Omega Systems Research Articles

Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields

Omega rings (Ω-rings) (and other related structures) are lattice-valued structures (with Ω being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, Ω-ideals are introduced, and natural connections with Ω-congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over Ω-fields is developed.

A rich legacy

This note describes the early developments at CERN of the Cherenkov Ring Imaging technique, inspired by the seminal works of Tom Ypsilantis and Jacques Séguinot, continuing by the construction and operation of the RICH counter for the experiment E605 at Fermilab and soon followed by the large OMEGA and DELPHI barrel RICH systems at CERN.

Distributed optimal control of lambda–omega systems

Distributed optimal control of lambda–omega systems

Distributed optimal control of lambda–omega systems

The formulation, analysis, and numerical solution of distributed optimal control problems governed by lambda-omega systems is presented. These systems provide a universal model for reaction-diffusion phenomena with turbulent behavior. Existence and regularity properties of solutions to the free and controlled lambda-omega models are investigated. To validate the ability of distributed control to drive lambda-omega systems from a chaotic to an ordered state, a space-time multigrid method is developed based on a new smoothing scheme. Convergence properties of the multigrid scheme are discussed and results of numerical experiments are reported.

Experiences with a space–time multigrid method for the optimal control of a chemical turbulence model

AbstractLambda–omega systems provide a universal model to investigate two‐species reaction diffusion problems. In the case of fast reaction kinetics and small diffusion, these systems evolve to turbulent behaviour. A class of open‐loop optimal control problems governed by lambda–omega systems in the turbulent regime is investigated. Optimal solutions are characterized by optimality systems consisting of two pairs of reaction diffusion equations with opposite time orientation. These systems are solved by a space–time multigrid scheme suitable for the turbulent setting. Numerical examples are given where the control drives the chaotic system to form regular patterns. Copyright © 2005 John Wiley & Sons, Ltd.

The amplitude of periodic plane waves depends on initial conditions in a variety of lambda - omega systems

lambda - omega systems are an important prototype for the study of reaction-diffusion equations whose kinetics possess a stable limit cycle. Here I use such systems to investigate the evolution of periodic plane waves from exponentially decaying initial data. I begin by considering the case in which lambda (.) and omega (.) are both monotonic functions. I show that in this case the reaction diffusion solution consists of a wave front moving across the domain, with periodic plane waves behind. I show that the amplitude of these periodic plane waves is the unique solution of a simple algebraic equation. For some parameter values, the waves of this amplitude are unstable as partial differential equation solutions and, in this case, the periodic plane waves degenerate into more irregular oscillations. I go on to consider a case in which lambda (.) is a cubic polynomial, of a form so that the algebraic equation governing periodic plane wave amplitude has more than one solution. I show that it is the waves of smallest possible amplitude that appear in the reaction-diffusion solutions, and that there is a novel bifurcation in the partial differential equations as these waves appear.

A Novel Method for Extending GPS to Underwater Applications

The need for accuracy, precision, and data registration in underwater positioning and navigation should be viewed as no less stringent than that existing on the surface or in the aerospace environment. This paper proposes a system that can be used to provide navigation service to free-ranging underwater users. This system uses buoys that act as roving pseudolites and translate GPS radio-based service to an acoustic-based service under water. Using this service, an unlimited number of users can independently locate themselves and navigate. Underwater extensions of Loran, Omega, or other radio-based navigation systems are also amenable to the technique.

Special Issue: Decision Support and Knowledge-Based Systems

Robert W. Blanning is Professor of Management Information Systems at the Owen Graduate School of Management at Vanderbilt University. He holds a B.S. in Physics from the Pennsylvania State University, an M.S. in Operations Research from the Case Institute of Technology, and a Ph.D. from the University of Pennsylvania, specializing in operations research and management information systems. He has been a member of the faculties of the School of Business at New York University and the Wharton School at the University of Pennsylvania. His teaching and research interests are in model management systems, information economics, and the management applications of artificial intelligence. He has published in Management Science, Decision Sciences, Communications of the ACM, Naval Research Logistics Quarterly, Decision Support Systems, Information and Management, Omega, Policy Analysis and Information Systems, International Journal of Policy and Information, Human Systems Management, Journal of Information Science, Long Range Planning, and Technological Forecasting and Social Change. He has presented papers at the National Computer Conference, the International Conference on Decision Support Systems, the Hawaii International Conference on Systems Sciences, the International Workshop on Expert Database Systems , and the International Workshop on Artificial Intelligence in Economics and Management. He is a member of the Board of Editors of JMIS, a member of the Editorial Boards of Decision Support Systems and Information Systems Research, and Associate Editor of Information and Decision Technologies and in the Decision Support Systems Department of Management Science.

Further eötvös correction error reduction through the utilization of baseline radio navigation systems

The current accuracy of sea‐going and airborne gravity measurements is not bounded by the precision of the gravimeter but by the precision with which external parameters such as vehicle velocity (speed), azimuthal heading, and geographic position can be determined. Uncertainties in these parameters are summed up in the Eötvös correction in the reduction of the measured data. This work investigates the suitability of baseline navigation systems, in particular Loran‐C and Omega, to further reduce the uncertainty of the Eötvös correction. Emphasis is placed on the velocity measurement error. A new algorithm is developed which derives velocity based upon the change in hyperbolic (or circular) grid readings, as opposed to the standard change in geographic position technique. A comparative analysis shows the new algorithm to be as precise as the currently used conventional calculation. Further, this simplified technique is accompanied with a 20‐fold reduction in computational complexity. Application of the results presented in this paper to the Loran‐C and Omega systems shows a velocity determination capability of 0.1 knot over a six minute integration time, and 0.05 knot for a 15 minute integration time for Loran‐C. The minimum error attainable in Omega is 0.1 knot when determined over a 17 minute measurement time. Further precision can be gleaned by applying the calculated error as a correction to subsequent velocity calculations.

Inshore Navigational System Conceptual Advances

The U.S. Navy, through a contract with MYSTECH ASSOCIATES, INC., has developed an advanced proto-type navigational system called MATCH-NAV, which utilizes a mini-computer to provide automated own-ship geographic position in inshore, coastal navigation situations. Conceptual development of MATCH-NAV has demonstrated the capability to provide ownship position display on digitized nautical charts, with overlay of the chart data on a radar Plan Position Indicator (PPI). Future plans include utilization of the MATCH-NAV concept in design of a completely automated Ownship Position Display having stored nautical chart capability, which can accept navigational data inputs from such ship's sensors as Loran-C, Omega, radar and other precision electronic navigation systems, including satelite systems. The goal—to provide continuous, accurate, real-time visual display of ship's position in restricted coastal waters. This paper discusses the MATCH-NAV concept and its potential applications in future inshore navigation.

The Impact of the Choice of Frequency and Modulation on Radio Navigation Systems

the choice of frequency for radio navigation is a subject of considerable depth and is inextricably intertwined with requirements for range, accuracy, reliability, cost and impact on competitive services using radiowaves. The basic information for passing judgment on these items comprises the limitations imposed by nature on the system. These limitations are the laws of physics governing the propagation of radio waves. We note in particular that great ranges and hence large coverage areas can be obtained at opposite ends of the spectrum in the OMEGA and SATELLITE systems. We find that great accuracy is accomplished with the ground wave propagation mechanism in the form of Loran–C and Loran–D. We observe that the choice of modulation is critical if high accuracy of position is an objective or requirement.

New Developments in Radar and Radio Sensors for Aircraft Navigation

Recent developments in airborne Doppler and ground mapping navigation radars and ground and satellite based radio systems are described. Simultaneous lobing and slope tracking techniques can remove the well-known Doppler sea bias error in fast and slowly moving vehicles. Doppler velocity information can be extracted from coherent forward-looking mapping radars, and high position fixing accuracy can be achieved by synthetic aperture radars. In radio navigation systems, such as Loran, Omega, and satellite systems, direct-ranging and differential techniques greatly reduce the geometric dilution and propagation effects which have plagued conventional radio navigation systems. The advantages gained by mixing of the data from these and other navigation sensors in a digital multisensor system are discussed and approaches for processing these data are suggested.

Navigation Aid Requirements for the U. S. Coastal/Confluence Region

A summary of a technical evaluation of the Decca, Differential Omega and Loran-C systems' capabilities to fulfill the navigation requirements of mariners in the U. S. Coastal Confluence Region is presented. This paper includes a summary of marine operational requirements, system evaluation criteria and system performance comparisons. The results of the evaluation lead to the recommendation of a system for implementation to satisfy the marine navigation needs in the U. S. Coastal Confluence Region. The work was completed by Polhemus Navigation Sciences, Inc., under contract to the U. S. Coast Guard.