In the recent development of LED technologies and market growth of LED luminaries, further study is needed in order for LEDs to replace the current incandescent bulb. Because of the LED radiation pattern, and it being a point-type light source, LED luminaries must employ similar and different methods than those of other luminaries in order to achieve a uniform irradiance. The methods presented in this paper can fasten the production of luminaries while cutting cost and still make luminaries with over 80% uniform irradiance. To achieve these methods reflectors, of 97% reflectivity, of multiple shapes and angles are combined with different arrays of LEDs. All luminaries are constructed using SolidWorks, and then ray data is simulated in TracePro commercial software. The final luminaries are then manufactured and the simulated results are compared and verified with experimental results. The purpose of this paper is to create luminaries for different situations that are affordable to produce while maximizing light efficiency.
The paper deals with eigenvalues and normalized eigenfunctions for a Strum-Liouville eigenvalue problem. The technique we have used is based on applying a Adomian decomposition method (ADM) to our eigenvalue problems. Doing some simple mathematical operations on the method, we can obtain ith eigenvalues and eigenfunctions one at a time. The computed results agree well with those analytical results given in the literature.
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