computationally, selection of a proper numerical value for infinitesimal non archimedean epsilon in dea models has some difficulties. although there are several algorithms for selecting the proper non-archimedean epsilon, it is important to introduce methods in order to calculate the efficiency of dmus without using epsilon. one of these methods is a two-phase method, which obtains the efficien...

To allow conditioning on counterfactual events, zero probabilities can be replaced by infinitesimal probabilities that range over a non-Archimedean ordered field. This paper considers a suitable minimal field that is a complete metric space. Axioms similar to those in Anscombe and Aumann (1963) and in Blume, Brandenburger and Dekel (1991) are used to characterize preferences which: (i) reveal u...

In an extensive form game, whether a player has a better strategy than in a presumed equilibrium depends on the other players’ equilibrium reactions to a counterfactual deviation. To allow conditioning on counterfactual events with prior probability zero, extended probabilities are proposed and given the four equivalent characterizations: (i) complete conditional probability systems; (ii) lexic...

Mehrabian, et. al. (1998) presented a procedure for determining overall assurance interval of ε . Solving n linear programs are needed for this propose, where n is the number of Decision Making Units involved in the evaluation. This paper proposes an efficient algorithm that can determine the overall assurance interval of ε by solving a few number of linear programs. KeywordsData Envelopment An...

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...

We construct a certain topological algebra Ext♯G∨X(χ) from a Deligne-Langlands parameter space X(χ) attached to the group of rational points of a connected split reductive algebraic group G over a non-Archimedean local field K. Then we prove the equivalence between the category of continuous modules of Ext♯G∨X(χ) and the category of unramified admissible modules of G(K) with a generalized infin...

We define the universal 1-adic thickening of the field of real numbers. This construction is performed in three steps which parallel the universal perfection, the Witt construction and a completion process. We show that the transposition of the perfection process at the real archimedean place is identical to the “dequantization” process and yields Viro’s tropical real hyperfield T R. Then we pr...

‎In 1897‎, ‎Hensel introduced a normed space which does‎ ‎not have the Archimedean property‎. ‎During the last three decades‎ ‎theory of non--Archimedean spaces has gained the interest of‎ ‎physicists for their research in particular in problems coming‎ ‎from quantum physics‎, ‎p--adic strings and superstrings‎. ‎In this paper‎, ‎we prove‎ ‎the generalized Hyers--Ulam--Rassias stability for a‎ ...

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.