2,536 research outputs found
Cubic spline prewavelets on the four-directional mesh
In this paper, we design differentiable, two dimensional, piecewise polynomial cubic prewavelets of particularly small compact support. They are given in closed form, and provide stable, orthogonal decompositions of L^2(\RR^2). In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain all cubic polynomials, whereas the more familiar box spline constructions cannot reproduce all cubic polynomials, unless resorting to a box spline of higher polynomial degree
Floristic diversity of steppe territories near Poltava town (Ukraine)
Current progress in botany requires new claims for floristic research. Now the latter is not a simple species inventory of a separate local or regional flora but it needs coordination with recent results of critical taxonomic, nomenclatural and molecular phylogenetic investigations. Based on the fact that detailed research on steppes as a zonal type of vegetation in the Forest-Steppe zone of Ukraine is very important for preservation of current steppe territories, the authors studied several territories with steppe vegetation near Poltava town (Poltava region, Ukraine). The key steppe territories found are situated near Abazivka, Rozhayivka, Kostochky, Buhayivka, Machukhy, Ivonchentsi and Zhuky villages. Data about steppe flora from only the first territory located between Abazivka and Rozhayivka villages including âRozhayivskyiâ local botanical reserve were early reported in literature sources while data about steppe vegetation of the other areas has never been published in detail. The full list of 401 vascular plant species found on these steppe territories with the frequency of distribution, major synonym names and references to current taxonomic papers for separate species are proposed. One of these species (Hemerocallis fulva (L.) L.) is a new alien for Poltava region. Taxonomy for all species was critically revised, nomenclature of several taxa (Dichoropetalum carvifolia (Vill.) Pimenov & Kljuykov, Erophila verna (L.) DC., Campanula canescens (Waldst. & Kit.) Roth) is discussed in detail. The name âDichoropetalum carvifolium-chabraei (Crantz) Soldano et al.â is an invalid designation based on trinominal and must be rejected. The names Selinum chabraei Jacq. ex Murray, Peucedanum euphimiae Kotov and Hemerocallis lilio-asphodelus var. fulva L. were lectotypified. The studied steppe territories have the great significance in the sozological aspect, they include 32 rare steppe plant species (seven from the Red Data Book of Ukraine and 25 from the list of locally rare plants within Poltava region) so the primary task for further research is to organize their protection as the most valuable steppe areas and the monitoring of their condition in the future
Theory of a Narrow roton Absorption Line in the Spectrum of a Disk-Shaped SHF Resonator
We calculate the probability of the birth of a circular phonon (c-phonon) in
He II by a c-photon of the resonator. It is shown that this probability has
sharp maxima at frequencies, where the effective group velocity of the c-phonon
is equal to zero; the density of states of c-phonons strongly grows at such
frequencies. For He II, these frequencies correspond to a roton and a maxon.
From the probability of the c-roton birth, we calculate the roto line width
which is found to approximately agree with the experimental one. We conclude
that the roton line observed in the super-high-frequency (SHF) absorption
spectrum of helium is related to the birth of c-rotons. A possible
interpretation of the Stark effect observed for the roton line is also
proposed.Comment: 13 pages, 1 figure, v2: journal variant, several minor correction
Microscopic derivation of Frenkel excitons in second quantization
Starting from the microscopic hamiltonian describing free electrons in a
periodic lattice, we derive the hamiltonian appropriate to Frenkel excitons.
This is done through a grouping of terms different from the one leading to
Wannier excitons. This grouping makes appearing the atomic states as a relevant
basis to describe Frenkel excitons in the second quantization. Using them, we
derive the Frenkel exciton creation operators as well as the commutators which
rule these operators and which make the Frenkel excitons differing from
elementary bosons. The main goal of the present paper is to provide the
necessary grounds for future works on Frenkel exciton many-body effects, with
the composite nature of these particles treated exactly through a procedure
similar to the one we have recently developed for Wannier excitons.Comment: 16 pages, 4 figure
Cylindrically symmetric solitons in Einstein-Yang-Mills theory
Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which
describe superconducting strings with Kasner asymptotic (hep-th/0610183). Here
we study the static cylindrically symmetric SU(2) EYM system in more detail.
The ansatz for the gauge field corresponds to superposition of the azimuthal
and the longitudinal components of the color magnetic field. We
derive sum rules relating data on the symmetry axis to asymptotic data and show
that generic asymptotic structure of regular solutions is Kasner. Solutions
starting with vacuum data on the axis generically are divergent. Regular
solutions correspond to some bifurcation manifold in the space of parameters
which has the low-energy limiting point corresponding to string solutions in
flat space (with the divergent total energy) and the high-curvature point where
gravity is crucial. Some analytical results are presented for the low energy
limit, and numerical bifurcation curves are constructed in the gravitating
case. Depending on the parameters, the solution looks like a straight string or
a pair of straight and circular strings. The existence of such non-linear
superposition of two strings becomes possible due to self-interaction terms in
the Yang-Mills action which suppress contribution of the circular string near
the polar axis.Comment: 21 pages, 11 figure
Level-rank duality via tensor categories
We give a new way to derive branching rules for the conformal embedding
(\asl_n)_m\oplus(\asl_m)_n\subset(\asl_{nm})_1. In addition, we show that
the category \Cc(\asl_n)_m^0 of degree zero integrable highest weight
(\asl_n)_m-representations is braided equivalent to \Cc(\asl_m)_n^0 with
the reversed braiding.Comment: 16 pages, to appear in Communications in Mathematical Physics.
Version 2 changes: Proof of main theorem made explicit, example 4.11 removed,
references update
Quantum coherence and carriers mobility in organic semiconductors
We present a model of charge transport in organic molecular semiconductors
based on the effects of lattice fluctuations on the quantum coherence of the
electronic state of the charge carrier. Thermal intermolecular phonons and
librations tend to localize pure coherent states and to assist the motion of
less coherent ones. Decoherence is thus the primary mechanism by which
conduction occurs. It is driven by the coupling of the carrier to the molecular
lattice through polarization and transfer integral fluctuations as described by
the hamiltonian of Gosar and Choi. Localization effects in the quantum coherent
regime are modeled via the Anderson hamiltonian with correlated diagonal and
non-diagonal disorder leading to the determination of the carrier localization
length. This length defines the coherent extension of the ground state and
determines, in turn, the diffusion range in the incoherent regime and thus the
mobility. The transfer integral disorder of Troisi and Orlandi can also be
incorporated. This model, based on the idea of decoherence, allowed us to
predict the value and temperature dependence of the carrier mobility in
prototypical organic semiconductors that are in qualitative accord with
experiments
Bivariate spline interpolation with optimal approximation order
Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181
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