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Interval linear regression analysis based on Minkowski difference – a bridge between traditional and interval linear regression models

Masahiro Inuiguchi, Tetsuzo Tanino (2006)

Kybernetika

In this paper, we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model, the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval...

Introduction to Rational Functions

Christoph Schwarzweller (2012)

Formalized Mathematics

In this article we formalize rational functions as pairs of polynomials and define some basic notions including the degree and evaluation of rational functions [8]. The main goal of the article is to provide properties of rational functions necessary to prove a theorem on the stability of networks

Invariance identity in the class of generalized quasiarithmetic means

Janusz Matkowski (2014)

Colloquium Mathematicae

An invariance formula in the class of generalized p-variable quasiarithmetic means is provided. An effective form of the limit of the sequence of iterates of mean-type mappings of this type is given. An application to determining functions which are invariant with respect to generalized quasiarithmetic mean-type mappings is presented.

Invariance in the class of weighted quasi-arithmetic means

Justyna Jarczyk, Janusz Matkowski (2006)

Annales Polonici Mathematici

Under the assumption of twice continuous differentiability of some of the functions involved we determine all the weighted quasi-arithmetic means M,N,K such that K is (M,N)-invariant, that is, K∘(M,N) = K. Some applications to iteration theory and functional equations are presented.

Invariant graphs of functions for the mean-type mappings

Janusz Matkowski (2012)

ESAIM: Proceedings

Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, ... , Mp : Ip → I the continuous means. We consider the problem of invariance of the graphs of functions ϕ : Jp−1 → I with respect to the mean-type mapping M = (M1, ... , Mp).Applying a result on the existence and uniqueness of an M -invariant mean [7], we prove that if the graph of a continuous function ϕ : Jp−1 → I ...

Invariant scrambled sets and maximal distributional chaos

Xinxing Wu, Peiyong Zhu (2013)

Annales Polonici Mathematici

For the full shift (Σ₂,σ) on two symbols, we construct an invariant distributionally ϵ-scrambled set for all 0 < ϵ < diam Σ₂ in which each point is transitive, but not weakly almost periodic.

Inverse Function Theorems and Jacobians over Metric Spaces

Luca Granieri (2014)

Analysis and Geometry in Metric Spaces

We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.

Inverse Limit Spaces Satisfying a Poincaré Inequality

Jeff Cheeger, Bruce Kleiner (2015)

Analysis and Geometry in Metric Spaces

We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces,...

Investigation of smooth functions and analytic sets using fractal dimensions

Emma D'Aniello (2004)

Bollettino dell'Unione Matematica Italiana

We start from the following problem: given a function f : 0 , 1 → 0 , 1 what can be said about the set of points in the range where level sets are «big» according to an opportune definition. This yields the necessity of an analysis of the structure of level sets of C n functions. We investigate the analogous problem for C n , a functions. These are in a certain way intermediate between C n and C n + 1 functions. The results involve a mixture of Real Analysis, Geometric Measure Theory and Classical Descriptive Set Theory.

Isomorphisms of AC(σ) spaces

Ian Doust, Michael Leinert (2015)

Studia Mathematica

Analogues of the classical Banach-Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if AC(σ₁) is algebra isomorphic to AC(σ₂) then σ₁ is homeomorphic to σ₂. The converse however is false. In a positive direction we show that the converse implication does hold if the sets σ₁ and σ₂ are confined to a restricted collection of compact sets, such as the set of all simple polygons.

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