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"Riemann's conditions for integrability and their influence on the birth of the concept of measure" (English translation of title) is an article on the history of measure theory, analyzing deeply and comprehensively every early contribution to the field, starting from Riemann's work and going to the works of Hermann Hankel, Gaston Darboux ...
Hankel matrices are formed when, given a sequence of output data, a realization of an underlying state-space or hidden Markov model is desired. [3] The singular value decomposition of the Hankel matrix provides a means of computing the A , B , and C matrices which define the state-space realization. [ 4 ]
In control theory, Hankel singular values, named after Hermann Hankel, provide a measure of energy for each state in a system. They are the basis for balanced model reduction, in which high energy states are retained while low energy states are discarded. The reduced model retains the important features of the original model.
One of the first mathematicians to appreciate Grassmann's ideas during his lifetime was Hermann Hankel, whose 1867 Theorie der complexen Zahlensysteme. [5] […], he developed […] some of Hermann Grassmann's algebras and W.R. Hamilton's quaternions. Hankel was the first to recognise the significance of Grassmann's long-neglected writings and ...
Indeed, beginning with Richard Dedekind in 1858, several mathematicians worked on the definition of the real numbers, including Hermann Hankel, Charles Méray, and Eduard Heine, but this is only in 1872 that two independent complete definitions of real numbers were published: one by Dedekind, by means of Dedekind cuts; the other one by Georg ...
Different kinds of learning and economically relevant types of knowledge can likewise be identified. It is argued that pure market economies, if such existed, would have severe problems in terms of learning and innovation. The 'learning economy' is a mixed economy in a fundamental sense.
Economics was the second Keynesian textbook in the United States, following the 1947 The Elements of Economics, by Lorie Tarshis.Like Tarshis's work, Economics was attacked by American conservatives (as part of the Second Red Scare, or McCarthyism), universities that adopted it were subject to "conservative business pressuring", and Samuelson was accused of Communism.
Price theory was a significant aspect of his legacy as a teacher, and he taught the subject from 1946 to 1964 and again from 1972 to 1976. Notable economists who took Friedman's price theory course include James M. Buchanan , Gary Becker , and Robert Lucas Jr. , all of whom later became Nobel laureates.