In this article, we formalize a matrix of Z-module and its properties. Specially, we formalize a matrix of a linear transformation of Z-module, a bilinear form and a matrix of the bilinear form (Gramian matrix). We formally prove that for a finite-rank free Z-module V , determinant of its Gramian matrix is constant regardless of selection of its basis. Z-module is necessary for lattice problems...

A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three-point tensor. The derivation explicitly shows that the Eulerian and Lagrangian strain tensors are two-point tensors, each a function of both the spatial and material coordinates....

We extend the well-known technique of constrained Maximum Likelihood Linear Regression (MLLR) to compute a projection (instead of a full rank transformation) on the feature vectors of the adaptation data. We model the projected features with phone-dependent Gaussian distributions and also model the complement of the projected space with a single class-independent, speaker-specific Gaussian dist...

A solution of the problem of calculating cartesian coordinates from a matrix of interpoint distances (the embedding problem) is reported. An efficient and numerically stable algorithm for the transformation of distances to coordinates is then obtained. It is shown that the embedding problem is intimately related to the theory of symmetric matrices, since every symmetric matrix is related to a g...

This paper studies the possibility of achieving indistinguishabilitybased security in privately outsourcing linear equation systems over real numbers. The particular task is to solve a full-rank n× n system Ax = b. Since the most complex part of this task is inverting A, the problem can be reduced to outsourcing of a square matrix inverse computation. Although outsourcing matrix inverse is triv...

Global sensitivity analysis can be used to identify and rank variables importance (sensitivities) for design objectives and constraints, where the solution space is sampled and a linear regression model is normally adopted in the stepwise manner. The relative importance of variables can be examined by three indicators: the order of variables entry into the linear regression model; the absolute ...