218 research outputs found
Tangent-point self-avoidance energies for curves
We study a two-point self-avoidance energy which is defined for all
rectifiable curves in as the double integral along the curve of .
Here stands for the radius of the (smallest) circle that is tangent to the
curve at one point and passes through another point on the curve, with obvious
natural modifications of this definition in the exceptional, non-generic cases.
It turns out that finiteness of for guarantees that
has no self-intersections or triple junctions and therefore must be
homeomorphic to the unit circle or to a closed interval. For the energy
evaluated on curves in turns out to be a knot energy separating
different knot types by infinite energy barriers and bounding the number of
knot types below a given energy value. We also establish an explicit upper
bound on the Hausdorff-distance of two curves in with finite -energy
that guarantees that these curves are ambient isotopic. This bound depends only
on and the energy values of the curves. Moreover, for all that are
larger than the critical exponent , the arclength parametrization of
is of class , with H\"{o}lder norm of the unit tangent
depending only on , the length of , and the local energy. The
exponent is optimal.Comment: 23 pages, 1 figur
Characterizing ~submanifolds by -integrability of global curvatures
We give sufficient and necessary geometric conditions, guaranteeing that an
immersed compact closed manifold of class and of
arbitrary dimension and codimension (or, more generally, an Ahlfors-regular
compact set satisfying a mild general condition relating the size of
holes in to the flatness of measured in terms of beta
numbers) is in fact an embedded manifold of class ,
where and . The results are based on a careful analysis of
Morrey estimates for integral curvature--like energies, with integrands
expressed geometrically, in terms of functions that are designed to measure
either (a) the shape of simplices with vertices on or (b) the size of
spheres tangent to at one point and passing through another point of
.
Appropriately defined \emph{maximal functions} of such integrands turn out to
be of class for if and only if the local graph
representations of have second order derivatives in and
is embedded. There are two ingredients behind this result. One of them is an
equivalent definition of Sobolev spaces, widely used nowadays in analysis on
metric spaces. The second one is a careful analysis of local Reifenberg
flatness (and of the decay of functions measuring that flatness) for sets with
finite curvature energies. In addition, for the geometric curvature energy
involving tangent spheres we provide a nontrivial lower bound that is attained
if and only if the admissible set is a round sphere.Comment: 44 pages, 2 figures; several minor correction
Minimal H\"older regularity implying finiteness of integral Menger curvature
We study two families of integral functionals indexed by a real number . One family is defined for 1-dimensional curves in and the other one
is defined for -dimensional manifolds in . These functionals are
described as integrals of appropriate integrands (strongly related to the
Menger curvature) raised to power . Given we prove that
regularity of the set (a curve or a manifold), with implies finiteness of both curvature functionals
( in the case of curves). We also show that is optimal by
constructing examples of functions with graphs of infinite
integral curvature
Recent Labour Market Trends in the Visegrad Group Countries
The large declines in the Slovak and Czech employment appeared because the countries' GDPs grew smaller while real wages grew bigger. Shorter working hours and limitations on labour productivity that the two countries introduced could not reverse the unfavourable employment trends that occurred during economic downturn.Duże spadki zatrudnienia w Słowacji i Czechach były związane ze słabym wzrostem PKB i silnym wzrostem płac realnych. Redukcje czasu pracy i wydajności pracy nie były w stanie odwrócić niekorzystnych tendencji w zatrudnieniu
Trash on Arctic beach: Coastal pollution along Calypsostranda, Bellsund, Svalbard
Beach pollution is one of the most common hazards in present-day anthropogenic environments. Even in the remote Svalbard Archipelago, pollution impacts the beach system and can pose environmental threats. The significant increase in human activity observed in Svalbard over the last 20–30 years has resulted in a visible change in the amount of coastal pollution. A 5 km long transect of modern beach developed along Calypsostranda (Recherchefjorden, Bellsund) was surveyed in the summer of 2015 in order to characterize the beach pollution. During the survey 296 pieces of trash were found on beach surface. 82% of found trash was plastic, followed by glass (8%), and metal (5%). The comparison with previous pollution survey showed the significant increase of plastic waste in local beach environment. Similar problem has been recently recorded in other parts of Svalbard suggesting an urgent need for coastal pollution monitoring
Structural and optical properties of as-grown and annealed Alq3 thin films
International audienc
System Response Kernel Calculation for List-mode Reconstruction in Strip PET Detector
Reconstruction of the image in Positron Emission Tomographs (PET) requires
the knowledge of the system response kernel which describes the contribution of
each pixel (voxel) to each tube of response (TOR). This is especially important
in list-mode reconstruction systems, where an efficient analytical
approximation of such function is required. In this contribution, we present a
derivation of the system response kernel for a novel 2D strip PET.Comment: 10 pages, 2 figures; Presented at Symposium on applied nuclear
physics and innovative technologies, Cracow, 03-06 June 201
A novel method for calibration and monitoring of time synchronization of TOF-PET scanners by means of cosmic rays
All of the present methods for calibration and monitoring of TOF-PET scanner
detectors utilize radioactive isotopes such as e.g. Na or Ge,
which are placed or rotate inside the scanner. In this article we describe a
novel method based on the cosmic rays application to the PET calibration and
monitoring methods. The concept allows to overcome many of the drawbacks of the
present methods and it is well suited for newly developed TOF-PET scanners with
a large longitudinal field of view. The method enables also monitoring of the
quality of the scintillator materials and in general allows for the continuous
quality assurance of the PET detector performance.Comment: 10 pages, 7 figure
Transparent amorphous zinc oxide thin films for NLO applications
This review focuses on the growth and optical properties of amorphous zinc oxide (ZnO) thin films. A high quality ZnO films fabricated by dip-coating (sol–gel) method were grown on quartz and glass substrates at temperature equal to 350 K. The amorphous nature of the films was verified by X-ray diffraction. Atomic Force Microscopy was used to evaluate the surface morphology of the films. The optical characteristics of amorphous thin films have been investigated in the spectral range 190–1100 nm. Measurement of the polarized optical properties was shows a high transmissivity (80–99%) and low absorptivity (<5%) in the visible and near infrared regions at different angles of incidence. Linear optical properties were investigated by classic and Time-Resolved Photoluminescence (TRPL) measurements. Photoluminescence spectrum exhibits a strong ultraviolet emission while the visible emission is very weak. An innovative TRPL technique has enabled the measurement of the photoluminescence decay time as a function of temperature. TRPL measurements reveal a multiexponential decay behavior typical for amorphous thin films. Second and third harmonic generation measurements were performed by means of the rotational Maker fringe technique using Nd:YAG laser at 1064 nm in picosecond regime for investigations of the nonlinear optical properties. The obtained values of second and third order nonlinear susceptibilities were found to be high enough for the potential applications in the optical switching devices based on refractive index changes. Presented spectra confirm high structural and optical quality of the investigated zinc oxide thin films
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