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Previous article Blending-Function Methods of Bivariate and Multivariate Interpolation and ApproximationWilliam J. GordonWilliam J. Gordonhttps://doi.org/10.1137/0708019PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. H. Ahlberg, , E. N. Nilson and , J. L. Walsh, The theory of splines and their applications, Academic Press, New York, 1967xi+284 MR0239327 0158.15901 Google Scholar[2] A. C. Ahlin, A bivariate generalization of Hermite's interpolation formula, Math. Comp., 18 (1964), 264–273 MR0164428 0122.12501 CrossrefISIGoogle Scholar[3] R. E. Barnhill, , W. J. Gordon and , D. H. Thomas, Decomposition methods for the approximate integration of multivariate functions, Res. Rep., General Motors, Warren, Mich., in preparation Google Scholar[4] Garrett Birkhoff and , Carl R. De Boor, H. L. Garabedian, Piecewise polynomial interpolation and approximation, Approximation of Functions (Proc. Sympos. General Motors Res. Lab., 1964 ), Elsevier Publ. Co., Amsterdam, 1965, 164–190 MR0189219 0136.04703 Google Scholar[5] Garrett Birkhoff and , William J. Gordon, The draftsman's and related equations, J. Approximation Theory, 1 (1968), 199–208 10.1016/0021-9045(68)90024-5 MR0235752 0189.40902 CrossrefGoogle Scholar[6] Garrett Birkhoff and , Saunders Mac Lane, A survey of modern algebra, Macmillan Co., New York, N. Y., 1953xi+472 MR0054551 0052.25402 Google Scholar[7] Garrett Birkhoff and , Gian-Carlo Rota, Ordinary differential equations, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass.-New York-Toronto, 1962vii+318 MR0138810 0102.29901 Google Scholar[8] R. C. Buck, Advanced Calculus, McGraw-Hill, New York, 1965 0125.30102 Google Scholar[9] S. A. Coons, Surfaces for Computer Aided Design of Space Forms, Project MAC, Design Div., Dept. of Mech. Engineering, MIT, 1964, Revised to MAC-TR-41, 1967. Available from CFSTI, Sills Building, 5285 Port Royal Road, Springfield, Virginia, 22151 Google Scholar[10] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963xiv+393 MR0157156 0111.06003 Google Scholar[11] Carl de Boor, Bicubic spline interpolation, J. Math. and Phys., 41 (1962), 212–218 MR0158512 0108.27103 CrossrefISIGoogle Scholar[12] Carl de Boor and , Robert E. Lynch, On splines and their minimum properties, J. Math. Mech., 15 (1966), 953–969 MR0203306 0185.20501 ISIGoogle Scholar[13] James Ferguson, Multivariable curve interpolation, J. Assoc. Comput. Mach., 11 (1964), 221–228 MR0162352 0123.33004 CrossrefISIGoogle Scholar[14] A. R. Forrest, Masters Thesis, Curves and surfaces for computer-aided design, Doctoral thesis, The University Mathematical Laboratory, Cambridge Univ., Cambridge, England, 1968 Google Scholar[15] A. R. Forrest, Coons surfaces and multivariable functional interpolation, 1971, J. Assoc. Comput. Mach., to appear Google Scholar[16] William J. Gordon, Spline-blended surface interpolation through curve networks, J. Math. Mech., 18 (1968/1969), 931–952 MR0246027 0192.42201 ISIGoogle Scholar[17] William J. Gordon, Blending: function methods of bivariate and multivariate interpolation and approximation, Res. Rep., GMR-834, General Motors, Warren, Mich., 1968 Google Scholar[18] William J. Gordon, I. J. Schoenberg, Distributive lattices and the approximation of multivariate functionsApproximations with Special Emphasis on Spline Functions (Proc. Sympos. Univ. of Wisconsin, Madison, Wis., 1969), Academic Press, New York, 1969, 223–277 MR0275021 0269.41029 Google Scholar[19] William J. Gordon, Free form surface interpolation through curve networks, Res. Rep., GMR-921, General Motors, Warren, Mich., 1969 Google Scholar[20] E. L. Ince, Ordinary Differential Equations, Dover, New York, 1956 Google Scholar[21] W. L. Johnson, Analytic surfaces for computer-aided design, Paper 660152, Proc. Society of Automobile Engineers Convention, 1966 Google Scholar[22] Saunders Mac Lane and , Garrett Birkhoff, Algebra, The Macmillan Co., New York, 1967xix+598 MR0214415 0153.32401 Google Scholar[23] D. Mangeron, Sopra un problema al contorno..., Rend. Accad. Sci. Fis Mat. Napoli, 2 (1932), 28–40 0005.35702 Google Scholar[24] W. W. Meyer, Remainders of derivative mean-value type for multivariate polynomial interpolation, Res. Rep., GMR-1001, General Motors, Warren, Mich., 1970 Google Scholar[25] Arthur Sard, Linear approximation, American Mathematical Society, Providence, R.I., 1963xi+544 MR0158203 0115.05403 CrossrefGoogle Scholar[26] D. D. Stancu, The remainder of certain linear approximation formulas in two variables, J. Soc. Indust. Appl. Math. Ser. B Numer. 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of Computational Physics, Vol. No. 1 Cross Ref Cross Ref Engineering Methods of Cross Ref The method of applied to June 2007 | Numerical Functional Analysis and Optimization, Vol. No. 2 Cross Ref On multivariate spline January | Mathematics of Vol. No. Cross Ref A of the and Design of Computer and Applications, Vol. 3, No. Cross Ref quadrature Vol. 22, No. 4 Cross Ref for solution of differential of Computational Physics, Vol. 47, No. 1 Cross Ref Generalized April | in Mathematics, Vol. No. 1-2 Cross Ref in Vol. 3, No. 1-2 Cross Ref transfinite for the and of surfaces using Journal for Numerical Methods in Engineering, Vol. 18, No. 1 Cross Ref of Cross Ref On Interpolation Cross Ref and their application to grid Mathematics and Vol. Cross Ref A general finite element transfinite Journal for Numerical Methods in Engineering, Vol. 17, No. Cross Ref OF INTERPOLATION OF Cross Ref spline and its Applications, Vol. Cross Ref April | in Mathematics, Vol. 3, No. 1-2 Cross Ref Approximation in Cross Ref Vol. 22, No. 4 Cross Ref Design of an Transactions on Mathematical Software, Vol. No. 1 Cross Ref Methods in Bivariate Hermite Interpolation Cross Ref On a Multivariate and the Interpolation Cross Ref for Cross Ref of Interpolation Cross Ref Polynomial and Spline Approximation Cross Ref Interpolation to Networks of Curves in A. July 2006 | Journal on Numerical Vol. No. of Approximation Theory, Vol. 22, No. 3 Cross Ref in the finite element methodInternational Journal for Numerical Methods in Engineering, Vol. No. 1 Cross Ref elements for boundary problemsInternational Journal for Numerical Methods in Engineering, Vol. No. 12 Cross Ref Bivariate and Multivariate Interpolation with Cross Ref A New Spline for of Vol. No. 1 Cross Ref The of surface of Approximation Theory, Vol. No. 3 Cross Ref of boundary and of solution in to boundary problemsJournal of Computational Physics, Vol. No. 2 Cross Ref for Polynomial S. July 2006 | Journal on Numerical Vol. No. for general of Journal for Numerical Methods in Engineering, Vol. No. 4 Cross Ref elements based on Journal for Numerical Methods in Engineering, Vol. No. 9 Cross Ref A on analysis and approximation on October 2006 Cross Ref bounds for bivariate spline October 2006 Cross Ref and Approximation of Surfaces Cross Ref in blending function Vol. 26, No. 2 Cross Ref A on Journal for Numerical Methods in Engineering, Vol. 10, No. 2 Cross Ref On the of conforming rectangular Journal for Numerical Methods in Engineering, Vol. 10, No. 4 Cross Ref Cross Ref A product interpolation and the of a and its Applications, Vol. 13, No. 3 Cross Ref Finite element generation for and shell type structures Vol. 10, No. 4 Cross Ref On surface of Approximation Theory, Vol. No. 3 Cross Ref using rectangular finite of Computational Physics, Vol. 19, No. 2 Cross Ref On the of bivariate interpolation Vol. No. 2 Cross Ref interpolation of of Computational Physics, Vol. 18, No. 1 Cross Ref Curved in the Finite Element Cross Ref of Boundary in the Finite Element Cross Ref Interpolation on J. Gordon and James A. July 2006 | Journal on Numerical Vol. No. of collocation and to linear parabolic Vol. No. Cross Ref Methods for the Design of Curves and of the Vol. No. 2 Cross Ref Collocation of August 2006 Cross Ref Some multidimensional spline approximation of Approximation Theory, Vol. 10, No. 1 Cross Ref INTERPOLATION Cross Ref INTERPOLATION Cross Ref INTERPOLATION A Cross Ref Natural and Bicubic Spline A. July 2006 | Journal on Numerical Vol. 10, No. interpolation in of Approximation Theory, Vol. No. 2 Cross Ref element interpolation arbitrary curved element Vol. No. 2 Cross Ref Spline interpolation techniques for Journal for Numerical Methods in Engineering, Vol. No. 4 Cross Ref Construction of curvilinear and applications to Journal for Numerical Methods in Engineering, Vol. 7, No. 4 Cross Ref On and methods for the of curved surfacesComputer and Vol. No. 4 Cross Ref Optimal approximation and error bounds in of bivariate of Approximation Theory, Vol. No. 1 Cross Ref OF Cross Ref der der Cross Ref Curve and surface generation and Cross Ref Modelling by a spline with shape Cross Ref of the using dynamic modeling and imaging Cross Ref Adaptive of using approximation Cross Ref Journal on Numerical Analysis April July 2006 Society for and Applied & for and Applied Mathematics

Previous article Next article Convergence Conditions for Ascent MethodsPhilip WolfePhilip Wolfehttps://doi.org/10.1137/1011036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractLiberal conditions on the steps of a “descent” method for finding extrema of a function are given; most known results are special cases.[1] Haskell B. Curry, The method of steepest descent for non-linear minimization problems, Quart. Appl. Math., 2 (1944), 258–261 MR0010667 0061.26801 CrossrefGoogle Scholar[2] Augustine Cauchy, Méthode générale pour la résolution des systèmes d'équations simultanées, C.R. Acad. Sci., 25 (1847), 536–538 Google Scholar[3] A. A. Goldstein, Minimizing functionals on normed-linear spaces, SIAM J. Control, 4 (1966), 81–89 10.1137/0304008 MR0196900 0147.12701 LinkGoogle Scholar[4] A. A. Goldstein, Cauchy's method of minimization, Numer. Math., 4 (1962), 146–150 10.1007/BF01386306 MR0141222 0105.10201 CrossrefGoogle Scholar[5] Alexander Ostrowski, Solution of equations and systems of equations, Second edition. Pure and Applied Mathematics, Vol. 9, Academic Press, New York, 1966xiv+338 MR0216746 0222.65070 Google Scholar[6] G. Zoutehdijk, 1967, Private communication Google Scholar[7] R. Fletcher and , C. M. Reeves, Function minimization by conjugate gradients, Comput. J., 7 (1964), 149–154 10.1093/comjnl/7.2.149 MR0187375 0132.11701 CrossrefISIGoogle Scholar[8] W. Oettli, 1967, Private communication Google Scholar[9] L. V. Kantorovich and , G. P. Akilov, Functional analysis in normed spaces, Translated from the Russian by D. E. Brown. Edited by A. P. Robertson. International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964xiii+771, Chap. 15 MR0213845 0127.06104 Google Scholar[10] Hirotugu Akaike, On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method, Ann. Inst. Statist. Math. Tokyo, 11 (1959), 1–16 10.1007/BF01831719 MR0107973 0100.14002 CrossrefISIGoogle Scholar[11] R. Fletcher and , M. J. D. Powell, A rapidly convergent descent method for minimization, Comput. J., 6 (1963/1964), 163–168 MR0152116 0132.11603 CrossrefISIGoogle Scholar[12] M. J. Box, A comparison of several current optimization methods, and the use of transformations in constrained problems, Comput. J., 9 (1966), 67–77 MR0192645 0146.13304 CrossrefISIGoogle Scholar[13] Donald M. Topkis and , Arthur F. Veinott, on the convergence of some feasible direction algorithms for nonlinear programming, J. SIAM control, 5 (1967), 268–274 10.1137/0305018 0158.18805 LinkGoogle Scholar[14] Philip Wolfe, on the convergence of gradient methods under constraints, Rep., RZ-204, IBM watson research center, yorktown heights, new york, 1966 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Two efficient modifications of AZPRP conjugate gradient method with sufficient descent propertyJournal of Inequalities and Applications, Vol. 2022, No. 1 | 10 January 2022 Cross Ref Optimal Transport Based Seismic Inversion:Beyond Cycle SkippingCommunications on Pure and Applied Mathematics, Vol. 75, No. 10 | 1 April 2021 Cross Ref A robust BFGS algorithm for unconstrained nonlinear optimization problemsOptimization, Vol. 17 | 19 September 2022 Cross Ref Two Methods for the Implicit Integration of Stiff Reaction SystemsComputational Methods in Applied Mathematics, Vol. 0, No. 0 | 14 September 2022 Cross Ref Simple and fast convergent procedure to estimate recursive path analysis modelBehaviormetrika, Vol. 107 | 6 September 2022 Cross Ref Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functionsNumerical Algorithms, Vol. 91, No. 1 | 20 January 2022 Cross Ref A Hybrid Stochastic Deterministic Algorithm for Solving Unconstrained Optimization ProblemsMathematics, Vol. 10, No. 17 | 23 August 2022 Cross Ref Pseudospectral methods and iterative solvers for optimization problems from multiscale particle dynamicsBIT Numerical Mathematics, Vol. 48 | 11 August 2022 Cross Ref An outlier-resistant κ -generalized approach for robust physical parameter estimationPhysica A: Statistical Mechanics and its Applications, Vol. 600 | 1 Aug 2022 Cross Ref An Active Set Trust-Region Method for Bound-Constrained OptimizationBulletin of the Iranian Mathematical Society, Vol. 48, No. 4 | 27 July 2021 Cross Ref Advancing Three-Dimensional Coupled Water Quality Model of Marine Ranches: Model Development, Global Sensitivity Analysis, and Optimization Based on Observation SystemJournal of Marine Science and Engineering, Vol. 10, No. 8 | 27 July 2022 Cross Ref Robust regression against heavy heterogeneous contaminationMetrika, Vol. 16 | 1 July 2022 Cross Ref A new class of nonlinear conjugate gradient coefficients for unconstrained optimizationAsian-European Journal of Mathematics, Vol. 15, No. 07 | 14 October 2021 Cross Ref New iterative conjugate gradient method for nonlinear unconstrained optimizationRAIRO - Operations Research, Vol. 56, No. 4 | 29 July 2022 Cross Ref Optimizing Oblique Projections for Nonlinear Systems using TrajectoriesSamuel E. 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Previous article Next article On the Construction and Comparison of Difference SchemesGilbert StrangGilbert Stranghttps://doi.org/10.1137/0705041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. Barkley Rosser, A Runge-Kutta for all seasons, SIAM Rev., 9 (1967), 417–452 10.1137/1009069 MR0219242 0243.65041 LinkISIGoogle Scholar[2] Robert D. Richtmyer and , K. W. Morton, Difference methods for initial-value problems, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967xiv+405 MR0220455 0155.47502 Google Scholar[3] Peter D. Lax and , Burton Wendroff, Difference schemes for hyperbolic equations with high order of accuracy, Comm. Pure Appl. Math., 17 (1964), 381–398 MR0170484 0233.65050 CrossrefISIGoogle Scholar[4] Samuel Z. Burstein, Numerical methods in multidimensional shocked flows, AIAA J., 2 (1964), 2111–2117 MR0180067 CrossrefGoogle Scholar[5] S. Z. Burstein, Finite-difference calculations for hydrodynamic flows containing discontinuities, J. Comp. Phys., 2 (1967), 198–222 0166.22103 Google Scholar[6] C. Berger, On the numerical range of powers of an operator, to appear Google Scholar[7] W. P. Crowley, Second-order numerical advection, J. Comp. Phys., 1 (1967), 471–484 10.1016/0021-9991(67)90053-8 0149.44403 CrossrefGoogle Scholar[8] Gilbert Strang, Accurate partial difference methods. I. Linear Cauchy problems, Arch. Rational Mech. Anal., 12 (1963), 392–402 MR0146970 0113.32303 CrossrefISIGoogle Scholar[9] A. R. Gourlay and , J. Ll. Morris, A multistep formulation of the optimized Lax-Wendroff method for nonlinear hyperbolic systems in two space variables, Math. Comp., 22 (1968), 715–719 MR0251931 0172.19904 CrossrefISIGoogle Scholar[10] Peter Lax and , Burton Wendroff, Systems of conservation laws, Comm. Pure Appl. Math., 13 (1960), 217–237 MR0120774 0152.44802 CrossrefISIGoogle Scholar[11] R. D. Richtmyer, A survey of difference methods for nonsteady fluid dynamics, Tech. Note, 63-2, National Center for Atmospheric Research, Boulder, Colorado, 1962 Google Scholar[12] Gilbert Strang, Accurate partial difference methods. II. Non-linear problems, Numer. Math., 6 (1964), 37–46 10.1007/BF01386051 MR0166942 0143.38204 CrossrefGoogle Scholar[13] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons Inc., New York, 1962xi+407 MR0135729 0112.34901 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Semiexplicit symplectic integrators for non-separable Hamiltonian systems23 September 2022 | Mathematics of Computation, Vol. 92, No. 339 Cross Ref A combined volume penalization / selective frequency damping approach for immersed boundary methods applied to high-order schemesJournal of Computational Physics, Vol. 472 Cross Ref Numerical computation for rogue waves in the coupled nonlinear Schrödinger equations with the coherent coupling effect29 April 2022 | International Journal of Computer Mathematics, Vol. 99, No. 12 Cross Ref A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systemsMathematics and Computers in Simulation, Vol. 202 Cross Ref Ultrafast laser matter interactions: modeling approaches, challenges, and prospects27 September 2022 | Modelling and Simulation in Materials Science and Engineering, Vol. 30, No. 8 Cross Ref An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gasesJournal of Computational Physics, Vol. 471 Cross Ref Implications of CO 2 mass transport dynamics for large-scale CCS in basalt formationsInternational Journal of Greenhouse Gas Control, Vol. 121 Cross Ref A charge-preserving compact splitting method for solving the coupled stochastic nonlinear Schrödinger equationsApplied Numerical Mathematics, Vol. 181 Cross Ref Local effects in vortex-flame interactions: Implications for turbulent premixed flame scaling and observablesCombustion and Flame, Vol. 245 Cross Ref Hamiltonian preserving nonlinear opticsPhysica D: Nonlinear Phenomena, Vol. 439 Cross Ref A fully coupled, fully implicit simulation method for unsteady flames using Jacobian approximation and clusteringCombustion and Flame, Vol. 245 Cross Ref Reactive Transport Modeling with a Coupled OpenFOAM®-PHREEQC Platform7 October 2022 | Transport in Porous Media, Vol. 145, No. 2 Cross Ref Multirate Exponential Rosenbrock MethodsVu Thai Luan, Rujeko Chinomona, and Daniel R. 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equationApplied Numerical Mathematics, Vol. Cross Ref Numerical simulation of in the of Journal of Multiphase Vol. Cross Ref approximation of and numerical October 2021 | in Applied Vol. No. 3 Cross Ref electron dynamics in high Accurate prediction of September 2021 | Physical Review Vol. No. 10 Cross Ref On the of by the hydrogen in July 2021 | Monthly Notices of the Royal Astronomical Society, Vol. No. 2 Cross Ref Reaction Effects on Nozzle Erosion in Paraffin/Oxygen Hybrid July 2021 Cross Ref modeling in July 2021 Cross Ref A fast and efficient numerical algorithm for equation with a nonlocal Mathematics Letters, Vol. Cross Ref An particle hydrodynamics method for modeling Methods in Applied and Engineering, Vol. Cross Ref A model for droplet Journal of Heat and Vol. Cross Ref Numerical for high frequency equation efficient time for Schrödinger equationJournal of Computational Physics, Vol. Cross Ref and for and simulation of Magnetic Vol. Cross Ref Local wave

Previous article Next article Fractional Brownian Motions, Fractional Noises and ApplicationsBenoit B. Mandelbrot and John W. Van NessBenoit B. Mandelbrot and John W. Van Nesshttps://doi.org/10.1137/1010093PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. Adelman, Long cycles—fact or artifact?, Amer. Economic Rev., 60 (1965), 444–463 Google Scholar[2] William Feller, The asymptotic distribution of the range of sums of independent random variables, Ann. Math. Statistics, 22 (1951), 427–432 MR0042626 0043.34201 CrossrefISIGoogle Scholar[3] I. M. Gel'fand and , N. Ya. Vilenkin, Generalized functions. Vol. 4, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1964 [1977]xiv+384 MR0435834 Google Scholar[4] C. W. J. Granger, The typical spectral shape of an economic variable, Econometrica, 34 (1966), 150–161 CrossrefISIGoogle Scholar[5] G. A. Hunt, Random Fourier transforms, Trans. Amer. Math. Soc., 71 (1951), 38–69 MR0051340 0043.30601 CrossrefISIGoogle Scholar[6] H. E. Hurst, , R. P. Black and , Y. M. Sinaika, Long Term Storage in Reservoirs. An Experimental Study, Constable, London, 1965 Google Scholar[7] A. N. Kolmogoroff, Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, C. R. (Doklady) Acad. Sci. URSS (N.S.), 26 (1940), 115–118 MR0003441 0022.36001 Google Scholar[8] John Lamperti, Semi-stable stochastic processes, Trans. Amer. Math. Soc., 104 (1962), 62–78 MR0138128 0286.60017 CrossrefGoogle Scholar[9] Paul Lévy, Random functions: General theory with special reference to Laplacian random functions, Univ. California Publ. Statist., 1 (1953), 331–390 MR0055607 0052.14402 Google Scholar[10] Michel Loève, Probability theory, 2nd ed. The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-New York-London, 1960xvi+685 MR0123342 0095.12201 Google Scholar[11] Benoı⁁t Mandelbrot, Une classe processus stochastiques homothétiques à soi; application à la loi climatologique H. E. Hurst, C. R. Acad. Sci. Paris, 260 (1965), 3274–3277 MR0176521 0127.09501 Google Scholar[12] B. Mandelbrot, Self-similar error-clusters in communication systems and the concept of conditional stationarity, IEEE Trans. Comet. Tech., COM-13 (1965), 71–90 10.1109/TCOM.1965.1089090 CrossrefISIGoogle Scholar[13] B. Mandelbrot, Noises with an $l/f$ spectrum, a bridge between direct current and white noise, IEEE Trans. Information Theory, IT-13 (1967), 289–298 10.1109/TIT.1967.1053992 0148.40507 CrossrefISIGoogle Scholar[14] Benoit Mandelbrot, Sporadic random functions and conditional spectral analysis: Self-similar examples and limitsProc. Fifth Berkeley Sympos. Mathematical Statistics and Probability (Berkeley, Calif., 1965/66), Vol. III: Physical Sciences, Univ. California Press, Berkeley, Calif., 1967, 155–179 MR0224243 0189.18302 Google Scholar[15] B. Mandelbrot and , J. R. Wallis, Noah, Joseph and operational hydrology, Water Resources Research, to appear Google Scholar[16] B. Mandelbrot and , J. R. Wallis, Computer experiments with fractional Gaussian noise, Water Resources Research, to appear Google Scholar[17] B. Mandelbrot and , J. R. Wallis, Some long run properties of geophysical records, Water Resources Research, to appear. Google Scholar[18] G. Maruyama, The harmonic analysis of stationary stochastic processes, Mem. Fac. Sci. Kyusyu Univ. A., 4 (1949), 45–106 MR0032127 0045.40602 CrossrefGoogle Scholar[19] M. Rosenblatt, Independence and dependenceProc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, Univ. California Press, Berkeley, Calif., 1961, 431–443 MR0133863 0105.11802 Google Scholar[20] G. I. Taylor, Statistical theory of turbulence, Proc. Roy. Sac. Ser. A, 151 (1935), 421–478 CrossrefGoogle Scholar[21] H. Weyl, Bemerkungen zum Begriff der Differential-Quotenten gebrochener Ordnung, Vierteljschr. Naturforsch. Ges. Zürich, 62 (1967), 296–302 Google Scholar[22] A. M. Yaglom, Correlation theory of processes with random stationary nth increments, Amer. Math. Soc. Transl. (2), 8 (1958), 87–141 MR0091554 0080.34903 CrossrefGoogle Scholar[23] A. M. Yaglom, L. M. LeCam and , J. Neyman, Stationary Gaussian processes satisfying the strong mixing condition and best predictable functionalsBernoulli-Bayes-Laplace Anniversary Volume, Springer-Verlag, New York, 1965, 241–252 0142.13904 CrossrefGoogle Scholar[24] A. M. Yaglom, Outline of some topics in linear extrapolation of stationary random processesProc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II:Contributions to Probability Theory, Part 1, Univ. California Press, Berkeley, Calif., 1967, 259–278 MR0215358 0189.18401 Google Scholar[25] Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952vi+329, 2nd ed. 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2022 IEEE International Conference on and Signal | 23 May 2022 Cross Ref estimation for the model driven by the complex fractional Brownian Vol. No. 4 | 28 July 2021 Cross Ref Anomalous diffusion and memory in Computational Biology, Vol. 18, No. 5 | 18 May 2022 Cross Ref OF OF A | 13 May 2022 Cross Ref On the of Vol. 10, No. 9 | 22 April 2022 Cross Ref Convergence of for for with of Computing, Vol. No. 2 | 21 March 2022 Cross Ref Entropy of in a Review E, Vol. No. 5 | 2 May 2022 Cross Ref Analysis of during 26 August Vol. 24, No. 5 | 14 May 2022 Cross Ref stability of stochastic A and Dynamics, Vol. 22, No. | 18 April 2022 Cross Ref behavior in a model with A, Vol. | 1 May 2022 Cross Ref Asymptotic for driven by fractional Brownian motion in the of Mathematical Analysis and Applications, Vol. No. 1 | 1 May 2022 Cross Ref Generalized and rough Ornstein–Uhlenbeck Vol. | 30 April 2022 Cross Ref The the distribution of processes for the estimation of the Sciences Journal, Vol. No. 6 | 12 April 2022 Cross Ref and Application of Some Fractional Driven by Fractional Economics, Vol. 2 | April 2022 Cross Ref for processes and to Vol. No. 4 | 1 March 2022 Cross Ref Stochastic with to fractional processes in of Analysis, Vol. No. 8 | 1 2022 Cross Ref of and in Hurst exponents from spectral analysis of atomic force microscopy topographic Science, Vol. | 1 2022 Cross Ref in Distribution to Stochastic Driven by a Fractional Brownian Journal of Mathematics, Vol. No. 2 | 21 2022 Cross Ref a Under Random and Stochastic and Transactions on Science and Engineering, Vol. No. 2 | 1 2022 Cross Ref A new fractional based on nonlinear structure to systems with and of and Vol. No. | 30 January 2021 Cross Ref and The Transactions on and Systems, Vol. No. 2 | 1 2022 Cross Ref Analysis on with of and Fractional, Vol. 6, No. 4 | 14 April 2022 Cross Ref The of the Fractional and Fractional, Vol. 6, No. 4 | 15 April 2022 Cross Ref A and for complex Review E, Vol. No. 4 | 18 April 2022 Cross Ref of under in Review E, Vol. No. 4 | April 2022 Cross Ref theory of of an Review A, Vol. No. 4 | 26 April 2022 Cross Ref method for model in fractal Solitons & Fractals, Vol. | 1 2022 Cross Ref Time fractional equation with a based fractional Solitons & Fractals, Vol. | 1 2022 Cross Ref stochastic and of with complex in Applied Mechanics and Engineering, Vol. | 1 2022 Cross Ref OF Journal, Vol. No. 2 | 18 August 2022 Cross Ref The of of Fractional by in Vol. 2 | 24 March 2022 Cross Ref Bayesian of scaled fractional Brownian motionJournal of Physics A: Mathematical and | 24 March 2022 Cross Ref Anomalous diffusion: fractional Brownian motion fractional motionJournal of Physics A: Mathematical and Theoretical, Vol. 55, No. 11 | 23 2022 Cross Ref process with noise as a anomalous diffusion of Physics A: Mathematical and | 8 March 2022 Cross Ref by and Analysis and Vol. | 4 March 2022 Cross Ref Stochastic for the stochastic differential equations with & Probability Letters, Vol. | 1 Mar 2022 Cross Ref Multivariate range A: Statistical Mechanics and its Applications, Vol. | 1 Mar 2022 Cross Ref the memory for and time with Vol. No. 3 | 31 January 2022 Cross Ref for the Fractional Ornstein–Uhlenbeck of Vol. No. 1 | 22 October 2020 Cross Ref Properties of a Generalized Fractional Brownian of Vol. No. 1 | 9 January 2021 Cross Ref The for Time of Stochastic Vol. 10, No. 3 | 23 2022 Cross Ref A for Long in Higher Vol. 10, No. 5 | 24 2022 Cross Ref The of time Journal of Statistics, Vol. No. 1 | 14 August 2021 Cross Ref Estimation on of time generalized Dynamics, Vol. No. 4 | 12 January 2022 Cross Ref of the in the of fields by the of the Vol. | 1 Mar 2022 Cross Ref Statistical of nonlinear time and application to Review Research, Vol. 4, No. 1 | 17 March 2022 Cross Ref Price Modeling of under for Vol. 13, No. 3 | 18 March 2022 Cross Ref and in Advances of Physical Sciences, Vol. 06 | 27 April 2022 Cross Ref of of under fractional Brownian motionStatistics & Probability Letters, Vol. | 1 Mar 2022 Cross Ref Fractional and Statistical An of the Indian of Science, Vol. 29 | 24 2022 Cross Ref diffusion with stochastic of Physics A: Mathematical and Theoretical, Vol. 55, No. 7 | 28 January 2022 Cross Ref On the fractional stochastic for random Analysis and Applications, Vol. | 2 2022 Cross Ref of and Systems to

A Complete Reference Covering the Latest Technology in Metal Cutting Tools, Processes, and Equipment Metal Cutting Theory and Practice, Third Edition shapes the future of material removal in new and lasting ways. Centered on metallic work materials and traditional chip-forming cutting methods, the book provides a physical understanding of conventional and high-speed machining processes applied to metallic work pieces, and serves as a basis for effective process design and troubleshooting. This latest edition of a well-known reference highlights recent developments, covers the latest research results, and reflects current areas of emphasis in industrial practice. Based on the authors’ extensive automotive production experience, it covers several structural changes, and includes an extensive review of computer aided engineering (CAE) methods for process analysis and design. Providing updated material throughout, it offers insight and understanding to engineers looking to design, operate, troubleshoot, and improve high quality, cost effective metal cutting operations. The book contains extensive up-to-date references to both scientific and trade literature, and provides a description of error mapping and compensation strategies for CNC machines based on recently issued international standards, and includes chapters on cutting fluids and gear machining. The authors also offer updated information on tooling grades and practices for machining compacted graphite iron, nickel alloys, and other hard-to-machine materials, as well as a full description of minimum quantity lubrication systems, tooling, and processing practices. In addition, updated topics include machine tool types and structures, cutting tool materials and coatings, cutting mechanics and temperatures, process simulation and analysis, and tool wear from both chemical and mechanical viewpoints. Comprised of 17 chapters, this detailed study: Describes the common machining operations used to produce specific shapes or surface characteristics Contains conventional and advanced cutting tool technologies Explains the properties and characteristics of tools which influence tool design or selection Clarifies the physical mechanisms which lead to tool failure and identifies general strategies for reducing failure rates and increasing tool life Includes common machinability criteria, tests, and indices Breaks down the economics of machining operations Offers an overview of the engineering aspects of MQL machining Summarizes gear machining and finishing methods for common gear types, and more Metal Cutting Theory and Practice, Third Edition emphasizes the physical understanding and analysis for robust process design, troubleshooting, and improvement, and aids manufacturing engineering professionals, and engineering students in manufacturing engineering and machining processes programs.

1R1. Boundary Element Programming in Mechanics. - Xiao-Wei Gao (Dept of Mech and Aerospace Eng, Arizona State Univ, Tempe AZ) and TG Davies (Glasgow Univ, UK). Cambridge UP, Cambridge, UK. 2002. 254 pp. (CD-Rom included). ISBN 0-521-77359-8. $69.95. Reviewed by DE Beskos (Dept of Civil Eng, Univ of Patras, Patras, GR-26500, Greece).This is a really excellent textbook as well as a reference book on the numerical implementation and computer programing of the direct boundary element method as applied to two and three-dimensional problems of linear elasticity and nonlinear elastoplasticity. The book is aimed at both graduate students and researchers as well as practicing engineers in mechanical, aeronautical, and civil engineering fields. The book consists of 254 pages plus a CD-Rom with the computer programs described. The whole book can be divided in two main components: The first one dealing with linear problems (elasticity) and the second one with nonlinear problems (time independent elastostoplasticity). In both parts, the chapter breakdown is the same and consists of the theory (of elasticity or plasticity), the corresponding boundary integral formulation of the problem, the numerical implementation, the detailed (subroutine by subroutine) description of the computer program and a number of applications—numerical examples to illustrate the code and demonstrate its accuracy. The book is completed by an introduction and an epilogue, eight appendices, a list of references, and a subject index. The figures and tables are of very good quality. The list of references is comprehensive, but selective, and the subject index is informative, but somewhat short. The unusual features of this book, in order of importance, are the following: the book is very clearly written and the English language is not just correct and easy to understand, but lively and enjoyable. The authors have proved they are not just very good on technical matters, but they also know to handle the English language superbly. The various computational aspects of the boundary element method, such as singular integration, treatment of edges and corners, computation of boundary stresses, solution of systems of linear equations, return mapping algorithms in plasticity, etc, are all treated in detail. In particular, the authors in every case, first discuss the problem, mention the work of others, and then offer their solution which they consider to be the most effective. The computer programs are explained in detail on a subroutine-by-subroutine basis and serve to illustrate the implementation of the method in the best possible way. In addition, they can be modified by the user, if he wishes to add or replace things. There is an emphasis on three-dimensional problems both in elasticity and plasticity, which cannot be found in other books on the subject. The book succeeds completely relative to the author’s stated aims and the subject matter. As a matter of fact, the book can be the ideal vehicle to teach the boundary element method to engineers who want the theory to go hand-in-hand with the numerical implementation and are not so much interested in mathematical details. Thus, the book can be used either as an ideal introductory text on boundary elements, in general, or as a specialized book on boundary element methods in plasticity. There are many introductory books available on boundary elements, but most of them deal with potential theory and elasticity, and they do not emphasize either the numerical implementation of the method nor 3D problems. This reviewer predicts that this book will prove to be, for boundary element programing, what has been the case with the two texts by Hinton and Owen on finite elements. The only slightly negative about this book has to do with the title, which employs the general and misleading term mechanics instead of the more appropriate term solid mechanics, which would more exactly reflect the contents of the book. Boundary Element Programming in Mechanics is highly recommended for purchase by both individuals and libraries.

Nonlinear continuum mechanics of solids is a fascinating subject. All the assumptions inherited from an overexposure to linear behaviour and analysis must be re-examined. The standard definitions of strain designed for small deformation linear problems may be totally misleading when finite motion or large deformations are considered. Nonlinear behaviour includes phenomena like `snap-through', where bifurcation theory is applied to engineering design. Capabilities in this field are growing at a fantastic speed; for example, modern automobiles are presently being designed to crumple in the most energy absorbing manner in order to protect the occupants. The combination of nonlinear mechanics and the finite element method is a very important field. Most engineering designs encountered in the fusion effort are strictly limited to small deformation linear theory. In fact, fusion devices are usually kept in the low stress, long life regime that avoids large deformations, nonlinearity and any plastic behaviour. The only aspect of nonlinear continuum solid mechanics about which the fusion community now worries is that rare case where details of the metal forming process must be considered. This text is divided into nine sections: introduction, mathematical preliminaries, kinematics, stress and equilibrium, hyperelasticity, linearized equilibrium equations, discretization and solution, computer implementation and an appendix covering an introduction to large inelastic deformations. The authors have decided to use vector and tensor notation almost exclusively. This means that the usual maze of indicial equations is avoided, but most readers will therefore be stretched considerably to follow the presentation, which quickly proceeds to the heart of nonlinear behaviour in solids. With great speed the reader is led through the material (Lagrangian) and spatial (Eulerian) co-ordinates, the deformation gradient tensor (an example of a two point tensor), the right and left Cauchy-Green tensors, the Eulerian or Almansi strain tensor, distortional components, strain rate tensors, rate of deformation tensors, spin tensors and objectivity. The standard Cauchy stress tensor is mentioned in passing, and then virtual work and work conjugacy lead to alternative stress representations such as the Piola-Kirchoff representation. Chapter 5 concentrates on hyperelasticity (where stresses are derived from a stored energy function) and its subvarieties. Chapter 6 proceeds by linearizing the virtual work statement prior to discretization and Chapter 7 deals with approaches to solving the formulation. In Chapter 8 the FORTRAN finite element code written by Bonet (available via the world wide web) is described. In summary this book is written by experts, for future experts, and provides a very fast review of the field for people who already know the topic. The authors assume the reader is familiar with `elementary stress analysis' and has had some exposure to `the principle of the finite element method'. Their goals are summarized by the statement, `If the reader is prepared not to get too hung up on details, it is possible to use the book to obtain a reasonable overview of the subject'. This is a very nice summary of what is going on in the field but as a stand-alone text it is much too terse. The total bibliography is a page and a half. It would be an improvement if there were that much reference material for each chapter.

This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to wide a range of research areas along with many numerical examples for a deep understanding of the usefulness of each method. This book will make it possible for the researchers to tackle difficult problems and deepen their understanding of problem solving using numerical methods. Multipoint methods are of great practical importance, as they determine sequences of successive approximations for evaluative purposes. This is especially helpful in achieving the highest computational efficiency. The rapid development of digital computers and advanced computer arithmetic have provided a need for new methods useful to solving practical problems in a multitude of disciplines such as applied mathematics, computer science, engineering, physics, financial mathematics, and biology. Provides a succinct way of implementing a wide range of useful and important numerical algorithms for solving research problems Illustrates how numerical methods can be used to study problems which have applications in engineering and sciences, including signal processing, and control theory, and financial computation Facilitates a deeper insight into the development of methods, numerical analysis of convergence rate, and very detailed analysis of computational efficiencyProvides a powerful means of learning by systematic experimentation with some of the many fascinating problems in scienceIncludes highly efficient algorithms convenient for the implementation into the most common computer algebra systems such as Mathematica, MatLab, and Maple

Abstract This paper presents a new linear tetrahedral element that overcomes the shortcomings in bending dominated problems of the average nodal pressure element presented in Bonet and Burton ( Communications in Numerical Methods in Engineering 1998; 14 :437–439) Zienkiewicz et al. ( Internatinal Journal for Numerical Methods in Engineering 1998; 43 :565–583) and Bonet et al. ( Internatinal Journal for Numerical Methods in Engineering 2001; 50 (1):119–133). This is achieved by extending some of the ideas proposed by Dohrmann et al. ( Internatinal Journal for Numerical Methods in Engineering 2000; 47 :1549–1568) to the large strain nonlinear kinematics regime. In essence, a nodal deformation gradient is defined by weighted average of the surrounding element values. The associated stresses and internal forces are then derived by differentiation of the corresponding simplified strain energy term. The resulting element is intended for use in explicit dynamic codes (Goudreau and Hallquist, Computer Methods in Applied Mechanics and Engineering 1982; 33 ) where the use of quadratic tetrahedral elements can present significant difficulties. Copyright © 2001 John Wiley & Sons, Ltd.

Abstract Although there is a consensus on the instructional potential of S erious G ames ( SG s), there is still a lack of methodologies and tools not only for design but also to support analysis and assessment. Filling this gap is one of the main aims of the G ames and L earning A lliance ( http://www.galanoe.eu ) E uropean N etwork of E xcellence on S erious G ames, which has a focus upon pedagogy‐driven SG s . This paper relies on the assumption that the fundamental aspect of SG design consists in the translation of learning goals/practices into mechanical element of gameplay, serving to an instructional purpose beside that of play and fun. This paper proposes the L earning M echanics– G ame M echanics ( LM‐GM ) model, which supports SG analysis and design by allowing reflection on the various pedagogical and game elements in an SG . The LM‐GM model includes a set of pre‐defined game mechanics and pedagogical elements that we have abstracted from literature on game studies and learning theories. Designers and analysts can exploit these mechanics to draw the LM‐GM map for a game, so as to identify and highlight its main pedagogical and entertainment features, and their interrelations. The tool may also be useful for teachers to evaluate the effectiveness of a given game and better understand how to implement it in educational settings. A case study is reported to illustrate the framework's support in determining how gameplay and pedagogy intertwine in an SG . Finally, the paper presents the results of two comparative user tests demonstrating the advantages of the proposed model with respect to a similar state‐of‐the‐art framework.

Mechanical Engineering Design, Third Edition strikes a balance between theory and application, and prepares students for more advanced study or professional practice. Updated throughout, it outlines basic concepts and provides the necessary theory to gain insight into mechanics with numerical methods in design. Divided into three sections, the text presents background topics, addresses failure prevention across a variety of machine elements, and covers the design of machine components as well as entire machines. Optional sections treating special and advanced topics are also included. Features: Places a strong emphasis on the fundamentals of mechanics of materials as they relate to the study of mechanical design Furnishes material selection charts and tables as an aid for specific uses Includes numerous practical case studies of various components and machines Covers applied finite element analysis in design, offering this useful tool for computer-oriented examples Addresses the ABET design criteria in a systematic manner Presents independent chapters that can be studied in any order Introduces optional MATLAB® solutions tied to the book and student learning resources Mechanical Engineering Design, Third Edition allows students to gain a grasp of the fundamentals of machine design and the ability to apply these fundamentals to various new engineering problems.

The Journal of Engineering Mechanics covers activity and development in the field of applied mechanics as it relates to civil engineering. Research on bioengineering, computational mechanics, computer-aided engineering, dynamics of structures, elasticity, experimental analysis and instrumentation, fluid mechanics, flow of granular media, inelastic behavior of solids and structures, probabilistic methods, properties of materials, fracture mechanics, stability of structural elements and systems, and turbulence is reported. Typically, published papers describe the development and implementation of new analytical models, innovative numerical methods, and novel experimental methods and results.

Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures–including high strength, high stiffness, low density and structural perfection–could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young’s modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references.

Abstract Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves 1 and in the first imaging of a black hole 2 . Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis.

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from experiments, field measurements, and large-scale simulations at multiple spatiotemporal scales. Machine learning (ML) offers a wealth of techniques to extract information from data that can be translated into knowledge about the underlying fluid mechanics. Moreover, ML algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of ML for fluid mechanics. We outline fundamental ML methodologies and discuss their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experiments, and simulations. ML provides a powerful information-processing framework that can augment, and possibly even transform, current lines of fluid mechanics research and industrial applications.

Core Ideas Review of selected capabilities of HYDRUS implemented since 2008 New standard and nonstandard specialized add‐on modules significantly expanded capabilities of the software Review of selected applications of the HYDRUS models published in VZJ and elsewhere in recent years The HYDRUS‐1D and HYDRUS (2D/3D) computer software packages are widely used finite‐element models for simulating the one‐ and two‐ or three‐dimensional movement of water, heat, and multiple solutes in variably saturated media, respectively. In 2008, Šimůnek et al. (2008b) described the entire history of the development of the various HYDRUS programs and related models and tools such as STANMOD, RETC, ROSETTA, UNSODA, UNSATCHEM, HP1, and others. The objective of this manuscript is to review selected capabilities of HYDRUS that have been implemented since 2008. Our review is not limited to listing additional processes that were implemented in the standard computational modules, but also describes many new standard and nonstandard specialized add‐on modules that significantly expanded the capabilities of the two software packages. We also review additional capabilities that have been incorporated into the graphical user interface (GUI) that supports the use of HYDRUS (2D/3D). Another objective of this manuscript is to review selected applications of the HYDRUS models such as evaluation of various irrigation schemes, evaluation of the effects of plant water uptake on groundwater recharge, assessing the transport of particle‐like substances in the subsurface, and using the models in conjunction with various geophysical methods.

This is a textbook written for mechanical engineering students at first-year graduate level. As such, it emphasizes the development of finite element methods used in applied mechanics. The book starts with fundamental formulations of heat conduction and linear elasticity and derives the weak form (i.e. the principle of virtual work in elasticity) from a boundary value problem that represents the mechanical behaviour of solids and fluids. Finite element approximations are then derived from this weak form. The book contains many useful exercises and the author appropriately provides the student with computer programs in both BASIC and FORTRAN for solving them. Furthermore, a workbook is available with additional computer listings, and also an accompanying disc that contains the BASIC programs for use on IBM-PC microcomputers and their compatibles. Thus the usefulness and versatility of this text is enhanced by the student's ability to practise problem solving on accessible microcomputers.

201-F6, was shown to exhibit the rare ability to grow on PET as a major carbon and energy source. Central to its PET biodegradation capability is a secreted PETase (PET-digesting enzyme). Here, we present a 0.92 Å resolution X-ray crystal structure of PETase, which reveals features common to both cutinases and lipases. PETase retains the ancestral α/β-hydrolase fold but exhibits a more open active-site cleft than homologous cutinases. By narrowing the binding cleft via mutation of two active-site residues to conserved amino acids in cutinases, we surprisingly observe improved PET degradation, suggesting that PETase is not fully optimized for crystalline PET degradation, despite presumably evolving in a PET-rich environment. Additionally, we show that PETase degrades another semiaromatic polyester, polyethylene-2,5-furandicarboxylate (PEF), which is an emerging, bioderived PET replacement with improved barrier properties. In contrast, PETase does not degrade aliphatic polyesters, suggesting that it is generally an aromatic polyesterase. These findings suggest that additional protein engineering to increase PETase performance is realistic and highlight the need for further developments of structure/activity relationships for biodegradation of synthetic polyesters.

SUMMARY A computational homogenization procedure for cohesive and adhesive crack modeling of materials with a heterogeneous microstructure has been recently presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI: 10.1016/j.cma.2010.10.013 ). The macroscopic material properties of the cohesive cracks are obtained from the inelastic deformation manifested in a localization band (modeled with a continuum damage theory) at the microscopic scale. The macroscopic behavior of the adhesive crack is derived from the response of a microscale sample representing the microstructure inside the adhesive crack. In this manuscript, we extend the theory presented in Computer Methods in Applied Mechanics and Engineering (2010, DOI: 10.1016/j.cma.2010.10.013 ) with implementation details, solutions for cyclic loading, crack propagation, numerical analysis of the convergence characteristics of the multiscale method, and treatment of macroscopic snapback in a multiscale simulation. Numerical examples including crack growth simulations with extended finite elements are given to demonstrate the performance of the method. Copyright © 2011 John Wiley & Sons, Ltd.