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Results for “Theorem Proving”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Establishing Fault Tolerance for a Class of Systems by Experiment

A long-standing problem in system verification is establishing fault tolerance at the ultra-high level by experiment. It is considered impossible because of system complexity and the enormous number of trials needed. This paper considers the problem for a class of digital systems that use redundancy to achieve reliability. The class is the systems that operate for a period of time without maintenance followed by a maintenance check that replaces components identified as faulty. The paper considers simulating a natural life test where a natural life test observes a number of operating periods. If the system does not fail during the test, it can be said to have a certain reliability at a certain confidence level. The approach in this paper is to make the simulated life test more efficient while maintaining realism by integrating structural arguments, information on fault occurrence, and fault injection in the lab. The major result of this paper is constructing a global fault model using the failure rate of the components and proving theorems about the model that tell how many, what kind, when, and where to inject faults. A simple example illustrates applying the theorems.

design of experiments↗
NASA NTRS1974

Elementary solutions of coupled model equations in the kinetic theory of gases

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

Kriese, J. T.↗
NASA NTRS1985

A theorem of equivalence on the methods of least-squares estimation

A theorem on the methods of least-squares estimation is stated and proved. This theorem enables the replacement of a system of correlated measurements by an equivalent system of uncorrelated measurements without a whitening process, thus simplifying the analysis while resulting in the same minimum-variance estimate.

Wu, S.-C.↗
NASA NTRS1979

Computing the Fast Fourier Transform on a vector computer

Two algorithms are presented for performing a Fast Fourier Transform on a vector computer and are compared on the Control Data Corporation STAR-100. The relative merits of the two algorithms are shown to depend upon whether only a few or many independent transforms are desired. A theorem is proved which shows that a set of independent transforms can be computed by performing a partial transformation on a single vector. The results of this theorem also apply to nonvector machines and have reduced the average time per transform by a factor of two on the CDC 6600 computer.

Korn, D. G.↗
NASA NTRS1982

Asymptotic freedom in solids - A theorem

A cusp theorem is proved that relates the zero-separation value and slope of two-particle position correlation functions in quantum many-body systems with Coulombic interactions. The theorem is independent of the particle type and symmetry of the wave function. Its proof uses only the integral form of the Schroedinger equation and the continuity and exponential decay of the wave function. It is used to derive a sum rule for the electron-gas structure factor and an exact statement about the screening of point charges. Applications to atomic-orbital-based calculations for H2 and metallic H are described.

Carlsson, A. E.↗
NASA NTRS1981

Observability for two dimensional systems

Sufficient conditions that a two-dimensional system with output is locally observable are presented. Known results depend on time derivatives of the output and the inverse function theorem. In some cases, no informaton is provided by these theories, and one must study observability by other methods. The observability problem is dualized to the controllability problem, and the deep results of Hermes on local controllability are applied to prove a theorem concerning local observability.

Hunt, L. R.↗
NASA NTRS1984

Observability for two-dimensional systems

Sufficient conditions that a two-dimensinal system with output is locally observable are presented. Known results depend on time derivatives of the output and the inverse function theorem. In some cases, no information is provided by these theories, and one must study observability by other methods. The observability problem is dualized to the controllability problems, and the deep results of Hermes on local controllability are applied to prove a theorem concerning local observability.

Hunt, L. R.↗
NASA NTRS1993

A theorem regarding roots of the zero-order Bessel function of the first kind

This paper investigates a problem on the steady-state, conduction-convection heat transfer process in cylindrical porous heat exchangers. The governing partial differential equations for the system are obtained using the energy conservation law. Solution of these equations and the concept of enthalpy lead to a new approach to prove a theorem that the sum of inverse squares of all the positive roots of the zero order Bessel function of the first kind equals to one-forth. As a corollary, it is shown that the sum of one over pth power (p greater than or equal to 2) of the roots converges to some constant.

Lin, X.-A.↗
NASA NTRS1964

On an Approximation Theorem of Kupka and Smale

Simplified and generalized geometrical proof of Kupka and Smale approximation theorem concerning differential equations defined on closed, compact, infinitely differentiable manifold

THEOREM PROVING↗