Bounds for the eigenvalues of a simply- supported rectangular plate under a compressive stress varying linearly in the direction of loading
Upper bounds of eigenvalues of simply-supported rectangular plate using Rayleigh-Ritz method
Fauconneau, G.↗
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The bounds of the heat production rate within the moon
A new approach is proposed to the evaluation of the lower and upper bounds of the global heat production rate within planetary interiors. The approach is based on the relationship between the internal energy change and the volume change of a planetary object. For illustration, the approach is applied to the moon. Using an average global surface heat flux of 18 erg/sq cm-sec, and assuming constancy of the lunar radius during the past 3.2 billion years. the lunar heat release within the past 3.2 billion years is estimated at (30 to 40) x 10 to the tenth erg/cu cm. This is equivalent to the present day uranium concentration of 35 to 50 ppb provided the radiogenic isotopes are of the same proportion as that given by Toksoz et al. (1978).
Hsui, A. T.↗
Formation of the Aerosol of Space Origin in Earth's Atmosphere
The problem of formation of the aerosol of space origin in Earth s atmosphere is examined. Meteoroids of the mass range of 10-18-10-8 g are considered as a source of its origin. The lower bound of the mass range is chosen according to the data presented in literature, the upper bound is determined in accordance with the theory of Whipple s micrometeorites. Basing on the classical equations of deceleration and heating for small meteor bodies we have determined the maximal temperatures of the particles, and altitudes at which they reach critically low velocities, which can be called as velocities of stopping . As a condition for the transformation of a space particle into an aerosol one we have used the condition of non-reaching melting temperature of the meteoroid. The simplified equation of deceleration without earth gravity and barometric formula for the atmosphere density are used. In the equation of heat balance the energy loss for heating is neglected. The analytical solution of the simplified equations is used for the analysis.
Kozak, P. M.↗
A bounds on the resonant frequency of rectangular microstrip antennas
The calculation of currents induced by a transverse electric plane wave normally incident upon an infinite strip embedded in a grounded dielectric slab is used to infer a lower bound on the resonant frequency (or resonant-E-plane dimension) for rectangular microstrip antennas. An upper bound is provided by the frequency for which the E-plane dimension is a half-wavelength.
Bailey, M. C.↗
Continued research on selected parameters to minimize community annoyance from airport noise
A mathematical model of the annoyance created at an airport by aircraft operations is developed. The model incorporates population distribution considerations around an airport and the annoyance caused by aircraft noise. The objective function of this model corresponds to seeking to minimize total population annoyance created by all aircraft operations in a 24-hour period. Several factors are included in this model as constraint bounded. Demand for flight services is incorporated by including lower bounds on the number of operations by type of aircraft, runway used and time period. Also upper bounds on the number of operations for each runway are included. The mathematical model as formulated is recognized as corresponding to a nonlinear integer mathematical programming problem.
Frair, L.↗
Upper and lower bounds for ground-state second-order perturbation energy
Upper and lower bounds for ground-state second- order perturbation energy
QUANTUM MECHANICS↗
Reliability of voting in fault-tolerant software systems for small output spaces
Under a voting strategy in a fault-tolerant software system there is a difference between correctness and agreement. An independent N-version programming reliability model is proposed for treating small output spaces which distinguishes between correctness and agreement. System reliability is investigated using analytical relationships and simulation. A consensus majority voting strategy is proposed and its performance is analyzed and compared with other voting strategies. Consensus majority strategy automatically adapts the voting to different component reliability and output space cardinality characteristics. It is shown that absolute majority voting strategy provides a lower bound on the reliability provided by the consensus majority, and 2-of-n voting strategy an upper bound. If r is the cardinality of the output space it is proved the 1/r is a lower bound on the average reliability of fault-tolerant system components below which the system reliability begins to deteriorate as more versions are added.
Mcallister, David F.↗
Did surface temperatures constrain microbial evolution?
The proposition that glaciation may not have occurred before the Cenozoic--albeit not yet a consensus position--nevertheless raises for reconsideration the surface temperature history of the earth. Glacial episodes, from the Huronian (2.3 billion years ago; BYA) through the late Paleozoic (320 to 250 million years ago; MYA) have been critical constraints on estimation of the upper bounds of temperature (Crowley 1983, Kasting and Toon 1989). Once removed, few if any constraints on the upper temperature limit other than life remain. Walker (1982) recognized that life provides an upper limit to temperature in the Precambrian. We propose a more radical concept: the upper temperature limit for viable growth of a given microbial group corresponds to the actual surface temperature at the time of the group's first appearance. In particular, we propose here that two major evolutionary developments--the emergence of cyanobacteria and aerobic eukaryotes--can be used to determine surface temperature in the Precambrian, and that only subsequent cooling mediated by higher plants and then angiosperms permitted what may possibly be the earth's first glaciation in the late Cenozoic.
NASA Program Exobiology↗
Reliability of voting in fault-tolerant software systems for small output spaces
Under a voting strategy in a fault-tolerant software system there is a difference between correctness and agreement. An independent N-version programming reliability model is proposed for treating small output spaces which distinguishes between correctness and agreement. System reliability is investigated using analytical relationships and simulation. A consensus majority voting stratey is proposed and its performance is analyzed and compared with other voting strategies. A consensus voting strategy automatically adapts the voting to diffeerent component reliability and output space cardinality characteristics. It is shown that absolute majority voting strategy provides a lower bound on the reliability provided by the consensus majority, and the 2-of-n voting strategy an upper bound. If r is the cardinality of output space it is proved that 1/r is a lower bound on the average reliability of fault-tolerant system components below which the system reliability begins to deteriorate as more versions are added.
Mcallister, David F.↗
An algorithm for the estimation of bounds on the emissivity and temperatures from thermal multispectral airborne remotely sensed data
The effective flux incident upon the detectors of a thermal sensor, after it has been corrected for atmospheric effects, is a function of a non-linear combination of the emissivity of the target for that channel and the temperature of the target. The sensor system cannot separate the contribution from the emissivity and the temperature that constitute the flux value. A method that estimates the bounds on these temperatures and emissivities from thermal data is described. This method is then tested with remotely sensed data obtained from NASA's Thermal Infrared Multispectral Scanner (TIMS) - a 6 channel thermal sensor. Since this is an under-determined set of equations i.e. there are 7 unknowns (6 emissivities and 1 temperature) and 6 equations (corresponding to the 6 channel fluxes), there exist theoretically an infinite combination of values of emissivities and temperature that can satisfy these equations. Using some realistic bounds on the emissivities, bounds on the temperature are calculated. These bounds on the temperature are refined to estimate a tighter bound on the emissivity of the source. An error analysis is also carried out to quantitatively determine the extent of uncertainty introduced in the estimate of these parameters. This method is useful only when a realistic set of bounds can be obtained for the emissivities of the data. In the case of water the lower and upper bounds were set at 0.97 and 1.00 respectively. Five flights were flown in succession at altitudes of 2 km (low), 6 km (mid), 12 km (high), and then back again at 6 km and 2 km. The area selected with the Ross Barnett reservoir near Jackson, Mississippi. The mission was flown during the predawn hours of 1 Feb. 1992. Radiosonde data was collected for that duration to profile the characteristics of the atmosphere. Ground truth temperatures using thermometers and radiometers were also obtained over an area of the reservoir. The results of two independent runs of the radiometer data averaged 7.03 plus or minus .70 for the first run and 7.31 plus or minus .88 for the second run. The results of the algorithm yield a temperature of 7.68 for the low altitude data to 8.73 for the high altitude data.
Jaggi, S.↗
Efficient diagnosis of multiprocessor systems under probabilistic models
The problem of fault diagnosis in multiprocessor systems is considered under a probabilistic fault model. The focus is on minimizing the number of tests that must be conducted in order to correctly diagnose the state of every processor in the system with high probability. A diagnosis algorithm that can correctly diagnose the state of every processor with probability approaching one in a class of systems performing slightly greater than a linear number of tests is presented. A nearly matching lower bound on the number of tests required to achieve correct diagnosis in arbitrary systems is also proven. Lower and upper bounds on the number of tests required for regular systems are also presented. A class of regular systems which includes hypercubes is shown to be correctly diagnosable with high probability. In all cases, the number of tests required under this probabilistic model is shown to be significantly less than under a bounded-size fault set model. Because the number of tests that must be conducted is a measure of the diagnosis overhead, these results represent a dramatic improvement in the performance of system-level diagnosis techniques.
Blough, Douglas M.↗
Bounds on effectiveness of software reuse
In an earlier work, the author developed a communication channel analogy model of the software development process, which established a quantifiable, parametric upper bound on human productivity in terms of information put into the process and yield of product output by the process. This paper extends this work to focus on factors of that bound associated with software reuse. Specifically, it is shown, that under policies of heavy reuse, human productivity associated with the language advantage grows at best logarithmically in the size of the reuse base.
Tausworthe, Robert C.↗
Microwave edge diffraction by features in Saturn's rings - Observations with Voyager 1
Classical edge diffraction patterns are formed at centimeter wavelengths by several features of Saturn's rings. These patterns were discovered in 3.6- and 13-centimeter radio signals from Voyager 1 during occultation by the rings. The observed shapes are in agreement with theoretical patterns computed for screens of perfectly abrupt edges having large but finite opacity. Comparison with models in which the opacity at the edge tapers to zero from a finite value sets a new bound of less than about 200 meters on the microwave edge thickness. Certain features of the data suggest a smaller upper bound of about 130 meters on the edge thickness.
Marouf, E. A.↗
Theoretical study of the low-lying bound states of O2
It is demonstrated that a complete-active-space self-consistent-field (CASSCF) (2p)/MRCI + Q (multireference configuration interaction with a Davidson correction) description in a (13s8p6d 4f2g)/((5s4p3d 2f1g) atomic natural orbits (ANO) basis set supplemented with diffuse functions provides a quantitative description of the six lowest states of O2. The calculated potentials are within 0.05 eV (1.2 kilocal/mol) of accurate experimental results. The importance of substantially expanding the primitive basis set has been investigated, and it is demonstrated that such expansions yield insignificant improvement in the spectroscopic constants. Potential energy curves have also been reported for the weakly bound states of O2. The 5Pi(g) state is estimated to have a D(e) of 0.16 +/- 0.03 eV. The upper bound of D(e) is found to be sufficiently large that the importance of this state as a precursor for the formation of O2 (b 1Sigma(t)(+)) and O(1S) should be reconsidered.
Partridge, Harry↗
On slowly varying systems - l-infinity to l-infinity performance and implications to robust adaptive control
The authors present a result on the l-infinity to l-infinity performance of slowly time varying systems. In particular, it is shown that the performance of such systems cannot be much worse than that of the frozen-time systems which are time invariant. This result is used to characterize a class of indirect adaptive controllers that can stabilize a time-invariant system subjected to both parametric and l-infinity to l-infinity bounded unstructured uncertainty. Pertaining to this class of controllers, a particular indirect adaptive scheme is proposed that provides the greatest upper bound on the size of the unstructured uncertainty for which stability is ensured.
Voulgaris, Petros G.↗
Biased Randomized Algorithm for Fast Model-Based Diagnosis
A biased randomized algorithm has been developed to enable the rapid computational solution of a propositional- satisfiability (SAT) problem equivalent to a diagnosis problem. The closest competing methods of automated diagnosis are described in the preceding article "Fast Algorithms for Model-Based Diagnosis" and "Two Methods of Efficient Solution of the Hitting-Set Problem" (NPO-30584), which appears elsewhere in this issue. It is necessary to recapitulate some of the information from the cited articles as a prerequisite to a description of the present method. As used here, "diagnosis" signifies, more precisely, a type of model-based diagnosis in which one explores any logical inconsistencies between the observed and expected behaviors of an engineering system. The function of each component and the interconnections among all the components of the engineering system are represented as a logical system. Hence, the expected behavior of the engineering system is represented as a set of logical consequences. Faulty components lead to inconsistency between the observed and expected behaviors of the system, represented by logical inconsistencies. Diagnosis - the task of finding the faulty components - reduces to finding the components, the abnormalities of which could explain all the logical inconsistencies. One seeks a minimal set of faulty components (denoted a minimal diagnosis), because the trivial solution, in which all components are deemed to be faulty, always explains all inconsistencies. In the methods of the cited articles, the minimal-diagnosis problem is treated as equivalent to a minimal-hitting-set problem, which is translated from a combinatorial to a computational problem by mapping it onto the Boolean-satisfiability and integer-programming problems. The integer-programming approach taken in one of the prior methods is complete (in the sense that it is guaranteed to find a solution if one exists) and slow and yields a lower bound on the size of the minimal diagnosis. In contrast, the present approach is incomplete and fast and yields an upper bound on the size of the minimal diagnosis.
Williams, Colin↗
Mean-square error bounds for reduced-error linear state estimators
The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Lyapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.
Baram, Y.↗
Mean-square-error bounds for reduced-order linear state estimators
The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Liapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.
Baram, Y.↗