In this section, we will develop some error bounds measuring the distance between any point and the exact solution of IMQVI (2.1) in Hilbert spaces.
Given the capacity bounds measured directly at the receive antenna of a real system, we can now assess the capacity loss due to a specific post-processing at the receiver.
Suppose that {σ k }k∈ℤis a sequence of uniformly bounded measures on ℝ d satisfying | σ ^ k ξ | ≤ C min | A 2 k L ξ |, ln | A 2 k L ξ | - 1 - β (2.3).
While the class of multipliers of the Sobolev space Wk,1(Rn) is strictly larger than the space of bounded measures for n > 1 [3], we show in this paper that it fails to contain certain natural operators of the singular integral type (Theorem 1).
Problem (0.1) admits a solution for every μ∈L1, but this need not be the case when μ is a general bounded measure.
Let be a bounded measure function on with values in symmetric linear transformations of, the linear space of -covectors in for.
The displacement is assumed to possess a Heaviside jump at the localization interface and the strain becomes bounded measure including a Dirac-delta function, but the traction must be continuous at the localization interface.
We study the boundary value problem with measures for (E1) −Δu+g(|∇u|)="0 in a bounded domain Ω in RN, satisfying (E2) u="μ on ∂Ω and prove that if g∈L1(1,∞;t−(2N+1)/Ndt) is nondecreasing (E1)–(E2) can be solved with any positive bounded measure.
we first generalize to systems a property established earlier by Hou and LeFloch for scalar conservation laws, and we prove that nonconservative schemes generate, at the level of the limiting hyperbolic system, an convergence error source-term which, provided the total variation of the approximations remains uniformly bounded, is a locally bounded measure.
In this paper we prove the existence of solutions for equations of the type −div(a(·, Du)) = f in a bounded open set Ω, u = 0 on ∂Ω, where a is a possibly non-linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure.
These were a result of 500 consecutive simulations and therefore, the bounds measured the variation in LCT load.
