The classical Mazur–Ulam theorem which states that every sur-jective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur–Ulam theorem in the non-Archimedean strictly convex normed spaces.

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

Boolean, free and monotone cumulants as well relations among them, have proven to be important in the study of non-commutative probability theory. Quite notably, Boolean were successfully used infinite divisibility via Bercovici--Pata bijection. On other hand, recent years concept infinitesimal has been developed, together with notion which can useful context combinatorial questions. In this ...

Tropical and non-Archimedean curves

Let $U$ be an affine log Calabi-Yau variety containing open algebraic torus. We show that the naive counts of rational curves in uniquely determine a commutative associative algebra equipped with compatible multilinear form. This proves variant Frobenius structure conjecture by Gross-Hacking-Keel mirror symmetry, and spectrum this is supposed to give hypothetical family. Although statement our ...

The Dezert-Smarandache theory of plausible and paradoxical reasoning is based on the premise that some elements θi of a frame Θ have a non-empty intersection. These elements are called exhaustive. In number theory, this property is observed only in non-Archimedean number systems, for example, in the ring Zp of p-adic integers, in the field Q of hyperrational numbers, in the field R of hyperreal...

we provide fuzzy quasi-metric versions of a fixed point theorem ofgregori and sapena for fuzzy contractive mappings in g-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.

Let C v be a complete, algebraically closed non-archimedean field, and let f ∈ ( z ) rational function of degree d ≥ 2 . If satisfies bounded contraction condition on its Julia set, we prove that small perturbations have dynamics conjugate to those their sets.