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For this reprint, we intend to cover theoretical as well as experimental works performed on small scale to predict the material properties and characteristics of any advanced and metamaterials. New studies on mechanics of small-scale structures such as MEMS/NEMS, carbon and non-carbon nanotubes (e.g., CNTs, Carbon nitride, and Boron nitride nanotubes), micro/nano-sensors, nanocomposites, macrocomposites reinforced by micro-/nano-fillers (e.g., graphene platelets), etc., are included in this reprint.

Technology: general issues --- History of engineering & technology --- carbon nanotube-reinforced composite --- forced vibration --- dynamic analysis --- beam --- harmonic load --- assembly --- metal-organic frameworks --- hydrogen evolution reaction --- Cu2−xS --- interfacial interaction --- conducting carbon black network --- mechanical property --- electromagnetic interference shielding --- CNT --- elastic foundations --- nonlinear free vibration --- nonlinear frequency --- shallow shell structures --- hyperelastic micro/nanobeam --- extended modified couple stress theory --- strain-stiffening effect --- nonlinear frequency response --- functionally graded material --- thermoelasticity --- sliding contact --- wear --- heating from friction --- thermoelastic instability --- wood --- nano-, micro-, meso-, and macro-structure --- multiscale mechanical properties --- size effects --- Hall-Petch law --- dendrochronology --- surface bonding --- nanoporous graphene --- atomic force microscopy --- hyperelastic microcantilever --- softening resonance --- non-contact cantilever --- shooting and arc-length continuation method --- developed Galerkin method --- graphene nanoplatelets --- recycle carbon fibers --- air nanobubbles --- cement-based composites and nanocomposites --- mechanical properties --- electrical properties

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The description for this book, Topological Methods in the Theory of Functions of a Complex Variable. (AM-15), Volume 15, will be forthcoming.

Functions of complex variables. --- Topology. --- 0O. --- 0Q. --- Absolute value. --- Addition. --- Additive group. --- Admissible representation. --- Arc (geometry). --- Arc length. --- Bernhard Riemann. --- Big O notation. --- Boundary (topology). --- Boundary value problem. --- Branch point. --- Canonical form. --- Cartesian coordinate system. --- Central angle. --- Clockwise. --- Compact space. --- Concentric. --- Conformal map. --- Continuous function. --- Contour line. --- Convex set. --- Corollary. --- Countable set. --- Critical value. --- Curve. --- Deformation theory. --- Diameter. --- Euclidean vector. --- Euler characteristic. --- Existential quantification. --- Family of curves. --- Finitary. --- Finite set. --- Function (mathematics). --- Harmonic function. --- Homeomorphism. --- Homotopy. --- Inference. --- Integer. --- Interior (topology). --- Intersection (set theory). --- Isolated point. --- Jordan curve theorem. --- Length. --- Limit point. --- Maxima and minima. --- Maximal arc. --- Meromorphic function. --- Metric space. --- Minimum distance. --- Normal family. --- Parameter. --- Parametrization. --- Partial derivative. --- Picard theorem. --- Point at infinity. --- Polar coordinate system. --- Polynomial. --- Quantity. --- Rado's theorem (Ramsey theory). --- Real variable. --- Rectangle. --- Remainder. --- Riemann surface. --- Rigid body. --- Saddle point. --- Sequence. --- Set (mathematics). --- Similarity (geometry). --- Simply connected space. --- Special case. --- Subset. --- Summation. --- Theorem. --- Theory. --- Topological property. --- Unit circle. --- Unit vector. --- Without loss of generality.

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The description for this book, Surface Area. (AM-35), Volume 35, will be forthcoming.

Surfaces. --- Absolute continuity. --- Addition. --- Admissible set. --- Arc length. --- Axiom. --- Axiomatic system. --- Bearing (navigation). --- Bounded variation. --- Calculus of variations. --- Circumference. --- Compact space. --- Complex analysis. --- Concentric. --- Connected space. --- Continuous function (set theory). --- Continuous function. --- Corollary. --- Countable set. --- Covering set. --- Curve. --- Derivative. --- Diameter. --- Differentiable function. --- Differential geometry. --- Direct proof. --- Dirichlet integral. --- Disjoint sets. --- Empty set. --- Equation. --- Equicontinuity. --- Existence theorem. --- Existential quantification. --- Function (mathematics). --- Functional analysis. --- Geometry. --- Hausdorff measure. --- Homeomorphism. --- Homotopy. --- Infimum and supremum. --- Integral geometry. --- Intersection number (graph theory). --- Interval (mathematics). --- Iterative method. --- Jacobian. --- Lebesgue integration. --- Lebesgue measure. --- Limit (mathematics). --- Limit point. --- Limit superior and limit inferior. --- Linearity. --- Line–line intersection. --- Locally compact space. --- Mathematician. --- Mathematics. --- Measure (mathematics). --- Metric space. --- Morphism. --- Natural number. --- Nonparametric statistics. --- Orientability. --- Parameter. --- Parametric equation. --- Parametric surface. --- Partial derivative. --- Potential theory. --- Radon–Nikodym theorem. --- Representation theorem. --- Representation theory. --- Right angle. --- Semi-continuity. --- Set function. --- Set theory. --- Sign (mathematics). --- Smoothness. --- Space-filling curve. --- Subset. --- Summation. --- Surface area. --- Tangent space. --- Theorem. --- Topological space. --- Topology. --- Total order. --- Total variation. --- Uniform convergence. --- Unit square.

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This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks-a sort of potato-stamp method-Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics.Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own.Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.

Symmetry (Mathematics) --- Symmetry (Art) --- Abstract algebra. --- Addition. --- Algorithm. --- Antisymmetry. --- Arc length. --- Boundary value problem. --- Cartesian coordinate system. --- Circular motion. --- Circumference. --- Coefficient. --- Complex analysis. --- Complex multiplication. --- Complex number. --- Complex plane. --- Computation. --- Coordinate system. --- Coset. --- Cyclic group. --- Derivative. --- Diagonal. --- Diagram (category theory). --- Dihedral group. --- Division by zero. --- Domain coloring. --- Dot product. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Eisenstein integer. --- Epicycloid. --- Equation. --- Euler's formula. --- Even and odd functions. --- Exponential function. --- Fourier series. --- Frieze group. --- Function (mathematics). --- Function composition. --- Function space. --- Gaussian integer. --- Geometry. --- Glide reflection. --- Group (mathematics). --- Group theory. --- Homomorphism. --- Horocycle. --- Hyperbolic geometry. --- Ideal point. --- Integer. --- Lattice (group). --- Linear interpolation. --- Local symmetry. --- M. C. Escher. --- Main diagonal. --- Mathematical proof. --- Mathematical structure. --- Mathematics. --- Mirror symmetry (string theory). --- Mirror symmetry. --- Morphing. --- Natural number. --- Normal subgroup. --- Notation. --- Ordinary differential equation. --- Parallelogram. --- Parametric equation. --- Parametrization. --- Periodic function. --- Plane symmetry. --- Plane wave. --- Point group. --- Polynomial. --- Power series. --- Projection (linear algebra). --- Pythagorean triple. --- Quantity. --- Quotient group. --- Real number. --- Reciprocal lattice. --- Rectangle. --- Reflection symmetry. --- Right angle. --- Ring of integers. --- Rotational symmetry. --- Scientific notation. --- Special case. --- Square lattice. --- Subgroup. --- Summation. --- Symmetry group. --- Symmetry. --- Tetrahedron. --- Theorem. --- Translational symmetry. --- Trigonometric functions. --- Unique factorization domain. --- Unit circle. --- Variable (mathematics). --- Vector space. --- Wallpaper group. --- Wave packet.

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This book builds upon the revolutionary discovery made in 1974 that when one passes from function f to a function J of paths joining two points A1≠A1 the connectivities R1 of the domain of f can be replaced by connectivities R1 over Q, common to the pathwise components of a basic Frechet space of classes of equivalent curves joining A1 to A1. The connectivities R1, termed "Frechet numbers," are proved independent of the choice of A1 ≠ A1, and of a replacement of Mn by any differential manifold homeomorphic to Mn.Originally published in 1976.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Differentiable manifolds. --- Global analysis (Mathematics) --- Calculus of variations. --- Algebraic topology. --- Analytic function. --- Arc length. --- Axiom. --- Bernhard Riemann. --- Boundary value problem. --- Cartesian coordinate system. --- Coefficient. --- Compact space. --- Computation. --- Conjugate points. --- Connectivity (graph theory). --- Continuous function. --- Corollary. --- Countable set. --- Counting. --- Cramer's rule. --- Curve. --- Deformation theory. --- Degeneracy (mathematics). --- Derivative. --- Diffeomorphism. --- Differentiable manifold. --- Differential equation. --- Differential geometry. --- Differential structure. --- Dimension. --- Domain of a function. --- Eilenberg. --- Einstein notation. --- Equation. --- Euclidean space. --- Euler characteristic. --- Euler equations (fluid dynamics). --- Euler integral. --- Existence theorem. --- Existential quantification. --- Exotic sphere. --- Family of curves. --- Finite set. --- First variation. --- Geometry. --- Global analysis. --- Homeomorphism. --- Homology (mathematics). --- Homotopy. --- Implicit function theorem. --- Inference. --- Integer. --- Intersection (set theory). --- Interval (mathematics). --- Invertible matrix. --- Jacobian matrix and determinant. --- Lagrange multiplier. --- Linear combination. --- Linear map. --- Line–line intersection. --- Mathematical proof. --- Maximal set. --- Metric space. --- N-sphere. --- Neighbourhood (mathematics). --- Null vector. --- Open set. --- Pairwise. --- Parameter. --- Parametric equation. --- Parametrization. --- Partial derivative. --- Partial function. --- Phase space. --- Positive definiteness. --- Projective plane. --- Quadratic form. --- Quadratic. --- Rate of convergence. --- Rational number. --- Real variable. --- Resultant. --- Riemannian manifold. --- Scientific notation. --- Sign (mathematics). --- Special case. --- Sturm separation theorem. --- Submanifold. --- Subsequence. --- Subset. --- Taylor's theorem. --- Tensor algebra. --- Theorem. --- Theory. --- Topological manifold. --- Topological space. --- Topology. --- Tuple. --- Unit vector. --- Variable (mathematics). --- Variational analysis. --- Weierstrass function. --- Without loss of generality.