169 research outputs found
Inverse spectral results for Schr\"odinger operators on the unit interval with potentials in L^P spaces
We consider the Schr\"odinger operator on with potential in . We
prove that two potentials already known on () and having
their difference in are equal if the number of their common eigenvalues
is sufficiently large. The result here is to write down explicitly this number
in terms of (and ) showing the role of
ΠΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²ΡΠΈΠΊΠΎΠ² Π±ΠΎΡΡΠΎΠ²ΠΎΠΉ ΡΠ°Π΄ΠΈΠΎΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ Π°ΠΏΠΏΠ°ΡΠ°ΡΡΡΡ ΠΊΠΎΡΠΌΠΈΡΠ΅ΡΠΊΠΈΡ Π°ΠΏΠΏΠ°ΡΠ°ΡΠΎΠ² Π½Π° Π±Π°Π·Π΅ ΠΈΠ½ΡΠ΅Π³ΡΠ°ΡΠΈΠΈ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΡ ΡΠΈΡΡΠ΅ΠΌ
ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²ΡΠΈΠΊΠΎΠ² Π±ΠΎΡΡΠΎΠ²ΠΎΠΉ ΡΠ°Π΄ΠΈΠΎΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ Π°ΠΏΠΏΠ°ΡΠ°ΡΡΡΡ, ΠΏΠΎΠ²ΡΡΠ°ΡΡΠΈΠΉ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅ΡΡΡΡΠΎΠ² ΠΈ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΡΠΌΠΈ ΠΏΡΠΎΡΠ΅ΡΡΠ°ΠΌΠΈ. ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π° ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΈΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° Π² ΡΡΠ΅Π΄Π΅ PLM-ΡΠΈΡΡΠ΅ΠΌΡ Enovia SmarTeam. Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΡΠΎΡ
ΡΠ°Π½Π΅Π½ΠΈΡ Π΄Π°Π½Π½ΡΡ
ΠΏΡΠΎΠ΅ΠΊΡΠΎΠ² EDA-ΡΠΈΡΡΠ΅ΠΌΡ Altium Designer Π² Ρ
ΡΠ°Π½ΠΈΠ»ΠΈΡΠ΅ Π΄Π°Π½Π½ΡΡ
PLM-ΡΠΈΡΡΠ΅ΠΌΡ Enovia SmarTeam. Π‘ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΎΡΡΠΊΠΈΡ
Π΄ΠΎΠΊΡΠΌΠ΅Π½ΡΠΎΠ² Π½Π° Π±Π°Π·Π΅ ΡΠΎΡΠΌΠ°ΡΠ° Ρ
ΡΠ°Π½Π΅Π½ΠΈΡ Π΄Π°Π½Π½ΡΡ
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The impact of using wordlists in the language classroom on studentsβ vocabulary acquisition
Vocabulary has always been an area of interest for many researchers since words represent βthe building block upon which knowledge of the second language can be builtβ and without them people cannot convey the intended meaning (Abrudan, 2010). Nation (1988) emphasised if teachers want to help their learners to deal with unknown words, it would be better to spend more time on vocabulary learning strategies rather than spending time on individual words. However, Schmitt in Schmitt and McCarthy (1997:200) stated that among vocabulary learning strategies only βguessing from contextβ and βkey word methodβ have been investigated in depth. Therefore, there is need for more research on vocabulary learning whose pedagogical implications may contribute to the field of second language learning. Considering the above-mentioned issues, vocabulary is a worthwhile field to investigate. Hence, this paper aims at proposing a framework for vocabulary teaching strategy in English as a foreign language context.publisher versio
Dirac Electrons on a Sharply Edged Surface of Topological Insulators
An unpaired gapless Dirac electron emergent at the surface of a strong
topological insulator (STI) is protected by the bulk-surface correspondence and
believed to be immune to backward scattering. It is less obvious, however, and
yet to be verified explicitly whether such a gapless Dirac state is smoothly
extended over the entire surface when the surface is composed of more than a
single facet with different orientations in contact with one another at sharp
corner edges (typically forming a steplike structure). In the realistic
situation that we consider, the anisotropy of the sample leads to different
group velocities in each of such facets. Here, we propose that much insight on
this issue can be obtained by studying the electronic states on a hyperbolic
surface of an STI. By explicitly constructing the surface effective
Hamiltonian, we demonstrate that no backward scattering takes place at a
concave step edge. A strong renormalization of the velocity in the
close vicinity of the step edge is also suggested.Comment: 4 pages, 2 figures, to be published in J. Phys. Soc. Jp
Spin Drag in Ultracold Fermi Mixtures with Repulsive Interactions
We calculate the spin-drag relaxation rate for a two-component ultracold
atomic Fermi gas with positive scattering length between the two spin
components. In one dimension we find that it vanishes linearly with
temperature. In three dimensions the spin-drag relaxation rate vanishes
quadratically with temperature for sufficiently weak interactions. This
quadratic temperature dependence is present, up to logarithmic corrections, in
the two-dimensional case as well. For stronger interaction the system exhibits
a Stoner ferromagnetic phase transition in two and three dimensions. We show
that the spin-drag relaxation rate is enhanced by spin fluctuations as the
temperature approaches the critical temperature of this transition from above.Comment: Submitted to New Journal of Physics Focus Issue "Strongly Correlated
Quantum Fluids: From Ultracold Quantum Gases to QCD Plasmas
Positive and negative well-being and objectively measured sedentary behaviour in older adults: evidence from three cohorts
Background:
Sedentary behaviour is related to poorer health independently of time spent in moderate to vigorous physical activity. The aim of this study was to investigate whether wellbeing or symptoms of anxiety or depression predict sedentary behaviour in older adults.
Method:
Participants were drawn from the Lothian Birth Cohort 1936 (LBC1936) (nβ=β271), and the West of Scotland Twenty-07 1950s (nβ=β309) and 1930s (nβ=β118) cohorts. Sedentary outcomes, sedentary time, and number of sit-to-stand transitions, were measured with a three-dimensional accelerometer (activPAL activity monitor) worn for 7βdays. In the Twenty-07 cohorts, symptoms of anxiety and depression were assessed in 2008 and sedentary outcomes were assessed ~β8βyears later in 2015 and 2016. In the LBC1936 cohort, wellbeing and symptoms of anxiety and depression were assessed concurrently with sedentary behaviour in 2015 and 2016. We tested for an association between wellbeing, anxiety or depression and the sedentary outcomes using multivariate regression analysis.
Results:
We observed no association between wellbeing or symptoms of anxiety and the sedentary outcomes. Symptoms of depression were positively associated with sedentary time in the LBC1936 and Twenty-07 1950s cohort, and negatively associated with number of sit-to-stand transitions in the LBC1936. Meta-analytic estimates of the association between depressive symptoms and sedentary time or number of sit-to-stand transitions, adjusted for age, sex, BMI, long-standing illness, and education, were Ξ²β=β0.11 (95% CIβ=β0.03, 0.18) and Ξ²β=βββ0.11 (95% CIβ=βββ0.19, β0.03) respectively.
Conclusion:
Our findings indicate that depressive symptoms are positively associated with sedentary behavior. Future studies should investigate the causal direction of this association
Fermi velocity engineering in graphene by substrate modification
The Fermi velocity is one of the key concepts in the study of a material, as
it bears information on a variety of fundamental properties. Upon increasing
demand on the device applications, graphene is viewed as a prototypical system
for engineering Fermi velocity. Indeed, several efforts have succeeded in
modifying Fermi velocity by varying charge carrier concentration. Here we
present a powerful but simple new way to engineer Fermi velocity while holding
the charge carrier concentration constant. We find that when the environment
embedding graphene is modified, the Fermi velocity of graphene is (i) inversely
proportional to its dielectric constant, reaching ~2.5 m/s, the
highest value for graphene on any substrate studied so far and (ii) clearly
distinguished from an ordinary Fermi liquid. The method demonstrated here
provides a new route toward Fermi velocity engineering in a variety of
two-dimensional electron systems including topological insulators.Comment: accepted in Scientific Report
Structural study of an amorphous NiZr2 alloy by anomalous wide angle X-ray scattering and Reverse Monte Carlo simulations
The local atomic structure of an amorphous NiZr2 alloy was investigated using
the anomalous wide-angle x-ray scattering (AWAXS), differential anomalous
scattering (DAS) and reverse Monte Carlo (RMC) simulations techniques. The
AWAXS measurements were performed at eight different incident photon energies,
including some close to the Ni and Zr K edges. From the measurements eight
total structure factor S(K,E) were derived. Using the AWAXS data four
differential structure factors DSFi(K,Em,En) were derived, two about the Ni and
Zr edges. The partial structure factors SNi-Ni(K), SNi-Zr(K) and SZr-Zr(K) were
estimated by using two different methods. First, the S(K,E) and DSFi(K,Em,En)
factors were combined and used in a matrix inversion process. Second, three
S(K,E) factors were used as input data in the RMC technique. The coordination
numbers and interatomic distances for the first neighbors extracted from the
partial structure factors obtained by these two methods show a good agreement.
By using the three-dimensional structure derived from the RMC simulations, the
bond-angle distributions were calculated and they suggest the presence of
distorted triangular-faced polyhedral units in the amorphous NiZr2 structure.
We have used the Warren chemical short-range order parameter to evaluate the
chemical short-range order for the amorphous NiZr2 alloy and for the NiZr2
compound. The calculated values show that the chemical short-range order found
in these two materials is similar to that found in a solid solution.Comment: Submitted to Phys. Rev. B, 8 figure
Inter-diffusion of Plasmonic Metals and Phase Change Materials
This work investigates the problematic diffusion of metal atoms into phase
change chalcogenides, which can destroy resonances in photonic devices.
Interfaces between Ge2Sb2Te5 and metal layers were studied using X-ray
reflectivity (XRR) and reflectometry of metal-Ge2Sb2Te5 layered stacks. The
diffusion of metal atoms influences the crystallisation temperature and optical
properties of phase change materials. When Au, Ag, Al, W structures are
directly deposited on Ge2Sb2Te5 inter-diffusion occurs. Indeed, Au forms AuTe2
layers at the interface. Diffusion barrier layers, such as Si3N4 or stable
diffusionless plasmonic materials, such as TiN, can prevent the interfacial
damage. This work shows that the interfacial diffusion must be considered when
designing phase change material tuned photonic devices, and that TiN is the
most suitable plasmonic material to interface directly with Ge2Sb2Te5.Comment: 23 pages, 8 figures, articl
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