0. App\Models\Prints
        Backtrace
        • 18. /app/Repositories/Pages/PagesRepository.php:156
        • 19. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:74
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1137 order by `id` asc
        1.62ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1137
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (305, 306, 671)
        740μs/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1137 order by `id` asc
        1.22ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1137
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (305, 306, 671)
        650μs/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1135 order by `id` asc
        1.45ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1135
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (138, 161, 252)
        750μs/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1135 order by `id` asc
        1.34ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1135
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (138, 161, 252)
        850μs/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1134 order by `id` asc
        1.4ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1134
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (181, 667, 668, 669, 670)
        1.14ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:78
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `same_authorsables` where `same_authors_id` = 1134 order by `id` asc
        1.52ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Bindings
        • 0. 1134
        Backtrace
        • 14. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 15. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      • select * from `members` where `members`.`id` in (181, 667, 668, 669, 670)
        1.02ms/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      App\Models\SameAuthorsables
      22
      App\Models\Prints
      3
      App\Models\Conference
      3
      App\Models\Posts
      3
      App\Models\PostsCategory
      5
      App\Models\Cadres
      7
      App\Models\Department
      16
      App\Models\Pages
      54
      App\Models\SerminarRoom
      1
      App\Models\Members
      34
      App\Models\Serminars
      1
          _token
          JHX252IONLAdahm9tjEAxPHURPxiilQNX3v69z9f
          _previous
          array:1 [ "url" => "https://beta.math.ac.vn/xemina-chi-tiet/bellmans-equation-and-the-value-functi...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /xemina-chi-tiet/bellmans-equation-and-the-value-function
          status_code
          200
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          request_request
          []
          request_headers
            0 of 0   
          array:15 [▼
  "accept-encoding" => array:1 [▶
    0 => "gzip, deflate, br, zstd"
  ]
  "sec-fetch-dest" => array:1 [▶
    0 => "document"
  ]
  "sec-fetch-user" => array:1 [▶
    0 => "?1"
  ]
  "sec-fetch-mode" => array:1 [▶
    0 => "navigate"
  ]
  "sec-fetch-site" => array:1 [▶
    0 => "none"
  ]
  "accept" => array:1 [▶
    0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7"
  ]
  "user-agent" => array:1 [▶
    0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
  ]
  "upgrade-insecure-requests" => array:1 [▶
    0 => "1"
  ]
  "sec-ch-ua-platform" => array:1 [▶
    0 => ""Windows""
  ]
  "sec-ch-ua-mobile" => array:1 [▶
    0 => "?0"
  ]
  "sec-ch-ua" => array:1 [▶
    0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129""
  ]
  "cache-control" => array:1 [▶
    0 => "no-cache"
  ]
  "pragma" => array:1 [▶
    0 => "no-cache"
  ]
  "connection" => array:1 [▶
    0 => "keep-alive"
  ]
  "host" => array:1 [▶
    0 => "beta.math.ac.vn"
  ]
]
          request_server
            0 of 0   
          array:41 [▼
  "USER" => "www-data"
  "HOME" => "/var/www"
  "HTTP_ACCEPT_ENCODING" => "gzip, deflate, br, zstd"
  "HTTP_SEC_FETCH_DEST" => "document"
  "HTTP_SEC_FETCH_USER" => "?1"
  "HTTP_SEC_FETCH_MODE" => "navigate"
  "HTTP_SEC_FETCH_SITE" => "none"
  "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7"
  "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
  "HTTP_UPGRADE_INSECURE_REQUESTS" => "1"
  "HTTP_SEC_CH_UA_PLATFORM" => ""Windows""
  "HTTP_SEC_CH_UA_MOBILE" => "?0"
  "HTTP_SEC_CH_UA" => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129""
  "HTTP_CACHE_CONTROL" => "no-cache"
  "HTTP_PRAGMA" => "no-cache"
  "HTTP_CONNECTION" => "keep-alive"
  "HTTP_HOST" => "beta.math.ac.vn"
  "REDIRECT_STATUS" => "200"
  "SERVER_NAME" => "beta.math.ac.vn"
  "SERVER_PORT" => "443"
  "SERVER_ADDR" => "119.17.215.180"
  "REMOTE_PORT" => "24919"
  "REMOTE_ADDR" => "18.220.47.149"
  "SERVER_SOFTWARE" => "nginx/1.18.0"
  "GATEWAY_INTERFACE" => "CGI/1.1"
  "HTTPS" => "on"
  "REQUEST_SCHEME" => "https"
  "SERVER_PROTOCOL" => "HTTP/1.1"
  "DOCUMENT_ROOT" => "/var/www/math.ac.vn/html/public"
  "DOCUMENT_URI" => "/index.php"
  "REQUEST_URI" => "/xemina-chi-tiet/bellmans-equation-and-the-value-function"
  "SCRIPT_NAME" => "/index.php"
  "CONTENT_LENGTH" => ""
  "CONTENT_TYPE" => ""
  "REQUEST_METHOD" => "GET"
  "QUERY_STRING" => ""
  "SCRIPT_FILENAME" => "/var/www/math.ac.vn/html/public/index.php"
  "FCGI_ROLE" => "RESPONDER"
  "PHP_SELF" => "/index.php"
  "REQUEST_TIME_FLOAT" => 1744121838.547
  "REQUEST_TIME" => 1744121838
]
          request_cookies
          []
          response_headers
            0 of 0   
          array:5 [▼
  "content-type" => array:1 [▶
    0 => "text/html; charset=UTF-8"
  ]
  "cache-control" => array:1 [▶
    0 => "no-cache, private"
  ]
  "date" => array:1 [▶
    0 => "Tue, 08 Apr 2025 14:17:18 GMT"
  ]
  "set-cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6IkpiV2pPY2tRWFlrT095dE0vOURoUGc9PSIsInZhbHVlIjoibTZMdlhxWEsvVlcvOXR4YWcyQ2JmTFBESVNsR3BZeWNoTGFOcVovaDJTTURKOW0vS2Q5bXVyUFhxWXluM2hxOFE1RGc2bjAzWHk4OXBZc0dGZndYNmdrLzAzbkFYYzJEc1Z2M3hqU3JjdnAraUM3bUg0SmluczUxaGpReVluK2UiLCJtYWMiOiI1MmNhMTNmZGNlZDc3ZjY3ZDkzN2Y5NzQ0ODZiZDJiMTdhMjc2MWY2ZTg3NmVjMmU2ZDkxMWI1NTQxNzUxOTljIiwidGFnIjoiIn0%3D; expires=Tue, 08-Apr-2025 16:17:18 GMT; Max-Age=7200; path=/; samesite=lax ◀XSRF-TOKEN=eyJpdiI6IkpiV2pPY2tRWFlrT095dE0vOURoUGc9PSIsInZhbHVlIjoibTZMdlhxWEsvVlcvOXR4YWcyQ2JmTFBESVNsR3BZeWNoTGFOcVovaDJTTURKOW0vS2Q5bXVyUFhxWXluM2hxOFE1RGc2b ▶"
    1 => "laravel_session=eyJpdiI6IlhKREhPbEFBUEZDenUxMjYrY2Q4OUE9PSIsInZhbHVlIjoiMmYwcFA5NUNmTWNMM1lQejZVd28wck16RjRWVXJJUzU1ZElVdlp5ZW1sbGZXSzR5K0hUcHpHRjloeHBlL2pEVzU2d0pvY0gxT0pHZWlzUUloelRkRDNVcUZ1TDJHOEZiVVVKc0s2ODBLODJJbjI0b3BuUDFVNmNHVE1NZGRYWTYiLCJtYWMiOiI5ZjkyOTBjZWM4ZDZlNmJjMjM2ODE2OGMyNWUxZjdjYjU5ZTlmYWEyYjYxYjgzNjA4YTkzZWUzYTFlY2JlOTc5IiwidGFnIjoiIn0%3D; expires=Tue, 08-Apr-2025 16:17:18 GMT; Max-Age=7200; path=/; httponly; samesite=lax ◀laravel_session=eyJpdiI6IlhKREhPbEFBUEZDenUxMjYrY2Q4OUE9PSIsInZhbHVlIjoiMmYwcFA5NUNmTWNMM1lQejZVd28wck16RjRWVXJJUzU1ZElVdlp5ZW1sbGZXSzR5K0hUcHpHRjloeHBlL2pEVzU2 ▶"
  ]
  "Set-Cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6IkpiV2pPY2tRWFlrT095dE0vOURoUGc9PSIsInZhbHVlIjoibTZMdlhxWEsvVlcvOXR4YWcyQ2JmTFBESVNsR3BZeWNoTGFOcVovaDJTTURKOW0vS2Q5bXVyUFhxWXluM2hxOFE1RGc2bjAzWHk4OXBZc0dGZndYNmdrLzAzbkFYYzJEc1Z2M3hqU3JjdnAraUM3bUg0SmluczUxaGpReVluK2UiLCJtYWMiOiI1MmNhMTNmZGNlZDc3ZjY3ZDkzN2Y5NzQ0ODZiZDJiMTdhMjc2MWY2ZTg3NmVjMmU2ZDkxMWI1NTQxNzUxOTljIiwidGFnIjoiIn0%3D; expires=Tue, 08-Apr-2025 16:17:18 GMT; path=/ ◀XSRF-TOKEN=eyJpdiI6IkpiV2pPY2tRWFlrT095dE0vOURoUGc9PSIsInZhbHVlIjoibTZMdlhxWEsvVlcvOXR4YWcyQ2JmTFBESVNsR3BZeWNoTGFOcVovaDJTTURKOW0vS2Q5bXVyUFhxWXluM2hxOFE1RGc2b ▶"
    1 => "laravel_session=eyJpdiI6IlhKREhPbEFBUEZDenUxMjYrY2Q4OUE9PSIsInZhbHVlIjoiMmYwcFA5NUNmTWNMM1lQejZVd28wck16RjRWVXJJUzU1ZElVdlp5ZW1sbGZXSzR5K0hUcHpHRjloeHBlL2pEVzU2d0pvY0gxT0pHZWlzUUloelRkRDNVcUZ1TDJHOEZiVVVKc0s2ODBLODJJbjI0b3BuUDFVNmNHVE1NZGRYWTYiLCJtYWMiOiI5ZjkyOTBjZWM4ZDZlNmJjMjM2ODE2OGMyNWUxZjdjYjU5ZTlmYWEyYjYxYjgzNjA4YTkzZWUzYTFlY2JlOTc5IiwidGFnIjoiIn0%3D; expires=Tue, 08-Apr-2025 16:17:18 GMT; path=/; httponly ◀laravel_session=eyJpdiI6IlhKREhPbEFBUEZDenUxMjYrY2Q4OUE9PSIsInZhbHVlIjoiMmYwcFA5NUNmTWNMM1lQejZVd28wck16RjRWVXJJUzU1ZElVdlp5ZW1sbGZXSzR5K0hUcHpHRjloeHBlL2pEVzU2 ▶"
  ]
]
          session_attributes
            0 of 0   
          array:4 [▼
  "_token" => "JHX252IONLAdahm9tjEAxPHURPxiilQNX3v69z9f"
  "_previous" => array:1 [▶
    "url" => "https://beta.math.ac.vn/xemina-chi-tiet/bellmans-equation-and-the-value-function"
  ]
  "_flash" => array:2 [▶
    "old" => []
    "new" => []
  ]
  "PHPDEBUGBAR_STACK_DATA" => []
]