950 research outputs found
On Convergence of Hermite-Fejér Interpolation Polynomials
AbstractHermite-Fejér interpolation operators based on the zeros of Jacobi polynomials, in general, are not uniformly convergent for all f ϵ C[−1, 1]. In this work we investigate weighted approximation by such operators with Jacobi weight functions. A necessary and sufficient condition for the weight function is given such that these interpolation polynomials converge in the weighted maximum norm for all f ϵ C[−1, 1]
Spatially Resolved X-Ray Study of Supernova Remnant G306.3-0.9 with Unusually High Calcium Abundance
The new chiral ligand 3-ethoxy-4-E(1R,2SS)-(2-hydroxy-1,2-diphenylethyl)amino -3-cyclobutene-1 ,2-dione
The asymmetric unit of C20H19NO4 contains two molecules with slightly different conformations, In the crystal,the molecules are linked by O-H ... O and N-H ... O hydrogen bonds [O ... O 2.764 (3) and 2.811 (3) Angstrom; N ... O 2.907 (3) and 3.968 (3) Angstrom] to form a two-dimensional network
Second Harmonic Generation for a Dilute Suspension of Coated Particles
We derive an expression for the effective second-harmonic coefficient of a
dilute suspension of coated spherical particles. It is assumed that the coating
material, but not the core or the host, has a nonlinear susceptibility for
second-harmonic generation (SHG). The resulting compact expression shows the
various factors affecting the effective SHG coefficient. The effective SHG per
unit volume of nonlinear coating material is found to be greatly enhanced at
certain frequencies, corresponding to the surface plasmon resonance of the
coated particles. Similar expression is also derived for a dilute suspension of
coated discs. For coating materials with third-harmonic (THG) coefficient,
results for the effective THG coefficients are given for the cases of coated
particles and coated discs.Comment: 11 pages, 3 figures; accepted for publication in Phys. Rev.
Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
In this paper we provide a sufficient condition, in terms of only one of the
nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity
vector field, for the global regularity of strong solutions to the
three-dimensional Navier-Stokes equations in the whole space, as well as for
the case of periodic boundary conditions
Pulse Shape Discrimination Techniques in Scintillating CsI(Tl) Crystals
There are recent interests with CsI(Tl) scintillating crystals for Dark
Matter experiments. The key merit is the capability to differentiate nuclear
recoil (nr) signatures from the background -events due to
ambient radioactivity on the basis of their different pulse shapes. One of the
major experimental challenges is to perform such pulse shape analysis in the
statistics-limited domain where the light output is close to the detection
threshold. Using data derived from measurements with low energy 's and
nuclear recoils due to neutron elastic scatterings, it was verified that the
pulse shapes between -events are different. Several methods of
pulse shape discrimination are studied, and their relative merits are compared.
Full digitization of the pulse shapes is crucial to achieve good
discrimination. Advanced software techniques with mean time, neural network and
likelihood ratios give rise to satisfactory performance, and are superior to
the conventional Double Charge method commonly applied at higher energies.
Pulse shape discrimination becomes effective starting at a light yield of about
20 photo-electrons. This corresponds to a detection threshold of about 5 keV
electron-equivalence energy, or 4050 keV recoil kinetic energy, in realistic
experiments.Comment: 20 pages, 7 figure
Measurement of the Intrinsic Radiopurity of Cs-137/U-235/U-238/Th-232 in CsI(Tl) Crystal Scintillators
The inorganic crystal scintillator CsI(Tl) has been used for low energy
neutrino and Dark Matter experiments, where the intrinsic radiopurity is an
issue of major importance. Low-background data were taken with a CsI(Tl)
crystal array at the Kuo-Sheng Reactor Neutrino Laboratory. The pulse shape
discrimination capabilities of the crystal, as well as the temporal and spatial
correlations of the events, provide powerful means of measuring the intrinsic
radiopurity of Cs-137 as well as the U-235, U-238 and Th-232 series. The event
selection algorithms are described, with which the decay half-lives of Po-218,
Po-214, Rn-220, Po-216 and Po-212 were derived. The measurements of the
contamination levels, their concentration gradients with the crystal growth
axis, and the uniformity among different crystal samples, are reported. The
radiopurity in the U-238 and Th-232 series are comparable to those of the best
reported in other crystal scintillators. Significant improvements in
measurement sensitivities were achieved, similar to those from dedicated
massive liquid scintillator detector. This analysis also provides in situ
measurements of the detector performance parameters, such as spatial
resolution, quenching factors, and data acquisition dead time.Comment: 28 pages, 12 figure
Studies of Prototype CsI(Tl) Crystal Scintillators for Low-Energy Neutrino Experiments
Crystal scintillators provide potential merits for the pursuit of low-energy
low-background experiments. A CsI(Tl) scintillating crystal detector is being
constructed to study low-energy neutrino physics at a nuclear reactor, while
projects are underway to adopt this technique for dark matter searches. The
choice of the geometrical parameters of the crystal modules, as well as the
optimization of the read-out scheme, are the results of an R&D program.
Crystals with 40 cm in length were developed. The detector requirements and the
achieved performance of the prototypes are presented. Future prospects for this
technique are discussed.Comment: 32 pages, 14 figure
The Casimir force and the quantum theory of lossy optical cavities
We present a new derivation of the Casimir force between two parallel plane
mirrors at zero temperature. The two mirrors and the cavity they enclose are
treated as quantum optical networks. They are in general lossy and
characterized by frequency dependent reflection amplitudes. The additional
fluctuations accompanying losses are deduced from expressions of the optical
theorem. A general proof is given for the theorem relating the spectral density
inside the cavity to the reflection amplitudes seen by the inner fields. This
density determines the vacuum radiation pressure and, therefore, the Casimir
force. The force is obtained as an integral over the real frequencies,
including the contribution of evanescent waves besides that of ordinary waves,
and, then, as an integral over imaginary frequencies. The demonstration relies
only on general properties obeyed by real mirrors which also enforce general
constraints for the variation of the Casimir force.Comment: 18 pages, 6 figures, minor amendment
Surface-impedance approach solves problems with the thermal Casimir force between real metals
The surface impedance approach to the description of the thermal Casimir
effect in the case of real metals is elaborated starting from the free energy
of oscillators. The Lifshitz formula expressed in terms of the dielectric
permittivity depending only on frequency is shown to be inapplicable in the
frequency region where a real current may arise leading to Joule heating of the
metal. The standard concept of a fluctuating electromagnetic field on such
frequencies meets difficulties when used as a model for the zero-point
oscillations or thermal photons in the thermal equilibrium inside metals.
Instead, the surface impedance permits not to consider the electromagnetic
oscillations inside the metal but taking the realistic material properties into
account by means of the effective boundary condition. An independent derivation
of the Lifshitz-type formulas for the Casimir free energy and force between two
metal plates is presented within the impedance approach. It is shown that they
are free of the contradictions with thermodynamics which are specific to the
usual Lifshitz formula for dielectrics in combination with the Drude model. We
demonstrate that in the impedance approach the zero-frequency contribution is
uniquely fixed by the form of impedance function and does not need any of the
ad hoc prescriptions intensively discussed in the recent literature. As an
example, the computations of the Casimir free energy between two gold plates
are performed at different separations and temperatures. It is argued that the
surface impedance approach lays a reliable framework for the future
measurements of the thermal Casimir force.Comment: 21 pages, 3 figures, to appear in Phys. Rev.
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