In this article, we introduce a class of the generalized mixed additive, quadratic and quartic functional equations and obtain their common solutions. We also investigate the stability of such modified functional equations in the non-Archimedean normed spaces by a fixed point method.

1.1. Motivation. This paper is largely concerned with constructing quotients by étale equivalence relations. We are inspired by questions in classical rigid geometry, but to give satisfactory answers in that category we have to first solve quotient problems within the framework of Berkovich’s k-analytic spaces. One source of motivation is the relationship between algebraic spaces and analytic s...

A complex manifold X is said to be hyperbolic (in the sense of Brody) if every analytic map from the complex plane C to X is constant. From Picard’s “little” theorem, an entire function missing more than two values must be constant. It is equivalent to say that P \ {0, 1,∞} is hyperbolic. Picard’s theorem also show that a Riemann surface of genus one omitting one point and Riemann surfaces of g...

The mixture property of the general multivariate Pareto MP distributions has been studied by Yeh (2004a). Arnold (1996) mentioned that any mixing distribution with support (0,∞) is a candidate for a frailty model. This fact drives Yeh to study the frailty structure of the MP distributions. It is discerned that the MP distributions is in the one-parameter kvariate Clayton family with k-variate A...

In this paper, we introduce a novel approach for modeling surface reflection. We focus on using a family of probability distributions called Archimedean copulas as BRDF models. The Archimedean representation has an attractive property in that the multivariate distributions are characterized by their marginal distributions through a single univariate function only. It is shown that the proposed ...

We examine a classical and quantum dynamics of systems described by the DBItype Lagrangian with tachyon-like potentials and corresponding DBI Lagrangians on (non-)Archimedean spaces. The dynamic of tachyon fields in spatially homogeneous and in zero-dimensional limits is analysed. A formalism for connecting a wide class of potentials and DBI Lagrangians with the locally equivalent canonical Lag...

Any cubic crystal structure can be divided into small units in the form of congruent semi-regular (Archimedean) truncated octahedra. The centers of these polyhedra can be chosen at invariant equivalent positions for most cubic space groups. The part of a 0567-7394/79/060946-07501.00 crystal structure enclosed by an Archimedean polyhedron is called a geometric unit (or unit for short); however, ...

The aim of this paper is to prove the uniqueness part of the Calabi–Yau theorem for metrized line bundles over non-archimedean analytic spaces, and apply it to endomorphisms with the same polarization and the same set of preperiodic points over a complex projective variety. The proof uses Arakelov theory (cf. [Ar, GS]) and Berkovich’s non-archimedean analytic spaces (cf. [Be]) even though the r...

In dose-finding clinical study, it is common that multiple endpoints are of interest. For instance, efficacy and toxicity endpoints are both primary in clinical trials. In this article, we propose a joint model for correlated efficacy-toxicity outcome constructed with Archimedean Copula, and extend the continual reassessment method (CRM) to a bivariate trial design in which the optimal dose for...

We present the results of an investigation into the representations of Archimedean polyhedra (those polyhedra containing only one type of vertex gure) as quotients of regular abstract polytopes. Two methods of generating these presentations are discussed, one of which may be applied in a general setting, and another which makes use of a regular polytope with the same automorphism group as the d...