Dreyfus

Variational calculus, Dreyfus (1962), may be employed to obtain a set of differential equations with certain boundary condition properties, known as the Euler-Lagrange equations. The maximum principle of Pontryagin (1962) can also be applied to provide the same boundary conditions by using a Hamiltonian function. 

Dreyfus, S.E. (1962) Variational Problems with Inequality Constraints, J. Math. Anal. Appl, 4, p. 297. 

The preparation of this manuscript and the research described herein was supported by grants form the Microgravity Sciences Program of the National Aeronautics and Space Adminsitration, by the Mobil Foundation and by a Teacher-Scholar Award from the Camille and Henry Dreyfus Foundation to RAB. 

Bellman, R., and Dreyfus, S Applied Dynamic Programming. Princeton University Press, Princeton, NJ, 1962. 

Financial support from Dow Coming Corporation and from the American Chemical Society (Grant CHE 93-18625) is gratefully acknowledged. BEB also gratefully acknowledges support from the Camille and Henry Dreyfus Foundation in the form of a Teacher-Scholar Award. 

J. Lorquin, G. Lortet, M. Ferro, N. Mear, B. Dreyfus, J.-C. Prome, and C. Boivin, Nod factors from Sinorhizobium saheli and 5. teranga bv. sesbaniae are both arabi-nosylated and fucosylated, a structural feature specific to Sesbania rostrata symbionts. Molec. Plant Microbe Interact. I0 il9 (1997). 

Brian Johnson and Margret Geselbracht are thanked for critically reading this manuscript. On behalf of the Ad Hoc Committee for Solid-State Instructional Materials, it is a pleasure to acknowledge the National Science Foundation (Grant USE—9150484), the Camille and Henry Dreyfus Foundation, the American Chemical Society, the Dow Chemical Company Foundation (Solid-State Model Kit), the University of Wisconsin—Madison Outreach Program (Solid-State Model Kit), and the Institute for Chemical Education for their generous support of this project. 

Santisteban, I., Arredondo-Vega, F. X., Kelly, S., Debre, M., Fischer, A., Pdrignon, J. L., Hilman, B., Eldahr, J., Dreyfus, D. H., Howell, P. L., and Hershfield, M. S Four new adenosine deaminase mutations, altering a zinc-binding histidine, two conserved alanine, and a 5 splice site. Hum. Mutat. 5,243-250 (1995). 

The author s research work on photochemistry of free radicals has been supported by US National Science Foundation, ACS Petroleum Research Fund, Camille and Henry Dreyfus Foundation, A. P. Sloan Foundation, and UC Regents Faculty Fellowships and Faculty Development Award. 

This project was initiated by JM and NH and continued by KH, and AT as part of the CHEM 1108 Freshman Chemistry Research Rotation taught by Prof. W. R. Murphy, Jr. at Seton Hall University. We thank Merck Co., Inc. for partial support of this research through an unrestricted grant. We also thank the Camille and Henry Dreyfus Foundation for support of TC through the Partners-in-Science Program and the ACS Project SEED program for support of MK. 

The NT-300 NMR spectrometer at Rockefeller University was purchased in part from funds from the National Science Foundation (PCM-7912083) and from the Camille and Henry Dreyfus Foundation. The WM-500 spectrometer is part of the Southern California Regional NMR Facility at Caltech and is supported by National Science Foundation Grant CHE-7916324. 

Acknowledgments We would like to thank the National Science Foundation (DMR-0135233, DMR-0703988, Chem-0456719, Chem-0723497), the ACS Petroleum Research Fund (36730-G7), the Dupont Company, the 3 M Company, the Simitomo Company, the Rhom and Haas Company, and the Univesity of California at Irvine for generous financial support. ZG gratefully acknowledges a Friedrich Wilhelm Bessel Research Award granted by the Alexander von Humboldt Foundation, a National Science Foundation CAREER Award, and a Camille Dreyfus Teacher-Scholar Award. CSP acknowledges an Allergan Fellowship, a UCI dissertation fellowship, and the Joan Rowland award from UCI. 

This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy under Contract No. W-7405 Eng-48. We thank Dr. H. Heinemann and Professors A. T. Bell, R. G. Bergman, and G. A. Somorjai for stimuu-lating comments. K.P.C.V. is an Alfred P. Sloan Fellow (1976-1980) and a Camille and Henry Dreyfus Teacher-Scholar (1978-1983). 

Yu, R. K. and Ando, S. Structures of some new complex gangliosides. In L. Svennerholm, P. Mandel, H. Dreyfus and P.-F. Urban (eds), Structure and Function of Gangliosides. New York Plenum Press, 1980, pp. 33M5. 

The tautomerisation of the N(9)H- and N(7)H-isomers of adenine (93) has been studied in aqueous solution using the temperature-jump technique with Joule heating (Dreyfus et al., 1975). The equilibrium constant K = [N(7)H]/[N(9)H] has a value of 0.28 at 20°C. The reciprocal relaxation time... 

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