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...

In this paper, we solve the additive ρ-functional inequalities ‖f(x+ y)− f(x)− f(y)‖ ≤ ∥∥∥∥ρ(2f (x+ y 2 ) − f(x)− f(y) )∥∥∥∥ , (1) ∥∥∥∥2f (x+ y 2 ) − f(x)− f(y) ∥∥∥∥ ≤ ‖ρ (f(x+ y)− f(x)− f(y))‖ , (2) where ρ is a fixed non-Archimedean number with |ρ| < 1 or ρ is a fixed complex number with |ρ| < 1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalit...

We develop the theory of Frobenioids associated to nonarchimedean [mixed-characteristic] and archimedean local fields. In particular, we show that the resulting Frobenioids satisfy the properties necessary to apply the main results of the general theory of Frobenioids. Moreover, we show that the reciprocity map in the nonarchimedean case, as well as a certain archimedean analogue of this recipr...

Earlier work (Hammond, 1988a, b) on dynamically consistent “consequentialist” behaviour in decision trees was unable to treat zero probability events satisfactorily. Here the rational probability functions considered in Hammond (1994), as well as other non-Archimedean probabilities, are incorporated into decision trees. As before, the consequentialist axioms imply the existence of a preference ...

We consider Baxter Q-operators for various versions of quantum affine Toda chain. The interpretation of eigenvalues of the finite Toda chain Baxter operators as local Archimedean L-functions proposed recently is generalized to the case of affine Lie algebras. We also introduce a simple generalization of Baxter operators and local L-functions compatible with this identification. This gives a con...

It is proved that if R is a valuation domain with maximal ideal P and if RL is countably generated for each prime ideal L, then R R is separable if and only RJ is maximal, where J = ∩n∈NP . When R is a valuation domain satisfying one of the following two conditions: (1) R is almost maximal and its quotient field Q is countably generated (2) R is archimedean Franzen proved in [2] that R is separ...