2,961 research outputs found

    Identities for field extensions generalizing the Ohno-Nakagawa relations

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    In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of `extra functional equations' involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper we generalize their result by proving a similar identity relating certain degree l fields with Galois groups D_l and F_l respectively, for any odd prime l, and in particular we give another proof of the Ohno-Nakagawa relation without appealing to binary cubic forms.Comment: Version 2, 16 pages, to appear in Compositi

    Simon Messing oral history interview by Mark I. Greenberg, January 16, 2004

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    Simon Messing, retired professor of Anthropology, discusses his career at USF and the work he did on campus and in Ethiopia. Dr. Messing\u27s daughter is following in his footsteps, as she is currently a professor of Anthropology at USF

    Can Music Increase Empathy? Interpreting Musical Experience Through the Empathizing–Systemizing (E-S) Theory: Implications for Autism

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    Recent research has provided evidence that musical interaction can promote empathy. Yet little is known about the underlying intrapersonal and social psychological processes that are involved when this occurs. For example, which types of music increase empathy and which types decrease it; what role, if any, does empathy play in determining individual differences in musical preference, perception, and performance; or, how do these psychological underpinnings help explain the musical experiences of people with autism spectrum conditions (ASC). To address these questions we employ the Empathizing–Systemizing (E-S) theory as a fruitful framework in which to understand these music-related phenomena. Specifically, we explore how individual differences in musical preference, perception, and performance can be explained by E-S theory. We provide examples from open-ended descriptions of strong musical experiences to demonstrate the ways in which empathy and music inter-relate. Importantly, we discuss the implications for the study of autism, and for how music therapists and clinicians can use music as a tool in their work with individuals diagnosed with ASC.

    Schwinger Representation for the Symmetric Group: Two explicit constructions for the Carrier Space

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    We give two explicit construction for the carrier space for the Schwinger representation of the group SnS_n. While the first relies on a class of functions consisting of monomials in antisymmetric variables, the second is based on the Fock space associated with the Greenberg algebra.Comment: Latex, 6 page
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