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A free group of piecewise linear transformations

Grzegorz Tomkowicz (2011)

Colloquium Mathematicae

We prove the following conjecture of J. Mycielski: There exists a free nonabelian group of piecewise linear, orientation and area preserving transformations which acts on the punctured disk {(x,y) ∈ ℝ²: 0 < x² + y² < 1} without fixed points.

A fuzzy approach to option pricing in a Levy process setting

Piotr Nowak, Maciej Romaniuk (2013)

International Journal of Applied Mathematics and Computer Science

In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets. We assume that some parameters of the financial instrument cannot be precisely described and therefore they are...

A fuzzy logic approach to assembly line balancing.

Daniel J. Fonseca, C. L. Guest, Matthew Elam, Charles L. Karr (2005)

Mathware and Soft Computing

This paper deals with the use of fuzzy set theory as a viable alternative method for modelling and solving the stochastic assembly line balancing problem. Variability and uncertainty in the assembly line balancing problem has traditionally been modelled through the use of statistical distributions. This may not be feasible in cases where no historical data exists. Fuzzy set theory allows for the consideration of the ambiguity involved in assigning processing and cycle times and the uncertainty contained...

A Game Theoretical Approach to The Algebraic Counterpart of The Wagner Hierarchy : Part II

Jérémie Cabessa, Jacques Duparc (2009)

RAIRO - Theoretical Informatics and Applications

The algebraic counterpart of the Wagner hierarchy consists of a well-founded and decidable classification of finite pointed ω-semigroups of width 2 and height ωω. This paper completes the description of this algebraic hierarchy. We first give a purely algebraic decidability procedure of this partial ordering by introducing a graph representation of finite pointed ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of any ω-rational language can therefore be computed...

A game theoretical approach to the algebraic counterpart of the Wagner hierarchy : Part I

Jérémie Cabessa, Jacques Duparc (2009)

RAIRO - Theoretical Informatics and Applications

The algebraic study of formal languages shows that ω-rational sets correspond precisely to the ω-languages recognizable by finite ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation on...

A general approach to decomposable bi-capacities

Susanne Saminger, Radko Mesiar (2003)

Kybernetika

We propose a concept of decomposable bi-capacities based on an analogous property of decomposable capacities, namely the valuation property. We will show that our approach extends the already existing concepts of decomposable bi-capacities. We briefly discuss additive and k -additive bi-capacities based on our definition of decomposability. Finally we provide examples of decomposable bi-capacities in our sense in order to show how they can be constructed.

A groupoid formulation of the Baire Category Theorem

Jonathan Brown, Lisa Orloff Clark (2014)

Fundamenta Mathematicae

We prove that the Baire Category Theorem is equivalent to the following: Let G be a topological groupoid such that the unit space is a complete metric space, and there is a countable cover of G by neighbourhood bisections. If G is effective, then G is topologically principal.

A López-Escobar theorem for metric structures, and the topological Vaught conjecture

Samuel Coskey, Martino Lupini (2016)

Fundamenta Mathematicae

We show that a version of López-Escobar’s theorem holds in the setting of model theory for metric structures. More precisely, let denote the Urysohn sphere and let Mod(,) be the space of metric -structures supported on . Then for any Iso()-invariant Borel function f: Mod(,) → [0,1], there exists a sentence ϕ of ω ω such that for all M ∈ Mod(,) we have f ( M ) = ϕ M . This answers a question of Ivanov and Majcher-Iwanow. We prove several consequences, for example every orbit equivalence relation of a Polish group...

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