1,627 research outputs found
C1,1 vector optimization and Riemann derivatives
No full textIn this paper we introduce a generalized second-order
Riemann-type derivative for C1,1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that these conditions are stronger
than those obtained by means of the second-order subdifferential in Clarke sense considered in Guerraggio, Luc (2001) and also to some extent than those obtained in Guerraggio, Luc, Minh (2001
C1,1 vector optimization problems and Riemann derivatives
No full textIn this paper we introduce a generalized second-order Riemann-type derivative for C^1'1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that, these conditions are stronger than those obtained by means of the second-order subdinerential in Clarke sense considered in Guerraggio, Luc (2001) and also to some extent than those obtained in Guerraggio, Luc, Minh (2001)
Vito Volterra
No full textVito Volterra (1860-1940) was one of the most famous representatives of Italian science in his day. Angelo Guerragio and Giovanni Paolini analyze Volterra’s most important contributions to mathematics and their applications, as well as his outstanding organizational achievements in scientific policy. Volterra was one of the founding fathers of functional analysis and the author of fundamental contributions in the field of integral equations, elasticity theory and population dynamics (Lotka-Volterra model). He delivered keynote lectures on the occasion of the International Congresses of Mathematicians held in Paris (1900), Rome (1908), Strasbourg (1920) and Bologna (1928). He became involved in the scientific development in united Italy and was appointed senator of the kingdom in 1905. One of his numerous non-mathematical activities was founding the National Research Council (Consiglio Nazionale delle Ricerche, CNR). During the First World War he was active in military research. After the war he took a clear stand against fascism, which was the starting point for his exclusion. In 1926 he resigned as president of the world famous Accademia Nazionale dei Lincei and was later on excluded from the academy. In 1931 he was one of the few university lecturers who denied to swear an oath of allegiance to the fascistic regime. In 1938 he suffered from the impact of the racial laws. The authors draw a comprehensive picture of Vito Volterra, both as a great mathematician and an organizer of science
Y=F(X). La storia del concetto di funzione in 15000 battute
No full textLa storia del concetto di funzione nella storia della Matematica
Y for y = f(x)
No full textThis paper surveys the history of the notion of function, back to its original identification with curves and (only) elementary functions. Making the definitions of the derivative and of limit rigorous leads to making calculus for functions of one and n variables rigorous as well, and to the subsequent extension to the functional calculus due to Vito Volterra
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