Author | Hua, Loo-Keng. author |
---|---|
Title | Popularizing Mathematical Methods in the People's Republic of China [electronic resource] : Some Personal Experiences / by Loo-Keng Hua, Yuan Wang ; edited by J. G. C. Heijmans |
Imprint | Boston, MA : Birkhรคuser Boston, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-6757-4 |
Descript | XXII, 209 p. online resource |
0 Introduction -- ยง 0.1 Three principles -- ยง 0.2 Looking for problems in the literature -- ยง 0.3 Looking for problems in the workshop -- ยง 0.4 Optimum seeking methods (O.S.M) -- ยง 0.5 The Fibonacci search -- ยง 0.6 The golden number and numerical integration -- ยง 0.7 Overall planning methods -- ยง 0.8 On the use of statistics -- ยง 0.9 Concluding remarks -- 1 On the Calculation of Mineral Reserves and Hillside Areas on Contour Maps -- ยง 1.1 Introduction -- ยง 1.2 Calculation of mineral reserves -- ยง 1.3 Calculation of hillside areas -- References -- 2 The Meshing Gear-Pair Problem -- ยง 2.1 Introduction -- ยง 2.2 Simple continued fractions -- ยง 2.3 Farey series -- ยง 2.4 An algorithm for the problem -- ยง 2.5 The solution to the meshing gear-pair problem -- References -- 3 Optimum Seeking Methods (single variable) -- ยง 3.1 Introduction -- ยง 3.2 Unimodal functions -- ยง 3.3 Method of trials by shifting to and fro -- ยง 3.4 The golden section method -- ยง 3.5 The proof of Theorem 3.1 -- ยง 3.6 The Fibonacci search -- ยง 3.7 The proof of Theorem 3.2 -- ยง 3.8 The bisection method -- ยง 3.9 The parabola method -- References -- 4 Optimum Seeking Methods (several variables) -- ยง 4.1 Introduction -- ยง 4.2 Unimodal functions (several variables) -- ยง 4.3 The bisection method -- ยง 4.4 The successive approximation method -- ยง 4.5 The parallel line method -- ยง 4.6 The discrete case with two factors -- ยง 4.7 The equilateral triangle method -- ยง 4.8 The gradient method -- ยง 4.9 The paraboloid method -- ยง 4.10 Convex bodies -- ยง 4.11 Qie Kuai Fa -- ยง4.12 The 0โ1 variable method -- References -- 5 The Golden Number and Numerical Integration -- ยง 5.1 Introduction -- ยง 5.2 Lemmas -- ยง 5.3 Error estimation for the quadrature formula -- ยง 5.4 A result for 0 and a lower bound for the quadrature formula -- ยง 5.5 Remarks -- References -- 6 Overall Planning Methods -- ยง 6.1 Introduction -- ยง 6.2 Critical Path Method -- ยง 6.3 Float -- ยง 6.4 Parallel operations and overlapping operations -- ยง 6.5 Manpower scheduling -- References -- 7 Program Evaluation and Review Technique (Pert) -- ยง 7.1 Introduction -- ยง 7.2 Estimation of the probability -- ยง 7.3 Computation process -- ยง 7.4 An elementary approach -- ยง 7.5 Remarks -- References -- 8 Machine Scheduling -- ยง 8.1 Introduction -- ยง 8.2 Two-machine problem -- ยง 8.3 A lemma -- ยง 8.4 Proof of Theorem 8.1 -- References -- 9 The Transportation Problem (Graphical Method) -- ยง 9.1 Introduction -- ยง 9.2 One cycle -- ยง 9.3 Proof of Theorem 9.1 -- References -- 10 The Transportation Problem (Simplex Method) -- ยง 10.1 Introduction -- ยง 10.2 Eliminated unknowns and feasible solutions -- ยง 10.3 Criterion numbers -- ยง 10.4 A criterion for optimality -- ยง 10.5 Characteristic numbers -- ยง 10.6 Substitution -- ยง 10.7 Linear programming -- References -- 11 The Postman Problem -- ยง 11.1 Introduction -- ยง 11.2 Euler paths -- ยง 11.3 A necessary and sufficient criterion for an optimum solution -- References