Search results for "Vector"

Distribution of Eigenvalues for Semi-classical Elliptic Operators with Small Random Perturbations, Results and Outline

2019

In this chapter we will state a result asserting that for elliptic semi-classical (pseudo-)differential operators the eigenvalues are distributed according to Weyl’s law “most of the time” in a probabilistic sense. The first three sections are devoted to the formulation of the results and in the last section we give an outline of the proof that will be carried out in Chaps. 16 and 17.

Bifurcations of Regular Limit Periodic Sets

1998

In this chapter, (X λ ) will be a smooth or analytic (in Section 3) family of vector fields on a phase space S, with parameter λ ∈ P, as in Chapter 1. Periodic orbits and elliptic singular points which are limits of sequences of limit cycles are called regular limit periodic sets. The reason for this terminology is that for such a limit periodic set Γ one can define local return maps on transversal segments, which are as smooth as the family itself. The limit cycles near Γ will be given by a smooth equation and the theory of bifurcations of limit cycles from Γ will reduce to the theory of unfoldings of differentiable functions. In fact, we will just need the Preparation Theorem and not the …

Invariants of equivariant algebraic vector bundles and inequalities for dominant weights

1998

Dimension of self-affine sets for fixed translation vectors

2016

An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self-affine set is the affinity dimension for Lebesgue almost every translation vectors. Similar statement was proven by Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine measures. In this article, we have an orthogonal approach. We introduce a class of self-affine systems in which, given translation vectors, we get the same results for Lebesgue almost all matrices. The proofs rely on Ledrappier-Young theory that was recently ver…

Hierarchies of Self-Organizing Maps for action recognition

2016

We propose a hierarchical neural architecture able to recognise observed human actions. Each layer in the architecture represents increasingly complex human activity features. The first layer consists of a SOM which performs dimensionality reduction and clustering of the feature space. It represents the dynamics of the stream of posture frames in action sequences as activity trajectories over time. The second layer in the hierarchy consists of another SOM which clusters the activity trajectories of the first-layer SOM and learns to represent action prototypes. The third - and last - layer of the hierarchy consists of a neural network that learns to label action prototypes of the second-laye…

Investigating the nature of light scalar mesons with semileptonic decays of D mesons

2015

We study the semileptonic decays of $D_{s}^{+}$, $D^{+}$, and $D^{0}$ mesons into the light scalar mesons [$f_{0} (500)$, $K_{0}^{\ast} (800)$, $f_{0} (980)$, and $a_{0}(980)$] and the light vector mesons [$\rho (770)$, $\omega (782)$, $K^{\ast} (892)$, and $\phi (1020)$]. With the help of a chiral unitarity approach in coupled channels, we compute the branching fractions for scalar meson processes of the semileptonic $D$ decays in a simple way. Using current known values of the branching fractions, we make predictions for the branching fractions of the semileptonic decay modes with other scalar and vector mesons. Furthermore, we calculate the $\pi ^{+} \pi ^{-}$, $\pi \eta$, $\pi K$, and $…

Value of the Axial-Vector Coupling Strength in β and ββ Decays : A Review

2017

In this review the quenching of the weak axial-vector coupling constant, $g_{\rm A}$, is discussed in nuclear $\beta$ and double-$\beta$ decays. On one hand, the nuclear-medium and nuclear many-body effects are separated, and on the other hand the quenching is discussed from the points of view of different many-body methods and different $\beta$-decay and double-$\beta$-decay processes. Both the historical background and the present status are reviewed and contrasted against each other. The theoretical considerations are tied to performed and planned measurements, and possible new measurements are urged, whenever relevant and doable. Relation of the quenching problem to the measurements of …

On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields

1986

Consider a fami ly of vector fCelds x~ on the plane. This fami ly depends on a parameter ~ ~ /R A, for some A ~ /~, and is supposed to be 0 ~ in (m,~) 6 /i~ 2X /~A. Suppose that for ~ = O, the vector f i e l d X o has a separatrix loop. This means that X o has an hyperbol ic saddle point s o and that one of the stable separatr ix of 8 o coincides with one of the unstable one. The union of th is curve and s o is the loop ?. A return map is defined on one side of r .

Yeast vectors for the integration/expression of any sequence at theTYR1 locus

2007

We have constructed new yeast vectors for targeted integration and conditional expression of any sequence at the Saccharomyces cerevisiae TYR1 locus which becomes disrupted. We show that vector integration is not neutral, causing prototrophy for tyrosine and auxotrophy for the vector's selectable marker (uracil or leucine, depending on the vector used). This feature allows a double screening of transformed yeast cells, improving the identification of colonies with the desired chromosomal structure. The GAL10 gene promoter has been added to drive conditional expression of cloned sequences. Using these vectors, chromosomal structure verification of recombinant clones is no longer necessary, s…

<title>Restoration of a short-exposure image sequence degraded by atmospheric turbulence</title>

2000

This paper deals with the restoration of the shape of an object observed with a high-resolution infrared imaging device, through atmospheric turbulence. The propagation path is quite long (a few tenth kilometer) and the image is thus disturbed. A sequence of short-exposure images of the interesting object is recorded. We can see that the object shape fluctuates randomly during the sequence, but that its edges remain sharp, thanks to the very short exposure time. A bayesian analysis of the Fourier descriptors associated to the edges shows that the optimal shape is the one corresponding to the mean Fourier descriptors. We thus propose two ways to estimate this shape. The first one consists in…