Application of localized molecular orbitals to the solution of semiempirical self-consistent field equations

When conventional matrix algebra is used to solve the semiempirical self-consistent field equations for large systems, the time required rises as the third power of the size of the system. A consequence of this is that self-consistent calculations of large systems such as enzymes are impractical. By using localized molecular orbitals instead of matrix methods, the time required for these systems can be made almost proportional to the size of the system. In partial geometry optimizations, the time required depends only upon the size of the fragment being optimized and is almost independent of the size of the whole system. © 1996 John Wiley & Sons, Inc.     

Three-component Heck–Diels–Alder cascade processes involving alkylallenes, aryl iodides and dienophiles

A wide variety of aryl/heteroaryl iodides undergo an intermolecular Heck reaction with alkylallenes to furnish 1,3-dienes. These subsequently react in situ with various dienophiles to give Diels–Alder adducts. The chemistry has been extended to incorporate cyclisation-anion capture methodology and the stereochemistry of the products has been determined.     

Dispersion of the nonlinear refractive index in sapphire

The nonlinear refractive index, n2, of sapphire was experimentally measured in the 550-1550-nm wavelength range by use of a picosecond Z-scan technique. It was found that in this spectral region the value of n2 decreases monotonically from approximately 3.3 x 10(-16) to approximately 2.8 x 10(-16) cm2/W. An empirical expression for the wavelength dependence of the nonlinear refractive index in the 270-1550-nm range was obtained.     

p-Wave Feshbach molecules

We have produced and detected molecules using a p-wave Feshbach resonance between 40K atoms. We have measured the binding energy and lifetime for these molecules and we find that the binding energy scales approximately linearly with the magnetic field near the resonance. The lifetime of bound p-wave molecules is measured to be 1.0+/-0.1 ms and 2.3+/-0.2 ms for the ml=+/-1 and ml=0 angular momentum projections, respectively. At magnetic fields above the resonance, we detect quasibound molecules whose lifetime is set by the tunneling rate through the centrifugal barrier.     

First observation of the point spread function of optical transition radiation

We represent the first experimental observation of the point spread function (PSF) of optical transition radiation (OTR) performed at KEK-Accelerator Test Facility extraction line. We have demonstrated that the PSF vertical polarization component has a central minimum with a two lobe distribution. However, the distribution width varied significantly with wavelength. We assume that we observed a severe effect from spherical or chromatic aberrations which are not taken into account in any existing theoretical model. We believe that the result of this work will encourage theoreticians to continue developing the theory as it is important for various transition radiation applications. Nonuniform distribution of the OTR PSF creates an opportunity for developing a submicrometer transverse beam size monitor.     

Experimental validation of the differential image motion lidar concept

We have experimentally validated the concept of a differential image motion (DIM) lidar for measuring vertical profiles of the refractive-index structure characteristic C(n)(2) by building a hard-target analog of the DIM lidar and testing it against a conventional scintillometer on a 300-m horizontal path throughout a range of turbulent conditions. The test results supported the concept and confirmed that structure characteristic C(n)(2) can be accurately measured with this method.     

Julia sets and periodic kneading sequences

We construct abstract Julia sets homeomorphic to Julia sets for complex polynomials of the form f _c (z) = z ² + c, having an associated periodic kneading sequence of the form [`(a*)]{\overline{\alpha\ast}} which is not a period n-tupling. We show that there is a single simply-defined space of “itineraries” which contains homeomorphic copies of all such Julia sets in a natural combinatorial way, with dynamical properties which are derivable directly from the combinatorics. This also leads to a natural definition of abstract Julia sets even for those kneading sequences which are not realized by any polynomial f _c , with similar dynamical properties.     

Singular measures without restrictive intervals

For the transformationT:[0,1][0,1] defined byT(x)=x(1–x) with 04, a is shown to exist for whichT has no restrictive intervals, hence is sensitive to initial conditions, but for which no finite absolutely continuous invariant measure exists forT.Supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University