Discrete Hilbert transforms on sparse sequences

Weighted discrete Hilbert transforms $(a_n)_n \mapsto \sum_n a_n v_n/(z-\gamma_n)$ from $\ell^2_v$ to a weighted $L^2$ space are studied, with $\Gamma=(\gamma_n)$ a sequence of distinct points in the complex plane and $v=(v_n)$ a corresponding sequence of positive numbers. In the special case when $|\gamma_n|$ grows at least exponentially, bounded transforms of this kind are described in terms of a simple relative to the Muckenhoupt $(A_2)$ condition. The special case when $z$ is restricted to another sequence $\Lambda$ is studied in detail; it is shown that a bounded transform satisfying a certain admissibility condition can be split into finitely many surjective transforms, and precise geometric conditions are found for invertibility of such two weight transforms. These results can be interpreted as statements about systems of reproducing kernels in certain Hilbert spaces of which de Branges spaces and model subspaces of $H^2$ are prime examples. In particular, a connection to the Feichtinger conjecture is pointed out. Descriptions of Carleson measures and Riesz bases of normalized reproducing kernels for certain "small" de Branges spaces follow from the results of this paper

Accurate Modelling of Left-Handed Metamaterials Using Finite-Difference Time-Domain Method with Spatial Averaging at the Boundaries

The accuracy of finite-difference time-domain (FDTD) modelling of left-handed metamaterials (LHMs) is dramatically improved by using an averaging technique along the boundaries of LHM slabs. The material frequency dispersion of LHMs is taken into account using auxiliary differential equation (ADE) based dispersive FDTD methods. The dispersive FDTD method with averaged permittivity along the material boundaries is implemented for a two-dimensional (2-D) transverse electric (TE) case. A mismatch between analytical and numerical material parameters (e.g. permittivity and permeability) introduced by the time discretisation in FDTD is demonstrated. The expression of numerical permittivity is formulated and it is suggested to use corrected permittivity in FDTD simulations in order to model LHM slabs with their desired parameters. The influence of switching time of source on the oscillation of field intensity is analysed. It is shown that there exists an optimum value which leads to fast convergence in simulations.Comment: 17 pages, 7 figures, submitted to Journal of Optics A Nanometa special issu

Ground increase of cosmic ray intensity on February 16, 1984

The event of February 16, 1984 is one of the two largest ground increases of solar cosmic rays (CR) in the last two cycles of solar activity. This event happended at a decrease of the 21-st cycle against a quiet background. Although at the beginning of 1984 the observed indices of solar activity were higher than those at the end of 1983, the day of February 16 16 may be characterized as very quiet. On that day the geomagnetic perturbance (Sigma F sub p = 14, A sub p = 7) was the lowest in February. After a small Forbush decrease due to the magnetic storm of February 12-13, the CR intensity almost completely recovered by February 16. Thus, the solar particles that came to the Earth on February 16 got into a practically unperturbed magnetosphere, and the variations of secondary CR induced by these particles were not superimposed on any other substantial variations of extraterrestrial or magnetospheric origin

MHC-linked and un-linked class I genes in the wallaby

Background: MHC class I antigens are encoded by a rapidly evolving gene family comprising classical and non-classical genes that are found in all vertebrates and involved in diverse immune functions. However, there is a fundamental difference between the organization of class I genes in mammals and non-mammals. Non-mammals have a single classical gene responsible for antigen presentation, which is linked to the antigen processing genes, including TAP. This organization allows co-evolution of advantageous class Ia/ TAP haplotypes. In contrast, mammals have multiple classical genes within the MHC, which are separated from the antigen processing genes by class III genes. It has been hypothesized that separation of classical class I genes from antigen processing genes in mammals allowed them to duplicate. We investigated this hypothesis by characterizing the class I genes of the tammar wallaby, a model marsupial that has a novel MHC organization, with class I genes located within the MHC and 10 other chromosomal locations. Results: Sequence analysis of 14 BACs containing 15 class I genes revealed that nine class I genes, including one to three classical class I, are not linked to the MHC but are scattered throughout the genome. Kangaroo Endogenous Retroviruses (KERVs) were identified flanking the MHC un-linked class I. The wallaby MHC contains four non-classical class I, interspersed with antigen processing genes. Clear orthologs of non-classical class I are conserved in distant marsupial lineages. Conclusion: We demonstrate that classical class I genes are not linked to antigen processing genes in the wallaby and provide evidence that retroviral elements were involved in their movement. The presence of retroviral elements most likely facilitated the formation of recombination hotspots and subsequent diversification of class I genes. The classical class I have moved away from antigen processing genes in eutherian mammals and the wallaby independently, but both lineages appear to have benefited from this loss of linkage by increasing the number of classical genes, perhaps enabling response to a wider range of pathogens. The discovery of non-classical orthologs between distantly related marsupial species is unusual for the rapidly evolving class I genes and may indicate an important marsupial specific function

Temperature evolution of magnetic structure of HoFeO3_3 by single crystal neutron diffraction

We have investigated the temperature evolution of the magnetic structures of HoFeO$_3$ by single crystal neutron diffraction. The three different magnetic structures found as a function of temperature for \hfo\ are described by the magnetic groups Pb$'$n$'2_1$, Pbn$2_1$ and Pbn$'2_1'$ and are stable in the temperature ranges $\approx$ 600-55~K, 55-37~K and 35$>T>2$~K respectively. In all three the fundamental coupling between the Fe sub-lattices remains the same and only their orientation and the degree of canting away from the ideal axial direction varies. The magnetic polarisation of the Ho sub-lattices in these two higher temperature regions, in which the major components of the Fe moment lie along $x$ and $y$, is very small. The canting of the moments from the axial directions is attributed to the antisymmetric interactions allowed by the crystal symmetry. They include contributions from single ion anisotropy as well as the Dzyaloshinski antisymmetric exchange. In the low temperature phase two further structural transitions are apparent in which the spontaneous magnetisation changes sign with respect to the underlying antiferromagnetic configuration. In this temperature range the antisymmetric exchange energy varies rapidly as the the Ho sub-lattices begin to order. So long as the ordered Ho moments are small the antisymmetric exchange is due only to Fe-Fe interactions, but as the degree of Ho order increases the Fe-Ho interactions take over whilst at the lowest temperatures, when the Ho moments approach saturation the Ho-Ho interactions dominate. The reversals of the spontaneous magnetisation found in this study suggest that in \hfo\ the sums of the Fe-Fe and Ho-Ho antisymmetric interactions have the same sign as one another, but that of the Ho-Fe terms is opposite

String Field Theory Projectors for Fermions of Integral Weight

The interaction vertex for a fermionic first order system of weights (1,0) such as the twisted bc-system, the fermionic part of N=2 string field theory and the auxiliary \eta\xi system of N=1 strings is formulated in the Moyal basis. In this basis, the Neumann matrices are diagonal; as usual, the eigenvectors are labeled by \kappa\in\R. Oscillators constructed from these eigenvectors make up two Clifford algebras for each nonzero value of \kappa. Using a generalization of the Moyal-Weyl map to the fermionic case, we classify all projectors of the star-algebra which factorize into projectors for each \kappa-subspace. At least for the case of squeezed states we recover the full set of bosonic projectors with this property. Among the subclass of ghost number-homogeneous squeezed state projectors, we find a single class of BPZ-real states parametrized by one (nearly) arbitrary function of \kappa. This class is shown to contain the generalized butterfly states. Furthermore, we elaborate on sufficient and necessary conditions which have to be fulfilled by our projectors in order to constitute surface states. As a byproduct we find that the full star product of N=2 string field theory translates into a canonically normalized continuous tensor product of Moyal-Weyl products up to an overall normalization. The divergent factors arising from the translation to the continuous basis cancel between bosons and fermions in any even dimension.Comment: LaTeX, 1+23 pages, minor improvements, references adde

Quantum phase transition in the dioptase magnetic lattice

The study of quantum phase transitions, which are zero-temperature phase transitions between distinct states of matter, is of current interest in research since it allows for a description of low-temperature properties based on universal relations. Here we show that the crystal green dioptase Cu_6Si_6O_18 . 6H_2O, known to the ancient Roman as the gem of Venus, has a magnetic crystal structure, formed by the Cu(II) ions, which allows for a quantum phase transition between an antiferromagnetically ordered state and a quantum spin liquid.Comment: 6 pages, 5 figures, EPL, in pres

Endomorphisms of quantized Weyl algebras

Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of (second) quantized Weyl algebras at roots of unity