A Point Balance Algorithm for the Spherical Code Problem

The Spherical Code (SC) problem has many important applications in such fields as physics, molecular biology, signal transmission, chemistry, engineering and mathematics. This paper presents a bilevel optimization formulation of the SC problem. Based on this formulation, the concept of balanced spherical code is introduced and a new approach, the Point Balance Algorithm (PBA), is presented to search for a 1-balanced spherical code. Since an optimal solution of the SC problem (an extremal spherical code) must be a 1-balanced spherical code, PBA can be applied easily to search for an extremal spherical code. In addition, given a certain criterion, PBA can generate efficiently an approximate optimal spherical code on a sphere in the n-dimensional space ⁿ. Some implementation issues of PBA are discussed and putative global optimal solutions of the Fekete problem in 3, 4 and 5-dimensional space are also reported. Finally, an open question about the geometry of Fekete points on the unit sphere in the 3-dimensional space is posed.     

Nanoscopic study of second-harmonic generation in organic crystals with collection-mode near-field scanning optical microscopy

Collection-mode near-field scanning optical microscopy (NSOM) is used to map nanoscopic second-harmonic generation (SHG) in N -(4-nitrophenyl)- (L) -prolinol crystals. A spatial resolution of 98 nm is achieved. Near-field polarization-dependent SHG measurement is performed, and a local effective SHG susceptibility of 224+/-18 pm/V is obtained.     

Analysis of planar waveguides with index discontinuity or index slope discontinuity

In this paper, we propose a novel analytic transfer matrix method (ATMM) to the analysis of planar waveguides with index discontinuity or index slope discontinuity, for the cases when the conventional WKB method is no longer valid. We also analyze the physical insight of the approximations in WKB theory, and according to our research, the phase shift at the turning point is not /2, but exactly . Test calculations are done for an index profile with a known solution and the comparison shows that our method gives extremely accurate propagation constant.     

A note on Hamilton sequences for extremal Beltrami coefficients

F. P. Gardiner gave a sufficient condition for a sequence to be a Hamilton sequence for an extremal Beltrami coefficient. In this note, we shall consider the converse problem, proving that the condition is not necessary.

     

Superconducting gap anisotropy in Nd1.85Ce0.15CuO4: results from photoemission

We have performed angle resolved photoelectron spectroscopy on the electron doped cuprate superconductor Nd1.85Ce0.15CuO4. A comparison of the leading edge midpoints between the superconducting and normal states reveals a small, but finite shift of 1.5-2 meV near the ( pi,0) position, but no observable shift along the zone diagonal near ( pi/2, pi/2). This is interpreted as evidence for an anisotropic superconducting gap in the electron doped materials, which is consistent with the presence of d-wave superconducting order in this cuprate superconductor.     

Motional effect in surface sum-frequency vibrational spectroscopy

Fast orientational motion of molecules at a surface can affect the sum-frequency vibrational spectra of the surface. Calculation shows that the effect is significant if the molecular orientation varies over a broad range within the vibrational relaxation time. The stretch vibration of the free OH bonds at the vapor/water interface is used to illustrate the importance of the effect.     

Long-Lived Luminescent Re(I) Complexes Containing cis-Carbonyl and Bidentate Phosphine Ligands

Highly emissive Re(I) complexes, hydrophobic cis-Re(CO)₂(c-dppene)(dpphen) and water-soluble cis-Re(CO)₂(c-dppene)(SO₃-dpphen) with a negative charge, were synthesized [where c-dppene is cis-(bis(diphenylphosphino)ethylene, dpphen is 4,7-diphenyl-1,10-phenanthroline, and SO₃-dpphen is its disulfonate derivative]. These Re(I) complexes have significantly higher molar absorption in the 350- to 490-nm region compared to their tricarbonyl Re(I) counterparts and their emission spectra are similar to those of Ru(II) polypyridyl complexes. The luminescence lifetimes of these Re(I) complexes approach 10 s in the absence of oxygen in both aqueous and less polar solvents. The complexes have limiting anisotropy values exceeding 0.3. As both ligands, the diimine and the bidentate phosphine, can be modified by adding different substituents, it should be possible to make cis-Re(CO)₂(diimine)(P-P) derivatives which are capable of labeling biomacromolecules for biochemical and biophysical studies.     

Delayed-focus pulses optimized using simulated annealing

Unlike prefocused pulses and shaped pulses based on the linear response theory, delayed-focus pulses (X.-L. Wu et al., 1991, Magn. Reson. Med. 20, 165--170) produce a selective spin echo after a predefined short delay without using a pi refocusing pulse. In this paper, a series of delayed-focus pulses of different flip angles are proposed based on optimization using Fourier series representation and simulated annealing. The resistance of these delayed-focus pulses to T(2) relaxation is also demonstrated using numerical simulation of Bloch equations.     

On the extremality of quasiconformal mappings and quasiconformal deformations

Given a family of quasiconformal deformations such that has a uniform bound , the solution of the Löwner-type differential equation

is an -quasiconformal mapping. An open question is to determine, for each fixed , whether the extremality of is equivalent to that of . The note gives this a negative approach in both directions.

     

Dirac Quantization in Kantowski—Sachs Spacetime

By forming the square root of the Wheeler-DeWitt equation and applying itto a minisuperspace composed of a Kantowski-Sachs universe, we derive acosmological wave function with conserved current and positive-definiteprobability density.