Author supplied: "This paper gives a linearised adjustment model for the affine, similarity and congruence transformations in 3D that is easily extendable with other parameters to describe deformations. The model considers all coordinates stochastic. Full positive semi-definite covariance matrices and correlation between epochs can be handled. The determination of transformation parameters between two or more coordinate sets, determined by geodetic monitoring measurements, can be handled as a least squares adjustment problem. It can be solved without linearisation of the functional model, if it concerns an affine, similarity or congruence transformation in one-, two- or three-dimensional space. If the functional model describes more than such a transformation, it is hardly ever possible to find a direct solution for the transformation parameters. Linearisation of the functional model and applying least squares formulas is then an appropriate mode of working. The adjustment model is given as a model of observation equations with constraints on the parameters. The starting point is the affine transformation, whose parameters are constrained to get the parameters of the similarity or congruence transformation. In this way the use of Euler angles is avoided. Because the model is linearised, iteration is necessary to get the final solution. In each iteration step approximate coordinates are necessary that fulfil the constraints. For the affine transformation it is easy to get approximate coordinates. For the similarity and congruence transformation the approximate coordinates have to comply to constraints. To achieve this, use is made of the singular value decomposition of the rotation matrix. To show the effectiveness of the proposed adjustment model total station measurements in two epochs of monitored buildings are analysed. Coordinate sets with full, rank deficient covariance matrices are determined from the measurements and adjusted with the proposed model. Testing the adjustment for deformations results in detection of the simulated deformations."
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Charitable donations constitute choices, and donors' values influence both the choice to donate and the selected nonprofit organization (NPO). The current study proposes a new instrument to measure NPO values. The proposed two-stage analytical procedure is novel in this research area. The first stage shows that the personal value of universalism drives the general decision to donate. The second stage reveals that donating to a specific NPO depends on the congruency between the NPO values of the organization and the individual donor's NPO values. Furthermore, distinct NPO values are relevant to donation decisions such that NPO values can attract a particular type of donor to an NPO. These findings have pertinent implications for NPOs' chosen positioning strategies as it allows NPOs to collectively guard the qualities that increase general donations and individually distinguish themselves based on the specific NPO values that ensure alignment with their own donors.
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