Mathematics document containing theorems and formulas.
Excerpt: Tight and Taut Submanifolds; Remembering Nicolaas Kuiper; Thomas F. Banchoff; and Geometry in Curvature Theory ...
Physics Literature
Excerpt: Symmetry and mechanics have been close partners since the time of the founding masters: Newton, Euler, Lagrange, Laplace, Poisson, Jacobi, Hamilton, Kelvin, Routh, Riemann, Noether, Poincare, Einstein, Schraodinger, Cartan, Dirac, and to this day, symmetry has continued to play a strong role, especially with the modern work of Kolmogorov, Arnold, Moser, Kirillov, Kostant, Smale, Souriau, Guillemin, Sternberg, and many others. This book is about these development...
Excerpt: Syzygies; Bounds In Polynomial Ideal Theory; Some Bounds In Polynomial Ideal Theory; The Hilbert?Serre Theorem; Homogeneous Sets; Cone Decomposition; Exact Decomposition Of Nf(I ); Exact Decomposition Of Ideals; Bounding The Macaulay Constants; Term-Rewriting Systems; A Quadratic Counter; Uniqueness Property; Lower Bounds; and Appendix A: Properties Of S0.
University of Connecticut Libraries ; University of Connecticut Libraries ; Boston Library Consortium
Excerpt: The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory are given in Chapter 8, using both invariant and index notation...
Vol. 3 has added t.-p. Leonhard Euler's Theorie der Bewegung fester oder starrer Kao'rper.
Excerpt: This chapter studies vector fields and the dynamical systems they determine. The ensuing chapters will study the related topics of tensors and differential forms. A basic operation introduced in this chapter is the Lie derivative of a function or a vector field. It is introduced in two different ways, algebraically as a type of directional derivative and dynamically as a rate of change along a flow. The Lie derivative formula asserts the equivalence of these two...
Excerpt: That d is a natural operator from the functor LkTL into functor Lk+1TL. If k > 0...
Osmania University ; Digital Library of India
Excerpt: In the previous chapter we studied vector fields and functions on manifolds. In this chapter these objects are generalized to tensor fields, whic h are sections of vector bundles built out of the tangent bundle. This study is continued in the next chapter when we discuss differential forms, which are tensors with special symmetry properties. One of the objectives of this chapter is to extend the pull-back and Lie derivative operations from functions and vector fields to tensor fields.