104 research outputs found
On Plouffe's Ramanujan Identities
Recently, Simon Plouffe has discovered a number of identities for the Riemann
zeta function at odd integer values. These identities are obtained numerically
and are inspired by a prototypical series for Apery's constant given by
Ramanujan: Such sums follow from a general relation given by Ramanujan, which is
rediscovered and proved here using complex analytic techniques. The general
relation is used to derive many of Plouffe's identities as corollaries. The
resemblance of the general relation to the structure of theta functions and
modular forms is briefly sketched.Comment: 19 pages, 3 figures; v4: minor corrections; modified intro; revised
concluding statement
Uncovering Ramanujan's "Lost" Notebook: An Oral History
Here we weave together interviews conducted by the author with three
prominent figures in the world of Ramanujan's mathematics, George Andrews,
Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the
"lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's
notes, and recent breakthroughs by Ono and others carrying certain important
aspects of the Indian mathematician's work into the future. Also presented are
historical details related to Ramanujan and his mathematics, perspectives on
the impact of his work in contemporary mathematics, and a number of interesting
personal anecdotes from Andrews, Berndt and Ono
Two-divisibility of the coefficients of certain weakly holomorphic modular forms
We study a canonical basis for spaces of weakly holomorphic modular forms of
weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a
relation between the Fourier coefficients of modular forms in this canonical
basis and a generalized Ramanujan tau-function, and use this to prove that
these Fourier coefficients are often highly divisible by 2.Comment: Corrected typos. To appear in the Ramanujan Journa
q-Newton binomial: from Euler to Gauss
A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made
less mysterious by virtue of being generalized through the introduction of an
additional parameter
Quantum non-demolition (QND) modulation of quantum interference
We propose an experiment where quantum interference between two different
paths is modulated by means of a QND measurement on one or both the arm of the
interferometer. The QND measurement is achieved in a Kerr cell. We illustrate a
scheme for the realisation of this experiment and some further developments.Comment: accepted for publicatio
Physical properties of FeSeTe single crystals grown under different conditions
We report on structural, magnetic, conductivity, and thermodynamic studies of
FeSeTe single crystals grown by self-flux and Bridgman methods.
The samples were prepared from starting materials of different purity at
various temperatures and cooling rates. The lowest values of the susceptibility
in the normal state, the highest transition temperature of 14.5 K, and
the largest heat-capacity anomaly at were obtained for pure (oxygen-free)
samples. The critical current density of A/cm (at 2
K) achieved in pure samples is attributed to intrinsic inhomogeneity due to
disorder at the cation and anion sites. The impure samples show increased
up to A/cm due to additional pinning centers of
FeO. The upper critical field of kOe is estimated
from the resistivity study in magnetic fields parallel to the \emph{c}-axis.
The anisotropy of the upper critical field reaches a value at . Extremely low values of the residual Sommerfeld coefficient for pure
samples indicate a high volume fraction of the superconducting phase (up to
97%). The electronic contribution to the specific heat in the superconducting
state is well described within a single-band BCS model with a temperature
dependent gap K. A broad cusp-like anomaly in the electronic
specific heat of samples with suppressed bulk superconductivity is ascribed to
a splitting of the ground state of the interstitial Fe ions. This
contribution is fully suppressed in the ordered state in samples with bulk
superconductivity.Comment: 11 pages, 11 figures, 3 table
Sum rules and energy scales in the high-temperature superconductor YBa2Cu3O6+x
The Ferrell-Glover-Tinkham (FGT) sum rule has been applied to the temperature
dependence of the in-plane optical conductivity of optimally-doped
YBa_2Cu_3O_{6.95} and underdoped YBa_2Cu_3O_{6.60}. Within the accuracy of the
experiment, the sum rule is obeyed in both materials. However, the energy scale
\omega_c required to recover the full strength of the superfluid \rho_s in the
two materials is dramatically different; \omega_c \simeq 800 cm^{-1} in the
optimally doped system (close to twice the maximum of the superconducting gap,
2\Delta_0), but \omega_c \gtrsim 5000 cm^{-1} in the underdoped system. In both
materials, the normal-state scattering rate close to the critical temperature
is small, \Gamma < 2\Delta_0, so that the materials are not in the dirty limit
and the relevant energy scale for \rho_s in a BCS material should be twice the
energy gap. The FGT sum rule in the optimally-doped material suggests that the
majority of the spectral weight of the condensate comes from energies below
2\Delta_0, which is consistent with a BCS material in which the condensate
originates from a Fermi liquid normal state. In the underdoped material the
larger energy scale may be a result of the non-Fermi liquid nature of the
normal state. The dramatically different energy scales suggest that the nature
of the normal state creates specific conditions for observing the different
aspects of what is presumably a central mechanism for superconductivity in
these materials.Comment: RevTeX 4 file, 9 pages with 7 embedded eps figure
Five new post-main-sequence debris disks with gaseous emission
Observations of debris disks, the products of the collisional evolution of rocky planetesimals, can be used to trace planetary activity across a wide range of stellar types. The most common end points of stellar evolution are no exception, as debris disks have been observed around several dozen white dwarf stars. But instead of planetary formation, post-main-sequence debris disks are a signpost of planetary destruction, resulting in compact debris disks from the tidal disruption of remnant planetesimals. In this work, we present the discovery of five new debris disks around white dwarf stars with gaseous debris in emission. All five systems exhibit excess infrared radiation from dusty debris, emission lines from gaseous debris, and atmospheric absorption features indicating ongoing accretion of metal-rich debris. In four of the systems, we detect multiple metal species in emission, some of which occur at strengths and transitions previously unseen in debris disks around white dwarf stars. Our first year of spectroscopic follow-up hints at strong variability in the emission lines that can be studied in the future, expanding the range of phenomena these post-main-sequence debris disks exhibit.Published versio
Error sources and data limitations for the prediction ofsurface gravity: a case study using benchmarks
Gravity-based heights require gravity values at levelled benchmarks (BMs), whichsometimes have to be predicted from surrounding observations. We use EGM2008 andthe Australian National Gravity Database (ANGD) as examples of model and terrestrialobserved data respectively to predict gravity at Australian national levelling network(ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BMgravity values and then into gravimetric height corrections (HCs). Our results indicatethat an approximate ±1 arc-minute horizontal position error of the BMs causesmaximum errors in EGM2008 BM gravity of ~ 22 mGal (~55 mm in the HC at ~2200 melevation) and ~18 mGal for ANGD BM gravity because the values are not computed atthe true location of the BM. We use RTM (residual terrain modelling) techniques toshow that ~50% of EGM2008 BM gravity error in a moderately mountainous regioncan be accounted for by signal omission. Non-representative sampling of ANGDgravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmertorthometric correction at ~2200 m elevation). For modelled gravity at BMs to beviable, levelling networks need horizontal BM positions accurate to a few metres, whileRTM techniques can be used to reduce signal omission error. Unrepresentative gravitysampling in mountains can be remedied by denser and more representative re-surveys,and/or gravity can be forward modelled into regions of sparser gravity
Mammalian Rif1 contributes to replication stress survival and homology-directed repair
Multifunctional protein Rif1 accumulates at stalled replication forks to facilitate DNA repair during S phase
- …