Axiomatizations of measurement systems usually require an axiom--called an Archimedean axiom-that allows quantities to be compared. This type of axiom has a different form from the other measurement axioms, and cannot-except in the most trivial cases-be empirically verified. In this paper, representation theorems for extensive measurement structures without Archimedean axioms are given. Such st...

Abstract We study homotopy epimorphisms and covers formulated in terms of derived Tate’s acyclicity for commutative $C^*$-algebras algebras continuous functions valued non-Archimedean fields. prove that a epimorphism between precisely corresponds to closed immersion the compact Hausdorff topological spaces associated with them cover $C^*$-algebra space it by immersions admitting finite subcover...

It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a d-monotone function. The class of d-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of d-dimensional l1-norm symmetric distributions that place no point mass at the origin. The d-monotone Archimedean copul...

Efficient sampling algorithms for both exchangeable and nested Archimedean copulas are presented. First, efficient sampling algorithms for the nested Archimedean families of Ali-Mikhail-Haq, Frank, and Joe are introduced. Second, a general strategy how to build a nested Archimedean copula from a given Archimedean generator is presented. Sampling this copula involves sampling an exponentiallytil...

In this paper, a new algebraic representation by the non-Archimedean fields is proposed to model stratified/ranked knowledge bases. The non-Archimedean representation is in the form of the non-Archimedean polynomials. With the nonArchimedean representation, the most widely used ordering strategies are easily induced and compared. Moreover, a framework of prioritized merging operators using the ...

We define and study the concept of non-Archimedean intuitionistic fuzzy normed space by using the idea of t-norm and t-conorm. Furthermore, by using the non-Archimedean intuitionistic fuzzy normed space, we investigate the stability of various functional equations. That is, we determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framewor...

We introduce an algorithm that can be used to compute the canonical height of a point on an elliptic curve over the rationals in quasi-linear time. As in most previous algorithms, we decompose the difference between the canonical and the naive height into an archimedean and a non-archimedean term. Our main contribution is an algorithm for the computation of the non-archimedean term that require...

In this paper I propose the non-Archimedean multiple-validity. Further, I build an infinite-order predicate logical language in that predicates of various order are considered as fuzzy relations. Such a language can have non-Archimedean valued semantics. For instance, infinite-order predicates can have an interpretation in the set [0, 1] of hyperreal (hyperrational) numbers. Notice that there e...

A Dedekind cut of an ordered abelian group G is a pair (X, Y) of nonempty subsets of G where Y=G−X and every member of X precedes every member of Y. A Dedekind cut (X, Y) is said to be continuous if X has a greatest member or Y has a least member, but not both; if every Dedekind cut of G is a continuous cut, G is said to be (Dedekind) continuous. The ordered abelian group R of real numbers is, ...

In the present paper, K denotes a complete, non-trivially valued, ultrametric (or non-archimedean) field. Entries of sequences, infinite series and matrices are in K. Following Kangro [2, 3, 4], we introduce concept boundedness with speed λ or λ-boundedness. We then obtain characterization matrix class (mλ , mµ ), where mλ set all λ-bounded sequences conclude paper remark about (c c λ-convergent