53,864 research outputs found
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
Super congruences and Euler numbers
Let be a prime. We prove that
, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of
combinatorial nature. We also formulate many conjectures concerning super
congruences and relate most of them to Euler numbers or Bernoulli numbers.
Motivated by our investigation of super congruences, we also raise a conjecture
on 7 new series for , and the constant
(with (-) the Jacobi symbol), two of which are
and
\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$
Decoherence-Based Quantum Zeno Effect in a Cavity-QED System
We present a decoherence-based interpretation for the quantum Zeno effect
(QZE) where measurements are dynamically treated as dispersive couplings of the
measured system to the apparatus, rather than the von Neumann's projections. It
is found that the explicit dependence of the survival probability on the
decoherence time quantitatively distinguishes this dynamic QZE from the usual
one based on projection measurements. By revisiting the cavity-QED experiment
of the QZE [J. Bernu, et al., Phys. Rev. Lett, 101, 180402 (2008)], we suggest
an alternative scheme to verify our theoretical consideration that frequent
measurements slow down the increase of photon number inside a microcavity due
to the nondemolition couplings with the atoms in large detuning.Comment: 4 pages, 3 figure
Hydrostatic pressure effects on the static magnetism in Eu(FeCo)As
The effects of hydrostatic pressure on the static magnetism in
Eu(FeCo)As are investigated by complementary
electrical resistivity, ac magnetic susceptibility and single-crystal neutron
diffraction measurements. A specific pressure-temperature phase diagram of
Eu(FeCo)As is established. The structural phase
transition, as well as the spin-density-wave order of Fe sublattice, is
suppressed gradually with increasing pressure and disappears completely above
2.0 GPa. In contrast, the magnetic order of Eu sublattice persists over the
whole investigated pressure range up to 14 GPa, yet displaying a non-monotonic
variation with pressure. With the increase of the hydrostatic pressure, the
magnetic state of Eu evolves from the canted antiferromagnetic structure in the
ground state, via a pure ferromagnetic structure under the intermediate
pressure, finally to a possible "novel" antiferromagnetic structure under the
high pressure. The strong ferromagnetism of Eu coexists with the
pressure-induced superconductivity around 2 GPa. The change of the magnetic
state of Eu in Eu(FeCo)As upon the application
of hydrostatic pressure probably arises from the modification of the indirect
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the Eu moments
tuned by external pressure.Comment: 9 pages, 6 figure
Time-Resolved Magnetic Relaxation of a Nanomagnet on Subnanosecond Time Scales
We present a two-current-pulse temporal correlation experiment to study the
intrinsic subnanosecond nonequilibrium magnetic dynamics of a nanomagnet during
and following a pulse excitation. This method is applied to a model
spin-transfer system, a spin valve nanopillar with perpendicular magnetic
anisotropy. Two-pulses separated by a short delay (< 500 ps) are shown to lead
to the same switching probability as a single pulse with a duration that
depends on the delay. This demonstrates a remarkable symmetry between magnetic
excitation and relaxation and provides a direct measurement of the magnetic
relaxation time. The results are consistent with a simple finite temperature
Fokker-Planck macrospin model of the dynamics, suggesting more coherent
magnetization dynamics in this short time nonequilibrium limit than near
equilibrium
Study on the effect of metallurgical waste on the water resistance of magnesium oxysulfate cement (MOS) coatings
In this paper, in order to achieve the resource utilization of metallurgical waste, this article studied the water resistance of magnesium oxysulfate cement coating using blast furnace slag powder and iron tailings powder as fillers, and characterized its hydration products using X-ray diffraction (XRD) and scanning electron microscopy (SEM). The results indicate that an appropriate amount of slag powder and iron tailings powder can make the internal structure of the coating more dense, effectively improve the softening coefficient, and enhance water resistance
Study on the effect of metallurgical waste on the cracking resistance of magnesium oxysulfate cement coatings
In this paper, in order to achieve the resource utilization of metallurgical industry waste, the cracking resistance of magnesium oxysulfate cement coatings using granulated blast furnace slag powder and iron tailings powder as fillers was studied, x-ray Diffraction (XRD) and scanning electron microscope (SEM) were used to characterize the hydration products. The results show that an appropriate amount of slag powder and iron tailings powder can make the internal structure of the coating more compact, the surface smooth and effectively reduce the generation of cracks
Determination of the magnetic anisotropy axes of single-molecule magnets
Simple methods are presented allowing the determination of the magnetic
anisotropy axes of a crystal of a single-molecule magnet (SMM). These methods
are used to determine an upper bound of the easy axis tilts in a standard
Mn12-Ac crystal. The values obtained in the present study are significately
smaller than those reported in recent high frequency electron paramagnetic
resonance (HF-EPR) studies which suggest distributions of hard-axes tilts.Comment: 10 pages, 6 figure
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