2011, ISBN 019957040X, xvii, 424

Isaac Newton's Scientific Method examines Newton's argument for universal gravity and his application of it to resolve the problem of deciding between geocentric and heliocentric world systems...

Cosmology | Gravitation | Newton, Isaac, 1642-1727 | Gravity | Physics | history of Western philosophy | 1642-1727 | Sir | Newton, Isaac | Einstein | Scientific progress | Newton | Empirical success | Prediction | Theory-mediated measurement

Cosmology | Gravitation | Newton, Isaac, 1642-1727 | Gravity | Physics | history of Western philosophy | 1642-1727 | Sir | Newton, Isaac | Einstein | Scientific progress | Newton | Empirical success | Prediction | Theory-mediated measurement

Book

International journal of machine tools & manufacture, ISSN 0890-6955, 2015, Volume 94, pp. 88 - 99

A shear-thickening polishing (STP) method utilizing the shear thickening mechanism of non-Newtonian power-law fluid based slurry is proposed for curved surface polishing...

Polishing | Shear-thickening effect | Curved surface | STP | Material removal model | Non-Newtonian fluid | FORM | VISCOSITY | ENGINEERING, MECHANICAL | FLUID | MODELS | MATERIAL REMOVAL RATE | ENGINEERING, MANUFACTURING | Newton's laws of motion | Analysis | Methods | Grain size | Computational fluid dynamics | Newtonian fluids | Fluid flow | Surface roughness | Abrasives | Slurries

Polishing | Shear-thickening effect | Curved surface | STP | Material removal model | Non-Newtonian fluid | FORM | VISCOSITY | ENGINEERING, MECHANICAL | FLUID | MODELS | MATERIAL REMOVAL RATE | ENGINEERING, MANUFACTURING | Newton's laws of motion | Analysis | Methods | Grain size | Computational fluid dynamics | Newtonian fluids | Fluid flow | Surface roughness | Abrasives | Slurries

Journal Article

ELECTROPHORESIS, ISSN 0173-0835, 06/2018, Volume 39, Issue 11, pp. 1329 - 1338

...‐physics process with hybrid boundary element method (BEM) and immersed boundary‐lattice Boltzmann method (IB‐LBM). The Carreau...

AC electrothermal phenomenon | Lattice Boltzmann method | Microfluidic pumping | Boundary element method | Non‐Newtonian blood flow | Non-Newtonian blood flow | CHEMISTRY, ANALYTICAL | PERFORMANCE | CONVECTION | BIOCHEMICAL RESEARCH METHODS | GPU | ENCLOSURE | RESISTIVE HEATERS | MODELS | NUMERICAL-SIMULATION | MICROFLUIDICS | Animals | Models, Cardiovascular | Humans | Rheology - instrumentation | Blood Flow Velocity | Lab-On-A-Chip Devices | Equipment Design | Electrical conductivity | Bacterial infections | Newton's laws of motion | Analysis | Dielectrics | Investigations | Methods | Electric properties | Blood flow | Electric potential | Energy consumption | Computational fluid dynamics | Computer simulation | Rheology | Dielectric properties | Fluid flow | Electrokinetics | Osmosis | Electrodes | Ohmic dissipation | Newtonian fluids | Pumping | Temperature effects | Scaling laws | Flow velocity | Rheological properties | Alternating current

AC electrothermal phenomenon | Lattice Boltzmann method | Microfluidic pumping | Boundary element method | Non‐Newtonian blood flow | Non-Newtonian blood flow | CHEMISTRY, ANALYTICAL | PERFORMANCE | CONVECTION | BIOCHEMICAL RESEARCH METHODS | GPU | ENCLOSURE | RESISTIVE HEATERS | MODELS | NUMERICAL-SIMULATION | MICROFLUIDICS | Animals | Models, Cardiovascular | Humans | Rheology - instrumentation | Blood Flow Velocity | Lab-On-A-Chip Devices | Equipment Design | Electrical conductivity | Bacterial infections | Newton's laws of motion | Analysis | Dielectrics | Investigations | Methods | Electric properties | Blood flow | Electric potential | Energy consumption | Computational fluid dynamics | Computer simulation | Rheology | Dielectric properties | Fluid flow | Electrokinetics | Osmosis | Electrodes | Ohmic dissipation | Newtonian fluids | Pumping | Temperature effects | Scaling laws | Flow velocity | Rheological properties | Alternating current

Journal Article

Journal of Engineering Mechanics, ISSN 0733-9399, 06/2019, Volume 145, Issue 6, p. 4019036

AbstractThis work aims at the unconstrained optimization of laminate plate problems by introducing a methodology that uses a decomposition method along with regularized Newton method...

Technical Papers | SANDWICH PLATES | FINITE-ELEMENTS | COMPOSITE PLATES | VIBRATION | SEARCH | LINEAR ELASTIC SYMMETRIES | RECURSIVE METHODOLOGY | DIFFERENTIAL-EQUATIONS | PROOF | FORMULATION | ENGINEERING, MECHANICAL | Rayleigh-Ritz method | Solution space | Mathematical analysis | Newton methods | Fiber orientation | Product design | Decomposition | Thin plates | Optimization

Technical Papers | SANDWICH PLATES | FINITE-ELEMENTS | COMPOSITE PLATES | VIBRATION | SEARCH | LINEAR ELASTIC SYMMETRIES | RECURSIVE METHODOLOGY | DIFFERENTIAL-EQUATIONS | PROOF | FORMULATION | ENGINEERING, MECHANICAL | Rayleigh-Ritz method | Solution space | Mathematical analysis | Newton methods | Fiber orientation | Product design | Decomposition | Thin plates | Optimization

Journal Article

Computers & mathematics with applications (1987), ISSN 0898-1221, 2005, Volume 50, Issue 10-12, pp. 1559 - 1568

In this paper, we present a sequence of iterative methods improving Newton's method for solving nonlinear equations...

Order of convergence | Newton's method | Nonlinear equations | Iterative methods | Adomian decomposition method | iterative methods | nonlinear equations | MATHEMATICS, APPLIED | adomian decomposition method | EQUATIONS | CONVERGENCE | order of convergence | VARIANT

Order of convergence | Newton's method | Nonlinear equations | Iterative methods | Adomian decomposition method | iterative methods | nonlinear equations | MATHEMATICS, APPLIED | adomian decomposition method | EQUATIONS | CONVERGENCE | order of convergence | VARIANT

Journal Article

2013, ISBN 9780199921850, xv, 177

...? This book proposes and defends several objective concepts of evidence. It then explores the question of whether a scientific method, such as that represented in the four...

Science | Newton, Isaac, 1642-1727 | Methodology | History | Maxwell, James Clerk, 1831-1879 | Verification (Empiricism) | philosophy of science | Newton, Isaac,-1642-1727 | Science-Methodology-History-18th century | Maxwell, James Clerk,-1831-1879 | Science-Methodology-History-19th century

Science | Newton, Isaac, 1642-1727 | Methodology | History | Maxwell, James Clerk, 1831-1879 | Verification (Empiricism) | philosophy of science | Newton, Isaac,-1642-1727 | Science-Methodology-History-18th century | Maxwell, James Clerk,-1831-1879 | Science-Methodology-History-19th century

Book

SIAM journal on optimization, ISSN 1095-7189, 2009, Volume 20, Issue 2, pp. 602 - 626

We propose an extension of Newton's method for unconstrained multiobjective optimization...

Multicriteria optimization | Newton's method | Multiobjective programming | Pareto points | multiobjective programming | MATHEMATICS, APPLIED | multicriteria optimization | VECTOR OPTIMIZATION | GENERATION | Studies | Optimization algorithms | Mathematical analysis | Applied mathematics | Mathematical programming

Multicriteria optimization | Newton's method | Multiobjective programming | Pareto points | multiobjective programming | MATHEMATICS, APPLIED | multicriteria optimization | VECTOR OPTIMIZATION | GENERATION | Studies | Optimization algorithms | Mathematical analysis | Applied mathematics | Mathematical programming

Journal Article

8.
Full Text
The cool-core bias in X-ray galaxy cluster samples: I. Method and application to HIFLUGCS

Astronomy and Astrophysics, ISSN 0004-6361, 02/2011, Volume 526, Issue 10, p. A79

.... We quantify this effect in the case of a well-known cluster sample, HIFLUGCS. Methods. We simulate a population of X-ray clusters with various surface-brightness profiles, and use the instrumental characteristics of the ROSAT All-Sky Survey (RASS...

galaxies: clusters: intracluster medium | X-rays: galaxies: clusters | galaxies: clusters: general | ROSAT | PROFILES | T RELATION | FLUX-LIMITED SAMPLE | LUMINOSITY FUNCTION | INTRACLUSTER MEDIUM | ASTRONOMY & ASTROPHYSICS | GAS | XMM-NEWTON OBSERVATIONS | DARK-MATTER | ENTROPY

galaxies: clusters: intracluster medium | X-rays: galaxies: clusters | galaxies: clusters: general | ROSAT | PROFILES | T RELATION | FLUX-LIMITED SAMPLE | LUMINOSITY FUNCTION | INTRACLUSTER MEDIUM | ASTRONOMY & ASTROPHYSICS | GAS | XMM-NEWTON OBSERVATIONS | DARK-MATTER | ENTROPY

Journal Article

Applied mathematics letters, ISSN 0893-9659, 2014, Volume 29, pp. 20 - 25

A simple modification to the standard Newton method for approximating the root of a univariate function is described and analyzed...

Newton’s method | Non-linear equations | Root-finding | Iterative methods | Newton's method | Newton-Raphson method | Approximation | Mathematical analysis | Newton methods | Mathematical models | Derivatives | Standards | Convergence

Newton’s method | Non-linear equations | Root-finding | Iterative methods | Newton's method | Newton-Raphson method | Approximation | Mathematical analysis | Newton methods | Mathematical models | Derivatives | Standards | Convergence

Journal Article

Mathematical Programming, ISSN 0025-5610, 8/2013, Volume 140, Issue 1, pp. 189 - 233

.... The bundle method uses an oracle that is able to compute separately the function and subgradient information for the convex function, and the function and derivatives for the smooth mapping...

Secondary 65K10 | Bundle methods | Composite functions | Theoretical, Mathematical and Computational Physics | Primary 90C26 | Mathematics | Mathematical Methods in Physics | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Nonsmooth optimization | 49M05 | Combinatorics | Nonconvex Optimization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | GAUSS-NEWTON METHOD | SMOOTH | ALGORITHMS | CONVEX-FUNCTIONS | Studies | Computer science | Optimization algorithms | Mathematical models | Mathematical programming | Bundling | Mathematical analysis | Eigenvalues | Minimization | Mapping | Derivatives | Optimization

Secondary 65K10 | Bundle methods | Composite functions | Theoretical, Mathematical and Computational Physics | Primary 90C26 | Mathematics | Mathematical Methods in Physics | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Nonsmooth optimization | 49M05 | Combinatorics | Nonconvex Optimization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | GAUSS-NEWTON METHOD | SMOOTH | ALGORITHMS | CONVEX-FUNCTIONS | Studies | Computer science | Optimization algorithms | Mathematical models | Mathematical programming | Bundling | Mathematical analysis | Eigenvalues | Minimization | Mapping | Derivatives | Optimization

Journal Article

Mathematical programming, ISSN 1436-4646, 2018, Volume 174, Issue 1-2, pp. 293 - 326

... of Newton’s method where the Hessian and/or gradients are randomly sub-sampled. For Hessian sub-sampling, using random matrix concentration inequalities, one can sub-sample in a way that second-order information, i.e...

65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Local and global convergence | Newton-type methods | Sub-sampling | 49M15 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Methods | Algebra | Mathematical analysis | Newton methods | Linear algebra | Sampling methods | Asymptotic methods | Curvature | Matrix methods | Convergence | Concentration gradient

65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Local and global convergence | Newton-type methods | Sub-sampling | 49M15 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Methods | Algebra | Mathematical analysis | Newton methods | Linear algebra | Sampling methods | Asymptotic methods | Curvature | Matrix methods | Convergence | Concentration gradient

Journal Article

Expert systems with applications, ISSN 0957-4174, 2019, Volume 117, pp. 166 - 175

...) Algorithm is integrated on (MOJH).•The performance of MOJH is improved with NR-based stochastic step size method...

Multiobjective | MOEAD | optimization | Hooke–Jeeves | 90C99 | Newton–Raphson | 90C29 | 90C15 | AGE-II | Hooke-Jeeves | OPTIMIZATION PROBLEMS | COORDINATION | DIFFERENTIAL EVOLUTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NEURAL-NETWORKS | STABILITY ANALYSIS | Multiobjective optimization | CONVERGENCE | Newton-Raphson | Algorithms | Mathematical optimization | Analysis | Methods

Multiobjective | MOEAD | optimization | Hooke–Jeeves | 90C99 | Newton–Raphson | 90C29 | 90C15 | AGE-II | Hooke-Jeeves | OPTIMIZATION PROBLEMS | COORDINATION | DIFFERENTIAL EVOLUTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NEURAL-NETWORKS | STABILITY ANALYSIS | Multiobjective optimization | CONVERGENCE | Newton-Raphson | Algorithms | Mathematical optimization | Analysis | Methods

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2013, Volume 35, Issue 2, pp. B401 - B437

Full waveform inversion (FWI) is a powerful method for reconstructing subsurface parameters from local measurements of the seismic wavefield...

Full waveform inversion | Seismic imaging | Numerical optimization | Large-scale inverse problems | large-scale inverse problems | VELOCITY | MATHEMATICS, APPLIED | full waveform inversion | ALGORITHM | CROSS-HOLE TOMOGRAPHY | SEISMIC DATA | seismic imaging | numerical optimization | GRADIENT | Reconstruction | Computation | Newton methods | Imaging | Inversions | Waveforms | Mathematical models | Descent | Earth Sciences | Geophysics | Mathematics | Sciences of the Universe | Optimization and Control | Physics | Environmental Sciences | Global Changes

Full waveform inversion | Seismic imaging | Numerical optimization | Large-scale inverse problems | large-scale inverse problems | VELOCITY | MATHEMATICS, APPLIED | full waveform inversion | ALGORITHM | CROSS-HOLE TOMOGRAPHY | SEISMIC DATA | seismic imaging | numerical optimization | GRADIENT | Reconstruction | Computation | Newton methods | Imaging | Inversions | Waveforms | Mathematical models | Descent | Earth Sciences | Geophysics | Mathematics | Sciences of the Universe | Optimization and Control | Physics | Environmental Sciences | Global Changes

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2015, Volume 289, pp. 332 - 354

.... These infinite-dimensional constraints are often addressed through aggregation methods that approximate the bound in a differentiable manner...

Kreisselmeier–Steinhauser function | Post-optimality sensitivities | Constraint aggregation | [formula omitted]-norm | Design optimization | P-norm | Kreisselmeier-Steinhauser function | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ADJOINT SENSITIVITY-ANALYSIS | ENGINEERING, MULTIDISCIPLINARY | p-norm | TOPOLOGY OPTIMIZATION | QUASI-NEWTON MATRICES | Analysis | Methods | Aerospace engineering | Approximation | Computer simulation | Aggregates | Mathematical analysis | Minimization | Mathematical models | Agglomeration | Optimization

Kreisselmeier–Steinhauser function | Post-optimality sensitivities | Constraint aggregation | [formula omitted]-norm | Design optimization | P-norm | Kreisselmeier-Steinhauser function | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ADJOINT SENSITIVITY-ANALYSIS | ENGINEERING, MULTIDISCIPLINARY | p-norm | TOPOLOGY OPTIMIZATION | QUASI-NEWTON MATRICES | Analysis | Methods | Aerospace engineering | Approximation | Computer simulation | Aggregates | Mathematical analysis | Minimization | Mathematical models | Agglomeration | Optimization

Journal Article