48,492 research outputs found
Semi-Finite Forms of Bilateral Basic Hypergeometric Series
We show that several classical bilateral summation and transformation
formulas have semi-finite forms. We obtain these semi-finite forms from
unilateral summation and transformation formulas. Our method can be applied to
derive Ramanujan's summation, Bailey's transformations,
and Bailey's summation.Comment: 8 pages. accepted by Proc. Amer. Math. So
Calibration of the Pulsed Electroacoustic Technique in the Presence of Trapped Charge
The influence of pulse voltage on the accuracy of charge density distribution in the pulsed electroacoustic technique (PEA) is discussed. It is shown that significant error can be introduced if a low dc voltage and high pulse voltage are used to calibrate charge density. However, our main focus in the present paper is to deal with one of the practical situations where space charge exists in the material prior to any measurements. The conventional calibration method can no longer be used to calibrate charge density due to the interference by the charge on the electrode induced by space charge. A method has been proposed which is based on two measurements. Firstly, the sample containing charge is measured without any applied voltage. The second measurement is carried out with a small external applied voltage. The applied voltage should be small enough so there is no disturbance of the existing charge in the sample. The difference of the two measurements can be used for calibration. An additional advantage of the proposed method avoids the influence of the pulse voltage on calibration and therefore gives a more accurate representation of space charge. The proposed method has been validated
Spherical to deformed shape transition in the nucleon-pair shell model
A study of the shape transition from spherical to axially deformed nuclei in
the even Ce isotopes using the nucleon-pair approximation of the shell model is
reported. As long as the structure of the dominant collective pairs is
determined using a microscopic framework appropriate to deformed nuclei, the
model is able to produce a shape transition. However, the resulting transition
is too rapid, with nuclei that should be transitional being fairly well
deformed, perhaps reflecting the need to maintain several pairs with each
angular momentum.Comment: 7 pages, 5 figure
Residual proton-neutron interactions and the scheme
We investigate the correlation between integrated proton-neutron interactions
obtained by using the up-to-date experimental data of binding energies and the
, the product of valence proton number and valence neutron
number with respect to the nearest doubly closed nucleus. We make corrections
on a previously suggested formula for the integrated proton-neutron
interaction. Our results demonstrate a nice, nearly linear, correlation between
the integrated p-n interaction and , which provides us
with a firm foundation of the applicability of the scheme
to nuclei far from the stability line.Comment: four pages, three figures, Physical Review C, in pres
Faulhaber's Theorem on Power Sums
We observe that the classical Faulhaber's theorem on sums of odd powers also
holds for an arbitrary arithmetic progression, namely, the odd power sums of
any arithmetic progression is a polynomial in
. While this assertion can be deduced from the original
Fauhalber's theorem, we give an alternative formula in terms of the Bernoulli
polynomials. Moreover, by utilizing the central factorial numbers as in the
approach of Knuth, we derive formulas for -fold sums of powers without
resorting to the notion of -reflexive functions. We also provide formulas
for the -fold alternating sums of powers in terms of Euler polynomials.Comment: 12 pages, revised version, to appear in Discrete Mathematic
Local Spin Susceptibility of the S=1/2 Kagome Lattice in ZnCu3(OD)6Cl2
We report single-crystal 2-D NMR investigation of the nearly ideal spin S=1/2
kagome lattice ZnCu3(OD)6Cl2. We successfully identify 2-D NMR signals
originating from the nearest-neighbors of Cu2+ defects occupying Zn sites. From
the 2-D Knight shift measurements, we demonstrate that weakly interacting Cu2+
spins at these defects cause the large Curie-Weiss enhancement toward T=0
commonly observed in the bulk susceptibility data. We estimate the intrinsic
spin susceptibility of the kagome planes by subtracting defect contributions,
and explore several scenarios.Comment: 4 figures; published in PR-B Rapid Communication
The structure of electronic polarization and its strain dependence
The \phi(\kpp)\sim \kpp relation is called polarization structure. By
density functional calculations, we study the polarization structure in
ferroelectric perovskite PbTiO, revealing (1) the \kpp point that
contributes most to the electronic polarization, (2) the magnitude of
bandwidth, and (3) subtle curvature of polarization dispersion. We also
investigate how polarization structure in PbTiO is modified by compressive
inplane strains. The bandwidth of polarization dispersion in PbTiO is shown
to exhibit an unusual decline, though the total polarization is enhanced. As
another outcome of this study, we formulate an analytical scheme for the
purpose of identifying what determine the polarization structure at arbitrary
\kpp points by means of Wannier functions. We find that \phi(\kpp) is
determined by two competing factors: one is the overlaps between neighboring
Wannier functions within the plane {\it perpendicular} to the polarization
direction, and the other is the localization length {\it parallel} to the
polarization direction. Inplane strain increases the former while decreases the
latter, causing interesting non-monotonous effects on polarization structure.
Finally, polarization dispersion in another paradigm ferroelectric BaTiO is
discussed and compared with that of PbTiO.Comment: 5 Figure
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