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Theory and olympiad problems involving modular arithmetic

En este informe se presentar\'a una opini\'on personal sobre la pel\'icula, c\'ual es la reseña que deja la pel\'icula y en que aspectos de la vida real se pueden presentar este tipo de situaciones. Adem\'as tambi\'en se hablar\'a sobre algunos de los experimentos que realizaron los personajes en la pel\'icula.

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📖 The classic and complete guide written in Traditional Chinese to help you get started on your journey with LaTeX: 《大家來學 LaTeX》. 此倉庫託管著李果正（Edward G.J. Lee）先生於 2004 年接受中華民國行政院研考會委辦的「政府機關資料文件交換之電子檔案格式應用研究」計畫補助所撰寫的《大家來學 LaTeX》原始程式代碼。 https://github.com/TeX-tw/LaTeX123/tree/legacy GNU Free Documentation License version 1.2

TRABAJO DE LA FUERZA ELECTRICA Y VARIACION DE ENERGIA POTENCIAL ELECTRICA

As LED systems have been evolving today in a great number of niche applications including automotive lighting, water purification, and skin imaging etc., extensive studies of scientists and engineers in the field have been constantly looking for ways to reduce generated heat loads and maximize the light output to reach the highest efficiency ratios. While the current systems developed over the last years achieved to reach even a 40% LED light efficiency, a higher portion of the electrical input energy of LEDs is still produced as heat and it hinders their development potential. In addition, the compact size of the LED systems poses some challenges to the reliable characterization of their performance at low uncertainties. Especially, the performance considerations associated with thermal loads over a limited size of LED chips require the effective characterization of these systems for various operational conditions. One of the techniques used for this purpose is that an LED package is characterized by a decrease in forward voltage with increasing junction temperature. As LEDs are operated at higher junction temperatures, the amount and quality of the light deteriorates significantly, and the less efficient use of the LEDs results in additional operating costs and reduced lifetime of LEDs. In fact, accurate identification of thermal behavior of LED packages is one of the essential tasks towards improving the design of LED systems. If thermal characterization of LEDs is accurately done, performance parameters of LED packages are more reliably optimized to yield the highest possible performance ratios. Thus, this study focused on the design and manufacturing of a thermally improved and fully operational rapid temperature controllable chamber in which calibration and test phases of junction temperature measurements are sensitively conducted under a low uncertainty.

In this paper novel approaches to optical beam shaping for lighting systems are presented. Application of various computer generated micro/nano-structured optical components is discussed.