We introduce normed Jordan ß-algebras, namely, normed Jordan algebras in which the set of quasi-invertible elements is open, and we prove that a normed Jordan algebra is a Q-algebra if and only if it is a full subalgebra of its completion. Homomorphisms from normed Jordan g-algebras onto semisimple Jordan-Banach algebras with minimality of norm topology are continuous. As a consequence, the topology of the norm of a 75*-algebra is the smallest normable topology making the product continuous, and /¿»"-algebras have minimality of the norm. Some applications to (associative) C*-algebras are also given: (i) the associative normed algebras that are ranges of continuous (resp. contractive) Jordan homomorphisms from C*-algebras are bicontinuously (resp. isometrically) isomorphic to C*-algebras, and (ii) weakly compact Jordan homomorphisms from C*-algebras are of finite rank.
Age, growth, and maturity of the bluewing searobin Prionotus punctatus were studied to assess its stock status in southern Brazil. Total length compositions, weight, sex, and maturity stage were recorded from commercial landings, and ages were estimated from transverse sections of the sagittal otolith. The oldest observed specimen was a 12-year-old female. Females grew to a larger asymptotic length (L ∞ = 384.4 mm) than males (L ∞ = 311.7 mm) but at a slower instantaneous rate (k females = 0.41 year −1 , k males = 0.75 year −1 ). Reproduction occurred from spring to early fall. Females sizeand age-at-maturity was estimated at 246.8 mm and 1.66 years, while males were at 237.2 mm and 1.38 years. Based on a statistical catch-at-age stock assessment, the spawning biomass declined 84% from 1976 to 2000 being classified as overfished and suffering from overfishing (B/B msy = 0.62; F/ Fmsy >1). P. punctatus was regularly discarded by industrial fisheries before 2000 but suffered from high exploitation in the last decades. These results highlight the need for the species to be included in Brazil's fishery management plans.
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