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]

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 $\beta / \gamma$-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 $\gamma$'s and nuclear recoils due to neutron elastic scatterings, it was verified that the pulse shapes between $\beta / \gamma$-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 40$-$50 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.