We present elements of a theory of translation-invariant integration on finite dimensional vector spaces and on GLn over a valuation field with local field as residue field. We then discuss the case of an arbitrary algebraic group. This extends the work of Fesenko. Introduction This paper addresses the problem of measure and integration on a finite dimensional vector space and on GLn over a val...

UNLABELLED BACKGROUND Statistical parametric mapping (SPM) procedure is an objective tool to analyze 18F-fluoro-2-deoxy-d-glucose-positron-emission tomography (FDG-PET) images and a useful complement to visual analysis. However, SPM requires a comparison to control data set that cannot be obtained in healthy children for ethical reasons. Using adults as controls showed some limitations. The ...

This paper extends current work in the field of Valuation Accuracy and Valuation Variance. These issues are examined in respect of Automated and Artificial Intelligent Valuation Systems. The issue of how accurate an automated system must be to compete with manual valuations is explored. The paper relies upon existing literature, a survey of practising valuers’ and a previous valuation variation...

Athreya, Bufetov, Eskin and Mirzakhani have shown the number of mapping class group lattice points intersecting a closed ball radius $R$ in Teichm\"{u}ller space is asymptotic to $e^{hR}$, where $h$ dimension space. We show for any pseudo-Anosov $f$, there exists power $n$, such that $f^n$ conjugacy coarsely $e^{\frac{h}{2}R}$.

We show that every set of n points in general position has a minimum pseudo-triangulation whose maximum vertex degree is five. In addition, we demonstrate that every point set in general position has a minimum pseudo-triangulation whose maximum face degree is four (i.e. each interior face of this pseudo-triangulation has at most four vertices). Both degree bounds are tight. Minimum pseudo-trian...

Embedding is the widely-observed phenomenon that a good is assigned a higher value if evaluated on its own rather than as part of a more inclusive set. Embedding is considered a serious problem affecting the quality of many environmental management and health risk policy judgments. This paper presents the results of an experiment involving of a structured, small-group approach for conducting en...

We investigate the complexity of enumerating pseudo-intents in the lectic order. We look at the following decision problem: Given a formal context and a set of n pseudo-intents determine whether they are the lectically first n pseudo-intents. We show that this problem is coNPhard. We thereby show that there cannot be an algorithm with a good theoretical complexity for enumerating pseudo-intents...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the center of such...

Let R be a complete rank-1 valuation ring of mixed characteristic (0, p), and let K be its field of fractions. A g-dimensional truncated Barsotti-Tate group G of level n over R is said to have a level-n canonical subgroup if there is a K-subgroup of G ⊗R K with geometric structure (Z/pZ) consisting of points “closest to zero”. We give a nontrivial condition on the Hasse invariant of G that guar...