Symmetric Modifications Research Articles

Extended measurements of the ν2 band of CD3 and the determination of the vibrational potential function for methyl

Measurements in the ν2 (umbrella) vibrational spectrum of CD3 are reported. The data include transitions up to and including the v2=4–3 bands and cover a wider range of rotational excitation than has been previously reported [Frye, Sears, and Leitner, J. Chem. Phys. 88, 5300 (1988)]. The spectroscopic data have been combined with all previously published data pertaining to the methyl radical and an estimate of the vibrational potential function for the species has been made. From this, we predict the positions of so far unobserved vibrational bands for all the various symmetric isotopic modifications and also extract an equilibrium structure. Preliminary results on the population distribution of v2 levels produced on the photofragmentation of acetone-d6 at 193 nm are reported and it is suggested that the methyl v3=1 and v3=0 levels may be produced in this reaction with a population inversion.

AC 0-collocation-like method for two-point boundary value problems

A method of a collocation type based onC0-piecewise polynomial spaces is presented for a two-point boundary value problem of the second order. The method has an optimal order of convergence under smoothness requirements on the exact solution which are weaker than forC1-collocation methods. If the differential operator is symmetric, a modification of this method leads to a symmetric system of linear equations. It is shown that if the collocation solution is a piecewise polynomial of degree not greater thanr, the method is stable and convergent with orderhr inH1-norm. A similar symmetric modification forC0-colloction-finite element method [7] is also obtained. Superconvergence at the nodes is established.

Accurate Petrov‐Galerkin methods for transient convective diffusion problems

AbstractThe Petrov‐Galerkin method is applied to transient convective diffusion problems with convection dominance. Weighting functions are used which differ from the shape functions by both symmetric and non‐symmetric modifications. It is proved that the symmetric modifications largely influence the accuracy. By a one‐dimensional and a two‐dimensional example it is shown how to choose this modification to maximize accuracy.

Infrared polarized spectra of single crystal of chloropentamethylbenzene above and below the temperature of transition

The i.r. spectra of polycrystalline sample and of single crystals of CPMB having ac and ab as predominant faces have been investigated above and below the temperature of transition to get information concerning the symmetrical modifications on the molecule or on the crystalline cell. Bands assigned to the stretching and bending vibrations CCH 3 groups become broader and less intense. Bands assigned to the rocking vibrations remain relatively unaffected. The general splitting of bands observed at low temperature is due to crystal field effect. Our results indicate a decrease of molecular symmetry through the phase transition I and III.

Influence of singularities on perturbation theory for the effective Hamiltonian

The energy-independent effective Hamiltonian $\mathcal{H}(z)$ is considered as an analytic function of the coupling parameter $z$. It is shown that a point ${z}_{b}$ is not a singularity of $\mathcal{H}(z)$ unless the energy of some state that is selected for representation in the model space (${L}_{P}$) coincides, at $z={z}_{b}$, with the energy of a state that is excluded from representation in ${L}_{P}$. This result establishes the correctness of previous conjectures by Schucan and Weidenm\uller, and implies that perturbation theory for $\mathcal{H}(z)$ will generally have a larger radius of convergence than perturbation theory for the individual energies. For the case of a cut (intruder-state cut) joining an isolated pair of branch points close to the real axis, the singular behavior of $\mathcal{H}(z)$ is examined in detail. The residue of the cut is expressed in terms of quantities that can be calculated by diagonalization of a real, symmetric modification (minimal smoothing) of the Hamiltonian matrix. A formula is given for the contribution of an intruder-state cut to the error incurred by $n\mathrm{th}$ order perturbation theory for the physical quantity $\mathcal{H}(1)$. Consideration of a numerical example shows that if the values of sufficiently high orders of perturbation theory are known, the residues of intruder-state cuts may be evaluated. This allows estimation of the errors that intruder-state cuts produce in perturbation theory summed to finite order, and yields a criterion for the optimal truncation of divergent perturbation series.NUCLEAR STRUCTURE Effective Hamiltonian for $^{18}O{J}^{\ensuremath{\pi}}={0}^{+}$; estimated errors of perturbation theory produced by intruder state.

Conditions favouring the emergence of host range variants during passage of a proxvirus.

SUMMARY The Rivers ‘revived’ strain of vaccinia virus (cvi), a population of virus particles produced in chorioallantoic membrane of eggs, is shown to be physically heterogeneous. Some cloned subpopulations isolated on RK cells interfere and others complement each other in mixed infection. Some are physically different, as shown by sedimentation velocity spectra, but none produce plaques on L cells. Yet pulse-inoculation (by centrifuging) at an input multiplicity of 20 virus particles per L cell produces progeny that make more plaques on L cells than on the RK cells from which they were selected. High multiplicity is essential to this process and the frequency of emerging L+ virus particles may be increased up to 400-fold if the recipient L cells are starved prior to inoculation. One cloned L+RK− virus, isolated from these progeny, is suppressed in plaque formation by antiserum to the original cvi virus but it no longer produces the characteristic necrotic lesions in rabbit skin. The sudden emergence of these large numbers of host-range variants in the absence of a mutagenic agent is similar in some respects to ‘symmetrical host-controlled modification’ observed with certain bacterial viruses.