A unified approach to the effects of symmetry and periodicity on boundary-value problems

A generalized approach to the effects of symmetry and periodicity on boundary-value problems is presented, especially as it pertains to the guiding structures encountered in electromagnetics. Several examples of structures and their dispersion behavior are given, and the theory predicts well that other authors claim.     

A unified approach to attractor reconstruction

In the analysis of complex, nonlinear time series, scientists in a variety of disciplines have relied on a time delayed embedding of their data, i.e., attractor reconstruction. The process has focused primarily on intuitive, heuristic, and empirical arguments for selection of the key embedding parameters, delay and embedding dimension. This approach has left several longstanding, but common problems unresolved in which the standard approaches produce inferior results or give no guidance at all. We view the current reconstruction process as unnecessarily broken into separate problems. We propose an alternative approach that views the problem of choosing all embedding parameters as being one and the same problem addressable using a single statistical test formulated directly from the reconstruction theorems. This allows for varying time delays appropriate to the data and simultaneously helps decide on embedding dimension. A second new statistic, undersampling, acts as a check against overly long time delays and overly large embedding dimension. Our approach is more flexible than those currently used, but is more directly connected with the mathematical requirements of embedding. In addition, the statistics developed guide the user by allowing optimization and warning when embedding parameters are chosen beyond what the data can support. We demonstrate our approach on uni- and multivariate data, data possessing multiple time scales, and chaotic data. This unified approach resolves all the main issues in attractor reconstruction.     

On the time to extinction from quasi-stationarity: A unified approach

This note provides a unified approach to the distribution of the time to extinction from quasi-stationarity for general Markov chains evolving both in discrete and in continuous time. Our results generalize a number of similar derivations which were established ad hoc for a variety of stochastic epidemic models. On the other hand, the obtained results unify the infinite irreducible case and the finite (reducible or irreducible) case which are typically presented under separate formulations in the literature for Markov chains.     

Optical measurement of atmospheric pollutants: accomplishments and problems

Two applications of optical methods to the measurement of atmospheric pollutants are discussed. The combination of Fourier Transform Spectrometer and long path infrared absorption cell has been used to measure many compounds simultaneously in polluted air samples at Pasadena, California. The detection limit for most pollutants has been about 10^–8 atmospheres partial pressure. A 4 km cell is being developed for use in 1976 with the objective of further lowering the detection limit by a factor of ten. Nondispersive spectral correlation techniques are also being applied in the ambient air. In this case a selected pollutant is measured by passing the infrared radiation from a thermal source through a train of passive components, including the atmospheric sample cell and a gas-filled filter cell. These spectral correlation methods show great sensitivity and selectivity and have a promising future for further application.     

A new approach to giant resonances in nuclei

The absorptive part of the response function for-transitions between the ground state and excited states of even-even nuclei is calculated using correlation function techniques. The absorptive part of the response function is expressed in terms of symmetrized correlation functions; these, in turn, are obtained as matrix elements of a properly defined resolvent operator using a generalization of Feshbach's projection operator technique. It is shown how the coupling of RPA states to the one-particle continuum and to more complicated excitations can be treated.     

Constrained systems: A unified geometric approach

A general geometric framework is devised in order to contain the presymplectic and Lagrangian formalisms as particular cases. We call these objectsconstrained dynamical systems, since their dynamics usually lead toconstraints. Their most elementary properties are studied, and several related structures, especially morphisms, are defined. In particular, a stabilization algorithm is performed. As a byproduct, the dynamics and constraints of the Lagrangian formalism (with the second-order condition) are intrinsically obtained.     

The box approach to resonances

The box approach to radial equation resonances is shown to lead to simple numerical calculations if R(E) is studied instead of E(R). Results for a test calculation differ slightly from those of some other workers.     

Shell model approach to intermediate resonances

Migdal's theory of nuclear structure is extended to treat the low energy intermediate scattering resonances. It is shown that the position and width of resonances can be calculated using the same effective force as for the calculation of response functions and nuclear moments.     

Non-coherent scattering in subordinate lines: A unified approach to redistribution functions

Within the scope of the quantum-mechanical result of Omont, Smith and Cooper, we have derived a laboratory-frame redistribution function for the scattering of radiation in subordinate lines where both atomic levels are radiatively broadened. This new function, denoted as R_V(x′, n′; x, n), is the correct counterpart of Hummer's redistribution function R_IV. Moreover, it follows from the formalism developed here that R_V contains all known redistributions R_i(i=I, II, III, IV) as special cases and we may therefore speak in some sense of a unified redistribution function. A simple method has been tested for the evaluation of R_V and our numerical examinations of the properties of R_V served, among others, as an independent verification of the results obtained by Reichel and Vardavas for R_III and R_IV. Finally, it is shown in the conclusion to this paper that the function R_V, discussed here, can be applied not only to the radiative redistribution, but also to a more general case of a collisional redistribution in subordinate lines.     

A “unified” phenomenological approach to the non-leptonic decays of hyperons

In analogy with the pole model for the non-leptonic hyperon decays, a new model is proposed, and which gives satisfactory results for all the non-leptonic decays of the hyperons (B→B′π,B→B′γ andB→B′πγ).     

Generalized entropies of chaotic maps and flows: A unified approach

A thermodynamic study of nonlinear dynamical systems, based on the orbits' return times to the elements of a generating partition, is proposed. Its grand canonical nature makes it suitable for application to both maps and flows, including autonomous ones. When specialized to the evaluation of the generalized entropies K(q), this technique reproduces a well-known formula for the metric entropy K(1) and clarifies the relationship between a flow and the associated Poincare maps, beyond the straightforward case of periodically forced nonautonomous systems. Numerical estimates of the topological and metric entropy are presented for the Lorenz and Rossler systems. The analysis has been carried out exclusively by embedding scalar time series, ignoring any further knowledge about the systems, in order to illustrate its usefulness for experimental signals as well. Approximations to the generating partitions have been constructed by locating the unstable periodic orbits of the systems up to order 9. The results agree with independent estimates obtained from suitable averages of the local expansion rates along the unstable manifolds. (c) 1997 American Institute of Physics.     

The unified approach to spectral analysis

We develop a new, unified, method to construct a closed (selfad-joint in ²) extension of a partial differential operator in all the spaces ^p ( ⁿ ) 1p. Our method is not only an unified approach but it is also very efficient. We obtain very weak conditions on the potentials.     

Top-down approach to unified supergravity models

We introduce a new approach for studying unified supergravity models. In this approach all the parameters of the grand unified theory (GUT) are fixed by imposing the corresponding number of low energy observables. This determines the remaining particle spectrum whose dependence on the low energy observables can now be investigated. We also include some SUSY threshold corrections that have previously been neglected. In particular the SUSY threshold corrections to the fermion masses can have a significant impact on the Yukawa coupling unification.