New Directions in the Search for the First Floridians
The authors cite two large research open-access databases developed in recent years, popularly kn... more The authors cite two large research open-access databases developed in recent years, popularly known by their acronyms PIDBA (Paleoindian Database of the Americas) and DINAA (Digital Index of North American Archaeology), for aiding in their study of early human settlements in Southeastern North America. With nearly half a million sites indexed so far, many with complex data records listing hundreds of attributes, DINAA has several orders of magnitude more information than PIDBA. PIDBA, however, encompasses image and attribute data on ca. 30,000 Paleoindian artifacts. Information recorded in both PIDBA and DINAA documents not only the number and distribution of Paleoindian artifacts and components found and recorded to date but also the possible proxy measures of human demography and settlement range, which can be compared with figures from later periods or from different states or regions.
Motivated by the Mathieu conjecture [Ma], the image conjecture [Z3] and the well-known Jacobian c... more Motivated by the Mathieu conjecture [Ma], the image conjecture [Z3] and the well-known Jacobian conjecture [K] (see also [BCW] and [E1]), the notion of Mathieu subspaces as a natural generalization of the notion of ideals has been introduced recently in [Z4] for associative algebras. In this paper, we first study algebraic elements in the radicals of Mathieu subspaces of associative algebras over fields and prove some properties and characterizations of Mathieu subspaces with algebraic radicals. We then give some characterizations or classifications for strongly simple algebras (the algebras with no non-trivial Mathieu subspaces) over arbitrary commutative rings, and for quasi-stable algebras (the algebras all of whose subspaces that do not contain the identity element of the algebra are Mathieu subspaces) over arbitrary fields. Furthermore, co-dimension one Mathieu subspaces and the minimal non-trivial Mathieu subspaces of the matrix algebras over fields are also completely determined.
New Directions in the Search for the First Floridians
The authors cite two large research open-access databases developed in recent years, popularly kn... more The authors cite two large research open-access databases developed in recent years, popularly known by their acronyms PIDBA (Paleoindian Database of the Americas) and DINAA (Digital Index of North American Archaeology), for aiding in their study of early human settlements in Southeastern North America. With nearly half a million sites indexed so far, many with complex data records listing hundreds of attributes, DINAA has several orders of magnitude more information than PIDBA. PIDBA, however, encompasses image and attribute data on ca. 30,000 Paleoindian artifacts. Information recorded in both PIDBA and DINAA documents not only the number and distribution of Paleoindian artifacts and components found and recorded to date but also the possible proxy measures of human demography and settlement range, which can be compared with figures from later periods or from different states or regions.
Motivated by the Mathieu conjecture [Ma], the image conjecture [Z3] and the well-known Jacobian c... more Motivated by the Mathieu conjecture [Ma], the image conjecture [Z3] and the well-known Jacobian conjecture [K] (see also [BCW] and [E1]), the notion of Mathieu subspaces as a natural generalization of the notion of ideals has been introduced recently in [Z4] for associative algebras. In this paper, we first study algebraic elements in the radicals of Mathieu subspaces of associative algebras over fields and prove some properties and characterizations of Mathieu subspaces with algebraic radicals. We then give some characterizations or classifications for strongly simple algebras (the algebras with no non-trivial Mathieu subspaces) over arbitrary commutative rings, and for quasi-stable algebras (the algebras all of whose subspaces that do not contain the identity element of the algebra are Mathieu subspaces) over arbitrary fields. Furthermore, co-dimension one Mathieu subspaces and the minimal non-trivial Mathieu subspaces of the matrix algebras over fields are also completely determined.
The Digital Index of North American Archaeology (DINAA) currently contains primary data from ov... more The Digital Index of North American Archaeology (DINAA) currently contains primary data from over 340,000 archaeological sites in 15 states in eastern North America. Two cases are used to explore the new research and management opportunities that are created by using DINAA in combination with other sources of data. First, the potential power of using DINAA as a “bridge” between specialized, independent datasets is considered using information compiled by the Eastern Woodlands Household Archaeology Data Project. Second, DINAA site data are combined with environmental data to model the effects of anticipated changes in sea level due to global climate change on cultural resources near the Atlantic and Gulf coasts. DINAA data were compiled in cooperation with State Historic Preservation Offices in our partner states to demonstrate the feasibility and research value of interoperating state-maintained site databases into a single, large-scale, freely-available archaeological dataset that protects sensitive site location information.
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Papers by Stephen Yerka