Recently, in [5], Najati and Moradlou proved Hyers-Ulam-Rassias stability of the following quadratic mapping of Apollonius type Q(z − x) + Q(z − y) = 1 2 Q(x− y) + 2Q ( z − x + y 2 ) in non-Archimedean space. In this paper we establish Hyers-Ulam-Rassias stability of this functional equation in random normed spaces by direct method and fixed point method. The concept of Hyers-Ulam-Rassias stabi...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...

There is a natural analytification functor from the category of locally separated algebraic spaces locally of finite type over C to the category of complex-analytic spaces [Kn, Ch. I, 5.17ff]. (Recall that a map of algebraic spaces X → S is locally separated if the diagonal ∆X/S : X → X ×S X is an immersion. We require algebraic spaces to have quasi-compact diagonal over SpecZ.) It is natural t...

This paper generalizes Yu. Manin’s approach toward a geometrical interpretation of Arakelov theory at infinity to linear cycles in projective spaces. We show how to interpret certain non-Archimedean Arakelov intersection numbers of linear cycles on Pn−1 with the combinatorial geometry of the Bruhat-Tits building associated to PGL(n). This geometric setting has an Archimedean analogue, namely, t...

In this paper we are concerned with the spectral analysis for classes of finte rank perturbations diagonal operators in form A = D+F where D is a operator and F u’1 ⊗v’1+...+u’m ⊗vm an finite non-archimedean Banach space countable type. We compute spectrum using theory Fredholm non archimedean setting concept essential linear operators.

We use a recent characterization of the d-dimensional Archimedean copulas as the survival copulas of d-dimensional simplex distributions (McNeil and Nešlehová (2009)) to construct new Archimedean copula families, and to examine the relationship between their dependence properties and the radial parts of the corresponding simplex distributions. In particular, a new formula for Kendall’s tau is d...

In the paper, we study behaviour of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behaviour of the system w.r.t. variety of word transformations performed by the system: We call a system completely transitive if, given arbitrary pair a, b of finite words that have equal lengths, the system A, while evolution during (discrete...