Brizolis asked the question: does every prime p have a pair (g, h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditio...

Campbell and Cochrane (1999) propose a preference speci cation that can explain a wide variety of asset pricing puzzles such as the high equity premium. They augment the basic power utility function with a time-varying subsistence level, or \habit", which is in the spirit of \catching up with the Joneses" but with a novel nonlinear mapping of consumption into habit. This paper demonstrates a su...

We study two related versions of the no-impatience postulate in the context of transitive and reflexive relations on infinite utility streams which are not necessarily complete. Both are excluded by the traditional (weak) anonymity axiom. We show explicit social welfare relations satisfying Strong Pareto and the weaker version of noimpatience that are compatible with continuity in all the tradi...

MARS. J. J Plaut 1 , A. Safaeinili 1 , B. A. Campbell 2 , R. J. Phillips 3 , N. E. Putzig 3 , D. C. Nunes 1 , R. Seu 4 . 1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 ([email protected]), 2 Center for Earth and Planetary Studies, National Air and Space Museum, Smithsonian Institution, Washington, D.C. 20560, 3 Southwest Research Institute, Boulder, CO 8030...

Problems in which abnormal or novel situations should be detected can be approached by describing the domain of the class of typical examples. These applications come from the areas of machine diagnostics, fault detection, illness identification, or, in principle, refer to any problem where little knowledge is available outside the typical class. In this paper, we explain why proximities are na...

We propose in this article a two-step testing procedure of fractional cointegration in macroeconomic time series. It is based on Robinson’s (1994) univariate tests and is similar in spirit to the one proposed by Engle and Granger (1987), testing initially the order of integration of the individual series and then, testing the degree of integration of the residuals from the cointegrating relatio...

b The University of Alabama at Birmingham Department of Computer and Information Sciences 115A Campbell Hall, 1300 University Boulevard, Birmingham, Alabama 35294-1170, United States { bryant, gray}@cis.uab.edu Phone: +1 205-934-2213 Fax: +1 205-934-5473 c University of Maribor Faculty of Electrical Engineering and Computer Science Smetanova ulica 17, 2000 Maribor, Slovenia marjan.mernik@uni-mb...

A central theme of this chapter is the following: to better understand the role of the teacher within a computer-supported collaborative learning (CSCL) environment, it is necessary to better conceptualize the CSCL construct. Toward this goal, this chapter will examine similarities and differences between cooperative and collaborative learning. Next, CSCL will be examined in the context of coop...

Kirill N. Alekseev, Ethan H. Cannon, Jonathan C. McKinney, Feodor V. Kusmartsev, and D.K. Campbell Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green St., Urbana, IL 61801, USA Department of Physical Sciences, Box 3000, University of Oulu FIN-90014, Finland Theory of Nonlinear Processes Laboratory, Kirensky Institute of Physics, Krasnoyarsk 660036, Russia Departm...

In many different fields of mathematics and physics Poincaré found many uses for the idea of a group, but not for group theory. He used the idea in his work on automorphic functions, in number theory, in his epistemology, Lie theory (on the so-called Campbell–Baker–Hausdorff and Poincaré–Birkhoff–Witt theorems), in physics (where he introduced the Lorentz group), in his study of the domains of ...