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Analysis of institutional authors

Fox, Daniel J FCorresponding Author

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FUNCTIONS DIVIDING THEIR HESSIAN DETERMINANTS AND AFFINE SPHERES

Publicated to:Asian Journal Of Mathematics. 20 (3): 503-530 - 2016-07-01 20(3), DOI: 10.4310/AJM.2016.v20.n3.a5

Authors: Fox Hornig, Daniel Jeremy

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Abstract

The nonzero level sets of a homogeneous, logarithmically homogeneous, or translationally homogeneous function are affine spheres if and only if the Hessian determinant of the function is a multiple of a power or an exponential of the function. In particular, the nonzero level sets of a homogeneous polynomial are proper affine spheres if some power of it equals a nonzero multiple of its Hessian determinant. The relative invariants of real forms of regular irreducible prehomogeneous vector spaces yield many such polynomials which are moreover irreducible. For example, the nonzero level sets of the Cayley hyperdeterminant are affine spheres.

Keywords

Affine sphereHyperdeterminantMonge-ampere equationPrehomogeneous vector spaceVector-spaces

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Asian Journal Of Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2016, it was in position 77/311, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 2.95, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-07, the following number of citations:

  • WoS: 4
  • Google Scholar: 4
  • OpenCitations: 3

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (FOX HORNIG, DANIEL JEREMY) and Last Author (FOX HORNIG, DANIEL JEREMY).

the author responsible for correspondence tasks has been FOX HORNIG, DANIEL JEREMY.