In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–Găvruţa. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces ...

AMS 2000 subject classifications: 62H20 62P05 Keywords: Tail dependence Heavy tails Copula Multivariate extreme value distribution Marshall–Olkin distribution Archimedean copula Contagion risk a b s t r a c t The orthant tail dependence describes the relative deviation of upper-(or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its c...

We prove an analog of the Yomdin–Gromov lemma for p-adic definable sets and more broadly in a non-Archimedean definable context. This analog keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the totally disconnected case. We apply this result to bound the number of rational points of bounded height on the transcendental part of p-adic subanalytic sets, and to ...

In the first part of the paper we generalize a descent technique due to HarishChandra to the case of a reductive group acting on a smooth affine variety both defined over arbitrary local field F of characteristic zero. Our main tool is Luna slice theorem. In the second part of the paper we apply this technique to symmetric pairs. In particular we prove that the pair (GLn(C), GLn(R)) is a Gelfan...

The commutative residuated lattices were first introduced by M. Ward and R.P. Dilworth as generalization of ideal lattices of rings. Non-commutative residuated lattices, called sometimes pseudo-residuated lattices, biresiduated lattices or generalized residuated lattices are algebraic counterpart of substructural logics, that is, logics which lack some of the three structural rules, namely cont...

We prove new patchworking theorems for singular algebraic curves, which state the following. Given a complex toric threefold Y which is fibred over C with a reduced reducible zero fiber Y0 and other fibers Yt smooth, and given a curve C0 ⊂ Y0, the theorems provide sufficient conditions for the existence of one-parametric family of curves Ct ⊂ Yt, which induces an equisingular deformation for so...

In the first part of the paper we generalize a descent technique due to Harish-Chandra to the case of a reductive group acting on a smooth affine variety both defined over arbitrary local field F of characteristic zero. Our main tool in that is Luna slice theorem. In the second part of the paper we apply this technique to symmetric pairs. In particular we prove that the pair (GLn(C), GLn(R)) is...

Two-dimensional colloidal suspensions subjected to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction (J. Mikhael et al., Nature 454, 501 (2008)). In experiments as well as in Monte Carlo and Brownian dynamics simulations, we identify a similar phase when the laser field posses...

Quasi-invariant measures with values in non-Archimedean fields on a group of diffeomorphisms were constructed for non-Archimedean manifolds M in [Lud96, Lud99t]. On non-Archimedean loop groups and semigroups they were provided in [Lud98s, Lud00a, Lud02b]. A Banach space over a local field also serves as the additive group and quasi-invariant measures on it were studied in [Lud03s2, Lud96c]. Thi...

The striking boundary dependency (the Arctic Circle phenomenon) exhibited in the ice model on the square lattice extends to other planar set-ups. We present these findings for the triangular and the Kagomé lattices. Critical connectivity results guarantee that ice configurations can be generated using the simplest and most efficient local actions. Height functions are utilized throughout the an...