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This result can be used to obtain a limit on $\\bar{\\nu}_{e}$ fluxes of any origin. Assuming that all $\\bar{\\nu}_e$ flux has its origin in the Sun and has the characteristic $^8$B solar $\\nu_e$ energy spectrum, we obtain an upper limit of 3.7 \\times 10$^2$ cm$^{-2}$ s$^{-1}$ (90% C.L.) on the $\\bar{\\nu}_e$ flux. 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