58,468 research outputs found
On the least common multiple of -binomial coefficients
In this paper, we prove the following identity \lcm({n\brack 0}_q,{n\brack
1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q},
where denotes the -binomial coefficient and
. This result is a -analogue of an identity of
Farhi [Amer. Math. Monthly, November (2009)].Comment: 5 page
Hemodynamic evaluation using four-dimensional flow magnetic resonance imaging for a patient with multichanneled aortic dissection
The hemodynamic function of multichanneled aortic dissection (MCAD) requires close monitoring and effective management to avoid potentially catastrophic sequelae. This report describes a 47-year-old man who underwent endovascular repair based on findings from four-dimensional (4D) flow magnetic resonance imaging of an MCAD. The acquired 4D flow data revealed complex, bidirectional flow patterns in the false lumens and accelerated blood flow in the compressed true lumen. The collapsed abdominal true lumen expanded unsatisfactorily after primary tear repair, which required further remodeling with bare stents. This case study demonstrates that hemodynamic analysis using 4D flow magnetic resonance imaging can help understand the complex pathologic changes of MCAD
Optimal transfer of an unknown state via a bipartite operation
A fundamental task in quantum information science is to transfer an unknown
state from particle to particle (often in remote space locations) by
using a bipartite quantum operation . We suggest the power of
for quantum state transfer (QST) to be the maximal average
probability of QST over the initial states of particle and the
identifications of the state vectors between and . We find the QST power
of a bipartite quantum operations satisfies four desired properties between two
-dimensional Hilbert spaces. When and are qubits, the analytical
expressions of the QST power is given. In particular, we obtain the exact
results of the QST power for a general two-qubit unitary transformation.Comment: 6 pages, 1 figur
Anomalous quantum glass of bosons in a random potential in two dimensions
We present a quantum Monte Carlo study of the "quantum glass" phase of the 2D
Bose-Hubbard model with random potentials at filling . In the narrow
region between the Mott and superfluid phases the compressibility has the form
with and vanishing or
very small. Thus, at the system is either incompressible (a Mott glass)
or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger
disorder, where a glass reappears from the superfluid, we find a conventional
highly compressible Bose glass. On a path connecting these states, away from
the superfluid at larger Hubbard repulsion, a change of the disorder strength
by only changes the low-temperature compressibility by more than four
orders of magnitude, lending support to two types of glass states separated by
a phase transition or a sharp cross-over.Comment: Published version including supplementary material, 11 pages total,
15 figure
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Two novel nonlinear companding schemes with iterative receiver to reduce PAPR in multi-carrier modulation systems
Companding transform is an efficient and simple method to reduce the Peak-to-Average Power Ratio (PAPR) for Multi-Carrier Modulation (MCM) systems. But if the MCM signal is only simply operated by inverse companding transform at the receiver, the resultant spectrum may exhibit severe in-band and out-of-band radiation of the distortion components, and considerable peak regrowth by excessive channel noises etc. In order to prevent these problems from occurring, in this paper, two novel nonlinear companding schemes with a iterative receiver are proposed to reduce the PAPR. By transforming the amplitude or power of the original MCM signals into uniform distributed signals, the novel schemes can effectively reduce PAPR for different modulation formats and sub-carrier sizes. Despite moderate complexity increasing at the receiver, but it is especially suitable to be combined with iterative channel estimation. Computer simulation results show that the proposed schemes can offer good system performances without any bandwidth expansion
Factors of sums and alternating sums involving binomial coefficients and powers of integers
We study divisibility properties of certain sums and alternating sums
involving binomial coefficients and powers of integers. For example, we prove
that for all positive integers , , and any
nonnegative integer , there holds {align*} \sum_{k=0}^{n_1}\epsilon^k
(2k+1)^{2r+1}\prod_{i=1}^{m} {n_i+n_{i+1}+1\choose n_i-k} \equiv 0 \mod
(n_1+n_m+1){n_1+n_m\choose n_1}, {align*} and conjecture that for any
nonnegative integer and positive integer such that is odd, where .Comment: 14 pages, to appear in Int. J. Number Theor
Metastable helium molecules as tracers in superfluid liquid He
Metastable helium molecules generated in a discharge near a sharp tungsten
tip operated in either pulsed mode or continuous field-emission mode in
superfluid liquid He are imaged using a laser-induced-fluorescence
technique. By pulsing the tip, a small cloud of He molecules is
produced. At 2.0 K, the molecules in the liquid follow the motion of the normal
fluid. We can determine the normal-fluid velocity in a heat-induced counterflow
by tracing the position of a single molecule cloud. As we run the tip in
continuous field-emission mode, a normal-fluid jet from the tip is generated
and molecules are entrained in the jet. A focused 910 nm pump laser pulse is
used to drive a small group of molecules to the vibrational state.
Subsequent imaging of the tagged molecules with an expanded 925 nm probe
laser pulse allows us to measure the velocity of the normal fluid. The
techniques we developed demonstrate for the first time the ability to trace the
normal-fluid component in superfluid helium using angstrom-sized particles.Comment: 4 pages, 7 figures. Submitted to Phys. Rev. Let
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