The following warnings occurred:
Warning [2] Undefined array key "extra" - Line: 100 - File: inc/plugins/google_seo/url.php PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/plugins/google_seo/url.php 100 errorHandler->error_callback
/inc/plugins/google_seo.php 317 require_once
/inc/class_plugins.php 38 require_once
/inc/init.php 263 pluginSystem->load
/global.php 20 require_once
/showthread.php 28 require_once
Warning [2] Undefined array key "parent" - Line: 447 - File: inc/plugins/google_seo/url.php PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/plugins/google_seo/url.php 447 errorHandler->error_callback
/inc/plugins/google_seo/url.php 1144 google_seo_url_create
/inc/plugins/google_seo/url.php 174 google_seo_url_hook
/inc/plugins/google_seo.php 317 require_once
/inc/class_plugins.php 38 require_once
/inc/init.php 263 pluginSystem->load
/global.php 20 require_once
/showthread.php 28 require_once
Warning [2] Trying to access array offset on value of type null - Line: 198 - File: inc/plugins/google_seo.php PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/plugins/google_seo.php 198 errorHandler->error_callback
/inc/plugins/google_seo/redirect.php 133 google_seo_tid
/inc/class_plugins.php 142 google_seo_redirect_hook
/global.php 100 pluginSystem->run_hooks
/showthread.php 28 require_once
Warning [2] Undefined array key 149165 - Line: 198 - File: inc/plugins/google_seo.php PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/plugins/google_seo.php 198 errorHandler->error_callback
/inc/plugins/google_seo/url.php 1453 google_seo_tid
/inc/functions.php 6608 google_seo_url_post
/inc/plugins/google_seo/redirect.php 134 get_post_link
/inc/class_plugins.php 142 google_seo_redirect_hook
/global.php 100 pluginSystem->run_hooks
/showthread.php 28 require_once
Warning [2] Undefined variable $unreadreports - Line: 38 - File: global.php(961) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/global.php(961) : eval()'d code 38 errorHandler->error_callback
/global.php 961 eval
/showthread.php 28 require_once
Warning [2] Undefined variable $mysupport_tech_notice - Line: 38 - File: global.php(961) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/global.php(961) : eval()'d code 38 errorHandler->error_callback
/global.php 961 eval
/showthread.php 28 require_once
Warning [2] Undefined variable $mysupport_assign_notice - Line: 38 - File: global.php(961) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/global.php(961) : eval()'d code 38 errorHandler->error_callback
/global.php 961 eval
/showthread.php 28 require_once
Warning [2] Undefined array key 149165 - Line: 198 - File: inc/plugins/google_seo.php PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/plugins/google_seo.php 198 errorHandler->error_callback
/inc/plugins/google_seo/url.php 1453 google_seo_tid
/inc/functions.php 6608 google_seo_url_post
/inc/functions_post.php 722 get_post_link
/showthread.php 1122 build_postbit
Warning [2] Undefined array key "additionalgroups" - Line: 7924 - File: inc/functions.php PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/functions.php 7924 errorHandler->error_callback
/inc/plugins/ougc_agi.php 307 is_member
/inc/class_plugins.php 142 ougc_agi_run
/inc/functions_post.php 917 pluginSystem->run_hooks
/showthread.php 1122 build_postbit
Warning [2] Undefined variable $theme - Line: 324 - File: inc/plugins/ougc_agi.php PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/plugins/ougc_agi.php 324 errorHandler->error_callback
/inc/class_plugins.php 142 ougc_agi_run
/inc/functions_post.php 917 pluginSystem->run_hooks
/showthread.php 1122 build_postbit
Warning [2] Trying to access array offset on value of type null - Line: 324 - File: inc/plugins/ougc_agi.php PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/plugins/ougc_agi.php 324 errorHandler->error_callback
/inc/class_plugins.php 142 ougc_agi_run
/inc/functions_post.php 917 pluginSystem->run_hooks
/showthread.php 1122 build_postbit
Warning [2] Undefined array key "mysupport_status" - Line: 23 - File: inc/functions_post.php(970) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/functions_post.php(970) : eval()'d code 23 errorHandler->error_callback
/inc/functions_post.php 970 eval
/showthread.php 1122 build_postbit
Warning [2] Undefined array key "mysupport_bestanswer" - Line: 25 - File: inc/functions_post.php(970) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/functions_post.php(970) : eval()'d code 25 errorHandler->error_callback
/inc/functions_post.php 970 eval
/showthread.php 1122 build_postbit
Warning [2] Undefined array key "mysupport_deny_support_post" - Line: 25 - File: inc/functions_post.php(970) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/functions_post.php(970) : eval()'d code 25 errorHandler->error_callback
/inc/functions_post.php 970 eval
/showthread.php 1122 build_postbit
Warning [2] Undefined variable $mysupport_options - Line: 52 - File: showthread.php(1651) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/showthread.php(1651) : eval()'d code 52 errorHandler->error_callback
/showthread.php 1651 eval
Warning [2] Undefined variable $mysupport_status - Line: 65 - File: showthread.php(1651) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/showthread.php(1651) : eval()'d code 65 errorHandler->error_callback
/showthread.php 1651 eval
Warning [2] Undefined variable $mysupport_options - Line: 88 - File: showthread.php(1651) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/showthread.php(1651) : eval()'d code 88 errorHandler->error_callback
/showthread.php 1651 eval
Warning [2] Undefined variable $mysupport_js - Line: 109 - File: showthread.php(1651) : eval()'d code PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/showthread.php(1651) : eval()'d code 109 errorHandler->error_callback
/showthread.php 1651 eval
Warning [2] Undefined variable $newurl - Line: 1609 - File: inc/plugins/google_seo/url.php PHP 8.1.33 (Linux)
File Line Function
/inc/class_error.php 157 errorHandler->error
/inc/plugins/google_seo/url.php 1609 errorHandler->error_callback
/inc/functions.php 1148 google_seo_url_multipage
/inc/functions.php 4819 multipage
/inc/functions.php 298 build_breadcrumb
/inc/functions.php 22 parse_page
/showthread.php 1652 output_page



  Register Account

Earn real money $$ through NewPoints: Click Here x


Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Multiplicative Partial Differential Equations
#1
[Image: e38nxpuzdt81.jpg]
Multiplicative Partial Differential Equations | 269 | Svetlin G. Georgiev |

Multiplicative Partial Differential Equations presents an introduction to the theory of multiplicative partial differential equations (MPDEs). It is suitable for all types of basic courses on MPDEs. The author's aim is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques. The text material of this book is presented in a highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques.

Features

Includes new classification and canonical forms of second-order MPDEs
Proposes a new technique to solving the multiplicative wave equation such as the method of separation of variables and the energy method
The proposed technique in the book can be used to give the basic properties of multiplicative elliptic problems, fundamental solutions, multiplicative integral representation of multiplicative harmonic functions, mean-value formulas, strong principle of maximum, multiplicative Poisson equation, multiplicative Green functions, method of separation of variables, and theorems of Liouville and Harnack



Contents of Download:
Multiplicative Partial Differential Equations.pdf (3.62 MB)


KatFile Link(s)

[To see links please register or login]

NitroFlare Link(s)

[To see links please register or login]

RapidGator Link(s)

[To see links please register or login]

[Image: signature.png]
Reply



Forum Jump:


Users browsing this thread:

DL Warez BB