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We report In0.4Ga0.6As quantum dot (QD) solar cells with In0.2Ga0.8As cap layers, which extends the photoabsorption spectra toward a wavelength longer than those of In0.4Ga0.6As QD solar cells without cap layers. Well-aligned 50-stack In0.4Ga0.6As QD structures with In0.2Ga0.8As cap layers can be grown without using a strain balancing technique. The photoluminescence wavelength of ten-stack In0.4Ga0.6As QDs with an In0.2Ga0.8As cap layer becomes longer, as a result of the reduced strain in the QDs achieved by using the cap layer. The cell characteristics of multistacked In0.4Ga0.6As QD solar cells are improved by employing In0.2Ga0.8As cap layers.

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We study skew-orthogonal polynomials with respect to the weight functionA finite subsequence of such skew-orthogonal polynomials arising in the study of orthogonal and symplectic ensembles of random matrices satisfies a system of differential-difference-deformation equation. The vectors formed by such subsequence have the rank equal to the degree of the potential in the quaternion sense. These solutions satisfy certain compatibility condition and hence admit a simultaneous fundamental system of solutions.

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