Comments on ''Lower-bound procedure for energy eigenvalues by the partitioning technique.''
Criticism of Choi-Smith extension of Lowdin lower bounds formalism to multidimensional reference manifold
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Criticism of Choi-Smith extension of Lowdin lower bounds formalism to multidimensional reference manifold
Quantum mechanical perturbation theory calculation of upper and lower bounds of energy eigenvalues using partitioning methods
Schroedinger equation eigenvalues lower bounds, noting relationship between intermediate Hamiltonians method and partitioning technique
This paper determines the information required about system recovery to compute the reliability of a class of reconfigurable systems. Upper and lower bounds are derived for these systems. The class consists of those systems that satisfy five assumptions: the components fail independently at a low constant rate, fault occurrence and system reconfiguration are independent processes, the reliability model is semi-Markov, the recovery functions which describe system configuration have small means and variances, and the system is well designed. The bounds are easy to compute, and examples are included.
The traditional approach used in the design of stability critical thin-walled circular cylin- ders, is to reduce unconservative buckling load predictions with an empirical knockdown factor. An alternative analysis-based approach to determine a lower bound buckling load for cylinders under axial compression is to use a lateral perturbation load to create an initial imperfection and determine the buckling load while that load is applied. This paper describes a preliminary e ort to develop a test capability to verify this approach. Results from tests of three aluminum alloy cylinders are described and compared to nite element predictions.
Calculations for the ground states of H, He, and Be, conducted by Steiner and Sykes (1972), show that the inclusion of a very small number of cusp functions can lead to a substantial enhancement of the quality of the Gaussian basis used in molecular wavefunction computations. The properties of the cusped-Gaussian basis are investigated by a calculation of lower bounds concerning the ground state energy of the hydrogen atom.
Dynamic polarizability at imaginary frequencies, deriving upper and lower variational bounds with functionals containing trial functions
Signals of opportunity (SoOp) reflectometry (SoOp-R) is a maturing field for geophysical remote sensing as evidenced by the growing number of airborne and spaceborne experiments. As this approach receives more attention, it is worth analyzing SoOp-R’s capabilities to retrieve subsurface soil moisture (SM) by leveraging communication and navigation satellite transmitters. In this research, the CRLB is used to identify the effects of variable SoOp-R parameters on the best achievable estimation error for root-zone soil moisture (RZSM). This study investigates the use of multiple frequency, polarization, and incidence angle measurement configurations on a two-layered dielectric profile. The results also detail the effects of variable SM conditions on the capability of SoOp-R systems to predict subsurface SM. The most prevalent observation is the importance of using at least two frequencies to limit uncertainties from subsurface SM estimates. If at least two frequencies are used, the CRLB of a profile is retrievable within the root-zone depending on the surface SM content as well as the number of independent measurements of the profile. For a depth of 30 cm, it is observed that a CRLB corresponding to 4% RZSM estimation accuracy is achievable with as few as 2 dual-frequency-based SoOp-R measurements. For this depth, increasing number of measurements provided by polarization and incidence angle allow for sensing of increasingly wet SM profile structures. This study, overall, details a methodology by which SoOp-R receiver system can be designed to achieve a desired CRLB using a trade-off study between the available measurements and SM profile.
Large deflection theory for determining the buckling pressure of spherical shells
Hydrostatic buckling pressure calculations for spherical shells
Low bounds to energy eigenvalues in quantum theory problems by partitioning technique for positive perturbation
There are no author-identified significant results in this report.
Astronomical observations of SN1987A, such as the light curve, spectral intensities of lines, the X-ray emissions, etc., constrain the lifetime for the decay of a heavy neutrino 1 MeV less than or equivalent to m sub nu H less than or equal to 50 MeV through nu sub H yields nu sub 1+e(+)+e(-) exceeds 4 x 10 to the 15th exp(-m sub nuH/5MeV) seconds. Otherwise. resulting ionization energy deposits and stronger X-ray emission would have been observed. This coupled with traditional cosmological considerations argues that the lifetime of tau-neutrinos probably exceeds the age of the universe. This in turn would imply the standard cosmological mass bound does apply to nu sub tau, namely m sub nu sub tau less than or equivalent to 100 h squared eV (where h is the Hubble constant in units of 100 km/sec/mpc). The only significant loophole for these latter arguments would be if nu sub tau primarily decays rapidly into particles having very weak interactions.
In this paper, we derive new Cramer-Rao bounds (CRBs) for the estimation of phase from a block of random M-PSK (M=2,4,8) symbols where the phase to be estimated is a random variable. Existing bounds for 2 and 4-PSK which model the phase as non-random are extended to obtain a new 8-PSK CRB. The new random phase bounds are compared to the new 8-PSK and existing 2,4-PSK bounds which model the phase as non-random. We see that the random phase CRBs more accurately model the behavior if the phase, as normally happens, is suppose to be constrained to the interval [-pi/M,pi/M).
Solar wind electrons, especially under conditions of relatively low speed flow, often can be represented as two bi-Maxwellian components, a cooler more dense core (denoted by the subscript c) and a hotter more tenuous halo.
The structured singular value, U, is an important linear algebra tool to study a class of matrix perturbation problems. It is useful for analyzing the robustness of stability and performance of uncertain, (nominally) linear systems. Computation of (M) is difficult, and usually, upper and lower bounds are all that can be reliably computed. Upper bounds give conservative estimates of the sizes of allowable perturbations. The maximum singular value of a matrix M is an upper bound for (M). As an upper bound, it can be improved by finding a transformations to the data (i.e. M) which do not change the structured singular value, but do reduce the maximum singular value. Typically, upper bound algorithms involve searches over sets of transformations to yield the tightest bound. Lower bound algorithms are intelligent searches for minimum-norm solutions to multivariable polynomial equations, and are based on various optimality conditions that hold at the global (and, unfortunately, some local) minima. The current methods to compute both of these types of bounds are reviewed. Theoretical justification and extensive numerical experience with the various algorithms are covered.
Measurements of neutral nitrogen density from mass spectrometers on five satellites (AE-B, Ogo 6, San Marco 3, Aeros A, and AE-C) and neutral temperatures inferred from incoherent scatter measurements at four ground stations are combined to produce a model of thermospheric neutral temperatures and nitrogen densities similar to the Ogo 6 empirical model (Hedin et al., 1974). This global model is designated MSIS (mass spectrometer and incoherent scatter). The global average temperature, the annual temperature variation, lower bound density, and lower bound temperature are discussed. The data set covers the time period from the end of 1965 to mid-1975 and also a wide range of solar activities. Diurnal and semidiurnal variations in lower bound density and temperature are considered, as is magnetic activity.
Both upper and lower bounds are established for state covariance matrices under parameter perturbations of the plant. The motivation for this study lies in the fact that many robustness properties of linear systems are given explicitly in terms of the state covariance matrix. Moreover, there exists a theory for control by covariance assignment. The results provide robustness properties of these covariance controllers.