Usually this theorem is proved by using continued fractions; see Theorem 193 in [2]. S. Hartman [3] has restricted the approximating numbers f to those fractions, where u and v belong to fixed residue classes a and b with respect to some modulus s. He proved the following: For any irrational number £, any s > 1, and integers a and b, there are infinitely many integers u and v > 0 satisfying 2s (1)

S. A. Isard and N. S. Dufault, Department of Plant Pathology, Pennsylvania State University, University Park, USA; M. R. Miles and G. L. Hartman, USDA/ARS, Department of Crop Sciences, University of Illinois, UrbanaChampaign, USA; J. M. Russo, ZedX Inc., Bellefonte, PA, USA; E. D. De Wolf, Department of Plant Pathology, Pennsylvania State University, University Park, USA; and W. Morel, Centro R...

P. Tenenbaum, D. Burke, S. Hartman, R. Helm, J. Irwin, R. Iverson, P. Raimondi, W. Spence Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 USA V. Bharadwaj, M. Halling, J. Holt Fermi National Accelerator Laboratory, Batavia, Illinois, USA J. Buon, J. Jeanjean, F. Le Diberder, V. Lepeltier, P. Puzo** Laboratoire de l’Accélérateur Linéaire, Orsay, France K. Oide, T. Shi...

2 Vickery, H. B., and Pucher, G. W., J. Biol. Chem., 90, 637 (1931). 3 Vickery, H. B., and Pucher, G. W., Connecticut Agric. Exp. Station, Bull. 352 (in press). 4 Dunbar, P. B., and Bacon, R. F., Ind. and Eng. Chem., 3, 826 (1911). 6 Hartman, B. G., and Hillig, F., J. Assn. Off. Agric. Chemists, 10, 264 (1927); 13, 99 (1930). 6 Vickery, H. B., and Pucher, G. W., Connecticut Agric. Exp. Station,...

Aharoni, R. and I. Ben-Arroyo Hartman, On Greene-Kleitman’s theorem for general digraphs, Discrete Mathematics 120 (1993) 13-24. Linial conjectured that Greene-Kleitman’s theorem can be extended to general digraphs. We prove a stronger conjecture of Berge for digraphs having k-optimal path partitions consisting of ‘long’ paths. The same method yields known results for acyclic digraphs, and exte...

T. A. Pham, Department of Crop Sciences, National Soybean Research Center (NSRC), University of Illinois, Urbana; M. R. Miles, United States Department of Agriculture–Agricultural Research Service (USDA-ARS), NSRC, Urbana, IL 61801; R. D. Frederick, USDA-ARS, Foreign Disease-Weed Science Research Unit, Ft. Detrick, MD 21702; C. B. Hill, Department of Crop Sciences, NSRC, University of Illinois;...

In this paper, we develop a general framework for studying Dirichlet Boundary Value Problems (BVP) for second order symmetric implicit differential systems satisfying the Hartman-Nagumo conditions, as well as a certain non-expandability condition. The main result, obtained by means of the equivariant degree theory, establishes the existence of multiple solutions together with a complete descrip...

We demonstrate the counterintuitive dispersion effect that the peaks (dips) in the gain spectrum correspond to abnormal (normal) dispersion, contrary to the usual Kramers-Kronig point of view. This effect may also lead to two unique features: a broadband abnormal dispersion region and an observable Hartman effect. These results are explained in terms of interference and boundary effects. Finall...

M. R. Miles, United States Department of Agriculture–Agricultural Research Service (USDA-ARS), National Soybean Research Center, University of Illinois, Urbana 61801; M. A. Pastor-Corrales, USDA-ARS, Vegetable Laboratory, Beltsville, MD 20705; G. L. Hartman, USDA-ARS, National Soybean Research Center, Department of Crop Sciences, University of Illinois, Urbana; and R. D. Frederick, Foreign Dise...

Allan R. Tunkel, Barry J. Hartman, Sheldon L. Kaplan, Bruce A. Kaufman, Karen L. Roos, W. Michael Scheld, and Richard J. Whitley Drexel University College of Medicine, Philadelphia, Pennsylvania; Weill Cornell Medical Center, New York, New York; Baylor College of Medicine, Houston, Texas; Medical College of Wisconsin, Milwaukee; Indiana University School of Medicine, Indianapolis; University of...