Search results for "Vector"
showing 10 items of 2660 documents
Weak separation condition, Assouad dimension, and Furstenberg homogeneity
2015
We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain sub-self-affine sets. In addition to dimension results for the limit set, we manage to express the Assouad dimension of any closed subset of a self-conformal set by means of the Hausdorff dimension. As an interesting consequence of this, we show that a Furstenberg homogeneous self-similar set in the real line satisfies the weak separation condition. We also exhibit a self-similar set which satisfies the open set condition but fails to be Furstenberg homogeneous.
Vector-valued Hardy inequalities and B-convexity
2000
Inequalities of the form $$\sum\nolimits_{k = 0}^\infty {|\hat f(m_k )|/(k + 1) \leqslant C||f||_1 } $$ for allf∈H 1, where {m k } are special subsequences of natural numbers, are investigated in the vector-valued setting. It is proved that Hardy's inequality and the generalized Hardy inequality are equivalent for vector valued Hardy spaces defined in terms ff atoms and that they actually characterizeB-convexity. It is also shown that for 1<q<∞ and 0<α<∞ the spaceX=H(1,q,γa) consisting of analytic functions on the unit disc such that $$\int_0^1 {(1 - r)^{q\alpha - 1} M_1^q (f,r) dr< \infty } $$ satisfies the previous inequality for vector valued functions inH 1 (X), defined as the space ofX…
Random cutout sets with spatially inhomogeneous intensities
2015
We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.
Mappings of Finite Distortion : Compactness of the Branch Set
2017
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, has a branch set homeomorphic to an (n - 2)-dimensional torus and distortion arbitrarily close to the asymptotic bound. Peer reviewed
Poisson Geometry in Mathematics and Physics
2008
We realize quantized anti de Sitter space black holes, building Connes spectral triples, similar to those used for quantized spheres but based on Universal Deformation Quantization Formulas (UDF) obtained from an oscillatory integral kernel on an appropriate symplectic symmetric space. More precisely we first obtain a UDF for Lie subgroups acting on a symplectic symmetric space M in a locally simply transitive manner. Then, observing that a curvature contraction canonically relates anti de Sitter geometry to the geometry of symplectic symmetric spaces, we use that UDF to define what we call Dirac-isospectral noncommutative deformations of the spectral triples of locally anti de Sitter black…
Some Improvements on Relativistic Positioning Systems
2018
[EN] We make some considerations about Relativistic Positioning Systems (RPS). Four satellites are needed to position a user. First of all we define the main concepts. Errors should be taken into account. Errors depend on the Jacobian transformation matrix. Its Jacobian is proportional to the tetrahedron volume whose vertexes are the four tips of the receiver-satellite unit vectors. If the four satellites are seen by the user on a circumference in the sky, then, the Jacobian and the tetrahedron volume vanish. The users we consider are spacecraft. Spacecraft to be positioned cannot be close to a null Jacobian satellites-user configuration. These regions have to be avoided choosing an appropr…
Genetically 'pure' Fasciola gigantica discovered in Algeria: DNA multimarker characterization, trans-Saharan introduction from a Sahel origin and spr…
2020
Fascioliasis is a freshwater snail-borne zoonotic helminth disease caused by two species of trematodes: Fasciola hepatica of almost worldwide distribution and the more pathogenic F. gigantica restricted to parts of Asia and most of Africa. Of high pathological impact in ruminants, it underlies large livestock husbandry losses. Fascioliasis is moreover of high public health importance and accordingly included within the main neglected tropical diseases by WHO. Additionally, this is an emerging disease due to influences of climate and global changes. In Africa, F. gigantica is distributed throughout almost the whole continent except in the north-western Maghreb countries of Morocco, Algeria a…
A Widrow–Hoff Learning Rule for a Generalization of the Linear Auto-associator
1996
Abstract A generalization of the linear auto-associator that allows for differential importance and nonindependence of both the stimuli and the units has been described previously by Abdi (1988). This model was shown to implement the general linear model of multivariate statistics. In this note, a proof is given that the Widrow–Hoff learning rule can be similarly generalized and that the weight matrix will converge to a generalized pseudo-inverse when the learning parameter is properly chosen. The value of the learning parameter is shown to be dependent only upon the (generalized) eigenvalues of the weight matrix and not upon the eigenvectors themselves. This proof provides a unified framew…
(K)over-bar* mesons in dense matter
2010
We study the properties of (K) over bar* mesons in nuclear matter using a unitary approach in coupled channels within the framework of the local hidden gauge formalism and incorporating the (K) over bar pi decay channel in matter. The in-medium (K) over bar *N interaction accounts for Pauli blocking effects and incorporates the (K) over bar* self-energy in a self-consistent manner. We also obtain the (K) over bar* (off-shell) spectral function and analyze its behavior at finite density and momentum. At a normal nuclear matter density, the (K) over bar* meson feels a moderately attractive potential, while the (K) over bar* width becomes five times larger than in free space. We estimate the t…
A Nullclines Approach to the Study of 2D Artificial Network
2019

 
 The system of two the first order ordinary differential equations arising in the gene regulatory networks theory is studied. The structure of attractors for this system is described for three important behavioral cases: activation, inhibition, mixed activation-inhibition. The geometrical approach combined with the vector field analysis allows treating the problem in full generality. A number of propositions are stated and the proof is geometrical, avoiding complex analytic. Although not all the possible cases are considered, the instructions are given what to do in any particular situation.