China
Africa
Explore chapters and articles related to this topic
Measurable Sets
Published in Hugo D. Junghenn, Principles of Analysis, 2018
Since A⊆Au $ \boldsymbol{{ \fancyscript {A}}}\subseteq \boldsymbol{{ \fancyscript {A}}}_ \mathfrak u $ , every sum s is also a sum t. On the other hand, since each Bn $ B_n $ is a finite disjoint union of members of A $ \boldsymbol{{ \fancyscript {A}}} $ and μu $ \mu _ \mathfrak u $ is additive, every t may be decomposed and written as an s. The infima over these sums are therefore the same.
∗-Algebras in Several Complex Variables
Published in Kehe Zhu, Handbook of Analytic Operator Theory, 2019
is a bounded symmetric domain of rank r — ℓ. For u ≠ 0 the translated set u + Ωu ⊂ ∂Ω is called a boundary component of Ω. One can show that these boundary components are pairwise disjoint. Taking the disjoint union () ∂lΩ=∪u∈Slu+Ωu
Algebraic Aspects of Autonomic Systems
Published in Phan Cong Vinh, Nature-Inspired Networking: Theory and Applications, 2018
Let AS and AS′ be autonomic systems. The coproduct of AS and AS′, denoted AS ⊔ AS′, is defined as the “disjoint union” of AS and AS′ (i.e., the autonomic system for which a state is either a state of AS or a state of AS′). If something is a state of both AS and AS′ then we include both copies, and distinguish between them, in AS ⊔ AS′. There are two natural inclusion actions self-*action1 : AS → AS ⊔ AS′ and self-*action2 : AS′ → AS ⊔ AS′.
Generalized left-localized Cayley parametrization for optimization with orthogonality constraints
Published in Optimization, 2022
Minimization of a continuous over the orthogonal group is a special instance of Problem 1.1 with p = N. This problem can be separated into two optimization problems over the special orthogonal group as and, with an arbitrarily chosen , because is the disjoint union of and . For the problem in (2), the Cayley transform and its inversion mapping1have been utilized in [18,20,21] because φ translates a subset [see (A3)]) of into the vector space of all skew-symmetric matrices, where is called, in this paper, the singular-point set of φ. More precisely, this is because φ is a diffeomorphism between the dense subset2 of and .
Asynchronous H∞ filtering for networked switched systems under effective DoS attacks
Published in International Journal of Systems Science, 2022
Lijie You, Xiaowu Mu, Zhe Yang
Let denotes subintervals that the condition (3) is satisfied in the interval and denotes subintervals that the condition (3) is not satisfied in the interval . The interval is the disjoint union of and , where and represent the union of and , respectively. Then, there exist two natural number sequences and such that where and .
Projections of patterns and mode interactions
Published in Dynamical Systems, 2018
Sofia B. S. D. Castro, Isabel S. Labouriau, Juliane F. Oliveira
Consider an (n + 1)-dimensional lattice with holohedry , and let . Let . Then there are , j − 2,… , r yielding k1 = k, k2 = δ2k,… , kr = δrk such that is the disjoint union and therefore the projection is a disjoint union of -orbits.