Index
987
Minimal surface, 92
Minimizing sequence, 457
Minkowski inequality, 73
Minor arc, 128
Mirror image adjoint Hamiltonian operator
train, 730
Mirror image conjugate Hamiltonian operator train, 730
Mirror image Hamiltonian operator train,
730
Mirror image transposition Hamiltonian
operator train, 730
Mixed functional, 344, 588
Mixed method, 473
Mixed self-adjoint operator, 409
Mixed self-conjugate operator, 409
Mixed type functional, 344, 588
Mixed variational problem, 345
Mobile endpoint, 239
Modified Ginzburg-Landau equations, 729
Modified variational principle, 384
Modulus of vector, 8
Mollifier, 46
Momentum operator, 635
Moving boundary, 239
Mutually disjoint (sets), 386
N
Nabla operator, 10, 412
Natural boundary conditions, 245
Natural numbers set, 385
Natural path, 516
Navier(’s) equations, 528
n-dimensional Euclidean distance, 391
n-dimensional Euclidean space, 394
n-dimensional Laplace(’s) equation, 162
n-dimensional point, 391
n-dimensional space, 391
Nearby curve, 110
Nearby path, 516
Necessary condition, 112
Negative element, 392
Neighborhood, 391
Neighboring curve, 110
Neighboring path, 516
Neumann boundary condition, 245
Neumann problem, 430
Next eigenvalue, 490
Node, 460
Noncontemporaneous variation, 99
Non-Darcy flow, 750, 960
Nonempty set, 385
Nonholonomic constraint, 515
Nonholonomic system, 515
Nontrivial solution, 490
Nonvariational principle, 513
Nonvariational principle in mechanics, 513
Nonvariational principle of mechanics, 513
Non-void set, 385
Norm, 393, 405
Normal characteristic function, 490
Normal derivative operator, 14
Normal eigenfunction, 490
Normal operator, 408
Normal orthogonal system, 401
Normed linear space, 393
Normed vector space, 393
Norm generated by the inner product, 396
Norm induced by the inner product, 396
Norm of an operator T , 407
Norm-preserving operator, 403
n-th approximate solution, 464
n-th derivative, 415
n-th homogeneous functional, 91
n-th linear differential operator, 412
n-th order δ approach degree, 93
n-th order δ neighborhood, 93
n-th order distance, 92
n-th order Lagrange(’s) remainder, 2
n-th variation, 232
Null element, 392
Null operator, 405
Null set, 385
Number domain, 388
Number field, 388
Number line, 385
Number of degrees of freedom, 553
Number space, 389
O
Oasis problem, 254
Objective functional of isoperimetric
problem, 331
Objective functional with differential
constraint, 326
Objective functional with holonomic
constraint, 320
Oil-film bearing problem, 124
One-element set, 385
One-one correspondence, 387
One-one mapping, 387
One-sided continuity, 90
One-sided variational problem, 303
Open ball, 391
987
Minimal surface, 92
Minimizing sequence, 457
Minkowski inequality, 73
Minor arc, 128
Mirror image adjoint Hamiltonian operator
train, 730
Mirror image conjugate Hamiltonian operator train, 730
Mirror image Hamiltonian operator train,
730
Mirror image transposition Hamiltonian
operator train, 730
Mixed functional, 344, 588
Mixed method, 473
Mixed self-adjoint operator, 409
Mixed self-conjugate operator, 409
Mixed type functional, 344, 588
Mixed variational problem, 345
Mobile endpoint, 239
Modified Ginzburg-Landau equations, 729
Modified variational principle, 384
Modulus of vector, 8
Mollifier, 46
Momentum operator, 635
Moving boundary, 239
Mutually disjoint (sets), 386
N
Nabla operator, 10, 412
Natural boundary conditions, 245
Natural numbers set, 385
Natural path, 516
Navier(’s) equations, 528
n-dimensional Euclidean distance, 391
n-dimensional Euclidean space, 394
n-dimensional Laplace(’s) equation, 162
n-dimensional point, 391
n-dimensional space, 391
Nearby curve, 110
Nearby path, 516
Necessary condition, 112
Negative element, 392
Neighborhood, 391
Neighboring curve, 110
Neighboring path, 516
Neumann boundary condition, 245
Neumann problem, 430
Next eigenvalue, 490
Node, 460
Noncontemporaneous variation, 99
Non-Darcy flow, 750, 960
Nonempty set, 385
Nonholonomic constraint, 515
Nonholonomic system, 515
Nontrivial solution, 490
Nonvariational principle, 513
Nonvariational principle in mechanics, 513
Nonvariational principle of mechanics, 513
Non-void set, 385
Norm, 393, 405
Normal characteristic function, 490
Normal derivative operator, 14
Normal eigenfunction, 490
Normal operator, 408
Normal orthogonal system, 401
Normed linear space, 393
Normed vector space, 393
Norm generated by the inner product, 396
Norm induced by the inner product, 396
Norm of an operator T , 407
Norm-preserving operator, 403
n-th approximate solution, 464
n-th derivative, 415
n-th homogeneous functional, 91
n-th linear differential operator, 412
n-th order δ approach degree, 93
n-th order δ neighborhood, 93
n-th order distance, 92
n-th order Lagrange(’s) remainder, 2
n-th variation, 232
Null element, 392
Null operator, 405
Null set, 385
Number domain, 388
Number field, 388
Number line, 385
Number of degrees of freedom, 553
Number space, 389
O
Oasis problem, 254
Objective functional of isoperimetric
problem, 331
Objective functional with differential
constraint, 326
Objective functional with holonomic
constraint, 320
Oil-film bearing problem, 124
One-element set, 385
One-one correspondence, 387
One-one mapping, 387
One-sided continuity, 90
One-sided variational problem, 303
Open ball, 391