background : accurate recording of the nursing care indicates the care performance and its quality, so that, any failure in documentation can be a reason for inadequate patient care. therefore, improving nurses’ skills in this field using effective educational methods is of high importance. since traditional teaching methods are not suitable for communities with rapid knowledge expansion and co...

We still need to show that the directions p0, p1, . . . , pn−1 generated by Algorithms 1 and (2) are conjugate wrt A. If so, then by Theorem 11.3, this algorithm will terminate in n steps. The next theorem shows this property, along with two other important properties: (i) the residuals ri are mutually orthogonal, and (ii) each pk and rk is contained in the Krylov subspace of degree k for r0, d...

This file of notes serves as a reference for Zeyuan himself about the materials to be delivered in class. It copies a lot of materials from Prof Michel X. Goemans’ lecture notes on 6.854 in 1994, (see http: //www-math.mit.edu/~goemans/notes-lp.ps), and Prof Sven O. Krumke’s report on interior point methods (see http://optimierung.mathematik.uni-kl.de/~krumke/Notes/interior-lecture. pdf). Ye’s i...

where L = (Lij)m×n is a block m×n matrix differential operator of at most first order, B = (Bij)l×n is a block l × n matrix operator, U = (Ui)n×1 is unknown, F = (Fi)m×1 is a given block vector-valued function defined in Ω, G = (Gi)l×1 is a given block vector-valued function defined on ∂Ω. Assume that first-order system (1.1) has a unique solution U . Boundary conditions in a least-squares form...

We now move on to a very interesting and powerful technique in combinatorics, called the probabilistic method. There is an excellent (really excellent!) textbook written by Noga Alon and Joel Spencer [AS16]. In fact, most materials that we will cover are from [AS16]. The method works as follows. Our goal is to prove the existence of certain object or structure with desired properties. We start ...

The approach combines second and fourth order statistics to perform BSS of instantaneous mixtures. It applies for any number of receivers if they are as many as sources. It is a batch algorithm that uses non-Gaussianity and stationarity of source signals. It is linear algebra based direct method, reliable and robust, though large dimensions of sources may slow down the computation significantly...