Lance D. Drager
Texas Tech University
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Featured researches published by Lance D. Drager.
Journal of The Franklin Institute-engineering and Applied Mathematics | 2007
Lance D. Drager; Jeffrey M. Lee; Clyde F. Martin
A number of numerical codes have been written for the problem of finding the circle of smallest radius in the Euclidean plane that encloses a finite set P of points, but these do not give much insight into the geometry of this circle. We investigate geometric properties of the minimal circle that may be useful in the theoretical analysis of applications. We show that a circle C enclosing P is minimal if and only if it is rigid in the sense that it cannot be translated while still enclosing P. We show that the center of the minimal circle is in the convex hull of P. We use this rigidity result and an analysis of the case of three points to find sharp estimates on the diameter of the minimal circle in terms of the diameter of P.
Systems & Control Letters | 1985
Lance D. Drager; Clyde F. Martin
Abstract It is shown that discrete time systems whose dynamics are governed by piecewise monotone maps of the interval are globally observable under a general class of observations. The results rest on the fact that the dynamics are ergodic.
Theory of Computing Systems \/ Mathematical Systems Theory | 1986
Lance D. Drager; Clyde F. Martin
Kroneckers theorem is used to show that the irrational flows on then-dimensional torus are globally observed by a large class of continuous functions. These results are used to study the observability of Riccati flows on the Grassman manifolds.
North-holland Mathematics Studies | 1984
Lance D. Drager; William J. Layton
Publisher Summary This chapter describes some results concerning the qualitative properties of bounded solutions of the nonlinear (scalar) delay differential equation. The chapter extends these results and places them in a general framework by considering certain subalgebras of the algebra of bounded continuous functions on the line.
IEEE Transactions on Information Theory | 2003
Robert E. Byerly; Lance D. Drager; Jeffrey M. Lee
We study the observability of a permutation on a finite set by a complex-valued function. The analysis is done in terms of the spectral theory of the unitary operator on functions defined by the permutation. Any function f can be written uniquely as a sum of eigenfunctions of this operator; we call these eigenfunctions the eigencomponents of f. It is shown that a function observes the permutation if and only if its eigencomponents separate points and if and only if the function has no nontrivial symmetry that preserves the dynamics. Some more technical conditions are discussed. An application to the security of stream ciphers is discussed.
conference on decision and control | 1987
Lance D. Drager; Robert L. Foote; Douglas Mcmahon
Doug McMahon was killed in a climbing accident in late 1986. He was a member of the Department of Mathematics at Arizona State University. The first two authors feel fortunate to have known Doug and to have worked with him. We would also like to thank Cris Brynes and Clyde Martin for getting us together with Doug.
Archive | 1986
Lance D. Drager; Clyde F. Martin
Harmonic analysis is used to show that an ergodic translation on a compact abelian group is observed by almost all continuous scalar functions.
conference on decision and control | 1985
Lance D. Drager; Clyde F. Martin
Aspects of global observability (GO) for some standard examples of chaotic systems are considered, the underlying philosophy being that such systems should be easy to observe and should be observed by large classes of scalar functions. Consideration is given to GO for piecewise monotone maps of the interval (a standard example of a chaotic system). Attention is then given to GO for ergodic translations on compact (metrizable) topological groups; the most familiar examples are the irrational translation flows on the n-torus.
North-holland Mathematics Studies | 1985
Lance D. Drager; William J. Layton
We study the non-linear delay differential equation x′(t) + g(x(t), x (t−τ))= f(t) under a non-resonance condition which assures the existence of a unique bounded solution. Using the algebra structure of the space of bounded continuous functions we investigate the properties of this solution. We discuss some generalizations and the initial value problem.
North-holland Mathematics Studies | 1985
Lance D. Drager; William J. Layton; Robert M.M. Mattheij
We consider the evolution equation (E) du/dt = au + f(t,u), u(0) = u0 in a Hilbert space H, where A is assumed to generate a C0 semigroup. The asymptotic-in-time behavior of solutions to (E) is studied together with the asymptotic-in-time behavior of methods for approximating (E).