A Note on Knights, Knaves, and Truth Tables

Student and teacher (in the order above) have taken on a project of trying to understand something about Boolean algebra, logic circuits, and applications with the aid of Mathematica. We quickly recognized that the logical puzzles popularized by Raymond Smullyan that involve Knights (truth tellers) and Knaves (liars) are ideally suited for analysis by Boolean methods and truth tables. with a big boost from Mathematica. Not only is there a lot of mathematics to be learned, there is a great deal of fun to be had. The topic seems to us to be an ideal vehicle for exposing young high school and undergraduate college students to wonderful mathematics outside of the standard Advanced Placement Calculus stream

Home Garden Hotbeds

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Mathematics from China to Virginia by Way of Singapore

Our article follows from an interesting concurrence of mathematical and educational lines. At least the concurrence seems so to us and we hope that those who read on will agree. The lines or streams are a joint minimester program at St. Catherine’s and St. Christopher‘s Schools, an interest in problem solving, and a Singapore connection. We shall describe the lines first and then describe the mathematics that we found at their intersection

Raman gain against a background of non-thermal ion fluctuations in a plasma

A complex stimulated Raman scattering event against a background of non-thermal ion acoustic waves in an inhomogeneous plasma is described. We obtain analytic forms for the Raman gain due to a five-wave interaction consisting of conventional three-wave Raman scattering followed by the decay of the Raman Langmuir wave into a second Langmuir wave (or a second scattered light wave) and an ion acoustic wave. Very modest levels of ion waves produce a. significant effect on Raman convective gain. A combination of plasma inhomogeneity and suprathermal ion fluctuations may offer a means for the control of Raman gain

LANDSAT range resource information system project, volume 1

There are no author-identified significant results in this report

Control law parameterization for an aeroelastic wind-tunnel model equipped with an active roll control system and comparison with experiment

Nominal roll control laws were designed, implemented, and tested on an aeroelastically-scaled free-to-roll wind-tunnel model of an advanced fighter configuration. The tests were performed in the NASA Langley Transonic Dynamics Tunnel. A parametric study of the nominal roll control system was conducted. This parametric study determined possible control system gain variations which yielded identical closed-loop stability (roll mode pole location) and identical roll response but different maximum control-surface deflections. Comparison of analytical predictions with wind-tunnel results was generally very good

The effect of composition on the mechanism of stress-corrosion cracking of titanium alloys in nitrogen tetroxide, and aqueous and hot- salt environments Annual summary report, 1 May 1967 - 30 Apr. 1968

Stress corrosion data for titanium alloys in aqueous, hot salt, and nitrogen dioxide environment

Interior Point Decoding for Linear Vector Channels

In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector channels include many practically important channels such as inter symbol interference channels and partial response channels. It is shown that the maximum likelihood decoding (MLD) rule for a linear vector channel can be relaxed to a convex optimization problem, which is called a relaxed MLD problem. The proposed decoding algorithm is based on a numerical optimization technique so called interior point method with barrier function. Approximate variations of the gradient descent and the Newton methods are used to solve the convex optimization problem. In a decoding process of the proposed algorithm, a search point always lies in the fundamental polytope defined based on a low-density parity-check matrix. Compared with a convectional joint message passing decoder, the proposed decoding algorithm achieves better BER performance with less complexity in the case of partial response channels in many cases.Comment: 18 pages, 17 figures, The paper has been submitted to IEEE Transaction on Information Theor

Overcoming observability problems in distributed test architectures

This paper investigates conditions that must be satisfied by an FSM for the existence of input sequences that can be applied in a distributed test architecture without encountering controllability and observability problems and without using external coordination messages. Such conditions have two potential values. First, they can be used to determine whether we require coordination messages and thus a network that connects the testers. Second, if we wish to avoid the use of coordination messages in testing then these conditions can be seen as testability conditions that can inform the design process. Results given in this paper differ from those in the following ways. First, the conditions are strictly weaker than those in since we are less restrictive in the ways we achieve our goals. Second, only considered observability problems; we consider both controllability and observability problems. In addition, only considered a particular type of observability problem and we generalize this. Finally, we investigate the situation in which we need only add input sequences to complement a given test/checking sequence ρ and prove that the conditions for this problem are equivalent to those for the original problem

Dynamic Energy Management

We present a unified method, based on convex optimization, for managing the power produced and consumed by a network of devices over time. We start with the simple setting of optimizing power flows in a static network, and then proceed to the case of optimizing dynamic power flows, i.e., power flows that change with time over a horizon. We leverage this to develop a real-time control strategy, model predictive control, which at each time step solves a dynamic power flow optimization problem, using forecasts of future quantities such as demands, capacities, or prices, to choose the current power flow values. Finally, we consider a useful extension of model predictive control that explicitly accounts for uncertainty in the forecasts. We mirror our framework with an object-oriented software implementation, an open-source Python library for planning and controlling power flows at any scale. We demonstrate our method with various examples. Appendices give more detail about the package, and describe some basic but very effective methods for constructing forecasts from historical data.Comment: 63 pages, 15 figures, accompanying open source librar