Search results for "Planar"
showing 10 items of 412 documents
"Table 124" of "Studies of QCD at e+ e- centre-of-mass energies between 91-GeV and 209-GeV."
2004
Aplanarity distribution at c.m. energy 200.00 GeV.
Multiple Canard Cycles in Generalized Liénard Equations
2001
AbstractThe paper treats multiple limit cycle bifurcations in singular perturbation problems of planar vector fields. The results deal with any number of parameters. Proofs are based on the techniques introduced in “Canard Cycles and Center Manifolds” (F. Dumortier and R. Roussarie, 1996, Mem. Amer. Math. Soc., 121). The presentation is limited to generalized Liénard equations εx+α(x, c)x+β(x, c)=0.
Removable sets for Sobolev spaces
1999
We study removable sets for the Sobolev space W1,p. We show that removability for sets lying in a hyperplane is essentially determined by their thickness measured in terms of a concept of p-porosity.
Uniform, Sobolev extension and quasiconformal circle domains
1991
This paper contributes to the theory of uniform domains and Sobolev extension domains. We present new features of these domains and exhibit numerous relations among them. We examine two types of Sobolev extension domains, demonstrate their equivalence for bounded domains and generalize known sufficient geometric conditions for them. We observe that in the plane essentially all of these domains possess the trait that there is a quasiconformal self-homeomorphism of the extended plane which maps a given domain conformally onto a circle domain. We establish a geometric condition enjoyed by these plane domains which characterizes them among all quasicircle domains having no large and no small bo…
Embedding of Sobolev Spaces into Lipschitz Spaces
1989
The main result of the paper is that if Ω is a bounded uniform domain in ℝn and p>n, then the Sobolev space Wl, p(Ω) embeds continously into Cα(Ω), α = 1 - n/p.
Structural re-arrangement in two hexanuclear CuIIcomplexes: from a spin frustrated trigonal prism to a strongly coupled antiferromagnetic soluble rin…
2014
The addition of water to a chloroform solution of the Cu6 trigonal prism complex [Cu6(μ6F)(μ2OH)(μ3OCH3)2(μ2OCH3)2(3,5-Me2pz)6] (1) (3,5-Me2pz− = 3,5-dimethylpyrazolate) results in the formation of the Cu6 planar hexagonal ring complex [Cu6(μ2OH)6(3,5-Me2pz)6]·CH3CN·CHCl3 (2). A simple mechanism for this structural re-arrangement is proposed, in which 2 can be viewed as a hydrolysis product of 1. This process is clearly noticeable in the magnetic properties, which change from spin frustrated with a weak antiferromagnetic coupling in 1, to strongly antiferromagnetic in 2. Interestingly, the hexagonal ring complex 2 self-assembles in the solid state to form a porous hexagonal tubular structur…
A Method to Extract the Complete Fiber Network Topology of Planar Fibrous Tissues and Scaffolds
2010
Improving fabrication protocols and design strategies, investigating on how fibrous ECM and synthetic architectures affect cell morphology, metabolism and phenotypic expression, predicting mechanical behaviors, have increasingly become crucial goals in the understanding of native tissues and in the development of engineered tissue. In the present study, an image-based analysis approach that provides an automatic tool to fully characterize engineered tissue fiber network topology was developed. The following micro architectural features were detected: fiber angle distribution, fiber connectivity, fiber overlap spatial density, and fiber diameter. In order to demonstrate the potential of this…
Stable maps from surfaces to the plane with prescribed branching data
2007
Abstract We consider the problem of constructing stable maps from surfaces to the plane with branch set a given set of curves immersed (except possibly with cusps) in the plane. Various constructions are used (1) piecing together regions immersed in the plane (2) modifying an existing stable map by a sequence of codimension one transitions (swallowtails etc) or by surgeries. In (1) the way the regions are pieced together is described by a bipartite graph (an edge C* corresponds to a branch curve C with the vertices of C* corresponding to the two regions containing C). We show that any bipartite graph may be realized by a stable map and we consider the question of realizing graphs by fold ma…
Morphology changes induced by intercellular gap junction blocking: A reaction-diffusion mechanism.
2021
Complex anatomical form is regulated in part by endogenous physiological communication between cells; however, the dynamics by which gap junctional (GJ) states across tissues regulate morphology are still poorly understood. We employed a biophysical modeling approach combining different signaling molecules (morphogens) to qualitatively describe the anteroposterior and lateral morphology changes in model multicellular systems due to intercellular GJ blockade. The model is based on two assumptions for blocking-induced patterning: (i) the local concentrations of two small antagonistic morphogens diffusing through the GJs along the axial direction, together with that of an independent, uncouple…
A generalization of the inhomogeneity measure for point distributions to the case of finite size objects
2008
The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the measure is modified in such a way that it relates to the smallest realizable value for each considered scale. To overcome the limitation of pattern partitions to scales with k being integer divisors of L we use a sliding cell-sampling approach. For given patterns, particularly in the case of clusters polydispersed in size, the comparison between the statistical measure and the entropic one reveals differences in detection of the first peak while at other sca…