Some new symmetric relations of quark masses and prediction of fourth-generation quark masses

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In this study, we discover a mass space defined by generalized Koide relations, named here as k-relations, and achieve some new symmetric relations. These relations can be further used to predict the fourth-generation quark masses in terms of dilation magnitude and angular rotation ratios in the general mass space. Thus far, no theory has been proposed that can constrain the number of generations of quarks; this theory naturally limits the number of generations of quarks.