In order to overcome above limitations, with the addition of the stress-free-state variables, the derivations of mechanical equilibrium equations for different types of elements neglecting the interim states of the structures utilizing the minimum potential energy theorem are briefly summarized. 2.2.1Pla...
Since [Math Processing Error]p∈[2N−μN,2N−μN−2), then by Hardy–Littlewood–Sobolev inequality and Sobolev embedding theorem, it is easy to prove that J is well defined on E and belongs to [Math Processing Error]C1(E,R). Moreover, there holds [Math Processing Error]⟨J′...
Von Neumann's proof of his “No go theorem” was based on a general assumption that has been, later, considered too strong. The condition asserts the following: Let sω be a dispersione-free state and let A, B be two (possibly noncompatible) observables. Then, Exp(A + B, sω) =...
Whether the theorem statement is true or not, I don’t know; but at the moment I am unable to prove it. I have to accept that there is a bug. As painful as it is I realize that I am writing this post from a relatively comfortable position. Who knows if I would have been able ...
With the Lagrange multiplier Theorem, they concluded that ū(x) := ŵ(x/tŵ) with tw^=N−22N∥∇w^∥2 is a least energy solution of (1.3). By noting the one-to-one correspondence between 𝓢 and 𝓜∞, Jeanjean-Tanaka [6] proved that ū is also a ground state solution ...
And, although the AMP algorithm can be derived as an approximation of loop belief propagation (LBP), this viewpoint provides little insight into why large i.i.d. \boldsymbol{A} \boldsymbol{A} matrices are important for AMP, and why AMP has a state evolution. In this work, we provide ...
Acknowledgments The author would like to thank the anonymous referees for their useful comments and suggestions to correct the errors and especially to improve the proof of Theorem 4.4. This work is partially supported by Natural Science Foundation of Shandong Province, PR China (ZR2019MA019).Refere...
(22) Theorem 1. Let us consider the spacecraft system (4) based on FxTESO (20). There exist the appro- priate observation gains α1, α2, β1, β2, and 0 < o < 1, θ > 1, such that E1 converges to zero in fixed time T1 without the initial conditions for t > T1, and ...
due to the Eastin–Knill theorem15, we also know that it is impossible to have a universal set of transversal gates, and although Clifford unitaries can be realized transversally16,17, one needs to find ways around the Eastin–Knill restriction. This can be achieved by injecting in quantum ...
The following theorem enables to prove the stability with decay-rate 0 < β ≤ 1 of the closed-loop system (1) with the control law (8) and the predictor-observer scheme (14), for any arbitrarily fast-time varying delays dkSC,dkCA. Theorem 1 Given K, L, and scalars σu,...