Tree series transformations computed by bottom-up tree series transducers are called bottom-up tree series transformations. (Functional) compositions of such transformations are investigated. It turns out that bottom-up tree series transformations over commutative and א0-complete semirings are closed under left-composition with linear bottom-up tree series transformations and right-composition ...

We show that the stationary quantum Hamilton–Jacobi equation of non–relativistic 1D systems, underlying Bohmian mechanics, takes the classical form with ∂q replaced by ∂q̂ where dq̂ = dq √ 1−β . The β term essentially coincides with the quantum potential that, like V − E, turns out to be proportional to a curvature arising in projective geometry. In agreement with the recently formulated equivale...

In these notes we study Lorentz transformations and focus on the group of proper, orthochronous Lorentz transformations, donated by L+. (These Lorentz transformations have determinant one and preserve the direction of time.) The 2×2 matrices with determinant one, denoted SL(2, C), play a key role, as there is a map from SL(2,C) onto L+, that is 2-to-1 and a homomorphism. In this correspondence,...

0

We develop a formal basis of correct schema transformations. Schemas are formalized as abstract data types, and correct schema transformations are formalized as information-preserving signature interpretations. Our formalism captures transformations of all schema components , making it possible to transform uniformly constraints and queries along with structures. In addition, our formalism capt...

In recent years, Model-Driven Engineering has taken a leading role in advancing a new paradigm shift in software development. Leveraging models to a first-class status is at the core of this methodology. Shifting the focus of software development from coding to modeling permits programs to transform models in order to generate other models which are amenable for a wide range of purposes, includ...

Heterogeneous transformations are translations between strings that are not characterized by a single function. E.g., nicknames, abbreviations and synonyms are heterogeneous transformations while edit distances are not. Such transformations are useful for information retrieval, information extraction and text understanding. They are especially useful in record linkage, where we determine whethe...

The n×m matrix AT obtained by exchanging rows and columns of A is called the transpose of A. A matrix A is said to be symmetric if A = AT . The sum of two matrices of equal size is the matrix of the entry-by-entry sums, and the scalar product of a real number a and an m× n matrix A is the m× n matrix of all the entries of A, each multiplied by a. The difference of two matrices of equal size A a...

These notes describe a number of ways by which a parameter vector (or matrix) β can be expressed as a function of an unrestricted parameter vector θ in such a way that any value of θ produces a β with a desired characteristic and such that any β with that characteristic can be obtained with some value of θ. Alternatively, it may be useful to have a transform that defines θ on a simple bounded r...

As model transformations are increasingly used in model-driven engineering, the dependability of model transformation systems becomes crucial to model-driven development deliverables. As any other software, model transformations can contain design faults, be used in inappropriate ways, or may be affected by problems arising in the transformation execution environment at run-time. We propose in ...