Industrial and applied mathematics in China

Contents......Page 8
Preface......Page 6
1 Introduction......Page 10
2.1 Properties of ascending chains......Page 12
2.2 Characteristic set method......Page 13
2.3 Wu\'s method of automated geometry theorem proving and discovering......Page 15
3.1 Rational and algebraic solutions of algebraic ODEs......Page 17
3.2 Rational solutions of algebraic O Es......Page 19
4.1 An algebraic setting......Page 21
4.2 Modules of formal solutions......Page 23
4.3 Picard-Vessiot extensions......Page 24
5 Determining all submodules of a LaurentOre module......Page 27
5.2 Determining one-dimensional submodules......Page 28
References......Page 30
Abstract......Page 34
1 Introduction......Page 35
1.1 Eddington or Diffusion Approximation......Page 38
1.2 Equilibrium diffusion approximation......Page 39
1.3 Boundary conditions for the diffusion approximation problem......Page 40
2 Mathematical results on radiation hydrodynamics......Page 41
3 A priori estimates......Page 45
References......Page 56
1 Introduction......Page 58
2 The high frequency limit......Page 59
3 The moment method......Page 61
4 The level set methods......Page 63
5.1 Notion of the solution......Page 66
5.2 Numerical flux at the interface......Page 68
References......Page 69
Abstract......Page 74
1.1 Basic PageRank model......Page 75
1.2 Limit of PageRank......Page 76
1.3 Comparison of different irreducible Markov chains......Page 78
1.4 N -step PageRank......Page 80
2.1 Traditional approaches of Websites-ranking......Page 81
2.2 AggregateRank algorithm......Page 82
3 Final remarks......Page 84
References......Page 85
1 Introduction......Page 88
2 A pricing mechanism of derivatives as an input-output black box......Page 90
3 BSDE pricing mechanism model and Black-Scholes formula......Page 91
3.1 Numerical calculation of solutions of BSDEs......Page 94
4 BSDE as a pricing mechanism of derivatives......Page 96
5 Testing the criteria (A5) by market data......Page 98
6 Characterization of g-pricing mechanism by its generating function 9......Page 103
References......Page 107
1 Introduction......Page 110
2.2 Finite element spaces and lemmas......Page 112
2.3 The discrete problem and the Korn inequality......Page 115
3 Error estimates......Page 116
References......Page 119
1 Introduction......Page 121
2 Mathematical model of heat conduction......Page 122
3 Inverse problem: least square method......Page 124
3.2 Discretization......Page 125
3.4 Shortcoming of the method......Page 126
4.1 Asymptotic solution......Page 127
4.2 The error of asymptotic solution......Page 129
4.4 Inverse problem and solution......Page 131
5.1 Test 1......Page 132
5.2 Real blast furnace, artificial data......Page 133
5.3 Real measurement......Page 135
References......Page 137
Abstract......Page 138
1 Introduction......Page 139
2.2 Gauss-Seidel projection method......Page 140
2.3 An efficient FFT in computing stray field......Page 141
2.4 Parallel computing......Page 143
3.1 The effects of wire number and length......Page 144
3.2 The effect of wire diameter, length, and interwire distance......Page 146
3.3 Switching dynamics......Page 147
4 Conclusion......Page 148
References......Page 149
1 Introduction......Page 150
2 Definition of the generalized B-spline......Page 151
3 Differential equation, basic properties......Page 152
4 Generalized spline, generalized B-spline......Page 154
5 Interpolation, knot insertion, recursive computation......Page 157
6 Polynomial reproducing, convergence order......Page 159
7 Uniform distributed knots, wavelets, cardinal spline......Page 166
References......Page 173
1 Introduction......Page 175
2.1 Background of static timing analysis (STA)......Page 178
A. Statistical MAX problem......Page 181
B. Review of existing methods......Page 182
2.2.2 Mathematical Challenges of (S)STA......Page 183
3.1 Parasitic Extraction and Maxwell\'s Equations......Page 184
3.2 Partial element equivalent circuit (PEEC) model......Page 185
3.3 Quasi assumptions for parasitic extraction......Page 186
3.4 Parasitic extraction methods......Page 187
3.5 Resistance, capacitance and susceptance (ReS) model for interconnects......Page 188
3.6 Variation-aware parasitic extraction......Page 189
3.7 Challenges of parasitic extraction......Page 190
4 Model order reduction......Page 191
4.1 Problem definition of model order reduction......Page 192
A. Moment-matching based methods......Page 194
4.2.2 Time-domain methods......Page 198
4.3 Problem definition of parameterized model order reduction......Page 199
4.4 Existing parameterized model order reduction techniques......Page 200
4.5 Mathematical challenges for model order reduction of interconnect......Page 201
5 Lithography simulation and optical proximity correction (Ope)......Page 202
A. Physical problem and mathematic model......Page 204
B. Available solutions for 3-D lithography simulation......Page 206
c. Mathematical challenges in 3-D lithography simulation......Page 209
5.2 Statistical lithography simulation......Page 210
A. Mathematical description for ope......Page 211
B. Existing ope algorithms......Page 212
C. Challenges for next generation OPC......Page 213
6 Summary......Page 214
Acknowledgements......Page 215
References......Page 216
1 Introduction......Page 224
2 RT two-scan mode with unilateral off-centered turntable and its virtual equivalence......Page 226
3 BPF algorithm for parallel-beam scan mode......Page 228
4.1 The derivation of the 3D DBP formula......Page 230
4.2 Hilbert inverse formula......Page 233
5 Numerical simulations and conclusion......Page 234
References......Page 237
1 Introduction......Page 238
2 RBF collocation method......Page 240
3.2 The variational EM method......Page 242
3.3 Some relevant issues......Page 244
4 Numerical experience......Page 245
5 Conclusion......Page 246
References......Page 248