(Contract W-7405-eng-36) (DE90-016566; LA-UR-90-2714; CONF-9005237-6) Avail: NTIS HC/MF A03 An analytically computable formula, based on the adiabatic Melnikov function, is established for lobe area in onedegree-of-freedom Hamiltonian systems depending on a parameter which varies slowly in time. This lobe area result is illustrated on a slowly parametrically forced pendulum, a paradigm problem for adiabatic chaos. The analysis unties the theory of action from classical mechanics with the theory of the adiabatic Melnikov function from the field of global bifurcation theory. N91-10664*# DOE Institute for Computer Applications in Science and Engineering, Hampton, VA. SPECTRAL METHODS FOR TIME DEPENDENT PROBLEMS Eitan Tadmor Sep. 1990 67 p (NASA-CR-187443; ICASE-IR-14; NAS 1.26:187443) Avail: NTIS HC/MF A04 CSCL 12A Spectral approximations are reviewed for time dependent problems. Some basic ingredients from the spectral Fourier and Chebyshev approximations theory are discussed. A brief survey was made of hyperbolic and parabolic time dependent problems which are dealt with by both the energy method and the related Fourier analysis. The ideas presented above are combined in the study of accuracy stability and convergence of the spectral Fourier approximation to time dependent problems. Author N91-10666# Technische Univ., Delft (Netherlands). Faculty of Technical Mathematics and Informatics. ON q-ANALOGUES OF THE FOURIER AND HANKEL Tom H. Koornwinder (Center for Mathematics and Computer Science, Amsterdam, Netherlands) and Rene F. Swarttouw 1989 19 p (Rept-89-89; ISSN-0922-5641; ETN-90-97696) Copyright Avail: NTIS HC/MF A03 Symmetry and orthogonality for q-Bessel functions are studied. Some limit transitions are considered. A q-analog of Graf's addition formula and q-analogs of the Fourier cosine and sine transforms are given. Rigorous proofs of some limit results are included. Exton's functions are considered to be more suitable than Jackson's q-Bessel functions for harmonic analysis, both within and outside the context of quantum groups, and within the study, Exton's notation is preserved and the results in terms of a given q-hypergeometric function are stated. ESA The number of limit cycles for a quadratic system of differential equations with the following real coefficients is given: dx/dt = a + (a sub 20)(x squared) + (a sub 11)(xy) + (a sub 02)(y squared) P(x,y); dy/dt b + (b sub 20)(x squared) + (b sub 11)(xy) + (b sub 02)(y squared) Q(x,y). The number of limit cycles for quadratic symmetric vector fields was shown to be at least two. It is proved that the system has at most two limit cycles. ESA = = = N91-10668# Technische Univ., Delft (Netherlands). Faculty of Technical Mathematics and Informatics. THE DIGITAL REGULATOR AND TRACKER FOR DETERMINISTIC CONTINUOUS-TIME LINEAR TIME-VARYING SYSTEMS L. G. vanWilligenburg and W. L. deKoning 1990 28 p (Rept-90-05; ISSN-0922-5641; ETN-90-97702) Copyright Avail: NTIS HC/MF A03 The regulator and tracking problem are solved for deterministic continuous time linear time varying systems with complete state information at the sampling instants and piecewise constant control. The solutions are in feedback form and generated by a Riccati type recursion which runs backwards in time. In case of the tracking problem the feedforward control component is also generated by a recursion that runs backwards in time. Both recursions can be calculated off line. ESA N91-10669# Technische Univ., Delft (Netherlands). Faculty of Technical Mathematics and Informatics. RELATIVE POSITION OF THE CRITICAL POINTS OF A CERTAIN CUBIC SYSTEM AND A GENERALIZATION OF THE BENDIXSON INDEX FORMULA 29 p Ye Yanqian (Nanjing Univ., China) 1990 (Rept-90-23; ISSN-0922-5641; ETN-90-97716) Copyright Avail: NTIS HC/MF A03 The configuration of saddle points on a cubic system are investigated. It is proved for a specific case that they cannot lie on a straight line. A configuration 3-3+3 and 4-3+2 is investigated. A generalization of the Bendixson formula is obtained. Using numerical calculation on a computer, a phase portrait with seven finite critical points is shown. ESA INVARIANT MEASURES EXIST UNDER A SUMMABILITY Tomasz Nowicki (Warsaw Univ., Poland) and Sebastian For unimodal maps with negative Schwarzian derivative a sufficient condition for the existence of an invariant measure, absolutely continuous with respect to Lebesgue measure, is given. Namely the derivatives of the iterations of the map in the (unique) critical value must be so large that sum of (some root of) the inverses is finite. ESA Bivariate quadratic simplicial B-splines defined by their corresponding set of knots derived from a (suboptimal) constrained Delaunay triangulation of the domain are employed to obtain a C1-smooth surface. The generation of triangle vertices is adjusted to the areal distribution of the data in the domain. It is emphasized that the vertices of the triangles initially define the knots of the B-splines and do generally not coincide with the abscissae of the data. Thus, this approach is well suited to process scattered data. An example for least squares approximation with simplex splines is presented. N91-10674# ESA Universiteit Twente, Enschede (Netherlands). Faculty of Applied Mathematics. SYMMETRIES OF THE THREE BODY PROBLEM (MEMO-843; ISSN-0169-2690; ETN-90-97734) Avail: NTIS A lot of insight into the three body problem for equal mass particles in a plane was evolved by the discovery of a remarkable symmetry which straightens out the problem. A study where all infinitesimal symmetries of the transformed and original three body problem are determined using computer algebra is presented. Mar. Dirk P. Kroese and Erhan Cinlar (Princeton Univ., NJ.) 1990 19 p Sponsored by Netherlands Organization for Applied Scientific Research TNO, Delft (MEMO-844; ISSN-0169-2690; ETN-90-97735) Avail: NTIS HC/MF A03 Most multi-component replacement models are formulated in discrete time and require dynamic programming techniques to obtain the optimal replacement policy. Some models however, admit an optimal policy that is characterized by only a few constants. A continuous time replacement model in which the simple structure of the replacement rule is exploited, using embedding techniques and Marko renewal theory, is considered. ESA N91-10676# Universiteit Twente, Enschede (Netherlands). Dept. of Applied Mathematics. LONG CYCLES, DEGREE SUMS, AND NEIGHBORHOOD H. J. Broersma, J. vanden Heuvel, and H. J. Veldman 25 Jun. 1990 24 p (MEMO-851; ISSN-0169-2690; ETN-90-97738) Avail: NTIS HC/MF A03 Graphs with defined parameters and independent sets of vertices are examined. Least cycle lengths of 1-tough graphs are determined. Analogous results for 2-connected graphs are established. N91-10677# ESA Universiteit Twente, Enschede (Netherlands). Faculty of Applied Mathematics. B. Mulansky (Technische Univ., Dresden, German D.R.) Apr. 1990 20 p (MEMO-853; ISSN-0169-2690; ETN-90-97739) Avail: NTIS HC/MF A03 The Chebyshev approximation of real continuous functions from the class (S sub n,k) of polynomial spline functions of degree n with k free knots is addressed. Using the notion of the tangent cone and a new sign rule for spline functions a necessary alternant condition for local best approximations from (S sub n,k) is derived. It shows that the corresponding error function must have an alternant of a certain length with a prescribed sign on a subinterval. This condition improves results by Braess and Cromme. A characterization of best approximations by fixed knots splines with coefficient constraints is obtained. ESA N91-10678# Universiteit Twente, Enschede (Netherlands). Faculty of Applied Mathematics. GENERATING ALL 3-CONNECTED 4-REGULAR PLANAR GRAPHS FROM THE OCTAHEDRON GRAPH H. J. Broersma, A. J. W. Duijvestijn, and F. Goebel Apr. 1990 12 P (MEMO-854; ISSN-0169-2690; ETN-90-97740) Avail: NTIS HC/MF A03 A proof that all 3-connected 4-regular planar graphs can be generated from the octahedron graph, using three operations is presented. These graphs are generated up to 15 vertices inclusive. By including a fourth operation, an alternative to a procedure by Lehel to generate all connected 4-regular planar graphs from the octahedron graph is obtained. ESA (NAL-TR-1055; ISSN-0389-4010) Avail: NTIS HC/MF A03 In a previous investigation it was shown that the determinant of a covariance matrix should be recognized as a reasonable criterion for comparing the quality of observation systems, and the determinant criterion was applied to find the optimum observation systems for two-dimensional vector sensing in cases where the observation errors were not correlated with each other and were normally distributed with zero means and equal variances. In the present investigation the determinant method is applied to cases where the observation errors contain not only random errors but also bias errors, provided that the values of these are mutually equal in each measuring instrument. The general properties of the optimum orientations are also shown. Furthermore the investigation is extended to include cases where some of the measuring instruments are out of order, as well as cases where there are misalignment errors in the configuration of the measuring instruments. Author N91-10682# Universiteit Twente, Enschede (Netherlands). A REMARK ON THE CONVEXITY OF PIECEWISE Bernd Mulansky (Technische Univ., Dresden, German D.R.) May 1990 13 p (MEMO-857; ISSN-0169-2690; ETN-90-97743) Avail: NTIS HC/MF A03 The restrictivity of the combination of the C1 smoothness conditions and of the convexity of the B-net for splines on certain triangulations is considered. It is pointed out that a negative result stated by Grandine does not hold for adjacent triangles forming a degenerate quadrilateral. This implies that some configurations do admit nonplanar convex B-nets satisfying the C1 conditions in contrast to the statements by Grandine. As an example, C1 piecewise quadratics on a Powel-Sabin-split are considered in more detail. ESA 16 P B. Kouvaritakis and M. S. Trimboli 1989 The presence of bounded noise in identification data implies uncertainty in the parameters of system models. Earlier results provide analytical means for determining optimal ellipsoidal regions that bound the vector of parameters. Parameter space information however is only of secondary interest in frequency response design when the main preoccupation is with the bounding of Nyquist diagrams. The projection of ellipsoidal regions from parameter space to the Nyquist plane are considered and results which are optimal from a frequency response point of view are obtained. As an illustration of the potential use for frequency response bounding regions, consideration is given to the problem of multivariable robust frequency response design and a numerical example is discussed. ESA function approximation problems, but are shown to be particularly effective in the approximation of eigenvalue/vector functions of transfer function matrices; as such the derived techniques provide some very useful tools for the characteristic locus design method. ESA N91-10685# Oxford Univ. (England). Dept. of Engineering Science. ROBUSTNESS EFFECTS OF A PREFILTER IN GENERALIZED B. D. Robinson and D. W. Clarke 27 Oct. 1989 30 p Simple stability bounds for closed-loop robustness in the presence of modeling errors are presented in terms of the steady state gain of the model. The effects of user specified prefilters upon these bounds are discussed, leading to guidelines for selection of the filters. This allows commissioning of the adaptive controller to be done on the basis of the robustness of the nominal closed loop to modeling errors, based only upon the estimated model and the particular control strategy to be employed. ESA 65 STATISTICS AND PROBABILITY Includes data sampling and smoothing; Monte Carlo method; and stochastic processes. N91-10686# Xerox Palo Alto Research Center, CA. L. D. Wilcox Dec. 1989 48 p (PB90-190588; PARC-EDL-89-4) Avail: NTIS HC/MF A03 CSCL 12A A method is derived for obtaining an optimal histogram estimate of a multivariate probability density function. In an optimal histogram, the location, shape, and size of each of the bins for the histogram are chosen to minimize the integrated mean square error to the density estimate. The mean square error is shown to be the sum of a variance term, which is proportional to the number of bins in the histogram divided by the sample size used for the estimate, and a bias term, which depends on the number of histogram bins and on their location, shape, and size. The bias can be expressed as a weighted Euclidean distance, with weighting matrix equal to the outer product of the gradient of the density. It shows that a local minimum of the bias term can be obtained with the k-means clustering algorithm used in vector quantization. Thus the optimal histogram is formed by vector quantizing the feature vector using the Euclidean distortion measure, and estimating the value of the density on the resulting quantization regions. The optimal number of bins for the density estimate is determined by minimizing an approximation to the integrated mean square error of the estimate, and is expressed in terms of the sample size and number of features. Author N91-10687# Technische Univ., Delft (Netherlands). Faculty of THE GENERALIZED MODUS PONENS CONSIDERED AS A Hans Hellendoorn 1990 35 p The generalized modus ponens in fuzzy logic is studied. The scheme of the inference rule is given. Basic assumptions for dealing with it are given. A number of theorems are shown to be incompatible with these. It is shown that it is arduous to construct an implication rule to meet two of the conditions, and a way to alter them which restores this is shown. ESA (Grant NWO-10-62-10) (Rept-90-04; ISSN-0922-5641; ETN-90-97701) Copyright Avail: NTIS HC/MF A03 The robustness and asymptotic behavior of tau-estimators for multivariate location and scatter are discussed. Estimators are shown to correspond with multivariate M-estimators defined by a weighted average of redescending psi functions, where the weights are adaptive. The study proves consistency and asymptotic normality under weak assumptions on the underlying distribution P, shows that tau-estimators have a high breakdown point, and obtains the influence function at general distributions P. In the special case of a location-scatter family tau-estimators are asymptotically equivalent to multivariate S-estimators defined by means of a weighted rho function. This enables a high breakdown point and bounded influence to be combined with good asymptotic efficiency for the location and covariance estimator. N91-10689# ESA Technische Univ., Delft (Netherlands). Faculty of Technical Mathematics and Informatics. THE DIGITAL REGULATOR AND TRACKER FOR L. G. vanWilligenburg and W. L. deKoning 1990 26 p The regulator and tracking problem are solved for continuous time linear time varying systems disturbed by additive white noise, with incomplete state information at the sampling instants corrupted by additive white Gaussian noise, and piecewise constant control. Both the regulator and tracking problem turn out to be certainty equivalent. The solutions to both the regulator and tracking problem therefore consist to the well known discrete time Kalman filter, and a feedback generated by a Riccati type recursion that runs backwards in time. In case of the tracking problem the feed forward is also generated by a recursion that runs backwards in time. Both recursions can be calculated off line. Explicit expressions for the minimum cost of both problems are derived. ESA N91-10690# Universiteit Twente, Enschede (Netherlands). Faculty of Applied Mathematics. THE DIFFERENCE OF TWO RENEWAL PROCESSES: LEVEL D. P. Kroese Mar. 1990 34 p The difference process N of two renewal processes studied by Kroese and Kallengerg (1989) is considered. First and second order approximations to the distribution function of the time that process N crosses level n, as n approaches infinity, are compared to simulation or exact results. Numerical results confirm that second order approximations give considerable improvement on known first order results. Direct application of the second order approximation is complicated by the occurrence of the term EM = E inf N(t) (t is greater than or = 0). Considerable attention is paid to the derivation of EM for important special cases. Earlier results on the sum and difference process are stated in more general form. M.G. N91-10694# Joint Publications Research Service, Arlington, VA. 30 Jul. 1990 57 p Transl. into ENGLISH from various Russian articles (JPRS-UPM-90-003) Avail: NTIS HC/MF A04 Abstracts of Soviet literature in various areas of physics and mathematics are compiled. The following subject areas are covered: acoustics; crystals, laser glasses, and semiconductors; fluid dynamics; lasers; magnetohydrodynamics; nuclear physics; optics and spectroscopy; plasma physics; superconductivity; and numerical analysis and algorithms. M.G. N91-10695*# Fermi National Accelerator Lab., Batavia, IL. Richard Holman, Edward W. Kolb, Sharon L. Vadas, and Yun (Grant NAGw-1340) (NASA-CR-186419; NAS 1.26:186419; CMU-HEP90-13; FNAL-PUB-90/147-A) Avail: NTIS HC/MF A03 CSCL 20C False-vacuum decay was studied in context of generalized extended inflationary theories, and the bubble nucleation rates was computed for these theories in the limit of G(sub N) yields 0. It was found that the time dependence of the nucleation rate can be exponentially strong through the time dependence of the Jordan-Brans-Dicke field. This can have a pronounced effect on whether extended inflation can be successfully implemented. N91-10696# Sandia National Labs., Albuquerque, NM. INTRINSIC (?) REFERENCE STANDARDS R. P. Reed 1990 12 p Author Presented at the 1990 National Conference of Standards Laboratories (NCSL) Symposium and Workshop, Washington, DC, 19-23 Aug. 1990 (Contract DE-AC04-76DP-00789) (DE90-015714; SAND-89-2877C; CONF-9008134-2) Avail: NTIS HC/MF A03 The term Intrinsic refers to something that is inherent in the nature of a thing. With regard to metrologic references, it usually concerns a characteristic property of a natural material or process. International standard scales, such as those for time, dimension, temperature, voltage, and resistance, are increasingly based on intrinsic natural properties rather than on physical artifacts. The objective is to provide accurate and reliable fiducials that are themselves reproducible independent of place, time, or observer. A distinction must be made, however, between intrinsic properties on which measurement scales are based and physical realizations of particular values of those intrinsic properties in actual reference devices used for practical calibration. Ideally, intrinsic references are not subject to calibration as they represent quantities that are exact by definition. It is sometimes asserted, for example, that such references do not require calibration traceability to a national laboratory. But, it must not be casually assumed that a calibration device that employs a class of natural phenomenon does, in fact, necessarily impose the standardized value on a calibration subject. Some of the problems associated with the practical use of so-called intrinsic standard references in industrial measurement practice are considered. In particular, distinctions between validation, qualification, and calibration are discussed in relation to intrinsic reference standards and measurement quality assurance. DOE N91-10697# Los Alamos National Lab., NM. Applied Theoretical PREDICTION AND CONTROL OF CHAOTIC PROCESSES R. D. Jones, C. W. Barnes, G. W. Flake, K. Lee, P. S. Lewis, M. (DE90-016505; LA-UR-90-2755; CONF-9007136-3) Avail: NTIS HC/MF A02 We present the theory of nonlinear adaptive networks and discuss a few applications. In particular, we review the theory of feedforward backpropagation networks. We then present the theory of the Connectionist Normalized Linear Spline network in both its feedforward and iterated modes. Also, we briefly discuss the theory of stochastic cellular automata. We then discuss applications to chaotic time series, tidal prediction in Venice lagoon, finite differencing, sonar transient detection, control of nonlinear processes, control of a negative ion source, balancing a double inverted pendulum and design advice for free electron lasers and laser fusion targets. DOE 71 ACOUSTICS Includes sound generation, transmission and attenuation. For noise pollution see 45 Environmental Pollution. N91-10698# Massachusetts Inst. of Tech., Cambridge. Presented at the MIT/Marine Industry Collegium, Cambridge, MA, 9 Jan. 1990 (Contract NA86AA-D-SG089) (PB90-183633; MITSG-89-33; OB-56) Avail: NTIS HC/MF A03 CSCL 20A The Massachusetts Institute of Technology (MIT) Sea Grant Marine Industry Collegium joined with the MIT-Industry Program in Structural Acoustics to sponsor a one-day workshop, on January 9, 1990. The workshop addressed current research efforts and provided an opportunity for attendees to actively interact through their questions and comments. Presentations covered such topics as the transmission properties of fluid storage tanks within vessels, recent developments in analytical models of machine systems for noise and vibration minimization, techniques to combine analytically and experimentally derive acoustic parameters for model definition, and the application of active and passive control techniques to minimize structural acoustic wave propagation. GRA N91-10699*# National Aeronautics and Space Administration. HELICOPTER FAR-FIELD ACOUSTIC LEVELS AS A Arnold W. Mueller, Charles D. Smith, and Philip LeMasurier During the design of a helicopter, the weight, engine, rotor speed, and rotor geometry are given significant attention when considering the specific operations for which the helicopter will be used. However, the noise radiated from the helicopter and its relationship to the design variables is currently not well modeled with only a limited set of full-scale field test data to study. In general, limited field data have shown that reduced main-rotor advancing blade-tip Mach numbers result in reduced far-field noise levels. The status of a recent helicopter noise research project is reviewed. It is designed to provide flight experimental data which may be used to further understand helicopter main-rotor advancing blade-tip Mach number effects on far-field acoustic levels. Preliminary results are presented relative to tests conducted with a Sikorsky S-76A helicopter operating with both the rotor speed and the flight speed as the control variable. The rotor speed was operated within the range of 107 to 90 percent NR at nominal forward speeds of 35, 100, and 155 knots. Author N91-10700# Sandia National Labs., Albuquerque, NM. Applied PREGO: A SIMULATION CODE FOR ONE-DIMENSIONAL Daniel J. Segalman Jul. 1990 34 p (DE90-014859; SAND-90-0593) Avail: NTIS HC/MF A03 A computer code, PREGO, has been developed to perform calculations for three related problems: reflection of an acoustic wave against a layered viscoelastic medium: (water/medium); transmission of an acoustic wave through such a medium (water/medium/water); and radiation of an acoustic wave through such a medium: (medium/water). This code draws on experience gained in writing and using a predecessor code, IMPEDE, which was devised to calculate the steady state reflection of an acoustic wave impinging on a layered substrate of elastic or viscoelastic materials. That code employed a finite element formulation to discretize the complex-valued, second order ordinary differential equations for monochromatic steady state acoustics. The principles of numerical analysis that underlie PREGO are different and less subject to discretization error than those used in IMPEDE. The |