Showing papers in "Advances in Mathematics in 1975"

TL;DR: In this paper, three integrable hamiltonian systems connected with isospectral deformations are discussed, where wave solutions of a nonlinear partial differential equation have a strong stability behavior.

TL;DR: In this paper, an explicitly soluble system of nonlinear differential equations related to certain Toda lattices was solved by applying a discrete version of the inverse scattering problem, and the solution of the finite system yielded also the solution to the finite Toda chain with two free ends, a problem that has been recently solved.

TL;DR: In this paper, a family of generic minimal free resolutions of the cokernel of a map of the form Ak C# or Sk+, where 4: F --t G is a map between free modules F and G over a noetherian commutative ring, with rank F >, rank G, and where A and Sk denote the kth exterior and symmetric powers, respectively.

TL;DR: In this paper, the existence of solutions for a general class of problems in the calculus of variations and optimal control involving ordinary differential equations or contingent equations is established, and the results of Cesari, Olech and the author are extended.

TL;DR: This article showed that deliberately induced biases can dramatically improve estimation properties when there are several parameters to be estimated, which represents a radical departure from the tradition of unbiased estimation which has dominated statistical thinking since the work of Gauss.

TL;DR: A Glimpse into Complex Analysis as mentioned in this paper discusses automorphic forms for Schottky groups, for which no standard fundamental region, no matter what generators one chooses, is bounded by circles.

TL;DR: In this article, the Hammerstein system is defined as an equation of the same form but with h and u r-vector functions for some positive integer Y, K a function from Q x Q to the (r x r)-matrices, and f a function between $2 x W to 172'

TL;DR: In this article, the signature and Euler characteristic of a Riemannian manifold with boundary was discussed. But the signature complex was not considered, and there is no corresponding uniqueness theorem for this case.

TL;DR: There is a homology theory on the category of ordered sets such that the Betti numbers of a geometric lattice are the Whitney numbers of the first kind and the chapter describes such a theory.

TL;DR: The renormalization group approach is a way of reducing the complexity of these problems to the point where numerical methods can be used to solve them as mentioned in this paper, where the Kondo problem is used as an illustration.

TL;DR: In this paper, the curvatures of a simple mechanical system relative to a total energy value h were studied in the setting of Riemannian geometry, where the Jacobi metric is defined relative to the energy value.

TL;DR: Some recent work in turbulence theory is reviewed in this article, with emphasis on methods related to renormalized perturbation theory, including constants of motion and equilibrium statistical mechanics of the Euler equations, cascade phenomena in turbulence and intermittency in the small scales, renormalization of viscosity, difficulty of distinguishing convection from distortion effects in turbulence dynamics, the need for Lagrangian description, and related difficulties in the quantum field theory of many-body systems.

TL;DR: In this paper, a simplification and unification of the techniques used by Furstenberg, Ellis, and Veech in their proofs of structure theorems about distal and point distal flows is presented.

TL;DR: Local class field theory as discussed by the authors is a generalization of algebraically closed residue field theory, which can be treated briefly and without using any of the involved machinery that one usually finds in this connection.

TL;DR: For a class of stopping times, such as passage times and independent exponential holding times, the local time is a diffusion relative to its spatial parameter as discussed by the authors, which is a remarkable result.

TL;DR: In this article, the authors discuss the real numbers as a wreath product and discuss the construction of real numbers by algorithmically describing the operations of binary addition, multiplication, and division on infinite strings of zeros and ones.

TL;DR: In the last decade some progress has been made in classifying measure-preserving transformations as discussed by the authors, and a new numerical invariant called entropy has been introduced by Shannon's work on information theory.