Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems

We study the growth with time of (the coefficients of the asymptoticexpansion of) the error in the numerical integration with linearmultistep methods of periodic solutions of systems of ordinarydifferential equations. Particular attention is devoted to reversiblesystems. It turns out that symmetric linear multistep methodscannot be recommended in spite of the fact that they mimic thereversibility of the true flow. For reversible second-ordersystems, linear multistep methods without parasitic double rootsare useful.     

Measuring the top quark mass in the eµ channel: A study

We describe a simple method to measure the top quark mass in the channel that may be useful in Run II of D? detector. The method is validated by applying it to the Run Ib eμ data.     

Level structures of 95,97Mo — A comparative study

High-spin states of ^95,97Mo (Z=42, N=53,55) nuclei have been investigated through ⁸²Se(¹⁸O, xn) reaction at Eb=60 MeV. The level scheme in ⁹⁵Mo has been observed upto ≏ 10 MeV in the present experiment. The level structure shows mainly single particle character. In ⁹⁷Mo, the ground state level sequence has been extended to ≏ 4.5 MeV while the previous information had been up to 2.4 MeV. A negative parity band built on 1437 keV (11/2⁻) excited state has been extended to 5.5 MeV. The structure seems to show a coexistence of single particle and collective modes of excitation. Properties of both the nuclei have been compared with shell model calculations using OXBASH.     

Development of a universal measure of quadrupedal forelimb-hindlimb coordination using digital motion capture and computerised analysis

Background  

Clinical spinal cord injury in domestic dogs provides a model population in which to test the efficacy of putative therapeutic interventions for human spinal cord injury. To achieve this potential a robust method of functional analysis is required so that statistical comparison of numerical data derived from treated and control animals can be achieved.     

18,18'-Dihexyl[9,9']biphenanthro[9,10-b]triphenylene: construction and consequences of a profoundly hindered aryl-aryl single bond

The title compound, 1-Hex, was synthesized by the Zr-mediated biphenylation of 4,4'-dihexyloctabromobiphenyl using (Li(THF)4)2 x Zr(biphe)3, where biphe is the 2,2'-biphenyldiyl ligand, in 5% isolated yield. Two independent X-ray diffraction analyses revealed that arene 1-Hex possesses a highly strained and hindered aryl-aryl single bond. This bond causes the phenanthro[9,10-b]triphenylene (PTP) moieties to twist (anthracene subunit dihedral, 69 degrees); the interlocked, helical, homochiral PTP moieties give rise to effective D2 symmetry. The calculated adiabatic homolytic bond dissociation energy of this strained bond is only 67 kcal/mol, but nonetheless the bond exhibits a surprisingly normal length (1.49 A); the reason is elongation only slowly releases strain. Variable temperature NMR revealed two dynamic processes: hexyl rotation (12.0 +/- 0.4 kcal/mol) and inversion of chirality (15.2 +/- 0.6 kcal/mol). DFT calculations provide rate-determining transitions states, whose energies agree with measured values, and provide insight to the mechanism of these processes. Rotation about the central bond is not involved in either observed process. Calculations demonstrate that rotation does not involve a simple torsion of the equilibrium structure, but rather a complex movement with a barrier of 49 kcal/mol from a slipped-parallel, C(2h) intermediate.