Search NASA⌕ Search

SEARCH · Search NASA

Results for “Generalization Bounds”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization

The problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case. The minimum value of the objective function can be obtained by solving a semiinfinite linear programming problem, and an iterative procedure for obtaining approximate solutions is introduced. Application of the l1-optimal problem to robustness is discussed. A mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations.

Dahleh, Munther A.↗
NASA NTRS1995

Harmonic oscillator representation in the theory of scattering and nuclear reactions

The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.

Smirnov, Yuri F.↗
NASA NTRS1988

Trapping Ne, Ar, Kr, and Xe in Si2O3 smokes

Simple Si2O3 smokes have been condensed at both low (less than 750 K) and high (greater than 1000 K) temperature at 35 torr H2 pressure in the presence of 0, 10, 100, and 1000 microns of a noble gas mixture containing Ne, Ar, Kr, and Xe. In general, both Ne and Ar are quite loosely bound in the smokes (6.0 x 10 to the -8th and 2.6 x 10 to the -4th ccSTP/g, respectively), and are degassed at temperatures below 1200 K. Both Kr and Xe are somewhat more strongly bound at concentrations of 1.0 x 10 to the -7th and 8.2 x 10 to the -8th ccSTP/g, respectively, and in addition show a double release with a second component at a temperature of about 1875 K. With the exception that Si2O3 smokes appear to show a particular affinity for argon, possibly due to an anomalous absorption of atmospheric argon, none of the other noble gases are found in sufficient concentration to explain the gases observed in meteorites as primary circumstellar condensates. However, this data in conjunction with observations of Honda et al. (1979) do seem to show a degree of dependence between noble gas retention and chemical composition.

Nuth, Joseph A., III↗
NASA NTRS2001

Exobiochemistry

Exobiochemistry is the putative biochemistry of extraterrestrial life. It suggests the possible energy and material bases of extraterrestrial life and could help detect it. The diverse biochemistry of Earth indicates that a wide range of exobiochemistry is possible on other planets. An exobiochemistry will probably use the same energy sources as Earths ecology, light, biological organic material, and more rarely abiotic chemicals. Extraterrestrial life will be based on familiar chemical principles and probably capture, store, and release energy using oxidation-reduction reactions. Extraterrestrial life will give chemical indications of its existence. Key elements will be concentrated, stored, and recycled, altering their availability and isotopic composition. Any significant departure from chemical equilibrium would be good evidence for exobiochemistry, but an integrated system of departures from the expected equilibrium would be better. Exobiochemistry can be expected to include closed biogeochemical cycles of the major life supporting elements and may well show the complex dynamic close-coupled interactions that characterize the terrestrial biosphere. Terrestrial biochemistry provides a basis for generalization and extrapolation but it does not set bounds on exobiochemistry. In exobiochemistry we can expect: 1. closed chemical cycles that recycle materials, nutrients, and catalysts, 2. organisms with complementary metabolisms that cooperate to close the chemical cycles, 3. a high probability of a carbon and water chemistry, but some possibility of a non-carbon or non-water chemistry in extreme environments, and, 4. life similar to bacteria more prevalent than higher plants and animals.

Jones, Harry↗
NASA NTRS1995

A Game Theoretic Fault Detection Filter

The fault detection process is modelled as a disturbance attenuation problem. The solution to this problem is found via differential game theory, leading to an H(sub infinity) filter which bounds the transmission of all exogenous signals save the fault to be detected. For a general class of linear systems which includes some time-varying systems, it is shown that this transmission bound can be taken to zero by simultaneously bringing the sensor noise weighting to zero. Thus, in the limit, a complete transmission block can he achieved, making the game filter into a fault detection filter. When we specialize this result to time-invariant system, it is found that the detection filter attained in the limit is identical to the well known Beard-Jones Fault Detection Filter. That is, all fault inputs other than the one to be detected (the "nuisance faults") are restricted to an invariant subspace which is unobservable to a projection on the output. For time-invariant systems, it is also shown that in the limit, the order of the state-space and the game filter can be reduced by factoring out the invariant subspace. The result is a lower dimensional filter which can observe only the fault to be detected. A reduced-order filter can also he generated for time-varying systems, though the computational overhead may be intensive. An example given at the end of the paper demonstrates the effectiveness of the filter as a tool for fault detection and identification.

Chung, Walter H.↗
NASA NTRS1973

On the error probability of general tree and trellis codes with applications to sequential decoding

An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random binary tree codes is derived and shown to be independent of the length of the tree. An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n is derived which separates the effects of the tail length T and the memory length M of the code. It is shown that the bound is independent of the length L of the information sequence. This implication is investigated by computer simulations of sequential decoding utilizing the stack algorithm. These simulations confirm the implication and further suggest an empirical formula for the true undetected decoding error probability with sequential decoding.

Johannesson, R.↗
NASA NTRS1949

Gas Motion in a Local Supersonic Region and Conditions of Potential-Flow Breakdown

For a certain Mach number of the oncoming flow, the local velocity first reaches the value of the local velocity of sound (M = 1) at some point on the surface of the body located within the flow. This Mach number is designated the critical Mach number M(sub cr). By increasing the flow velocity, a supersonic local region is formed bounded by the body contour and the line of transition from subsonic to supersonic velocity. As is shown by observations with the Toepler apparatus, at a certain flow Mach number M > M(sub cr) a shock wave is formed near the body that closes the local supersonic region from behind. The formation of the shock wave is associated with the appearance of an additional resistance defined as the wave drag. In this paper, certain features are described of the flow in the local supersonic region, which is bounded by the contour of the body and the transition line, and conditions are sought for which the potential flow with the local supersonic region becomes impossible and a shock wave occurs. In the first part of the paper, the general properties of the potential flow in the local supersonic region, bounded by the contour of the profile and the transition line, are established. It is found that at the transition line, if it is not a line of discontinuity, the law of monotonic variation of the angle of inclination of the velocity vector holds (monotonic law). An approximation is given for the change in velocity at the contour of the body. The flow about a contour having a straight part is studied. In the second part of the paper, an approximation is given of the magnitudes of the accelerations at the interior points of the supersonic region. With the aid of these approximations, it is shown that for profiles convex to the flow the breakdown of the potential flow,associated with an increase of the Mach number of the oncoming flow, cannot be due to the formation of an envelope of the characteristics within the supersonic region. On the basis of the monotonic law, the transitional Mach number M is found, beyond which the potential flow with local supersonic region becomes impossible.

Nikolskii, A. A.↗
NASA NTRS1988

Finite-state codes

A class of codes called finite-state (FS) codes is defined and investigated. The codes, which generalize both block and convolutional codes, are defined by their encoders, which are finite-state machines with parallel inputs and outputs. A family of upper bounds on the free distance of a given FS code is derived. A general construction for FS codes is given, and it is shown that in many cases the FS codes constructed in this way have a free distance that is the largest possible. Catastrophic error propagation (CEP) for FS codes is also discussed. It is found that to avoid CEP one must solve the graph-theoretic problem of finding a uniquely decodable edge labeling of the state diagram.

Pollara, Fabrizio↗
NASA NTRS1980

The composition of the Martian dark regions: Observations and analysis

Near infrared telescopic spectrophotometry for dark regions is present and interpreted using laboratory studies of iron bearing mineral mixtures and terrestrial oxidized and unoxidized basalts. Upon closer inspection (by spacecraft) the telescopic dark regions were found to consist of large scale intermixtures of bright soil (aeolian dust) and dark materials. The dark materials themselves consist of an intimate physical association of very fine grained ferric oxide bearing material with relatively high near infrared reflectance and darker, relatively unoxidized rocks or rock fragments. While these two components could exist finely intermixed in a soil, a number of lines of evidence indicate that the usual occurrence is probably a thin coating of physically bound oxidized material. The coated rocks are dark and generally clinopyroxene bearing. The shallow band depths and low overall reflectances indicate that opaque minerals such as magnetite are probably abundant.

Singer, R. B.↗
NASA NTRS1985

Fluvial Drainage Basins and Valley Networks: Eastern Margaritifer Sinus, Mars

The fluvial drainage of the eastern Margaritifer Sinus (MC-19NE, SE) and northeastern Argyre (MC-26NE) Quadrangles is dominated by two major longitudinal valley networks, the Parana/Loire system on the east, and the Samara Himera system to the west. It is believed that both of these drainages are through-going to the northwest and debouch into Margaritifer Chaos (general location: 12S, 22.5W). The Parana/Loire drainage is bounded on the east in part by an ancient multi-ringed impact basin. The Parana multi-digitate network drains northwest into a depositional basin, and impact basin floor, characterized by positive relief chaos. It is believed that Loire Vallis heads in the basin; thus Parana and Loire Valles may be treated as one system. Samara Valles heads in the northeastern Argyre Quadrangle and extends as a major truck valley to the northwest. Samara Valles cuts through the hills forming one of the concentric rings of the Ladon impact basin and joins the Himera drainage to trend in a more northerly direction to Margaritifer Chaos. The downstream portion of Himera is considered to be part of the Samara

Boothroyd, J. C.↗
NASA NTRS1986

Migration of the separation point on a deforming cylinder

An iterative scheme of solving the Navier-Stokes equations for unsteady two-dimensional flow about a deforming and translating cylinder is given. In the kth iteration, the convected vorticity appears as the source term in an equation of transient diffusion of vorticity. A novel integral transform is used to reduce this transient vorticity equation to a k-dimensional heat equation. The bounded solution of this equation is obtained with a general method of superposition for problems involving a moving boundary. An equation describing the migration of the separation point on a deforming cylinder in unsteady cross flows is derived from the analytically obtained velocity field. The radial expansion of the cylinder surface is shown to hasten the separation time and to increase the separation angle. The results imply that in the steady flow past a body that is moving forward and sinking at constant rates, the locus of points at which the azimuthal component of skin friction changes sign originates on the leeward ray at a point downstream of the front tip.

Lin, S. P.↗
NASA NTRS2001

Complex Correlation Calculation of e-H Total Cross Sections

Calculation of e-H total and elastic partial wave cross sections is being carried out using the complex correlation variational T-matrix method. In this preliminary study, elastic partial wave phase shifts are calculated with the correlation functions which are confined to be real. In that case the method reduces to the conventional optical potential approach with projection operators. The number of terms in the Hylleraas-type wave function for the S phase shifts is 95 while for the S it is 56, except for k=0.8 where it is 84. Our results, which are rigorous lower bounds, are given. They are seen to be in general agreement with those of Schwartz, but they are of 0 greater accuracy and outside of his error limits for k=0.3 and 0.4 for S. The main aim of this approach' is the application to higher energy scattering. By virtue of the complex correlation functions, the T matrix is not unitary so that elastic and total scattering cross sections are independent of each other. Our results will be compared specifically with those of Bray and Stelbovics.

Bhatia, A. K.↗
NASA NTRS2004

Bounding the Resource Availability of Partially Ordered Events with Constant Resource Impact

We compare existing techniques to bound the resource availability of partially ordered events. We first show that, contrary to intuition, two existing techniques, one due to Laborie and one due to Muscettola, are not strictly comparable in terms of the size of the search trees generated under chronological search with a fixed heuristic. We describe a generalization of these techniques called the Flow Balance Constraint to tightly bound the amount of available resource for a set of partially ordered events with piecewise constant resource impact We prove that the new technique generates smaller proof trees under chronological search with a fixed heuristic, at little increase in computational expense. We then show how to construct tighter resource bounds but at increased computational cost.

Frank, Jeremy↗
NASA NTRS1979

Application of the relative energy release criteria to enclosure fire testing

The five relative energy release criteria (RERC) which are a first step towards formulating a unified concept that can be applied to the development of fires in enclosures, place upper bounds on the rate and amount of energy released during a fire. They are independent, calculated readily, and may be applied generally to any enclosure regardless of size. They are useful in pretest planning and for interpreting experimental data. Data from several specific fire test programs were examined to evaluate the potential use of RERC to provide test planning guidelines. The RERC were compared with experimental data obtained in full-scale enclosures. These results confirm that in general the RERC do identify the proper limiting constraints on enclosure fire development and determine the bounds of the fire development envelope. Plotting actual fire data against the RERC reveals new valid insights into fire behavior and reveals the controlling constraints in fire development. The RERC were calculated and plotted for several descrpitions of full-scale fires in various aircraft compartments.

Roschke, E. J.↗
NASA NTRS1996

Generalization of the Time-Energy Uncertainty Relation of Anandan-Aharonov Type

A new type of time-energy uncertainty relation was proposed recently by Anandan and Aharonov. Their formula, to estimate the lower bound of time-integral of the energy-fluctuation in a quantum state is generalized to the one involving a set of quantum states. This is achieved by obtaining an explicit formula for the distance between two finitely separated points in the Grassman manifold.

Hirayama, Minoru↗
NASA NTRS1987

High gain feedback and telerobotic tracking

Asymptotically stable linear time invariant systems are capable of tracking arbitrary reference signals with a bounded error proportional to the magnitude of the reference signal (and its derivatives). It is shown that a similar property holds for a general class of nonlinear dynamical systems which includes all robots. As in the linear case, the error bound may be made arbitrarily small by increasing the magnitude of the feedback gains which stabilize the system.

Koditschek, D. E.↗
NASA NTRS1975

Asymptotic form of the charge exchange cross section in the three body rearrangement collisions

A three body general rearrangement collision is considered where the initial and final bound states are described by the hydrogen-like wave functions. Mathematical models are developed to establish the relationships of quantum number, the reduced mass, and the nuclear charge of the final state. It is shown that for the low lying levels, the reciprocal of n cubed scaling law at all incident energies is only approximately satisfied. The case of the symmetric collisions is considered and it is shown that for high n and high incident energy, E, the cross section behaves as the reciprocal of E cubed. Zeros and minima in the differential cross sections in the limit of high n for protons on atomic hydrogen and positrons on atomic hydrogen are given.

Omidvar, K.↗