Park (2010) [8] presented a method to obtain the upper bound on efficiency in imprecise data envelopment analysis (IDEA) in which the envelopment model with imprecise data had been used. In this paper, we consider the dual model, the multiplier model, which involves the non-Archimedean element ε . Then, we define a model to determine the upper bound of ε . An assurance interval for the non-Arch...

The copula function is an effective and elegant tool useful for modeling dependence between random variables. Among the many families of this function, one most prominent family Archimedean family, which has its unique structure features. Most functions in have only a single parameter limits scope structure. In paper we modify generator copulas way maintains membership while increasing number p...

We prove that if q > 5 is an integer, then every q-th power of an integer contains at least 5 nonzero digits in its binary expansion. This is a particular instance of one of a collection of rather more general results, whose proofs follow from a combination of refined lower bounds for linear forms in Archimedean and non-Archimedean logarithms with various local arguments.

In Part I of this paper ([PW12]), the minimal regular covers of three of the eight Archimedean tilings were determined. However, the computations described in that work grow more complicated as the number of flag orbits of the tilings increases. In Part II, we develop a new technique in order to present the minimal regular covers of certain periodic abstract polytopes. We then use that techniqu...

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...