Application of Poincare's Sweeping-Out Process
نویسندگان
چکیده
منابع مشابه
Sweeping out on a Set of Integers
Let (X, ®, m) be a Lebesgue space, m(X) = 1, and let T be an invertible measurable nonsingular aperiodic transformation of X onto X. If S is a set of r integers, r > 2, then there exists a set A of measure less than /•"' S*_! k~l such that X = U,es T"A. Thus for every infinite set of integers W there exist sets A of arbitrarily small measure such that X = U nniv T"A.
متن کاملSweeping by a tame process
We show that any semi-algebraic sweeping process admits piecewise absolutely continuous solutions, and any such bounded trajectory must have finite length. Analogous results hold more generally for sweeping processes definable in o-minimal structures. This extends previous work on (sub)gradient dynamical systems beyond monotone sweeping sets.
متن کاملDiscrete Approximations of a Controlled Sweeping Process
The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhedral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It ...
متن کاملTrajectory length of the tame sweeping process
We show that bounded trajectories of the semi-algebraic, or more generally o-minimally definable, sweeping process have finite length. This result generalizes previous work on gradient/subgradient dynamical systems and paves the way for further extensions in control systems and mathematical mechanics.
متن کاملBroom: Sweeping Out Garbage Collection from Big Data Systems
Many popular systems for processing “big data” are implemented in high-level programming languages with automatic memory management via garbage collection (GC). However, high object churn and large heap sizes put severe strain on the garbage collector. As a result, applications underperform significantly: GC increases the runtime of typical data processing tasks by up to 40%. We propose to use ...
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: Proceedings of the National Academy of Sciences
سال: 1933
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.19.4.457