Sentence examples for systems we prove from inspiring English sources

Using the instability of completeness of orthogonal systems we prove that every contractive operator-valued function S t),t ∈ T, on a Hilbert space E is the scattering operator of a pair (U, Ů) of unitary operators on L2(E), where Ů is the shift Ůƒ = z · ƒ.

By means of dual transformation and generalized Riccati equation systems, we prove the existence of eigenvalues and construct the corresponding eigenfunctions.

Under these conditions and considering only the case where the spectrum is simultaneously utilized by the two systems, we prove that the best response dynamics are globally convergent.

On the basis of the proposed computational integration of the two systems, we prove analytically that reward-seeking and physiological stability are two sides of the same coin, and also provide a normative explanation for temporal discounting of reward.

On finite horizons and for arbitrary exo-systems, we prove that our control is an agreeable plan as it approximates the computational expensive, time-varying optimal control of any suitably large horizon.

For the proposed overall system, we prove hierarchical consistency and that the closed-loop behavior is nonblocking.

In the case of anN-body system we prove that the high velocity limit of any one of the Dollard scattering operators determines uniquely the potential.

For an interval system, we prove that the maximal H∞ norm of its sensitivity function is achieved at twelve (out of sixteen) Kharitonov vertices.

With this innovative microgravity simulation system, we prove through experiments and tests that our innovative method is feasible and effective and that the simulation fidelity is even higher than the neutral buoyancy system.

Employing a nominal feedback law, not necessarily satisfying a linear growth restriction, which globally asymptotically, and not necessarily exponentially, stabilizes a nominal transformed system, we prove global asymptotic stability of the original closed-loop system, under the predictor-based version of the nominal feedback law, utilizing estimates on solutions.

For the corresponding auxiliary system, we prove the existence of solutions by using relatively suitable conditions.