Escape rate and Hausdorff measure for entire functions

The escaping set of an entire function is the set of points that tend to infinity under iteration. We consider subsets of the escaping set defined in terms of escape rates and obtain upper and lower bounds for the Hausdorff measure of these sets with respect to certain gauge functions.Comment: 24 pages; some errors corrected, proof of Theorem 2 shortene

Combined potential and spin impurity scattering in cuprates

We present a theory of combined nonmagnetic and magnetic impurity scattering in anisotropic superconductors accounting for the momentum-dependent impurity potential. Applying the model to the d-wave superconducting state, we obtain a quantitative agreement with the initial suppression of the critical temperature due to Zn and Ni substitutions as well as electron irradiation defects in the cuprates. We suggest, that the unequal pair-breaking effect of Zn and Ni may be related to a different nature of the magnetic moments induced by these impurities.Comment: 5 pages, 3 tables, RevTex, to be published in Phys. Rev.

Are Devaney hairs fast escaping?

Beginning with Devaney, several authors have studied transcendental entire functions for which every point in the escaping set can be connected to infinity by a curve in the escaping set. Such curves are often called Devaney hairs. We show that, in many cases, every point in such a curve, apart from possibly a finite endpoint of the curve, belongs to the fast escaping set. We also give an example of a Devaney hair which lies in a logarithmic tract of a transcendental entire function and contains no fast escaping points.Comment: 22 pages, 1 figur

Magnetic polarons in weakly doped high-Tc superconductors

We consider a spin Hamiltonian describing $d$-$d$ exchange interactions between localized spins $d$ of a finite antiferromagnet as well as $p$-$d$ interactions between a conducting hole ($p$) and localized spins. The spin Hamiltonian is solved numerically with use of Lanczos method of diagonalization. We conclude that $p$-$d$ exchange interaction leads to localization of magnetic polarons. Quantum fluctuations of the antiferromagnet strengthen this effect and make the formation of polarons localized in one site possible even for weak $p$-$d$ coupling. Total energy calculations, including the kinetic energy, do not change essentially the phase diagram of magnetic polarons formation. For parameters reasonable for high-$T_c$ superconductors either a polaron localized on one lattice cell or a small ferron can form. For reasonable values of the dielectric function and $p$-$d$ coupling, the contributions of magnetic and phonon terms in the formation of a polaron in weakly doped high-$T_c$ materials are comparable.Comment: revised, revtex-4, 12 pages 8 eps figure

Coherent Potential Approximation for `d - wave' Superconductivity in Disordered Systems

A Coherent Potential Approximation is developed for s-wave and d-wave superconductivity in disordered systems. We show that the CPA formalism reproduces the standard pair-breaking formula, the self-consistent Born Approximation and the self-consistent T-matrix approximation in the appropriate limits. We implement the theory and compute T_c for s-wave and d-wave pairing using an attractive nearest neighbor Hubbard model featuring both binary alloy disorder and a uniform distribution of scattering site potentials. We determine the density of states and examine its consequences for low temperature heat capacity. We find that our results are in qualitative agreement with measurements on Zn doped YBCO superconductors.Comment: 35 pages, 23 figures, submitted to Phys Rev.

Is FLT3 internal tandem duplication an unfavorable risk factor for high risk children with acute myeloid leukemia? : Polish experience

According to the AML-BFM 2004 Interim, a treatment protocol used in Poland since 2005, presence of FLT3 internal tandem duplication (FLT3/ITD) qualifies a patient with acute myeloid leukemia (AML) to a high-risk group (HRG). The present study was aimed to identify the prevalence of FLT3/ITD in children with AML in Poland and to evaluate its prognostic significance in the HRG patients. Out of 291 children with de novo AML treated in 14 Polish centers between January 2006 and December 2012, samples from 174 patients were available for FLT3/ITD analysis. Among study patients 108 children (61.7%) were qualified to HRG. Genomic DNA samples from bone marrow were tested for identification of FLT3/ITD mutation by PCR amplification of exon 14 and 15 of FLT3 gene. Clinical features and treatment outcome in patients with and without FLT3/ITD were analyzed in the study. The FLT3/ITD was found in 14 (12.9%) of 108 HRG children. There were no significant differences between children with and without FLT3/ITD in age and FAB distribution. The white blood cells count in peripheral blood at diagnosis was significantly higher (p <0.01) in the children with FLT3/ITD. Over 5-year overall survival rate for FLT3/ITD positive children was worse (42.4%) comparing to FLT3/ITD negative children (58.9%), but the statistical difference was not significant. However, over 5-year survivals free from treatment failures were similar. The FLT3/ITD rate (12.9%) observed in the study corresponded to the published data. There was no significant impact of FLT3/ITD mutation on survival rates, although further studies are needed on this subject

Cross-talk between high light stress and plant defence to the two-spotted spider mite in Arabidopsis thaliana

Little is known about how plants deal with arthropod herbivores under the fluctuating light intensity and spectra which occur in natural environments. Moreover, the role of simultaneous stress such as excess light (EL) in the regulation of plant responses to herbivores is poorly characterized. In the current study, we focused on a mite-herbivore, specifically, the two-spotted spider mite (TSSM), which is one of the major agricultural pests worldwide. Our results showed that TSSM-induced leaf damage (visualized by trypan blue staining) and oviposition rate (measured as daily female fecundity) decreased after EL pre-treatment in wild-type Arabidopsis plants, but the observed responses were not wavelength specific. Thus, we established that EL pre-treatment reduced Arabidopsis susceptibility to TSSM infestation. Due to the fact that a portion of EL energy is dissipated by plants as heat in the mechanism known as non-photochemical quenching (NPQ) of chlorophyll fluorescence, we tested an Arabidopsis npq4-1 mutant impaired in NPQ. We showed that npq4-1 plants are significantly less susceptible to TSSM feeding activity, and this result was not dependent on light pre-treatment. Therefore, our findings strongly support the role of light in plant defence against TSSM, pointing to a key role for a photo-protective mechanism such as NPQ in this regulation. We hypothesize that plants impaired in NPQ are constantly primed to mite attack, as this seems to be a universal evolutionarily conserved mechanism for herbivores

The Eurasian Modern Pollen Database (EMPD), version 2

The Eurasian (née European) Modern Pollen Database (EMPD) was established in 2013 to provide a public database of high-quality modern pollen surface samples to help support studies of past climate, land cover, and land use using fossil pollen. The EMPD is part of, and complementary to, the European Pollen Database (EPD) which contains data on fossil pollen found in Late Quaternary sedimentary archives throughout the Eurasian region. The EPD is in turn part of the rapidly growing Neotoma database, which is now the primary home for global palaeoecological data. This paper describes version 2 of the EMPD in which the number of samples held in the database has been increased by 60 % from 4826 to 8134. Much of the improvement in data coverage has come from northern Asia, and the database has consequently been renamed the Eurasian Modern Pollen Database to reflect this geographical enlargement. The EMPD can be viewed online using a dedicated map-based viewer at https://empd2.github.io and downloaded in a variety of file formats at https://doi.pangaea.de/10.1594/PANGAEA.909130 (Chevalier et al., 2019)Swiss National Science Foundation | Ref. 200021_16959