Search results for "DIMENSION"

Effect of inter-crystal scatter on estimation methods for random coincidences and subsequent correction.

2008

Random coincidences can contribute substantially to the background in positron emission tomography (PET). Several estimation methods are being used for correcting them. The goal of this study was to investigate the validity of techniques for random coincidence estimation, with various low-energy thresholds (LETs). Simulated singles list-mode data of the MADPET-II small animal PET scanner were used as input. The simulations have been performed using the GATE simulation toolkit. Several sources with different geometries have been employed. We evaluated the number of random events using three methods: delayed window (DW), singles rate (SR) and time histogram fitting (TH). Since the GATE simula…

Some Numerical Invariants of Multilinear Identities

2017

We consider non-necessarily associative algebras over a field of characteristic zero and their polynomial identities. Here we describe most of the results obtained in recent years on two numerical sequences that can be attached to the multilinear identities satisfied by an algebra: the sequence of codimensions and the sequence of colengths.

Multiplicative loops of 2-dimensional topological quasifields

2015

We determine the algebraic structure of the multiplicative loops for locally compact $2$-dimensional topological connected quasifields. In particular, our attention turns to multiplicative loops which have either a normal subloop of positive dimension or which contain a $1$-dimensional compact subgroup. In the last section we determine explicitly the quasifields which coordinatize locally compact translation planes of dimension $4$ admitting an at least $7$-dimensional Lie group as collineation group.

Baer cones in finite projective spaces

1987

Let R and V be two skew subspaces with dimensions r and v of P=PG(d,q). If q is a square, then there is a Baer subspace V* of V, i.e. a subspace of dimension v and order √q. We call the set C(R,V*)=\(\mathop \cup \limits_p \), where the union is taken over all PeV*, aBaer cone oftype (r,v).

Classification générique de synthèses temps minimales avec cible de codimension un et applications

1997

In this article we consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraints belonging to a manifold of codimension one, for systems of the form v = X + uY, v ϵ R2, R3, |u| ≤ 1 under generic assumptions. The analysis is localized near the terminal manifold and is motivated by the problem of controlling a class of chemical systems.

Invariant ordering of surface groups and 3-manifolds which fibre over $S^1$

2006

Hausdorff dimension from the minimal spanning tree

1993

A technique to estimate the Hausdorff dimension of strange attractors, based on the minimal spanning tree of the point distribution is extensively tested in this work. This method takes into account in some sense the infimum requirement appearing in the definition of the Hausdorff dimension. It provides accurate estimates even for a low number of data points and it is especially suited to high-dimensional systems.

A simple proof of the polylog counting ability of first-order logic

2007

The counting ability of weak formalisms (e.g., determining the number of 1's in a string of length N ) is of interest as a measure of their expressive power, and also resorts to complexity-theoretic motivations: the more we can count the closer we get to real computing power. The question was investigated in several papers in complexity theory and in weak arithmetic around 1985. In each case, the considered formalism (AC 0 -circuits, first-order logic, Δ 0 ) was shown to be able to count up to a polylogarithmic number. An essential part of the proofs is the construction of a 1-1 mapping from a small subset of {0, ..., N - 1} into a small initial segment. In each case the expressibility of …

Packing dimension, intersection measures, and isometries

1997

Polynomial Identities of Algebras of Small Dimension

2009

It is well known that given an associative algebra or a Lie algebra A, its codimension sequence c n (A) is either polynomially bounded or grows at least as fast as 2 n . In [2] we proved that for a finite dimensional (in general nonassociative) algebra A, dim A = d, the sequence c n (A) is also polynomially bounded or c n (A) ≥ a n asymptotically, for some real number a > 1 which might be less than 2. Nevertheless, for d = 2, we may take a = 2. Here we prove that for d = 3 the same conclusion holds. We also construct a five-dimensional algebra A with c n (A) < 2 n .