Showing papers in "Theory of Computing Systems \/ Mathematical Systems Theory in 1988"

Realization theory in Hilbert space

Abstract: A representation theorem for infinite-dimensional, linear control systems is proved in the context of strongly continuous semigroups in Hilbert spaces. The result allows for unbounded input and output operators and is used to derive necessary and sufficient conditions for the realizability in a Hilbert space of a time-invariant, causal input-output operator ℐ. The relation between input-output stability and stability of the realization is discussed. In the case of finite-dimensional input and output spaces the boundedness of the output operator is related to the existence of a convolution kernel representing the operator ℐ.

The monadic second-order logic of graphs, II: Infinite graphs of bounded width

Abstract: A countable graph can be considered as the value of a certain infinite expression, represented itself by an infinite tree. We establish that the set of finite or infinite (expression) trees constructed with a finite number of operators, the value of which is a graph satisfying a property expressed in monadic second-order logic, is itself definable in monadic second-order logic. From Rabin's theorem, the emptiness of this set of (expression) trees is decidable. It follows that the monadic second-order theory of an equational graph, or of the set of countable graphs of width less than an integerm, is decidable.

Equivalence of input-output stability and exponential stability for infinite-dimensional systems

Abstract: For a wide class of infinite-dimensional linear systems it is shown that if the state-space realization is exponentially stabilizable and detectable then exponential stability is equivalent to input-output stability of the transfer function. Exponential stabilizability (or detectability) is a strong assumption as it implies that the system operator satisfies the spectrum decomposition assumption and has finitely many unstable eigenvalues of finite multiplicity. In addition, the finite-dimensional unstable projection of the system is controllable (or observable).

Exact Linearization of Nonlinear Systems with Outputs

Abstract: This paper discusses the problem of using feedback and coordinates transformation in order to transform a given nonlinear system with outputs into a controllable and observable linear one. We discuss separately the effect of change of coordinates and, successively, the effect of both change of coordinates and feedback transformation. One of the main results of the paper is to show what extra conditions are needed, in addition to those required for input-output-wise linearization, in order to achieve full linearity of both state-space equations and output map.

Functional expansions for nonlinear discrete-time systems

Abstract: Given an input-output map associated with a nonlinear discrete-time state equationx(t + 1) =f(x(t);u(t)) and a nonlinear outputy(t) =h(x(t)), we present a method for obtaining a “discrete Volterra series” representation of the outputy(t) in terms of the controlsu(0), ...,u(t − 1). The proof is based on Taylor-type expansions of the iterated composition of analytic functions. It allows us to make an explicit construction of each kernel, that is, each coefficient of the series expansion ofy(t) in powers of the controls. This is achieved by making use of successive directional derivatives associated with a family of vector fields which are deduced from the discrete state equations. We discuss the use of these vector fields for the analysis and control of nonlinear discrete-time systems.

Variants of top-down tree transducers with look-ahead

Abstract: In this article we consider deterministic and strongly deterministic top-down tree transducers with regular look-ahead, with regular check, with deterministic top-down look-ahead, and with deterministic top-down check We compare the transformational power of these tree transducer classes by giving a correct inclusion diagram of the tree transformation classes induced by them Along with the comparison we decompose some of the examined classes into simpler classes and we introduce the concept of the deterministic top-down tree automata with deterministic top-down look-ahead We show that these recognizers recognize a tree language class which is strictly between the class of regular tree languages and the class of tree languages recognizable by deterministic top-down tree automata We also study the closure properties of the examined tree transformation classes We show that some classes are closed under composition while others, for example the class of tree transformations induced by deterministic top-down tree transducers with deterministic top-down look-ahead, are not

Sublogarithmic-space turing machines, nonuniform space complexity, and closure properties

Abstract: We show that some of the fundamental closure properties (such as concatenation) that hold for Turing machines (TMs) operating in space above logn, do not hold for TMs operating in space below logn. We also compare the powers of TMs andsweeping TMs operating in space below logn. While the proof that the powers of TMs and sweeping TMs are the same is trivial for space greater than or equal to logn, it is not obvious when the space is sublogarithmic. To explore the nature of sublogarithmic space computations further, we introduce a nonuniform space complexity measure and study some of its fundamental properties (such as closure, hierarchy, and gap) in the sublogarithmic range.

A convolution method for inverse heat conduction problems

Abstract: The problem of determining the temperature at one end of a rod by means of interior temperature measurements has considerable practical importance and has been well studied, however, few exact solutions have been found Most of the applicable results therefore, have been obtained from the (numerical) analysis of discretized systems In this paper we present an analytic method for obtaining solutions to this problem which does not require differentiation (only integration) of the interior temperature readings and is valid for general finite energy boundary data and for general radiation boundary conditions at the known end of the rod

A second step toward the strong polynomial-time hierarchy

Abstract: In this paper we discuss the concepts ofimmunity andsimplicity in levels of the relativized Polynomial-time Hierarchy just aboveP. We consider various diagonalization techniques with which oracle sets can be constructed relative to which strong separations between language classes in the first two levels of this hierarchy are established. In particular, we build oracle sets for separation of relativized Σ2P from relativizedNP with immunity, of relativized Σ2P from relativizedNP with bi-immunity, of relativized Σ2P from relativized Δ2P with immunity, of relativized Π2P from relativized Δ2P with immunity, and finally of relativized Σ2P from relativized Π2P with simplicity.

Atmospheric angular momentum and length of day

Abstract: : Changes in the globally integrated absolute angular momentum of the atmosphere were computed from the Fleet Numerical Oceanography Center NOGAPS wind analyses and compared to astronomically measured changes in length of day (LOD) obtained from the U.S. Naval Observatory, Washington D.C. The two time series were subjected to both time and frequency domain analysis. In the time domain, digital filters were used to isolate seasonal and subseasonal components. In the frequency domain, energy density, coherence and phase were computed over periods from 2 days to 1000 days. Over 90% of the total variance in astronomically determined LOD can be explained by meteorological phenomena. Fluctuations in LOD are coherent and in phase with fluctuations in the globally integrated angular momentum of the Earth's shell (crust, mantle and oceans; liquid core is excluded) at almost all periods less than 365 days. Annual fluctuations in LOD appear to originate in the midlatitudes and propagate equatorward. Subseasonal fluctuations (30 to 100 day periods) appear to be a tropical phenomena. Keywords: Length of Day; Atmospheric angular momentum; Theses; Computer programs.

Minimum-diameter cyclic arrangements in mapping data-flow graphs onto VLSI arrays

Abstract: Regular arrays of processing elements in VLSI have proved to be suitable for high-speed execution of many matrix operations. To execute an arbitrary computational algorithm on such processing arrays, it has been suggested mapping the given algorithm directly onto a regular array. The computational algorithm is represented by a data-flow graph whose nodes are to be mapped onto processors in the VLSI array. This study examines the complexity of mapping data-flow graphs onto square and hexagonal arrays of processors. We specifically consider the problem of routing data from processors in a given (source) sequence to another (target) sequence. We show that under certain conditions, the above problem is equivalent to the one of finding a minimum-diameter cyclic arrangement. The complexity of the latter problem is analyzed and upper and lower bounds on the number of intermediate rows of processors (between the source and target rows) are derived.

Position, Scale, and Rotation Invariant Optical Pattern Recognition for Target Extraction and Identification

Abstract: : This thesis investigates the feasibility of optically implementing a real-time, pattern recognition system using correlation techniques in a position, scale, and rotation invariant (PSRI) feature space. Input target templates were optically Fourier transformed using an improved high-resolution, high-pass filter positioned in the focal plane of the transforming lens. A logarithmic-polar coordinate transform of the magnitude-squared of the Fourier transform (/FT/2) was performed with an improved method of focusing the magnified /FT/2 onto a computer generated hologram (CGH), which was shown to scale linearly along the horizontal axis and logarithmically along the vertical axis. Optical, matched-filter correlations on the magnitude-squared Fourier transform logarithmic-polar (FLRT) feature space were performed using thermoplastic, phase-relief holography and Vander Lugt filtering. Correlation results prove that scale and rotation changes of the input can be predicted accurately based on linear shifts of the correlation peak. Also, the FLRT feature space is shown to provide excellent discrimination for multiple-input scenes. The need for a cyclic correlation is verified, and digital simulations prove the validity of the

Comparisons between some pumping conditions for context-free languages

Abstract: We present a systematic investigation of the relationships between various pumping properties—the classic pumping condition of Bar-Hillelet al., Ogden's condition, a generalized Ogden condition of Bader and Moura, Sokolowski's condition, an extended Sokolowski condition of Grant, and linear versions of some of these conditions. We define special language operations that allow us to produce, in a systematical and uniform way, languages that satisfy some combinations of the pumping conditions but not the others. We show, among others, that the general and the linear pumping conditions are “orthogonal,” whereas the generalized Ogden condition is stronger than the extended Sokolowski condition.

Modeling of jet vane heat-transfer characteristics and simulation of thermal response

Abstract: : The development of a dynamic computational model capable of predicting, with the requisite design certainty, the transient thermal response of jet vane thrust control systems has been undertaken. The modeling and simulation procedures utilized are based on the concept that the thermal processes associated with jet vane operation can be put into a transfer function form commonly found in the discipline of automatic controls. Well established system identification methods are employed to formulate and verify the relationships between the various gains and frequencies of the transfer function model and experimental data. Keywords: Dynamic systems modeling; Modeling; Model simulation; Thermal response; Parametric system identification; Theses.

Evaluation of the Spatial and Temporal Characteristics of the Conducting PRIZ

Abstract: : The imaging properties of the conducting PRIZ were re-evaluated using crystals which were carefully ground and polished to minimize surface layer damage. Resolution was quantified as a function of the energy density of the write-beam for both incoherent and coherent light sources. Maximum resolution from a standardized bar chart was determined using a model derived from a hybrid of luminance ratios used to evaluate image quality and the Rayleigh criteria for two point resolution. In addition, the spatial-temporal frequency dependence of the conducting PRIZ in the dynamic imaging mode was demonstrated and, quantified for coherent illumination over a range of spatial and temporal frequencies. The write-beam- induced damage threshold for these carefully prepared crystals was determined in terms of energy density. Optical memory of the device was found to last for 20-60 minutes, depending on the specific spatial frequency, at these peak energy densities when a single pulse of write-beam was applied. When multiple pulses of write-beam energy were applied, the frequency of the pulses (temporal frequency) as well as the energy density of the beam and spatial frequency of the object influenced memory decay. Keywords: Bismouth silicon oxide; Spatial light modulators; Theses.

Corona Wind Cooling Comparisons for Horizontal Cylinders

Abstract: : Corona wind 'refers to the movement of gas induced by the repulsion of ions from the vicinity of high voltage discharge electrode' A typical corona test configuration (13:4) is illustrated in Figure 1 Free charges are produced in the ionized region surrounding the high field active electrode These charged particles migrate and collide with neutral air particles in the drift Experiments were conducted to determine the effect of the corona wind on the convective heat transfer rate form each of three horizontally mounted, heated aluminum cylinders The cylinder was maintained at ground potential and an emitter was connected to a high voltage source Stretched wire and multipoint emitter devices were used Emitter-to-cylinder spacing and field voltage were parameters Blown air was also used to simulate the corona wind generated from the stretched wire emitter An energy balance method was used for data analysis Free convection heat transfer rates were used as a baseline The results of all experiments were compared and contrasted The multipoint emitter was a more efficient emitter device than the stretched wire emitter The convection heat transfer rate due to the corona wind with an applied high voltage field of 15kV was as much as 65 times the free convection heat transfer rate Keywords: Electrostatic cooling Theses

Bubble Detection Using a Dual Frequency Sound Field

Abstract: : The design, testing and analysis of a dual frequency system to detect and determine the resonance frequency (and hence the size) of bubbles ranging from 100 to 7 micro radius is reported. The resonance frequencies were compared to estimates based on the rise time of the bubbles. In general these comparisons agreed to within five percent. Although the system is not ideal for field measurements, it identifies important requirements concerning the size of the sample volume, the frequency and amplitude ranges of the sound fields and signal processing techniques to make an effective system. Bubbles are distinguished from non-gaseous particles by the nature of their nonlinear response to the dual sound field. The system is versatile and can be modified to suit many research purposes. Keyword: Bubble resonance frequency; Nonlinear bubble dynamics; Bubble detection; Bubble size; Dual frequency. Theses.

Optical Activity and Its Influence on Photorefractive Materials

Abstract: : The purpose of this study was to investigate the combined effects of optical activity and linear birefringence on photorefractive crystals. The relation of input-output intensity was determined. These results were discussed with regard to the operation and optimization of the conducting PRIZ. The study focused on the crystal Bi12SiO20 (BSO) in order to correlate results with current experimental work at AFIT. The combination of optical activity and the photorefractive effect caused the crystal to be elliptically birefringent; this birefringence was modeled using Jones matrices for computer simulation. The simulation results showed that optical activity does have a noticeable effect, but for the application investigated the effect was small enough that it could be ignored. Recommendations were made to improve the quality of the output image of the PRIZ. More work should be performed in this area to investigate other applications of this phenomenon and also different crystal materials. Bismuth compounds, theses, Silicon oxides.

Modified backward error propagation for tactical target recognition

Abstract: : This thesis explores a new approach to the classification of tactical targets using a new biologically-based neural network. The targets of interest were generated from doppler imagery and forward looking infrared imagery, and consisted of tanks, trucks, armored personnel carriers, jeeps and petroleum, oil, and lubricant tankers. Each target was described by feature vectors, such as normalized moment invariants. The features were generated from the imagery using a segmenting process. These feature vectors were used as the input to a neural network classifier for tactical target recognition. The neural network consisted of a multilayer perceptron architecture, employing a backward error propagation learning algorithm. The minimization technique used was an approximation to Newton's method. This second order algorithm is a generalized version of well known first order techniques, i.e., gradient of steepest descent and momentum methods. Classification using both first and second order techniques was performed, with comparisons drawn.

Measuring atmospheric free radicals using chemical amplification

Abstract: : Atmospheric free radicals play an important role in early all atmospheric cycles. The focus of this research was to continue characterizing the PEroxy Radical measurement by Chemical Amplification (PERCA) method first investigated by Cantrell (1983, 1984), then Buhr (1986). Experiments proved the original model of the PERCA method developed by Cantrell was too simple. New instrument modifications have insured optimum performance for peroxy radical measurement in clean, dry environments. The instrument is currently calibrated under laboratory conditions by observing the decay of HO2 radicals in a formaldehyde photolysis system. The reported chain lengths of 600 are in reasonable agreement with previously reported methods. Theses.

Construction of Gallium Arsenide Solar Concentrator for space use

Abstract: : A Gallium Arsenide (GaAs) Solar Concentrator Array (SCA) was constructed using the recently developed fresnel lens technology. The parts used were a mixture of space qualified components and readily available off-the-shelf items. THe objective of the test to verify that the SCA would substantially increase the array's power output and reject the high thermal radiation it would encounter in space. It was found that the 3 by 3 GaAs SCA power output increased from 29.88 mW to 433.71 mW. The thermal analysis and the steady state cell operating temperature calculation showed that the SCA's thermal design would keep the GaAs solar cells at a steady state temperature of 50.7 C. However, because of the low intensity level of the light source available for use the cell operating temperature was only 27 C. This was considered to be inconclusive in determining the adequacy of the thermal design.

Microwave characteristics of interdigitated photoconductors on a HEMT structure

Abstract: Interdigitated photoconductive detectors of various geometries were fabricated on AlGaAs/GaAs heterostructure material. The processes used in the fabrication of these devices are described, and the results of a study of their optical and electrical characteristics are presented.

Electromagnetic coupling by a wire through a cavity-backed circular aperture in an infinite screen

Abstract: The problem of a wire penetrating a circular aperture in an infinite screen and coupling energy into a cavity behind that screen is considered. We formulate an integral equation in terms of the electric field in the aperture. This integral equation is solved using two approximate methods: a zeroth-order approximation valid at low frequencies, and the method of moments. In addition, we introduce an equivalent circuit model to aid in our physical interpretation of the problem. Numerical results for the interior current on the wire and for the equivalent circuit admittance parameters are presented in order to provide a comparison between the two approximations.

Synthesis of 165-1165-1165-1-optimal linear feedback systems

Abstract: TheH ∞-optimization approach to feedback system design was introduced in the context of sensitivity minimization. This problem formulation yielded improper optimal controllers and did not incorporate design issues related to robustness and plant input cost. A more realistic problem formulation incorporating a weighting on the plant input was suggested earlier by the author and is pursued further in this paper. The optimization problem which results from this problem formulation is of mixed-sensitivity minimization and is solved by using tools from interpolation and approximation theory. This synthesis approach is believed to be of considerable promise for the design of linear feedback systems.

Observation of Brewster angle light scattering from air bubbles rising in water

Abstract: : Air bubbles rising freely through distilled water were illuminated by laser light with incident polarization of the electric field parallel to the plane of incidence. The radii a of the bubbles investigated were from 50 to 100 micrometers. At Brewster's angle of incidence i sub B = arctan (m) = 36.9, the Fresnel reflection coefficient vanishes, where m is the relative index of refraction for a water-air interface, m= 0.75. Therefore a minimum in scattered intensity should be observed at the Brewster scattering angle Theta sub B = 180 deg - 2i sub B = 106.2 deg. Furthermore interference patterns caused by different classes of rays should change drastically for angles around Brewster scattering angle Theta sub b. Experiments were done to detect these two phenomena by photographing the scattering light. The scattered intensity as a function of angle was inferred by scanning the photographs with a microdensitometer. To confirm the experimental results, they were compared with Mie theory calculation for scattering from spherical bubbles. Features of the scattering pattern due to ray interference could be understood using geometrical optics. The experiment confirmed that the observed features of the scattering pattern near Theta sub B are those predicted of a bubble having a clean surface. Since it has been previously calculated that the scattering pattern would be significantly different near Theta sub B if the surface of the bubble is coated by contamination, it is plausible that such a coating could be characterized optically. It is thought that the acoustics and dynamics of microbubbles in the ocean, or in other environments, may be affected by such coatings. Theses.

Optimal Low Thrust Trajectories for Planetary Capture

Abstract: : The purpose of this study is to find optimal low thrust capture trajectories in the restricted three body problem. The region of phase space which corresponds to capture by a body is bounded by the curve of zero velocity passing through the equilibrium point (Lagrange point) L2. If the spacecraft is driven to rest at L2, capture has been achieved by adding the least amount of energy. An optimal control law is developed to achieve this based on maximizing the Jacobi integral. The dynamics are then linearized around L2 for the Earth Moon system and the shooting method is used to solve the two point boundary value problem. This problem was found to be singular so the shooting method was modified to avoid making corrections along the null eigenvector. Four trajectories were found which demonstrate the optimal control law successfully caused the spacecraft to be captured by the Moon. Theses.