Phòng Phương trình vi phân

phong-phuong-trinh-vi-phan

Ngay từ khi thành lập Viện Toán học năm 1970, hướng nghiên cứu phương pháp toán lý đã được hình thành dưới sự chủ trì của GS Lê Văn Thiêm.


Các vấn đề chính được quan tâm như hàm số biến phức, các hệ phương trình đạo hàm riêng trong lớp giải tích suy rộng và các vấn đề ứng dụng vào những lĩnh vực khác nhau của vật lý toán như lý thuyết thấm, cơ học đàn hồi … Thành phần ban đầu của nhóm nghiên cứu bao gồm các anh Ngô Văn Lược, Hoàng Đình Dung, Nguyễn Văn Gia, Trần Gia Lịch, Lê Văn Thành, … Năm 1978 phòng Phương pháp toán lý được thành lập do GS Ngô Văn Lược làm phó phòng, rồi trưởng phòng vào năm 1981.

Từ năm 1981 trong phòng hình thành nhóm nghiên cứu về chuyên ngành phương trình đạo hàm riêng do GS Trần Đức Vân phụ trách gồm các cán bộ nghiên cứu Trần Đức Vân, Hà Tiến Ngoạn, Lê Hữu Diện. Năm 1982 nhóm này tách riêng thành nhóm nghiên cứu độc lập trực thuộc Viện và năm 1983 phòng Phương trình đạo hàm riêng được thành lập do GS Trần Đức Vân lãnh đạo.

Năm 1998 hai phòng Phương pháp toán lý và Phương trình đạo hàm riêng được sát nhập lại và lấy tên là Phòng phương trình vật lý toán do PGS Hà Tiến Ngoạn làm trưởng phòng. Năm 2009 phòng được đổi tên thành phòng Phương trình vi phân do GS. TSKH Đinh Nho Hào làm trưởng phòng. Từ tháng 3-2011, PGS. TSKH Nguyễn Minh Trí làm trưởng phòng.


Các hướng nghiên cứu chính của phòng:

  1. Các vấn đề của vật lý toán
  2. Phương trình cấp vô hạn và toán tử giả vi phân giải tích
  3. Phương trình đạo hàm riêng phi tuyến
  4. Phương trình elliptic suy biến
  5. Bài toán ngược và bài toán đặt không chỉnh.

Danh sách cán bộ

PGS. TS Hoàng Thế Tuấn

Trưởng phòng

Email: httuan@math.ac.vn

GS. TSKH Đinh Nho Hào

Email: hao@math.ac.vn

TS Lương Thái Hưng

Email: lthung@math.ac.vn

TS Đào Quang Khải

Email: dqkhai@math.ac.vn


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        710μs/app/Repositories/Pages/PagesRepository.php:119beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Pages/PagesRepository.php:119
        • 20. view::d5c804409edad40678fd57625e1b8fa2f6d266d9:67
        • 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 `pages`
        2.29ms/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`
        1.95ms/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
        1.01ms/app/Repositories/Department/DepartmentRepository.php:17beta_math_vn
        Metadata
        Bindings
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        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
        990μs/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
        2.92msview::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
        800μsview::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
        660μsview::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
        710μsview::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
        780μsview::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
        730μsview::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
        600μsview::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
        630μsview::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
        670μsview::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
        730μsview::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`
        870μs/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
        5.82ms/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
        3.59ms/app/Repositories/Conferences/ConferencesRepository.php:39beta_math_vn
        Metadata
        Bindings
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        • 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
        4ms/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'
        2.51ms/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
        1.39ms/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)
        720μs/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
        1.44ms/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)
        730μs/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
        1.69ms/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)
        700μs/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
        1.31ms/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)
        700μs/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
        1.28ms/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)
        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` = 1134 order by `id` asc
        1.37ms/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)
        770μs/app/Repositories/Conferences/ConferencesRepository.php:70beta_math_vn
        Metadata
        Backtrace
        • 19. /app/Repositories/Conferences/ConferencesRepository.php:70
        • 20. view::4fd68d67ec55e7902e23cc158b632c528a6199cd:79
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