A tall space with a small bottom

We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if kappa(<kappa) = kappa then there is such a space of height kappa(+) with only kappa many isolated points. This implies that there is a locally compact scattered space of height omega(2) with omega(1) isolated points in ZFC, solving an old problem of the first author

Exact relationship between the entanglement entropies of XY and quantum Ising chains

We consider two prototypical quantum models, the spin-1/2 XY chain and the quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of l spins in homogeneous or inhomogeneous systems of length L. By using two different approaches, free-fermion techniques and perturbational expansion, an exact relationship between the entropies is revealed. Using this relation we translate known results between the two models and obtain, among others, the additive constant of the entropy of the critical homogeneous quantum Ising chain and the effective central charge of the random XY chain.Comment: 6 page

Entanglement entropy of aperiodic quantum spin chains

We study the entanglement entropy of blocks of contiguous spins in non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg, XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and relevant aperiodic modulations, the entanglement entropy is found to be a logarithmic function of the block size with log-periodic oscillations. The effective central charge, c_eff, defined through the constant in front of the logarithm may depend on the ratio of couplings and can even exceed the corresponding value in the homogeneous system. In the strong modulation limit, the ground state is constructed by a renormalization group method and the limiting value of c_eff is exactly calculated. Keeping the ratio of the block size and the system size constant, the entanglement entropy exhibits a scaling property, however, the corresponding scaling function may be nonanalytic.Comment: 6 pages, 2 figure

Entanglement evolution after connecting finite to infinite quantum chains

We study zero-temperature XX chains and transverse Ising chains and join an initially separate finite piece on one or on both sides to an infinite remainder. In both critical and non-critical systems we find a typical increase of the entanglement entropy after the quench, followed by a slow decay towards the value of the homogeneous chain. In the critical case, the predictions of conformal field theory are verified for the first phase of the evolution, while at late times a step structure can be observed.Comment: 15 pages, 11 figure

Entanglement entropy in aperiodic singlet phases

We study the average entanglement entropy of blocks of contiguous spins in aperiodic XXZ chains which possess an aperiodic singlet phase at least in a certain limit of the coupling ratios. In this phase, where the ground state constructed by a real space renormalization group method, consists (asymptotically) of independent singlet pairs, the average entanglement entropy is found to be a piecewise linear function of the block size. The enveloping curve of this function is growing logarithmically with the block size, with an effective central charge in front of the logarithm which is characteristic for the underlying aperiodic sequence. The aperiodic sequence producing the largest effective central charge is identified, and the latter is found to exceed the central charge of the corresponding homogeneous model. For marginal aperiodic modulations, numerical investigations performed for the XX model show a logarithmic dependence, as well, with an effective central charge varying continuously with the coupling ratio.Comment: 18 pages, 9 figure

A generalized exponential relationship between the surface-enhanced Raman scattering (SERS) efficiency of gold/silver nanoisland arrangements and their non-dimensional interparticle distance/particle diameter ratio

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Effects of Temperature–Climate Patterns on the Production of Some Competitive Species on Grounds of Modelling

Climate change has serious effects on the setting up and the operation of natural ecosystems. Small increase in temperature could cause rise in the amount of some species or potential disappearance of others. During our researches, the dispersion of the species and biomass production of a theoretical ecosystem were examined on the effect of the temperature–climate change. The answers of the ecosystems which are given to the climate change could be described by means of global climate modelling and dynamic vegetation models. The examination of the operation of the ecosystems is only possible in huge centres on supercomputers because of the number and the complexity of the calculation. The number of the calculation could be decreased to the level of a PC by considering the temperature and the reproduction during modelling a theoretical ecosystem, and several important theoretical questions could be answered

Monitoring Space Weather: Using Automated, Accurate Neural Network Based Whistler Segmentation for Whistler Inversion

It is challenging, yet important, to measure the - ever-changing - cold electron density in the plasmasphere. The cold electron density inside and outside of the plasmapause is a key parameter for radiation belt dynamics. One indirect measurement is through finding the velocity dispersion relation exhibited by lightning induced whistlers. The main difficulty of the method comes from low signal-to-noise ratios for most of the ground-based whistler components. To provide accurate electron density and L-shell measurements, whistler components need to be detectable in the noisy background, and their characteristics need to be reliably determined. For this reason precise segmentation is needed on a spectrogram image. Here we present a fully automated way to perform such an image segmentation by leveraging the power of convolutional neural networks, a state-of-the-art method for computer vision tasks. Testing the proposed method against a manually, and semi-manually segmented whistler dataset achieved <10% relative electron density prediction error for 80% of the segmented whistler traces, while for the L-shell, the relative error is <5% for 90% of the cases. By segmenting more than 1 million additional real whistler traces from Rothera station Antarctica, logged over 9 years, seasonal changes in the average electron density were found. The variations match previously published findings, and confirm the capabilities of the image segmentation technique