We consider a problem of simultaneous reduction of a sequence of matrices by means of orthogonal transformations. We show that such reduction can be performed by a series of the deflation steps. At each deflation step a simultaneous eigenvalue problem, which is a direct generalization of the generalized eigenvalue problem, is solved. A fast variant of Gauss-Newton algorithm for its solution was...

Reduced rank regression analysis provides maximum likelihood estimators of a matrix of regression coefficients of specified rank and of corresponding linear restrictions on such matrices. These estimators depend on the eigenvectors of an ‘‘effect’’ matrix in the metric of an error covariance matrix. In this paper it is shown that the maximum likelihood estimator of the restrictions can be appro...

Simultaneous editing is a new method for automating repetitive text editing. After describing a set of regions to edit (the records), the user can edit any one record and see equivalent edits applied simultaneously to all other records. The essence of simultaneous editing is generalizing the user’s selection in one record to equivalent selections in the other records. We describe a generalizati...

In recent years, there has been increasing emphasis in the rural development literature on the multiple income-generating activities undertaken by rural households and the importance of assets in determining the capacity to undertake these activities. Controlling for endogeneity choice and applying Lee's generalization of Amemiya's two-step estimator to a simultaneous equation model, household ...

MOTIVATION Datasets resulting from metabolomics or metabolic profiling experiments are becoming increasingly complex. Such datasets may contain underlying factors, such as time (time-resolved or longitudinal measurements), doses or combinations thereof. Currently used biostatistics methods do not take the structure of such complex datasets into account. However, incorporating this structure int...

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact triangulated categories. In this paper, we show that the idempotent completion an extriangulated category admits natural structure. As application, prove recollement is still recollement.

This paper is concerned with the problem of nonlinear best simultaneous approximations in K?the Bochner function spaces respect to Minkowski? norms Euclidean spaces. Characterization results generalized approximation are established. These considered a generalization concerning Lebesgue and Orlicz

Aziz and Stursberg [1] propose an “Egalitarian Simultaneous Reservation”rule (ESR), a generalization of Serial rule, one of the most discussed mechanisms in random assignment problem, to the more general random social choice domain. We provide an alternative definition, or characterization, of ESR as the unique most ordinally-egalitarian one. Specifically, given a lottery p over alternatives, f...

This paper instigates the multivariate generalization of widely used Cauchy inequality 1 + x ≤ ex where can be any non-negative real number. The results this study solution for Cauchy’s problem particular Ordinary Differential Equation (ODE). is also related to complete monotone function and divided differences theory. proof based on empty product convention notion Beppo Levi theorem Monotone c...