. . . . . "\u7269\u7406\u5B78\u4E2D\uFF0C\u5C24\u5176\u662F\u91CF\u5B50\u5834\u8AD6\uFF0C\u6B63\u898F\u5316\uFF08\u82F1\u8A9E\uFF1Aregularization\uFF09\u662F\u4E00\u9805\u8655\u7406\u7121\u9650\u5927\u3001\u767C\u6563\u4EE5\u53CA\u4E00\u4E9B\u4E0D\u5408\u7406\u8868\u793A\u5F0F\u7684\u65B9\u6CD5\uFF0C\u5176\u65B9\u6CD5\u900F\u904E\u5F15\u5165\u4E00\u9805\u8F14\u52A9\u6027\u7684\u6982\u5FF5\u2014\u2014\u6B63\u898F\u5B50(regulator)\u3002\u8209\u4F8B\u4F86\u8AAA\uFF0C\u82E5\u77ED\u8DDD\u96E2\u7269\u7406\u6548\u61C9\u51FA\u73FE\u767C\u6563\uFF0C\u5247\u8A2D\u5B9A\u4E00\u9805\u7A7A\u9593\u4E2D\u6700\u5C0F\u8DDD\u96E2\u4F86\u89E3\u6C7A\u9019\u60C5\u5F62\u3002\u6B63\u78BA\u7684\u7269\u7406\u7D50\u679C\u662F\u8B93\u6B63\u898F\u5B50\u6D88\u5931(\u6B64\u4F8B\u662F)\u7684\u6975\u9650\u60C5\u5F62\uFF0C\u4E0D\u904E\u6B63\u898F\u5B50\u7684\u7528\u610F\u5C31\u5728\u65BC\u7576\u5B83\u662F\u6709\u9650\u503C\uFF0C\u7406\u8AD6\u7D50\u679C\u4E5F\u662F\u6709\u9650\u503C\u7684\u3002\u6B63\u898F\u5316\u662F\u5C07\u6578\u5B78\u4E2D\u7684\u767C\u6563\u7D1A\u6578\u7684(summability methods)\u7528\u5728\u7269\u7406\u5B78\u554F\u984C\u4E0A\u3002 \u7136\u800C\uFF0C\u7406\u8AD6\u7D50\u679C\u901A\u5E38\u5305\u542B\u4E86\u4E00\u4E9B\u9805\uFF0C\u662F\u6B63\u6BD4\u65BC\u4F8B\u5982\u7684\u5F0F\u5B50\uFF0C\u82E5\u53D6\u6975\u9650\u5247\u6703\u6C92\u6709\u826F\u597D\u5B9A\u7FA9\u3002\u6B63\u898F\u5316\u662F\u7372\u5F97\u4E00\u500B\u5B8C\u6574\u3001\u6709\u9650\u4E14\u6709\u610F\u7FA9\u7684\u7D50\u679C\u7684\u7B2C\u4E00\u6B65\uFF1B\u5728\u91CF\u5B50\u5834\u8AD6\uFF0C\u901A\u5E38\u6703\u63A5\u8457\u4E00\u500B\u76F8\u95DC\u4F46\u662F\u7368\u7ACB\u7684\u6280\u8853\u65B9\u6CD5\u7A31\u4F5C\u91CD\u6574\u5316\u3002\u91CD\u6574\u5316\u5247\u662F\u57FA\u65BC\u5C0D\u4E00\u4E9B\u6709\u8457\u985E\u4F3C\u8868\u793A\u5F0F\u7684\u7269\u7406\u91CF\u7684\u8981\u6C42\uFF0C\u8981\u6C42\u5176\u61C9\u8A72\u7B49\u65BC\u89C0\u6E2C\u503C\u3002\u5982\u6B64\u7684\u7D04\u675F\u689D\u4EF6\u5247\u5141\u8A31\u6211\u5011\u8A08\u7B97\u4E00\u4E9B\u770B\u4F3C\u767C\u6563\u7684\u7269\u7406\u91CF\u7684\u6709\u9650\u503C\u3002"@zh . . "\u0420\u0435\u0433\u0443\u043B\u044F\u0440\u0438\u0437\u0430\u0301\u0446\u0438\u044F \u2014 \u0442\u0435\u0445\u043D\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u043F\u0440\u0438\u0451\u043C \u0432 \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u043E\u0439 \u0442\u0435\u043E\u0440\u0438\u0438 \u043F\u043E\u043B\u044F, \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0449\u0438\u0439 \u0438\u0437\u0431\u0435\u0433\u0430\u0442\u044C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0438 \u043D\u0435\u043A\u043E\u0440\u0440\u0435\u043A\u0442\u043D\u044B\u0445 \u0432\u044B\u0440\u0430\u0436\u0435\u043D\u0438\u0439 \u0432 \u043F\u0440\u043E\u043C\u0435\u0436\u0443\u0442\u043E\u0447\u043D\u044B\u0445 \u0432\u044B\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u044F\u0445 (\u0442\u043E \u0435\u0441\u0442\u044C \u0432\u043C\u0435\u0441\u0442\u043E \u044F\u0432\u043D\u044B\u0445 \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0441\u0442\u0435\u0439 \u043C\u044B \u043E\u043F\u0435\u0440\u0438\u0440\u0443\u0435\u043C \u043A\u043E\u043D\u0435\u0447\u043D\u044B\u043C\u0438 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0430\u043C\u0438). \u041F\u043E\u0434\u0440\u0430\u0437\u0443\u043C\u0435\u0432\u0430\u0435\u0442\u0441\u044F, \u0447\u0442\u043E \u043F\u043E\u0441\u043B\u0435 \u043F\u043E\u043B\u0443\u0447\u0435\u043D\u0438\u044F \u043E\u043A\u043E\u043D\u0447\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0433\u043E \u043E\u0442\u0432\u0435\u0442\u0430 \u0440\u0435\u0433\u0443\u043B\u0438\u0440\u0443\u044E\u0449\u0438\u0439 \u043F\u0430\u0440\u0430\u043C\u0435\u0442\u0440 \u0443\u0441\u0442\u0440\u0435\u043C\u043B\u044F\u0435\u0442\u0441\u044F \u043A \u043D\u0443\u043B\u044E, \u0438 \u043F\u0440\u0438 \u044D\u0442\u043E\u043C \u043E\u043A\u043E\u043D\u0447\u0430\u0442\u0435\u043B\u044C\u043D\u044B\u0439 \u043E\u0442\u0432\u0435\u0442 \u0434\u043B\u044F \u0441\u0442\u0440\u0435\u043C\u0438\u0442\u0441\u044F \u043A \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u043C\u0443 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u044E."@ru . . . . . . . "\u0420\u0435\u0433\u0443\u043B\u044F\u0440\u0438\u0437\u0430\u0301\u0446\u0438\u044F \u2014 \u0442\u0435\u0445\u043D\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u043F\u0440\u0438\u0451\u043C \u0432 \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u043E\u0439 \u0442\u0435\u043E\u0440\u0438\u0438 \u043F\u043E\u043B\u044F, \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0449\u0438\u0439 \u0438\u0437\u0431\u0435\u0433\u0430\u0442\u044C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0438 \u043D\u0435\u043A\u043E\u0440\u0440\u0435\u043A\u0442\u043D\u044B\u0445 \u0432\u044B\u0440\u0430\u0436\u0435\u043D\u0438\u0439 \u0432 \u043F\u0440\u043E\u043C\u0435\u0436\u0443\u0442\u043E\u0447\u043D\u044B\u0445 \u0432\u044B\u0447\u0438\u0441\u043B\u0435\u043D\u0438\u044F\u0445 (\u0442\u043E \u0435\u0441\u0442\u044C \u0432\u043C\u0435\u0441\u0442\u043E \u044F\u0432\u043D\u044B\u0445 \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0441\u0442\u0435\u0439 \u043C\u044B \u043E\u043F\u0435\u0440\u0438\u0440\u0443\u0435\u043C \u043A\u043E\u043D\u0435\u0447\u043D\u044B\u043C\u0438 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0430\u043C\u0438). \u041F\u043E\u0434\u0440\u0430\u0437\u0443\u043C\u0435\u0432\u0430\u0435\u0442\u0441\u044F, \u0447\u0442\u043E \u043F\u043E\u0441\u043B\u0435 \u043F\u043E\u043B\u0443\u0447\u0435\u043D\u0438\u044F \u043E\u043A\u043E\u043D\u0447\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0433\u043E \u043E\u0442\u0432\u0435\u0442\u0430 \u0440\u0435\u0433\u0443\u043B\u0438\u0440\u0443\u044E\u0449\u0438\u0439 \u043F\u0430\u0440\u0430\u043C\u0435\u0442\u0440 \u0443\u0441\u0442\u0440\u0435\u043C\u043B\u044F\u0435\u0442\u0441\u044F \u043A \u043D\u0443\u043B\u044E, \u0438 \u043F\u0440\u0438 \u044D\u0442\u043E\u043C \u043E\u043A\u043E\u043D\u0447\u0430\u0442\u0435\u043B\u044C\u043D\u044B\u0439 \u043E\u0442\u0432\u0435\u0442 \u0434\u043B\u044F \u0441\u0442\u0440\u0435\u043C\u0438\u0442\u0441\u044F \u043A \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u043C\u0443 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u044E."@ru . "En physique th\u00E9orique, la r\u00E9gularisation est une proc\u00E9dure ad-hoc qui consiste \u00E0 modifier une grandeur physique qui pr\u00E9sente une singularit\u00E9 afin de la rendre r\u00E9guli\u00E8re. La r\u00E9gularisation est par exemple abondamment utilis\u00E9e en th\u00E9orie quantique des champs en relation avec la proc\u00E9dure de renormalisation, ainsi qu'en relativit\u00E9 g\u00E9n\u00E9rale pour le calcul du probl\u00E8me \u00E0 deux corps en param\u00E9trisation post-newtonienne."@fr . . . . . . . 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\u0627\u0644\u062A\u0646\u0638\u064A\u0645 \u062C\u062F\u0627\u0644\u064B\u0627 \u0645\u0633\u062A\u0645\u0631\u064B\u0627 \u0644\u0639\u062F\u0629 \u0639\u0642\u0648\u062F \u0628\u064A\u0646 \u0627\u0644\u0639\u062F\u064A\u062F \u0645\u0646 \u0627\u0644\u0646\u0627\u0633 \u0628\u0645\u0646 \u0641\u064A\u0647\u0645 \u0645\u062E\u062A\u0631\u0639\u0648 \u0627\u0644\u0623\u0633\u0644\u0648\u0628 \u0630\u0627\u062A\u0647\u0645\u060C \u0641\u0647\u0648 \u064A\u0648\u062D\u062F \u0628\u064A\u0646 \u0627\u0644\u062F\u0639\u0627\u0648\u064A \u0627\u0644\u0641\u064A\u0632\u064A\u0627\u0626\u064A\u0629 \u0648\u0627\u0644\u0645\u0639\u0631\u0641\u064A\u0629 \u0641\u064A \u0646\u0641\u0633 \u0627\u0644\u0645\u0639\u0627\u062F\u0644\u0629. \u0648\u0631\u063A\u0645 \u0630\u0644\u0643\u060C \u0623\u062B\u0628\u062A \u0647\u0630\u0627 \u0627\u0644\u0623\u0633\u0644\u0648\u0628 \u062C\u062F\u0627\u0631\u062A\u0647 \u0641\u064A \u0625\u0646\u062A\u0627\u062C \u062A\u0646\u0628\u0624\u0627\u062A \u062F\u0642\u064A\u0642\u0629 \u0648\u0645\u0641\u064A\u062F\u0629\u060C \u0648\u0623\u0635\u0628\u062D \u0645\u0641\u0647\u0648\u0645\u064B\u0627 \u0628\u0634\u0643\u0644 \u062C\u064A\u062F."@ar . . "Regularizaci\u00F3n (f\u00EDsica)"@es . "Regularisatie is een begrip uit de theoretische natuurkunde. Het is een techniek om met oneindigheden en divergente uitdrukkingen om te gaan, vooral gebruikt voor problemen die opduiken in kwantumveldentheorie\u00EBn."@nl . "En physique th\u00E9orique, la r\u00E9gularisation est une proc\u00E9dure ad-hoc qui consiste \u00E0 modifier une grandeur physique qui pr\u00E9sente une singularit\u00E9 afin de la rendre r\u00E9guli\u00E8re. La r\u00E9gularisation est par exemple abondamment utilis\u00E9e en th\u00E9orie quantique des champs en relation avec la proc\u00E9dure de renormalisation, ainsi qu'en relativit\u00E9 g\u00E9n\u00E9rale pour le calcul du probl\u00E8me \u00E0 deux corps en param\u00E9trisation post-newtonienne."@fr . . . . . "Regularization (physics)"@en . . . . . . . "En f\u00EDsica, en particular en teor\u00EDa cu\u00E1ntica de campos, la regularizaci\u00F3n es un m\u00E9todo para lidiar con resultados infinitos o divergentes que aparecen en el c\u00E1lculo de algunas cantidades f\u00EDsicas. En general consiste en modificar la teor\u00EDa o f\u00F3rmula en cuesti\u00F3n de manera controlada mediante uno o varios par\u00E1metros a priori no f\u00EDsicos, de forma que el resultado sea finito. La interpretaci\u00F3n f\u00EDsica del resultado final suele requerir la eliminaci\u00F3n de estos reguladores en un proceso subsiguiente denominado renormalizaci\u00F3n. Existen diversas maneras de regularizar una teor\u00EDa: \n* La modifica la propagaci\u00F3n de las part\u00EDculas de la teor\u00EDa a\u00F1adiendo part\u00EDculas ficticias de masa muy alta. \n* La elimina las divergencias efectuando el c\u00E1lculo en un espacio-tiempo de dimensi\u00F3n m\u00E1s alta. \n* La (lattice regularization) sustituye un campo continuo por una versi\u00F3n discretizada en una ."@es . . "Em f\u00EDsica, especialmente na teoria qu\u00E2ntica de campos , a regulariza\u00E7\u00E3o \u00E9 um m\u00E9todo de lidar com express\u00F5es infinitas, divergentes, e n\u00E3o sensicais atrav\u00E9s da introdu\u00E7\u00E3o de um conceito auxiliar de um regulador."@pt . . . . "\u0420\u0435\u0433\u0443\u043B\u044F\u0440\u0438\u0437\u0430\u0446\u0456\u044F"@uk . . "Em f\u00EDsica, especialmente na teoria qu\u00E2ntica de campos , a regulariza\u00E7\u00E3o \u00E9 um m\u00E9todo de lidar com express\u00F5es infinitas, divergentes, e n\u00E3o sensicais atrav\u00E9s da introdu\u00E7\u00E3o de um conceito auxiliar de um regulador."@pt . "\u0420\u0435\u0433\u0443\u043B\u044F\u0440\u0438\u0437\u0430\u0446\u0456\u044F \u2014 \u0442\u0435\u0445\u043D\u0456\u043A\u0430, \u0449\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0432 \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u0447\u043D\u0456\u0439 \u0444\u0456\u0437\u0438\u0446\u0456, \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u0443 \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u0456\u0439 \u0442\u0435\u043E\u0440\u0456\u0457 \u043F\u043E\u043B\u044F \u0434\u043B\u044F \u0432\u0438\u043A\u043E\u043D\u0430\u043D\u043D\u044F \u043F\u0440\u043E\u043C\u0456\u0436\u043D\u0438\u0445 \u0440\u043E\u0437\u0440\u0430\u0445\u0443\u043D\u043A\u0456\u0432, \u0443 \u044F\u043A\u0438\u0445 \u0432\u0438\u043D\u0438\u043A\u0430\u044E\u0442\u044C \u0440\u043E\u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456. \u0421\u0443\u0442\u044C \u0442\u0435\u0445\u043D\u0456\u043A\u0438 \u0443 \u0432\u0432\u0435\u0434\u0435\u043D\u043D\u0456 \u0434\u043E\u043F\u043E\u043C\u0456\u0436\u043D\u043E\u0433\u043E \u0447\u0438\u0441\u043B\u0430, \u0440\u0435\u0433\u0443\u043B\u044F\u0442\u043E\u0440\u0430, \u044F\u043A\u0438\u0439 \u043E\u0431\u043C\u0435\u0436\u0443\u0454 \u043E\u0431\u043B\u0430\u0441\u0442\u0456 \u0456\u043D\u0442\u0435\u0433\u0440\u0443\u0432\u0430\u043D\u043D\u044F \u0447\u0438 \u0441\u0443\u043C\u0443\u0432\u0430\u043D\u043D\u044F \u0442\u0430\u043A\u0438\u043C \u0447\u0438\u043D\u043E\u043C, \u0449\u043E \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u0437\u0430\u043B\u0438\u0448\u0430\u0454\u0442\u044C\u0441\u044F \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0438\u043C, \u043E\u0434\u043D\u0430\u043A \u0437\u0430\u043B\u0435\u0436\u043D\u0438\u043C \u0432\u0456\u0434 \u0440\u0435\u0433\u0443\u043B\u044F\u0442\u043E\u0440\u0430. \u041F\u0440\u043E\u0446\u0435\u0434\u0443\u0440\u0430 \u0440\u0435\u0433\u0443\u043B\u044F\u0440\u0438\u0437\u0430\u0446\u0456\u0457 \u0432\u0438\u043F\u0440\u0430\u0432\u0434\u0430\u043D\u0430 \u0432 \u0442\u043E\u043C\u0443 \u0432\u0438\u043F\u0430\u0434\u043A\u0443, \u043A\u043E\u043B\u0438 \u043A\u0456\u043D\u0446\u0435\u0432\u0438\u0439 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u043E\u0431\u0440\u0430\u0445\u0443\u043D\u043A\u0456\u0432, \u044F\u043A\u0438\u0439 \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u0430\u0454 \u0444\u0456\u0437\u0438\u0447\u043D\u0456\u0439 \u0441\u043F\u043E\u0441\u0442\u0435\u0440\u0435\u0436\u0443\u0432\u0430\u043D\u0456\u0439 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0456, \u043D\u0435 \u0437\u0430\u043B\u0435\u0436\u0438\u0442\u044C \u0432\u0456\u0434 \u0440\u0435\u0433\u0443\u043B\u044F\u0442\u043E\u0440\u0430 \u0439 \u0437\u0430\u043B\u0438\u0448\u0430\u0454\u0442\u044C\u0441\u044F \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0438\u043C."@uk . . . "Regulariza\u00E7\u00E3o (f\u00EDsica)"@pt . . . . . . . "Regolarizzazione (fisica)"@it . "\u0420\u0435\u0433\u0443\u043B\u044F\u0440\u0438\u0437\u0430\u0446\u0456\u044F \u2014 \u0442\u0435\u0445\u043D\u0456\u043A\u0430, \u0449\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0432 \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u0447\u043D\u0456\u0439 \u0444\u0456\u0437\u0438\u0446\u0456, \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u0443 \u043A\u0432\u0430\u043D\u0442\u043E\u0432\u0456\u0439 \u0442\u0435\u043E\u0440\u0456\u0457 \u043F\u043E\u043B\u044F \u0434\u043B\u044F \u0432\u0438\u043A\u043E\u043D\u0430\u043D\u043D\u044F \u043F\u0440\u043E\u043C\u0456\u0436\u043D\u0438\u0445 \u0440\u043E\u0437\u0440\u0430\u0445\u0443\u043D\u043A\u0456\u0432, \u0443 \u044F\u043A\u0438\u0445 \u0432\u0438\u043D\u0438\u043A\u0430\u044E\u0442\u044C \u0440\u043E\u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456. \u0421\u0443\u0442\u044C \u0442\u0435\u0445\u043D\u0456\u043A\u0438 \u0443 \u0432\u0432\u0435\u0434\u0435\u043D\u043D\u0456 \u0434\u043E\u043F\u043E\u043C\u0456\u0436\u043D\u043E\u0433\u043E \u0447\u0438\u0441\u043B\u0430, \u0440\u0435\u0433\u0443\u043B\u044F\u0442\u043E\u0440\u0430, \u044F\u043A\u0438\u0439 \u043E\u0431\u043C\u0435\u0436\u0443\u0454 \u043E\u0431\u043B\u0430\u0441\u0442\u0456 \u0456\u043D\u0442\u0435\u0433\u0440\u0443\u0432\u0430\u043D\u043D\u044F \u0447\u0438 \u0441\u0443\u043C\u0443\u0432\u0430\u043D\u043D\u044F \u0442\u0430\u043A\u0438\u043C \u0447\u0438\u043D\u043E\u043C, \u0449\u043E \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u0437\u0430\u043B\u0438\u0448\u0430\u0454\u0442\u044C\u0441\u044F \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0438\u043C, \u043E\u0434\u043D\u0430\u043A \u0437\u0430\u043B\u0435\u0436\u043D\u0438\u043C \u0432\u0456\u0434 \u0440\u0435\u0433\u0443\u043B\u044F\u0442\u043E\u0440\u0430. \u041F\u0440\u043E\u0446\u0435\u0434\u0443\u0440\u0430 \u0440\u0435\u0433\u0443\u043B\u044F\u0440\u0438\u0437\u0430\u0446\u0456\u0457 \u0432\u0438\u043F\u0440\u0430\u0432\u0434\u0430\u043D\u0430 \u0432 \u0442\u043E\u043C\u0443 \u0432\u0438\u043F\u0430\u0434\u043A\u0443, \u043A\u043E\u043B\u0438 \u043A\u0456\u043D\u0446\u0435\u0432\u0438\u0439 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u043E\u0431\u0440\u0430\u0445\u0443\u043D\u043A\u0456\u0432, \u044F\u043A\u0438\u0439 \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u0430\u0454 \u0444\u0456\u0437\u0438\u0447\u043D\u0456\u0439 \u0441\u043F\u043E\u0441\u0442\u0435\u0440\u0435\u0436\u0443\u0432\u0430\u043D\u0456\u0439 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0456, \u043D\u0435 \u0437\u0430\u043B\u0435\u0436\u0438\u0442\u044C \u0432\u0456\u0434 \u0440\u0435\u0433\u0443\u043B\u044F\u0442\u043E\u0440\u0430 \u0439 \u0437\u0430\u043B\u0438\u0448\u0430\u0454\u0442\u044C\u0441\u044F \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0438\u043C."@uk . "En f\u00EDsica, en particular en teor\u00EDa cu\u00E1ntica de campos, la regularizaci\u00F3n es un m\u00E9todo para lidiar con resultados infinitos o divergentes que aparecen en el c\u00E1lculo de algunas cantidades f\u00EDsicas. En general consiste en modificar la teor\u00EDa o f\u00F3rmula en cuesti\u00F3n de manera controlada mediante uno o varios par\u00E1metros a priori no f\u00EDsicos, de forma que el resultado sea finito. La interpretaci\u00F3n f\u00EDsica del resultado final suele requerir la eliminaci\u00F3n de estos reguladores en un proceso subsiguiente denominado renormalizaci\u00F3n. Existen diversas maneras de regularizar una teor\u00EDa:"@es . . . . . . . . . . . . "\u062A\u064F\u0639\u0631\u0641 \u0639\u0645\u0644\u064A\u0629 \u0627\u0644\u062A\u0646\u0638\u064A\u0645 \u0641\u064A \u0633\u064A\u0627\u0642 \u0627\u0644\u0641\u064A\u0632\u064A\u0627\u0621 (\u0648\u0628\u0627\u0644\u0623\u062E\u0635 \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u062D\u0642\u0644 \u0627\u0644\u0643\u0645\u0648\u0645\u064A) \u0628\u0623\u0646\u0647\u0627 \u0637\u0631\u064A\u0642\u0629 \u0644\u062A\u0639\u062F\u064A\u0644 \u0627\u0644\u0643\u0645\u064A\u0627\u062A \u0627\u0644\u0645\u064F\u0642\u0627\u0633\u0629 \u063A\u064A\u0631 \u0627\u0644\u0645\u064F\u0639\u0631\u0641\u0629 (\u0645\u062B\u0644 \u0627\u0644\u0643\u0645\u064A\u0627\u062A \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064A\u0629) \u0644\u062A\u062D\u0648\u064A\u0644\u0647\u0627 \u0625\u0644\u0649 \u0643\u0645\u064A\u0627\u062A \u0645\u062A\u0646\u0627\u0647\u064A\u0629 \u0628\u0648\u0627\u0633\u0637\u0629 \u0628\u0627\u0631\u0627\u0645\u062A\u0631 \u0645\u0646\u0627\u0633\u0628 \u064A\u0639\u0631\u0641 \u0628\u0627\u0644\u0645\u064F\u0646\u0638\u0645 \u0623\u0648 \u062D\u062F \u0627\u0644\u0642\u0637\u0639. \u064A\u0646\u0645\u0630\u062C \u0627\u0644\u0645\u0646\u0638\u0645 \u0639\u062F\u0645 \u0645\u0639\u0631\u0641\u062A\u0646\u0627 \u0628\u0642\u0648\u0627\u0646\u064A\u0646 \u0627\u0644\u0641\u064A\u0632\u064A\u0627\u0621 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062A\u0648\u064A\u0627\u062A \u0627\u0644\u062A\u064A \u0644\u0627 \u0646\u0633\u062A\u0637\u064A\u0639 \u0631\u0635\u062F\u0647\u0627 (\u0645\u062B\u0644 \u0627\u0644\u0623\u062D\u062C\u0627\u0645 \u0627\u0644\u0635\u063A\u064A\u0631\u0629 \u0648\u0645\u0633\u062A\u0648\u064A\u0627\u062A \u0627\u0644\u0637\u0627\u0642\u0629 \u0627\u0644\u0647\u0627\u0626\u0644\u0629). \u064A\u0639\u0648\u0636 \u0627\u0644\u0645\u0646\u0638\u0645 \u0639\u0646 \u0627\u062D\u062A\u0645\u0627\u0644\u064A\u0629 \u0627\u0643\u062A\u0634\u0627\u0641 \u00AB\u0641\u064A\u0632\u064A\u0627\u0621 \u062C\u062F\u064A\u062F\u0629\u00BB (\u0648\u0648\u062C\u0648\u062F\u0647 \u0645\u0642\u062A\u0631\u0646 \u0628\u062A\u0644\u0643 \u0627\u0644\u0627\u062D\u062A\u0645\u0627\u0644\u064A\u0629) \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062A\u0648\u064A\u0627\u062A \u0627\u0644\u062A\u064A \u0644\u0627 \u062A\u0633\u062A\u0637\u064A\u0639 \u0646\u0638\u0631\u064A\u0627\u062A\u0646\u0627 \u0627\u0644\u062D\u0627\u0644\u064A\u0629 \u0646\u0645\u0630\u062C\u062A\u0647\u0627\u060C \u0648\u0641\u064A \u0627\u0644\u0648\u0642\u062A \u0630\u0627\u062A\u0647 \u064A\u0645\u0643\u0651\u0646 \u0627\u0644\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u062D\u0627\u0644\u064A\u0629 \u0645\u0646 \u0625\u0646\u062A\u0627\u062C \u062A\u0646\u0628\u0624\u0627\u062A \u0635\u062D\u064A\u062D\u0629 \u0628\u0635\u0641\u062A\u0647\u0627 \u00AB\u0627\u0644\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0641\u0639\u0627\u0644\u0629\u00BB \u0641\u064A \u0646\u0637\u0627\u0642 \u0627\u0644\u0627\u0633\u062A\u062E\u062F\u0627\u0645 \u0627\u0644\u0645\u062E\u0635\u0635 \u0644\u0647\u0627."@ar . . . "In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a \"cutoff\", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility that \"new physics\" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an \"effective theory\" within its intended scale of use."@en . . . . . "\u6B63\u898F\u5316"@zh . . "In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a \"cutoff\", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility that \"new physics\" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an \"effective theory\" within its intended scale of use. It is distinct from renormalization, another technique to control infinities without assuming new physics, by adjusting for self-interaction feedback. Regularization was for many decades controversial even amongst its inventors, as it combines physical and epistemological claims into the same equations. However, it is now well understood and has proven to yield useful, accurate predictions."@en . . . . "1120457745"^^ . . . "\uBB3C\uB9AC\uD559\uC5D0\uC11C \uC870\uC808(\u8ABF\u7BC0, regularization)\uC774\uB780 \uC774\uB860\uC5D0\uC11C \uC0DD\uAE30\uB294 \uAC01\uC885 \uBB34\uD55C\uD55C \uAC12\uC744 \uB2E4\uB8E8\uAE30 \uC704\uD574, \uADF8 \uBB34\uD55C\uD55C \uC815\uB3C4\uB97C \uC5B4\uB5A4 \uC870\uC808 \uBCC0\uC218(regulator)\uB85C \uD45C\uD604\uD558\uC5EC \uC720\uD55C\uD558\uAC8C \uB9CC\uB4DC\uB294 \uC218\uD559\uC801 \uACFC\uC815\uC774\uB2E4. \uC591\uC790\uC7A5\uB860\uC5D0\uC11C \uC8FC\uB85C \uC4F0\uC778\uB2E4. \uC77C\uBC18\uC801\uC73C\uB85C, \uC870\uC808 \uC774\uD6C4 \uC870\uC808 \uBCC0\uC218\uC758 \uBB34\uD55C\uD568\uC744 \uC7AC\uADDC\uACA9\uD654\uB85C\uC11C \uC774\uB860\uC758 \uC0C1\uC218\uC5D0 \uC228\uAE34\uB2E4. \uC8FC\uC5B4\uC9C4 \uC774\uB860\uC744 \uC870\uC808\uD558\uB824\uBA74 \uC5EC\uB7EC \uBC29\uBC95\uC774 \uC788\uB2E4. \uB300\uAC1C \uC11C\uB85C \uB2E4\uB978 \uADDC\uCE59\uD654 \uBC29\uBC95\uC744 \uC368\uB3C4 \uB3D9\uC77C\uD55C \uACC4\uC0B0 \uACB0\uACFC\uB97C \uC5BB\uB294\uB370, \uC774\uB294 \uBCF4\uD3B8\uC131(universality)\uACFC 2\uCC28 \uC0C1\uC804\uC774\uC758 \uC874\uC7AC \uB54C\uBB38\uC774\uB2E4. \uC774\uB294 \uCF00\uB124\uC2A4 G. \uC70C\uC2A8\uACFC \uB9AC\uC624 \uCE74\uB2E4\uB178\uD504\uC5D0 \uC758\uD574 \uBC1D\uD600\uC84C\uB2E4. \uB2E4\uB9CC \uC870\uC808\uC5D0 \uB530\uB77C \uACC4\uC0B0 \uACB0\uACFC\uAC00 \uB2E4\uB97C \uB54C\uAC00 \uC788\uB294\uB370, \uC774\uB294 \uACE0\uC804 \uC774\uB860\uC744 \uC591\uC790\uD654\uD558\uB294 \uB3D9\uC548, \uACE0\uC804\uC801\uC778 \uB300\uCE6D\uC774 \uAE68\uC84C\uAE30 \uB54C\uBB38\uC774\uB2E4. \uC774\uB7F0 \uACBD\uC6B0 \uC774\uB860\uC774 \uBCC0\uCE59\uC801\uC774\uB77C\uACE0 \uD558\uACE0, \uAE68\uC9C4 \uB300\uCE6D\uC744 \uBCC0\uCE59\uC774\uB77C\uACE0 \uBD80\uB978\uB2E4. \uD754\uD788 \uC4F0\uC774\uB294 \uADDC\uCE59\uD654\uB294 \uB2E4\uC74C\uACFC \uAC19\uB2E4. \n* \uC790\uC678 \uC808\uB2E8 \uC870\uC808 (ultraviolet cutoff) -- \uAC00\uC7A5 \uB2E8\uC21C\uD55C \uBC29\uBC95. \uAC8C\uC774\uC9C0 \uB300\uCE6D\uC774\uB098 \uB85C\uB7F0\uCE20 \uB300\uCE6D\uC744 \uBB34\uC2DC\uD55C\uB2E4. \n* \uCC28\uC6D0 \uC870\uC808\u2014\uAC8C\uC774\uC9C0 \uB300\uCE6D\uC744 \uBCF4\uC874\uD55C\uB2E4. \n* \uD30C\uC6B8\uB9AC-\uBE44\uC57C\uB974 \uC870\uC808\u2014\uAC00\uC0C1\uC758 \uBB34\uAC70\uC6B4 \uC785\uC790\uB97C \uB77C\uADF8\uB791\uC9C0\uC5B8\uC5D0 \uC0BD\uC785. \uC785\uC790\uC758 \uC9C8\uB7C9\uC774 \uB9E4\uC6B0 \uD06C\uBA74, \uC774 \uD56D\uC740 \uC774\uB860\uC5D0\uC11C \uBD84\uB9AC(decoupling)\uB41C\uB2E4. \n* \uACA9\uC790\uC870\uC808 (lattice) -- \uC2DC\uACF5\uC744 \uC5F0\uC18D\uCCB4\uC5D0\uC11C \uACA9\uC790\uB85C \uB300\uCCB4. \uB85C\uB7F0\uCE20 \uB300\uCE6D\uC744 \uAE68\uB728\uB9AC\uC9C0\uB9CC, \uC218\uCE58\uC801 \uACC4\uC0B0\uC5D0 \uC6A9\uC774\uD558\uB2E4. \n* \uC81C\uD0C0 \uD568\uC218 \uC870\uC808 (zeta function) \n* \uC778\uACFC\uC131 \uC870\uC808 (causal) \n* \uC544\uB2E4\uB9C8\uB974 \uC870\uC808 (Hadamard) \n* Point-splitting regularization"@ko . . . . . "\uC870\uC808 (\uBB3C\uB9AC\uD559)"@ko . . . . . . . "\u7269\u7406\u5B78\u4E2D\uFF0C\u5C24\u5176\u662F\u91CF\u5B50\u5834\u8AD6\uFF0C\u6B63\u898F\u5316\uFF08\u82F1\u8A9E\uFF1Aregularization\uFF09\u662F\u4E00\u9805\u8655\u7406\u7121\u9650\u5927\u3001\u767C\u6563\u4EE5\u53CA\u4E00\u4E9B\u4E0D\u5408\u7406\u8868\u793A\u5F0F\u7684\u65B9\u6CD5\uFF0C\u5176\u65B9\u6CD5\u900F\u904E\u5F15\u5165\u4E00\u9805\u8F14\u52A9\u6027\u7684\u6982\u5FF5\u2014\u2014\u6B63\u898F\u5B50(regulator)\u3002\u8209\u4F8B\u4F86\u8AAA\uFF0C\u82E5\u77ED\u8DDD\u96E2\u7269\u7406\u6548\u61C9\u51FA\u73FE\u767C\u6563\uFF0C\u5247\u8A2D\u5B9A\u4E00\u9805\u7A7A\u9593\u4E2D\u6700\u5C0F\u8DDD\u96E2\u4F86\u89E3\u6C7A\u9019\u60C5\u5F62\u3002\u6B63\u78BA\u7684\u7269\u7406\u7D50\u679C\u662F\u8B93\u6B63\u898F\u5B50\u6D88\u5931(\u6B64\u4F8B\u662F)\u7684\u6975\u9650\u60C5\u5F62\uFF0C\u4E0D\u904E\u6B63\u898F\u5B50\u7684\u7528\u610F\u5C31\u5728\u65BC\u7576\u5B83\u662F\u6709\u9650\u503C\uFF0C\u7406\u8AD6\u7D50\u679C\u4E5F\u662F\u6709\u9650\u503C\u7684\u3002\u6B63\u898F\u5316\u662F\u5C07\u6578\u5B78\u4E2D\u7684\u767C\u6563\u7D1A\u6578\u7684(summability methods)\u7528\u5728\u7269\u7406\u5B78\u554F\u984C\u4E0A\u3002 \u7136\u800C\uFF0C\u7406\u8AD6\u7D50\u679C\u901A\u5E38\u5305\u542B\u4E86\u4E00\u4E9B\u9805\uFF0C\u662F\u6B63\u6BD4\u65BC\u4F8B\u5982\u7684\u5F0F\u5B50\uFF0C\u82E5\u53D6\u6975\u9650\u5247\u6703\u6C92\u6709\u826F\u597D\u5B9A\u7FA9\u3002\u6B63\u898F\u5316\u662F\u7372\u5F97\u4E00\u500B\u5B8C\u6574\u3001\u6709\u9650\u4E14\u6709\u610F\u7FA9\u7684\u7D50\u679C\u7684\u7B2C\u4E00\u6B65\uFF1B\u5728\u91CF\u5B50\u5834\u8AD6\uFF0C\u901A\u5E38\u6703\u63A5\u8457\u4E00\u500B\u76F8\u95DC\u4F46\u662F\u7368\u7ACB\u7684\u6280\u8853\u65B9\u6CD5\u7A31\u4F5C\u91CD\u6574\u5316\u3002\u91CD\u6574\u5316\u5247\u662F\u57FA\u65BC\u5C0D\u4E00\u4E9B\u6709\u8457\u985E\u4F3C\u8868\u793A\u5F0F\u7684\u7269\u7406\u91CF\u7684\u8981\u6C42\uFF0C\u8981\u6C42\u5176\u61C9\u8A72\u7B49\u65BC\u89C0\u6E2C\u503C\u3002\u5982\u6B64\u7684\u7D04\u675F\u689D\u4EF6\u5247\u5141\u8A31\u6211\u5011\u8A08\u7B97\u4E00\u4E9B\u770B\u4F3C\u767C\u6563\u7684\u7269\u7406\u91CF\u7684\u6709\u9650\u503C\u3002"@zh . . "20277"^^ . . . . . "Regularisatie (natuurkunde)"@nl . . "\uBB3C\uB9AC\uD559\uC5D0\uC11C \uC870\uC808(\u8ABF\u7BC0, regularization)\uC774\uB780 \uC774\uB860\uC5D0\uC11C \uC0DD\uAE30\uB294 \uAC01\uC885 \uBB34\uD55C\uD55C \uAC12\uC744 \uB2E4\uB8E8\uAE30 \uC704\uD574, \uADF8 \uBB34\uD55C\uD55C \uC815\uB3C4\uB97C \uC5B4\uB5A4 \uC870\uC808 \uBCC0\uC218(regulator)\uB85C \uD45C\uD604\uD558\uC5EC \uC720\uD55C\uD558\uAC8C \uB9CC\uB4DC\uB294 \uC218\uD559\uC801 \uACFC\uC815\uC774\uB2E4. \uC591\uC790\uC7A5\uB860\uC5D0\uC11C \uC8FC\uB85C \uC4F0\uC778\uB2E4. \uC77C\uBC18\uC801\uC73C\uB85C, \uC870\uC808 \uC774\uD6C4 \uC870\uC808 \uBCC0\uC218\uC758 \uBB34\uD55C\uD568\uC744 \uC7AC\uADDC\uACA9\uD654\uB85C\uC11C \uC774\uB860\uC758 \uC0C1\uC218\uC5D0 \uC228\uAE34\uB2E4. \uC8FC\uC5B4\uC9C4 \uC774\uB860\uC744 \uC870\uC808\uD558\uB824\uBA74 \uC5EC\uB7EC \uBC29\uBC95\uC774 \uC788\uB2E4. \uB300\uAC1C \uC11C\uB85C \uB2E4\uB978 \uADDC\uCE59\uD654 \uBC29\uBC95\uC744 \uC368\uB3C4 \uB3D9\uC77C\uD55C \uACC4\uC0B0 \uACB0\uACFC\uB97C \uC5BB\uB294\uB370, \uC774\uB294 \uBCF4\uD3B8\uC131(universality)\uACFC 2\uCC28 \uC0C1\uC804\uC774\uC758 \uC874\uC7AC \uB54C\uBB38\uC774\uB2E4. \uC774\uB294 \uCF00\uB124\uC2A4 G. \uC70C\uC2A8\uACFC \uB9AC\uC624 \uCE74\uB2E4\uB178\uD504\uC5D0 \uC758\uD574 \uBC1D\uD600\uC84C\uB2E4. \uB2E4\uB9CC \uC870\uC808\uC5D0 \uB530\uB77C \uACC4\uC0B0 \uACB0\uACFC\uAC00 \uB2E4\uB97C \uB54C\uAC00 \uC788\uB294\uB370, \uC774\uB294 \uACE0\uC804 \uC774\uB860\uC744 \uC591\uC790\uD654\uD558\uB294 \uB3D9\uC548, \uACE0\uC804\uC801\uC778 \uB300\uCE6D\uC774 \uAE68\uC84C\uAE30 \uB54C\uBB38\uC774\uB2E4. \uC774\uB7F0 \uACBD\uC6B0 \uC774\uB860\uC774 \uBCC0\uCE59\uC801\uC774\uB77C\uACE0 \uD558\uACE0, \uAE68\uC9C4 \uB300\uCE6D\uC744 \uBCC0\uCE59\uC774\uB77C\uACE0 \uBD80\uB978\uB2E4. \uD754\uD788 \uC4F0\uC774\uB294 \uADDC\uCE59\uD654\uB294 \uB2E4\uC74C\uACFC \uAC19\uB2E4."@ko . "R\u00E9gularisation (physique)"@fr . . . "In fisica, in particolare nella teoria quantistica dei campi, la regolarizzazione \u00E8 un metodo per modificare osservabili che hanno singolarit\u00E0 al fine di renderle finite mediante l'introduzione di un opportuno parametro chiamato regolatore. Il regolatore, noto anche come \"cutoff\" (valore di taglio), modella la mancanza di conoscenza della fisica su scale non osservate (ad esempio scale di piccole dimensioni o grandi livelli di energia). Compensa per (e richiede) la possibilit\u00E0 che la \"nuova fisica\" possa essere scoperta a quelle scale che la presente teoria non \u00E8 in grado di modellizzare, mentre consente alla teoria attuale di fornire previsioni accurate come una \"teoria efficace\" all'interno della scala di utilizzo prevista. Non va confusa con la rinormalizzazione, un'altra tecnica per controllare gli infiniti senza assumere una nuova fisica, regolandosi per il feedback dell'autointerazione. La regolarizzazione \u00E8 stata per molti decenni oggetto di discussione anche tra i suoi inventori, poich\u00E9 combina le affermazioni fisiche ed epistemologiche nelle stesse equazioni. Tuttavia, ora \u00E8 ben compresa e ha dimostrato di fornire previsioni utili e accurate."@it . "Regularisatie is een begrip uit de theoretische natuurkunde. Het is een techniek om met oneindigheden en divergente uitdrukkingen om te gaan, vooral gebruikt voor problemen die opduiken in kwantumveldentheorie\u00EBn."@nl . . . . "\u0420\u0435\u0433\u0443\u043B\u044F\u0440\u0438\u0437\u0430\u0446\u0438\u044F (\u0444\u0438\u0437\u0438\u043A\u0430)"@ru . "In fisica, in particolare nella teoria quantistica dei campi, la regolarizzazione \u00E8 un metodo per modificare osservabili che hanno singolarit\u00E0 al fine di renderle finite mediante l'introduzione di un opportuno parametro chiamato regolatore. Il regolatore, noto anche come \"cutoff\" (valore di taglio), modella la mancanza di conoscenza della fisica su scale non osservate (ad esempio scale di piccole dimensioni o grandi livelli di energia). Compensa per (e richiede) la possibilit\u00E0 che la \"nuova fisica\" possa essere scoperta a quelle scale che la presente teoria non \u00E8 in grado di modellizzare, mentre consente alla teoria attuale di fornire previsioni accurate come una \"teoria efficace\" all'interno della scala di utilizzo prevista."@it . "2009062"^^ . . "\u062A\u0646\u0638\u064A\u0645 (\u0641\u064A\u0632\u064A\u0627\u0621)"@ar .