Convex integration

Xem 1-7 trên 7 kết quả Convex integration
  • In this paper we study Lipschitz solutions of partial differential relations of the form (1) ∇u(x) ∈ K a.e. in Ω, where u is a (Lipschitz) mapping of an open set Ω ⊂ Rn into Rm , ∇u(x) is its gradient (i.e. the matrix ∂ui (x)/∂xj , 1 ≤ i ≤ m, 1 ≤ j ≤ n, defined for almost every x ∈ Ω), and K is a subset of the set M m×n of all real m × n matrices. In addition to relation (1), boundary conditions and other conditions on u will also be considered. Relation (1)...

    pdf29p tuanloccuoi 04-01-2013 26 6   Download

  • We find a sharp combinatorial bound for the metric entropy of sets in Rn and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central Limit Theorem if the square root of its combinatorial dimension is integrable. 2. The uniform entropy is equivalent to the combinatorial dimension under minimal regularity. Our method also constructs a nicely bounded coordinate section of a symmetric convex body in Rn . ...

    pdf47p noel_noel 17-01-2013 26 5   Download

  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Convexity Property for an Integral Operator on the Class SP β

    pdf4p sting10 24-02-2012 19 4   Download

  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Convex Solutions of a Nonlinear Integral Equation of Urysohn Type

    pdf13p sting08 18-02-2012 16 2   Download

  • We resolve these issues as follows. We show that a nonincreasing returns to scale (nrs) model is usually appropriate when modeling rational choice among investors. We show when multiple risk and return measures can justifiably be combined and identify some suitable measures. We show we need a nonlinear model to justify the assumption of convexity and to model diversification. We develop a method to approximate a solution to this model as accurately as needed using a sequence of linear models. Coherent measures of risk come up again and again in our discussion.

    pdf18p thangbienthai 20-11-2012 19 1   Download

  • This chapter provides a brief introduction to the theory of morphological signal processing and its applications toimage analysis andnonlinear filtering. By “morphological signal processing”we mean a broad and coherent collection of theoretical concepts, mathematical tools for signal analysis, nonlinear signal operators, design methodologies, and applications systems that are based on or related to mathematical morphology (MM), a set- and lattice-theoreticmethodology for image analysis. MM aims at quantitatively describing the geometrical structure of image objects.

    pdf32p longmontran 18-01-2010 55 9   Download

  • báo cáo này, chúng ta xem xét một lớp học của các chức năng starlike thống nhất được định nghĩa bởi nhà điều hành tách rời nhất định. Chúng tôi xác định một điều kiện đủ cho một hàm f được thống nhất starlike chức năng đó cũng là cần thiết khi e có hệ số tiêu cực.

    pdf16p phalinh21 01-09-2011 19 2   Download


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