Weil representations via abstract data and Heisenberg groups: A comparison

In this paper we deal with a well known problem of specifying abstract data types. Up to now there were many approaches to this problem. We follow the axiomatic style of specifying abstract data types (cf. e.g. [1, 2, 6, 8, 9, 10]). We apply, however, the first-order temporal logic. We introduce a notion of first-order completeness of axiomatic specifications and show a general method for obtaining first-order complete axiomatizations. Some examples illustrate the method.

Download Full-text

A comparison of abstract data type and constraint database approaches to GIS query languages

Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - GIS '09 ◽

10.1145/1653771.1653824 ◽

2009 ◽

Author(s):

Peter Revesz

Keyword(s):

Query Languages ◽

Data Type ◽

Abstract Data Type ◽

Abstract Data ◽

Constraint Database

Download Full-text

Abstract data types and Data Bases

Proceedings of the 1980 workshop on Data abstraction, databases and conceptual modeling - ◽

10.1145/800227.806912 ◽

1980 ◽

Cited By ~ 1

Author(s):

Paolo Paolini

Keyword(s):

Abstract Data Types ◽

Data Types ◽

Data Bases ◽

Abstract Data

Download Full-text

Optimistic concurrency control for abstract data types

Proceedings of the fifth annual ACM symposium on Principles of distributed computing - PODC '86 ◽

10.1145/10590.10608 ◽

1986 ◽

Cited By ~ 8

Author(s):

Maurice Herlihy

Keyword(s):

Concurrency Control ◽

Abstract Data Types ◽

Data Types ◽

Optimistic Concurrency Control ◽

Abstract Data

Download Full-text

Counting and equidistribution in quaternionic Heisenberg groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004121000426 ◽

2021 ◽

pp. 1-38

Author(s):

JOUNI PARKKONEN ◽

FRÉDÉRIC PAULIN

Keyword(s):

Hyperbolic Geometry ◽

Quaternion Algebra ◽

Rational Points ◽

Hyperbolic Spaces ◽

Heisenberg Groups ◽

Arithmetic Groups ◽

Hermitian Forms ◽

Dimension 2 ◽

Counting Formula ◽

The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

Download Full-text