The Pauli equation with complex boundary conditions

We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.Comment: 16 pages, 4 figure

Palynomorphs of the Normapolles group and related plant mesofossils from the Iharkút vertebrate site, Bakony Mountains (Hungary)

Abstract Palynological and paleobotanical investigation of bonebeds and other strata of the Csehbánya Formation from the vertebrate locality at Iharkút (Bakony Mts, Hungary) reveals well-preserved Santonian palynological assemblages dominated by the Normapolles group, with a minor component consisting of other angiosperm pollen, some gymnosperm pollen, and spores. Eleven species of Normapolles-type pollen grains belonging to seven genera and fruit remains of a new taxon, Sphaeracostata barbackae gen. et sp. nov., are described. The new species is very abundant in the material, represented by ca. 1000 specimens. The genus Caryanthus Friis and an unnamed form previously reported from Haţeg by Lindfors et al. (2010) are also present. Plants producing Normapolles-type pollen grains diversified during the Late Cretaceous, with a bloom in the Santonian. The palynostratigraphy of the Upper Cretaceous terrestrial sediments in the studied region is based on Normapolles-related species. The studied assemblage is assigned to the Oculopollis zaklinskaiae-Tetracolporopollenites (Brecolpites) globosus Zone (or Zone C) indicating a late Santonian age. Comparison of the Iharkút palynoflora with other known Upper Cretaceous palynofloras of Central Europe shows diachronous occurrence of Normapolles taxa at different geographic localities and warrants further investigation. The ecological requirements of the amphibian fauna reflect azonal conditions controlled by the availability of water, which is in agreement with the inferred ecological conditions based on the paleobotanical investigations. The fauna is of entirely non-marine character, further supported by isotope studies, in line with our data showing that the palynological samples contain no marine forms

PT-symmetric models in curved manifolds

We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.Comment: 37 pages, PDFLaTeX with 11 figure

Differences in preservice teachers’ readiness to use ICT in education and development of TPACK

Education for the 21st century society requires the use of Information and Communication Technology (ICT) in education. This presents challenges for preservice teacher education. Thus, more cognate understanding about preservice teachers’ readiness to use ICT in education, coupled with knowledge related to ICT in education, is needed. Furthermore, it is important to understand that preservice teachers have various levels of readiness to use ICT in education, thereby creating a demand to investigate sub-groups within preservice teachers. This study focuses on differences of readiness and development of knowledge between preservice teachers’ based on two theoretical constructs: Theory of Planned Behavior and TPACK. Results indicate differences in readiness of preservice teachers’ sub-groups. Still, positive development trends in terms of knowledge of ICT in education can be found during the first two years of preservice teacher education. Limitations and future research are discussed

Implementing concurrent-training and nutritional strategies in professional football: a complex challenge for coaches and practitioners

Purpose: To study concurrent-training (CT) and nutritional practices within a professional soccer team. Methods: Twenty-one professional football players competing in the English professional league participated in this study (mean ± standard deviations [M ± SD] 26 ± 4 years, stature 1.84 ± 0.1 m, body mass 83 ± 7 kg, VO2max; 58 ± 3 ml · kg−1 · min−1). A range of internal and external training metrics, the organisation of CT (training sequence, training rest period between bouts) and the nutritional intake around CT (timing, type and quantity) was collected for 10 weeks. Results: CT; n = 17 (endurance-training [ET] + resistance-training [RT]; n = 11; RT + ET; n = 6) rest period between bouts was not consistent and varied depending on the sequence of CT (RT + ET, 75 ± 48 min; ET + RT; 60 ± 5 min; P = 0.04). sRPE of football-specific ET was higher in RT + ET (RT + ET, 7 ± 1; ET + RT, 6 ± 1; P = 0.05). The timing of meals around training was influenced by the organisation of CT. Subsequently, CHO consumption before training session one was significantly less in RT + ET (CHO 0.10 ± 0.5 g · kg−1 vs. CHO 0.45 ± 0.2 g · kg−1). Conclusion: The present data demonstrate that the organisation of CT (i.e., exercise order and/or recovery time between bouts) and nutrition (i.e., timing of meal intake) can be unsystematic in the applied environment. The organisation of training and nutrition might influence the players’ ability to perform high-intensity actions in secondary training sessions and could potentially impact acute metabolic processes associated with muscle recovery and muscle adaptation

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.Comment: version accepted for publication in J. Math. Phys.: criterion excluding basis property (Proposition 6) added, unbounded time-evolution discussed, new reference

Beta-delayed-neutron studies of 135,136^{135,136}Sb and 140^{140}I performed with trapped ions

Beta-delayed-neutron ($\beta$n) spectroscopy was performed using the Beta-decay Paul Trap and an array of radiation detectors. The $\beta$n branching ratios and energy spectra for $^{135,136}$Sb and $^{140}$I were obtained by measuring the time of flight of recoil ions emerging from the trapped ion cloud. These nuclei are located at the edge of an isotopic region identified as having $\beta$n branching ratios that impact the r-process abundance pattern around the A~130 peak. For $^{135,136}$Sb and $^{140}$I, $\beta$n branching ratios of 14.6(11)%, 17.6(28)%, and 7.6(28)% were determined, respectively. The $\beta$n energy spectra obtained for $^{135}$Sb and $^{140}$I are compared with results from direct neutron measurements, and the $\beta$n energy spectrum for $^{136}$Sb has been measured for the first time