In this paper, we describe the Grothendieck group $$K_0(V)$$ of an absolute matrix order unit space V. For purpose, discuss direct limit spaces. We show that $$K_0$$ is a functor from category spaces with morphisms as unital completely $$\vert \cdot \vert$$ -preserving maps to abelian groups. study structure in and prove under certain condition, ordered group. also additive on orthogonal maps.

We consider the dynamics of the Hénon and Ikeda maps in the presence of additive and dynamical noise. We show that, from the point of view of computations of some statistical quantities, dynamical noise corrupting these deterministic systems can be considered effectively as an additive "pseudonoise" with the Cauchy distribution. In the case of the Hénon and Ikeda maps, this effect occurs only f...

Large populations of globally coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that, for strong coupling, the collective dynamics can be described in terms of a few effective macroscopic degrees of freedom, whose deterministic equations of motion are systematically derived throug...

The problem considered in the paper can be described as follows. We are given a continuous mapping from one metric space into another which is regular (in the sense of metric regularity or, equivalently, controllability at a linear rate) near a certain point. How small may be an additive perturbation of the mapping which destroys regularity? The paper contains a new proof of a recent theorem of...

Let ψ1, . . . , ψk be maps from Z to an additive abelian group with positive periods n1, . . . , nk respectively. We show that the function ψ = ψ1 + · · ·+ψk is constant if ψ(x) equals a constant for |S| consecutive integers x where S = {r/ns : r = 0, . . . , ns − 1; s = 1, . . . , k}; moreover, there are periodic maps f0, . . . , f|S|−1 : Z → Z only depending on S such that ψ(x) = |S|−1 r=0 fr...

Let ψ1, . . . , ψk be maps from Z to an additive abelian group with positive periods n1, . . . , nk respectively. We show that the function ψ = ψ1 + · · ·+ψk is constant if ψ(x) equals a constant for |S| consecutive integers x where S = {r/ns : r = 0, . . . , ns − 1; s = 1, . . . , k}; moreover, there are periodic maps f0, . . . , f|S|−1 : Z → Z only depending on S such that ψ(x) = ∑|S|−1 r=0 f...

1. Historical backgrounds: the Airy function in Physics 2 2. The area-Airy distributions: Brownian motion, linear probing hashing, additive parameters in grammars 4 2.1. Area under a Brownian excursion 4 2.2. On the analysis of linear probing hashing 4 2.3. Analytic variations on the Airy distribution 5 2.4. Hachage, arbres, chemins & graphes 6 3. Random matrices, Airy kernel and the Tracy–Wido...

The present paper generalises some results for spectrally negative Lévy processes to the setting of Markov additive processes (MAPs). A prominent role is assumed by the first passage times, which will be determined in terms of their Laplace transforms. These have the form of a phase-type distribution, with a rate matrix that can be regarded as an inverse function of the cumulant matrix. A numer...

Article history: Received 20 December 2014 Received in revised form 20 January 2015 Accepted 16 February 2015 Available online 23 February 2015 QTL IciMapping is freely available public software capable of building high-density linkage maps and mapping quantitative trait loci (QTL) in biparental populations. Eight functionalities are integrated in this software package: (1) BIN: binning of redu...