منابع مشابه
A Review of Non-archimedean Elliptic Functions
This expository article consists of two parts. The first is an old manuscript dating from 1959, entitled “Rational points on elliptic curves over complete fields” containing my first proof of the isomorphism k∗/tZ Et(k). The second part is a discussion of some further aspects of the theory. It begins with a sketch of some topics I had hoped to add to the old manuscript before publishing it, nam...
متن کاملNon-Archimedean analysis, T-functions, and cryptography
These are lecture notes of a 20-hour course at the International Summer School Mathematical Methods and Technologies in Com-Loosely speaking, a T-function is a map of n-bit words into n-bit words such that each i-th bit of image depends only on low-order bits 0,. .. , i of the pre-image. For example, all arithmetic operations (addition , multiplication) are T-functions, all bitwise logical oper...
متن کاملNon - Archimedean Analysis and Rigorous Computation
An introduction to recent work on analysis over the non-Archimedean Levi-Civita field related to applications for common numerical tasks is provided. After studying the algebraic, order, and topological properties, a calculus is developed under which central concepts like the intermediate value theorem, mean value theorem, and Taylor’s theorem with remainder hold under slightly stronger conditi...
متن کاملNon-Archimedean Probabilities and Non-Archimedean Bayesian Networks
In the paper we consider non-Archimedean fuzziness and probabilities. The idea of non-Archimedean multiple-validities is that (1) the set of values for the vagueness and probability is uncountable infinite and (2) this set is not wellordered. For the first time the non-Archimedean logical multiple-validity was proposed in [13], [14]. We propose non-Archimedean fuzziness that is defined on an in...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1986
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1986-15490-x