Contents Preface ix I. Research and Expository Papers 1 A lower bound for the chromatic number of a graph EARL R. BARNES 3 The fractional parts of ~ M. R. CURRIE AND E. H. GOINS 13 Ultrafilters and Ramsey theory DENNIS E. DAVENPORT 33 Artin's conjecture and elliptic curves EDRAY HERBER GOINS 39 Chaoticity results for "join the shortest queue" CARL GRAHAM 53 Maintenance of deteriorating machines with probabilistic monitoring and silent failures JULIE SIMMONS IVY AND STEPHEN M. POLLOCK 69 The application of numerical grid generation to problems in computational fluid dynamics BONITA V. SAUNDERS 95 The elementary residual method DESMOND STEPHENS AND GARY HOWELL 107 The response of the upper ocean to surface buoyancy forcing: A characteristic solution to wave propagation MONICA Y. STEPHENS AND ZHENGYU LIU 117 An overview of integro-differential equations and variational Lyapunov method SONYA A. F. STEPHENS AND V. LAKSHMIKANTHAM II. Papers on Philosophy of Mathematics The art of mathematics JERRY P. KING vii 129 137 139
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