Constructive proof of the Min-Max theorem
نویسندگان
چکیده
منابع مشابه
A constructive fixed point theorem for min-max functions∗
Min-max functions, F : R → R, arise in modelling the dynamic behaviour of discrete event systems. They form a dense subset of those functions which are homogeneous, Fi(x1 + h, · · · , xn + h) = Fi(x1, · · · , xn) + h, monotonic, ~x ≤ ~y ⇒ F (~x) ≤ F (~y), and nonexpansive in the `∞ norm—so-called topical functions—which have appeared recently in the work of several authors. Our main result char...
متن کاملApplications of the Gaussian Min-Max theorem
We show how the Gaussian min-max theorem provides direct proofs of several famous results in asymptotic geometric analysis, such as, the Dvoretzky theorem, the Johnson-Lindenstrauss Lemma, Gluskin’s theorem on embedding in `1 , and others.
متن کاملThe Duality Theorem for Min-max Functions
The set of min-max functions F : R → R is the least set containing coordinate substitutions and translations and closed under pointwise max, min, and function composition. The Duality Conjecture asserts that the trajectories of a min-max function, considered as a dynamical system, have a linear growth rate (cycle time) and shows how this can be calculated through a representation of F as an inf...
متن کاملThe Duality Theorem for Min - Max Functionsst
The set of min-max functions F : R n ! R n is the least set containing coordinate substitutions and translations and closed under pointwise max, min, and function composition. The Duality Conjecture asserts that the trajectories of a min-max function, considered as a dynamical system, have a linear growth rate (cycle time) and shows how this can be calculated through a representation of F as an...
متن کاملConstructive Proof of the Carpenter’s Theorem
We give a constructive proof of Carpenter’s Theorem due to Kadison [14, 15]. Unlike the original proof our approach also yields the real case of this theorem. 1. Kadison’s theorem In [14] and [15] Kadison gave a complete characterization of the diagonals of orthogonal projections on a Hilbert space H. Theorem 1.1 (Kadison). Let {di}i∈I be a sequence in [0, 1]. Define a = ∑ di<1/2 di and b = ∑ d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1956
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1956.6.25