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Equations are derived for the general terms of the series obtained when certain operations are carried out on one or several given series. Explicit and recurrence relations are given for the literal groups which are common to the given series. A general method is shown to obtain the multipliers which depend on the operation being performed, and the method is illustrated for several examples.
The equilibrium properties of a two-dimensional plasma are examined theoretically within the framework of the random-phase approximation. The guiding-center case is of most interest because of the formal equivalence to two-dimensional discrete-line vortex fluids and because of the formal admissibility of negative temperatures. Using a judicious treatment of the periodic boundary conditions, extensive thermodynamics for nonnegative temperatures and a new value for the energy at which the temperature becomes negative are found. An explicit form for the structure function is derived and compared with the result of a Monte Carlo calculation. Good agreement is found for the negative-temperature-threshold prediction and for the general shape of the structure function. An equilibrium energy spectrum is calculated, which for positive temperatures, is the Debye-Hueckel result; for negative temperatures, it predicts an enhanced excitation of the lowest mode, corresponding to macroscopic charge separation.
The reported investigation is concerned with a stochastic inverse radiation problem in a uniform medium. The problem is illustrated with the aid of a simple model consisting of an array of point sources. The entropy functional is chosen to be the structural functional in determining the source distribution. A general theory for the stochastic inverse problem is introduced. It is shown that the general procedure yields the methods of the Lagrangian multiplier, when the structural and residual functionals are specialized. Tihonov's regularization and a method related to generalized or pseudoinverses are also obtained. Examples considered for purposes of illustration are related to a continuous source with the least noise intensity, a continuous source with a potential, and an axisymmetric line source.
An alternative structure for control systems is proposed. The structure is represented by a three-element block diagram and three functional definitions. It is argued that the three functional elements form a canonical set. The set includes the functions description, estimation and control. General overlay of the structure on parallel state and nested-state control systems is discussed. Breakdown of two real nested-state control systems into the proposed functional format is displayed. Application of the process to the mapping of complex control systems R and D efforts is explained with the Mars Rover Sample and Return mission as an example. A previous application of this basic functional structure to Space Station performance requirements organization is discussed.
This paper directly examines the claims of Segal (1976) that the (m,z) Hubble diagram is fitted best by a square law z = Kr-squared rather than by the traditional Hubble law z = Hr in the low-redshift range, z no more than about 0.01, corresponding to galaxies brighter than 14th mag. Segal attempts to fit a distance relation to the (m,z) scatter diagram in which each individual galaxy is plotted. The exact relation between the mean redshift for all galaxies in a small magnitude interval and the apparent magnitude is calculated. This relation is independent of luminosity function and peculiar velocity distribution about the general expansion, and is not affected by sample incompleteness as a function of apparent magnitude or the clustering of galaxies in the sample. Segal's method is affected by all of these and requires a highly sophisticated statistical analysis to deal with the non-Gaussian pointwise scatter. The present analysis favors the Hubble law and conclusively rules out the square law for the small redshift region.
This dissertation develops a new general method of solving Prony's problem. Two special cases of this new method have been developed previously. They are the Matrix Pencil and the Osculatory Interpolation. The dissertation shows that they are instances of a more general solution type which allows a wide ranging class of linear functional to be used in the solution of the problem. This class provides a continuum of functionals which provide new methods that can be used to solve Prony's problem.
At NASA, the Crew Health and Performance (CHP) system represents the span of countermeasures, capabilities, interventions, and tested processes and procedures that in combination work to mitigate the human component of spaceflight mission risk. Across the varying NASA mental models of the CHP system, the different functionalities needed to meet human flight systems standards can be broken down into specific categories (i.e. medical capability, environmental health, behavioral health). These categories can be further broken down into specific subgroups generally associated with the CHP functionalities meant to mitigate or buy down individual human system risks. Taking a similar development approach we seek to leverage dynamic probabilistic risk assessment as a means to quantify and relatively assess the human risk state within the crew health and performance domain. By utilizing existing tools as integrators, we propose a rapid development strategy for incorporating research and operational data that represent the influence of the CHP system functionalities, in order to provide order of magnitudes estimates of the influence on most human system risks outcomes. The model system utilizes a modest cumulative risk approach and that limits the scope to primary paths of influence between the CHP functionalities and human system risks, thus enabling quick prototypes of the integrative effects of CHP functional combinations to solicit valuable feedback from stakeholders and customers on the data, relationship, and structure of the integration.
This paper is the first in a series that will examine image formation in optical systems with polarization aberrations. The present paper derives the point-spread function (PSF) and the optical transfer function for optical systems with polarization aberration and explores how image formation depends on the coherence and polarization state of the source. It is shown that the scalar PSF of Fourier optics can be generalized in the presence of polarization aberration to a 4 x 4 point-spread matrix (PSM) in Mueller matrix notation. A similar 4 x 4 optical transfer matrix (OTM) is shown to be an appropriate generalization of the optical transfer function. The PSM and the OTM are associated with the optical system and are independent of the incident polarization state but dependent on the coherence of the illumination. Since an optical system with polarization aberrations will have a different PSF and optical transfer function for different incident polarization states, the PSM and the OTM act as filters with regard to the incident polarization state. Example calculations are performed for a circularly retarding lens.
We consider the design of multi-agent systems so as to optimize an overall world utility function when (1) those systems lack centralized communication and control, and (2) each agents runs a distinct Reinforcement Learning (RL) algorithm. A crucial issue in such design problems is to initialize/update each agent's private utility function, so as to induce best possible world utility. Traditional 'team game' solutions to this problem sidestep this issue and simply assign to each agent the world utility as its private utility function. In previous work we used the 'Collective Intelligence' framework to derive a better choice of private utility functions, one that results in world utility performance up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we extend these results. We derive the general class of private utility functions that both are easy for the individual agents to learn and that, if learned well, result in high world utility. We demonstrate experimentally that using these new utility functions can result in significantly improved performance over that of our previously proposed utility, over and above that previous utility's superiority to the conventional team game utility.
This paper introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing-edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio, and number of control surfaces. Using this information, the generalized forces are computed using the doublet-lattice method. Using Roger's approximation, a rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. All parameters can be easily modified if desired. The focus of this paper is on tool presentation, verification, and validation. These processes are carried out in stages throughout the paper. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool, therefore, the flutter speed and frequency for a clamped plate are computed using damping-versus-velocity and frequency-versus-velocity analysis. The computational results are compared to a previously published computational analysis and wind-tunnel results for the same structure. A case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to damping-versus-velocity and frequency-versus-velocity analysis, including the analysis of the model in response to a 1-cos gust.
This report introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing-edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio, and number of control surfaces. Using this information, the generalized forces are computed using the doublet-lattice method. Using Roger's approximation, a rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. All parameters can be easily modified if desired. The focus of this report is on tool presentation, verification, and validation. These processes are carried out in stages throughout the report. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool, therefore, the flutter speed and frequency for a clamped plate are computed using damping-versus-velocity and frequency-versus-velocity analysis. The computational results are compared to a previously published computational analysis and wind-tunnel results for the same structure. A case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to damping-versus-velocity and frequency-versus-velocity analysis, including the analysis of the model in response to a 1-cos gust.
Finite field arithmetic logic is central in the implementation of some error-correcting coders and some cryptographic devices. There is a need for good multiplication algorithms which can be easily realized. Massey and Omura recently developed a new multiplication algorithm for finite fields based on a normal basis representation. Using the normal basis representation, the design of the finite field multiplier is simple and regular. The fundamental design of the Massey-Omura multiplier is based on a design of a product function. In this article, a generalized algorithm to locate a normal basis in a field is first presented. Using this normal basis, an algorithm to construct the product function is then developed. This design does not depend on particular characteristics of the generator polynomial of the field.
The assumed modes method is used to investigate the stability of the GEOS satellite. The system is discretized by representing the continuous displacement by finite series of space-dependent admissible functions multiplied by time-dependent generalized coordinates. The spatial dependence is eliminated by integration over the elastic domains, so that the testing functional reduces to a testing function. The sign properties of the testing function are then tested and the equilibrium defined as nontrivial. In considering the stability of small motions about nontrivial equilibrium, it is shown that if the analysis performed by ignoring the motion of the mass center indicates stability, then the system remains stable if the motion of the mass center is included.
A five-parameter gamma distribution (BGD) having two shape parameters, two location parameters, and a correlation parameter is investigated. This general BGD is expressed as a double series and as a single series of the modified Bessel function. It reduces to the known special case for equal shape parameters. Practical functions for computer evaluations for the general BGD and for special cases are presented. Applications to wind gust modeling for the ascent flight of the space shuttle are illustrated.
A five parameter gamma distribution (BGD) having two shape parameters, two location parameters, and a correlation parameter is investigated. This general BGD is expressed as a double series and as a single series of the modified bessel function, and reduces to the known special case for equal shape parameters. Practical functions for computer evaluations for the general BGD and for special cases are presented. Applications are to be bound in reliability theory, signal noise, and meteorology. Applications to wind gust modeling for the ascent flight of the space shuttle are illustrated.
RNA molecules that are assembled from the four standard nucleotides contain a limited number of chemical functional groups, a characteristic that is generally thought to restrict the potential for catalysis by ribozymes. Although polypeptides carry a wider range of functional groups, many contemporary protein-based enzymes employ coenzymes to augment their capabilities. The coenzymes possess additional chemical moieties that can participate directly in catalysis and thereby enhance catalytic function. In this work, we demonstrate a mechanism by which ribozymes can supplement their limited repertoire of functional groups through RNAcatalyzed incorporation of various coenzymes and coenzyme analogues. The group I ribozyme of Tetrahymena thermophila normally mediates a phosphoester transfer reaction that results in the covalent attachment of guanosine to the ribozyme. Here, a shortened version of the ribozyme is shown to catalyze the self-incorporation of coenzymes and coenzyme analogues, such as NAD+ and dephosphorylated CoA-SH. Similar ribozyme activities may have played an important role in the "RNA world," when RNA enzymes are thought to have maintained a complex metabolism in the absence of proteins and would have benefited from the inclusion of additional functional groups.
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
A simple problem of a two-body system perturbed by the disturbing function epsilon/r-squared is considered to show that the time-averaged equations of the true and mean anomaly are not necessarily equal. Secular effects due to perturbations in the mean and true anomalies are different not only in value but also in sign. A more general case where the disturbing function is periodic with respect to the mean anomaly is also considered. Here a discrepancy in the time-averaged solutions is due to the fact that the mean anomaly is an action-angle variable conjugate to the action variable L, while the true anomaly is not. When the action-angle variables are chosen as dependent variables, the Hamiltonian is a function only of action variables. One must first derive first-order solutions, substitute them into the right-hand side of the equations of motion, and then take time averages.