From the duality concept discussed in Section 8.6, this is equivalent to the observability of the pair (A¯4,A¯2). Theorem 9.4 gives a necessary and sufficient condition for the observability of the pair. Theorem 9.4 The pair (A¯4,A¯2) is observable if and only if system (A...
Infinite-state games are a commonly used model for the synthesis of reactive systems with unbounded data domains. Symbolic methods for solving such games need to be able to construct intricate arguments to establish the existence of winning strategies. O
Then we prove that the Kreps–Yan theorem is valid for topological vector spaces in separating duality 〈 X , Y 〉, provided Y satisfies both a "completeness condition" and a "Lindelf-like condition". We apply this result to the characterization of the no-arbitrage assumption in a general ...
What is the duality theorem? What values of the boolean variables x and y satisfy xy = x + y? What are the equivalence classes of the equivalence relation {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} on the set {0, 1, 2, 3}? How is the Miller-Rabin tes...
anykplayers holding the reserved qumodes can still obtain the secret. Hence, by choosing arbitrarynplayers from the total2k−1players, a(k,2k−1)threshold protocol can be transformed into a(k,n)protocol. Thus, to prove Theorem 1, we only need to show that any(k,2k−1)protocol can...
It's a mathematical theorem about vectors in a Hilbert space and Hermitian operators. The theorem basically says that every vector in a Hilbert space is an eigenvector of some Hermitian operator. I can't find a specific reference at the moment. Opus_723 said: For example, what such operat...
on-shell generating a CP conserving phase and thus A dir CP , which is usually quite small for the experimentally feasible decays, O(1%). It is believed that larger asymmetries can be obtained in exclusive decays. However, a simple picture is lost because of the absence of the duality argu...
The spectral duality axiom is introduced in the next subsection and used together with the atomic decomposition to give a geometric characterization of the dual ball of a JB ∗ -triple (Theorem 3.14). The final subsection applies the latter to give an operator space characterization of one-...
Abstract In this paper, we study the existence of ground state solutions of nonlinear elliptic equation with logarithmic nonlinearity by the Linking theorem and logarithmic Sobolev inequality. Our results are quite different from those in the case of polynomial nonlinearity....
·K(s)). Consequently, 1+λt(s) is the eigenvalue of the 1+L(s). Therefore, for the every encirclement of the point −1+j0 by the Nyquist contour there will be an eigenvalue on the RHP. The proof of the duality for the eigenvalue theorem and generalized Nyquist theorem is ...