Polynomial Lie algebra methods in solving the second-harmonic generation model: some exact and approximate calculations

We compare exact and SU(2)-cluster approximate calculation schemes to determine dynamics of the second-harmonic generation model using its reformulation in terms of a polynomial Lie algebra $su_{pd}(2)$ and related spectral representations of the model evolution operator realized in algorithmic forms. It enabled us to implement computer experiments exhibiting a satisfactory accuracy of the cluster approximations in a large range of characteristic model parameters.Comment: LaTex file, 13 pages, 3 figure

Sub-collision hyperfine structure of nonlinear-optical resonance with field scanning

Some experimental evidences for methane are produced that the simple transition from frequency scanning of nonlinear-optical resonances to magnetic one may be accompanied with transition from sub-Doppler collisionally broadened structure to sub-collision hyperfine one. It is conditioned by nonlinearity of splitting of hyperfine sublevel for molecules in the adiabatically varied magnetic field and respectively breaking the analogy of magnetic and frequency scannings. The exact calculation of the resonance structure is considered for molecules with only one spin subsystem. The approximately spin-additive calculation of the structure is given for sufficiently fast rotating molecules with greater number of spin subsystems. Within the same approximation an example of hyperfine doubling in the magnetic and electric spectra of nonlinear-optical resonance is considered for fluoromethane.Comment: 56 pages, 10 figures, accepted for publication in J. Mol. Spectrosc

On metric-connection compatibility and the signature change of space-time

We discuss and investigate the problem of existence of metric-compatible linear connections for a given space-time metric which is, generally, assumed to be semi-pseudo-Riemannian. We prove that under sufficiently general conditions such connections exist iff the rank and signature of the metric are constant. On this base we analyze possible changes of the space-time signature.Comment: 18 standard LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are require

Assessing and predicting sustainability for maintaining silver collections. In Working Towards a Sustainable Past

Sustainability data for materials and electric energy consumed vary with national location. Addition ally, local climate can have a dramatic effect on the amount of energy needed to maintain cultural heritage environments. The first part of this re search focused on the energy needed to maintain a showcase at 55% RH. Measurements with a Munters dehumidifier were made in different loca tions. The variability of the showcase was removed by estimates from a developed model. The vari ability from the building fabric was removed by estimates from an Energy Plus model. The focus of the second part of this research was silver tarnish and its prevention. Performance models allowed geographic location effects to be estimated, and a simple model was developed mainly from existing data on the rate and prevention of silver tarnish. Small areas of missing data were investigated. Carbon footprint information was developed and added to the model to allow predictions of differ ent interventive, preventive and mixed scenarios