Data compression - A lower bound for epsilon entropy
Lower bound for asymptotic behavior of epsilon entropy of Gaussian stochastic process on unit interval under square-error fidelity criterion - data compression
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Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately
The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.
Huang, Zhaofeng↗
Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately
The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.
Huang, Zhaofeng↗
Lower Bounds for the Energy Levels of Anharmonic Oscillators
The lower‐bounds method presented by Löwdin in the preceding paper has been applied to oscillators perturbed by third‐ and fourth‐power terms in the potential‐energy expression. For favorable cases agreement between upper and lower bounds is easily carried to many more figures than are likely to be physically significant. In many cases the lower bounds agreed more closely to the true eigenvalue than did the corresponding upper bounds. For a given basis set, this method gives closer bounds than that of Bazley and Fox, except for energy levels too high to be satisfactorily treated in the given basis. The only disadvantage found was that for close bounds double precision proved necessary, indicating more than ordinary loss of computational accuracy.
Reid, Charles E.↗
Studies in perturbation theory. x - lower bounds to energy eigenvalues in perturbation- theory ground state.
Lower bounds to energy eigenvalues in perturbation theory ground state, studying lower bounds to ground state energies of helium-like ions
ATOMIC EXCITATION↗
The Effects of Geometric and Loading Imperfections on the Response and Lower-Bound Buckling Load of a Compression-Loaded Cylindrical Shell
Results from a numerical study of the buckling response of a thin-walled compressionloaded isotropic circular cylindrical shell with initial geometric and loading imperfections are used to determine a lower bound buckling load estimate suitable for preliminary design. The lower bound prediction techniques presented herein include an imperfection caused by a lateral perturbation load, an imperfection in the shape of a single stress-free dimple (similar to the lateral pertubation imperfection), and a distributed load imperfection that induces a nonuniform load in the shell. The ABAQUS finite element code is used for the analyses. Responses of the cylinders for selected imperfection amplitudes and imperfection types are considered, and the effect of each imperfection is compared to the response of a geometrically perfect cylinder. The results indicate that compression-loaded shells subjected to a lateral perturbation load or a single dimple imperfection, and a nonuniform load imperfection, exhibit similar buckling behavior and lower bound trends and the predicted lower bounds are much less conservative than the corresponding design recommendation NASA SP-8007 for the design of buckling-critical shells. In addition, the lateral perturbation technique and the distributed load imperfection produce response characteristics that are physically meaningful and can be validated via laboratory testing.
Kriegesmann, Benedikt↗
A lower bound procedure for energy eigenvalues.
Lower bound procedure for energy eigenvalues and helium ground state calculations
HELIUM ATOM↗
A lower bound on the minimum Euclidean distance of trellis-coded modulation schemes
A lower bound on the minimum free Euclidean distance of trellis-coded modulation (TCM) is derived that guarantees the existence of good TCM codes of any complexity. The bound is used to compare trellis codes combined with phase-shift keying, pulse amplitude modulation, and quadrature amplitude-shift keying modulation. This random coding bound is the first lower bound on the free distance of trellis codes, is tighter than any upper bound for large constraint lengths, and predicts the asymptotic performance of TCM when the complexity of the code becomes large. The bound can be used with any code rate and any modulation scheme and shows that the free distance increases linearly with the constraint length for large values of the constraint length.
Rouanne, Marc↗
Comparison of Methods to Predict Lower Bound Buckling Loads of Cylinders Under Axial Compression
Results from a numerical study of the buckling response of two different orthogrid stiffened circular cylindrical shells with initial imperfections and subjected to axial compression are used to compare three different lower bound buckling load prediction techniques. These lower bound prediction techniques assume different imperfection types and include an imperfection based on a mode shape from an eigenvalue analysis, an imperfection caused by a lateral perturbation load, and an imperfection in the shape of a single stress-free dimple. The STAGS finite element code is used for the analyses. Responses of the cylinders for ranges of imperfection amplitudes are considered, and the effect of each imperfection is compared to the response of a geometrically perfect cylinder. Similar behavior was observed for shells that include a lateral perturbation load and a single dimple imperfection, and the results indicate that the predicted lower bounds are much less conservative than the corresponding results for the cylinders with the mode shape imperfection considered herein. In addition, the lateral perturbation technique and the single dimple imperfection produce response characteristics that are physically meaningful and can be validated via testing.
Haynie, Waddy T.↗
A lower bound for the decoder error probability of the linear MDS code
A lower bound for the decoder error probability (P sub E (u)) of a linear maximum distance separable (MDS) code is derived by counting the dominant types of decoding words around code words. It is shown that the lower bound derived is similar in form, and close numerically, to the upper bound derived.
Cheung, K.-M.↗
Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited States
The bracketing theorem in the partitioning technique for solving the Schrödinger equation may be used in principle to determine upper and lower bounds to energy eigenvalues. Practical lower bounds of any accuracy desired may be evaluated by utilizing the properties of ``inner projections'' on finite manifolds in the Hilbert space. The method is here applied to the ground state and excited states of a Hamiltonian H=H(sub 0)+V having a positive definite perturbation V. Even if inspiration is derived from the method of intermediate Hamiltonians, the final results are of bracketing type and independent of this approach. The method is numerically illustrated in some accompanying papers.
Loewdin, Per-Olov↗
Primary-backup protocols: Lower bounds and optimal implementations
A formal specification of primary-backup is presented. We then prove lower bounds on the degree of replication, failover time, and worst-case response time to client requests assuming different failure models. Finally, we outline primary-backup protocols and indicate which of our lower bounds are tight.
Budhiraja, Navin↗
The variational method 4. Lower bounds for the energy
Variational method and lower bound calculations
Epstein, S. T.↗
LOWER BOUNDS FOR THE BUCKLING PRESSURE OF SPHERICAL SHELLS.
Lower bounds of buckling pressure of spherical shells
PRESSURE↗
Lower bounds to eigenvalues of the Schroedinger equation. I.
Optimum lower bounds to excited states of Hamiltonian having known set of eigenfunctions
Wilson, T. M.↗
Lower bounds to eigenvalues of the Schroedinger equation. II.
Lower bounds of low lying levels of Li ion and helium calculated using partitioning technique with multivalued bracketing function
Reid, C. E.↗
Variational lower bounds on electron hydrogen S-wave phase shifts.
Variational bound method applied to calculation of lower bounds on S-wave phase shifts for scattering of electrons by hydrogen atoms
PHASE SHIFT↗
Lower-bound procedure for energy eigenvalues by the partitioning technique.
Lower bound procedure in quantum mechanical energy equation eigenvalue problem by partitioning and bracketing Hilbert space
PARTITION FUNCTION↗