For instance, the sequence of Fock states \(\left( \vert n\rangle \!\langle n\vert \right) _n\) converges to 0 in the weak operator topology, but it is not convergent in the norm topology (for instance because it is not of Cauchy type). 2.2 Continuous variable systems Among all ...
The different forms of Rolle Theorem,Lagrange Theorem and Cauchy Theorem unified in differential mean-value theorems are also discussed. 从几何直观出发,立足于整体角度,研究微分中值定理之间的关系,讨论R o lle定理、L agrange定理、C auchy定理统一于微分学中值定理的各种形式;并以R o lle定理为基础,借助...
To enhance the “robustness” of the kernel parameter selection on the resultant filtering performance, the Cauchy kernel function is adopted to calculate the corresponding correntropy. The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy ...
A result for such a small gap in the classical setting follows directly from a very elementary analysis based on the Cook-Levin theorem. So then why did we have to write so many pages (and so many applications of Cauchy-Schwarz!) to arrive at basically the same result (with a )?
This paper is concerned with the study of equations of viscous compressible and heat-conducting full magnetohydrodynamic (MHD) steady flows in a horizontal layer under the gravitational force and a large temperature gradient across the layer. We assume a
Cauchys mean value theorem View Solution State triangle inequality. View Solution For any two vectors vecaandvecb , we always have |veca*vecb|le|veca||vecb| (Cauchy- Schwartz inequality). View Solution For any two vectors →aand→b , we always have ∣∣→a⋅→b∣∣≤|→a|∣∣→...
Taking an expectation over \(\gamma \) and then using Cauchy–Schwarz inequality and the natural order in I to simplify the notations, we obtain $$\begin{aligned}&\left\langle \left| \phi ^{I+y} - (\phi ')^{I+y} \right| \right\rangle _{\gamma } \le \sum _{x\in I} \...
In recent times, an upsurge in the investigation related to the effects of meditation in reconditioning various cardiovascular and psychological disorders is seen. In majority of these studies, heart rate variability (HRV) signal is used, probably for it
s deviation from the true value of the parameter, and takes advantage of quantum local asymptotic normality, a useful asymptotic characterization of identically prepared states in terms of Gaussian states. We first prove our results for the mean square error of a special class of models, calledD...
Let A be the adjacency matrix of a graph G and suppose U ( t ) = exp( itA ). We say that we have perfect state transfer in G from the vertex u to the vertex v at time t if there is a scalar γ of unit modulus such that U ( t ) e u = γ e v . It is known