a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

a model for missing data in mixed binary and continuous responses, which can be used on cross-sectional data, is presented. in this model response indicator for the binary response can be dependent on the continuous response. a closed form for the likelihood is found. for data with a complicated pattern of missing responses some new residuals are also proposed. the model of multiplicative heter...

We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension incompressible Navier–Stokes equations, observational measurements given by finite volume elements or nodal points of the velocity field and measurement errors which...

this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...

Suppose we want to benchmark a quantum device held by remote party, e.g. testing its ability carry out challenging measurements outside of free set $\mathcal{M}$. A very simple way do so is up binary state discrimination task that cannot be solved efficiently means measurements. If one can find pairs orthogonal states become arbitrarily indistinguishable under in $\mathcal{M}$, the sense error ...