The transformations generated by an infinitesimal projective transformation in function space

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

Infinitesimal Fourier Transformation for the Space of Functionals

The purpose is to formulate a Fourier transformation for the space of functionals, as an infinitesimal meaning. We extend R to ( ∗R) under the base of nonstandard methods for the construction. The domain of a functional is the set of all internal functions from a ∗-finite lattice to a ∗-finite lattice with a double meaning. Considering a ∗-finite lattice with a double meaning, we find how to tr...

on the teacher-generated v.s. leaner-generated noticing-the-gap activities in language classes

abstract the purpose of this study is twofold: on the one hand, it is intended to see what kind of noticing-the –gap activity (teacher generated vs. learner generated) is more efficient in teaching l2 grammar in classroom language learning. on the other hand, it is an attempt to determine which approach of the noticing-the-gap- activity is more effective in the long- term retention of grammar...

On infinitesimal ~-fields generated by random processes

Let X(t) , t >1 O, be a Polish space-valued r a n d o m process defined on a probabi l i ty space (~, ~ , P), where ~ is the P-comple t ion of a countab ly generated a-field ~ o . Let ~(t + ) (the ' l ook-ahead ' a-field at t) and r ) (the ' l ook-back ' a-field at t) denote the P-comple t ions of c~>,a(X(y), t <~ y <~ s) and c~s<ta(X(y), s ~< y ~< t) respectively. The aim of this note is to p ...

The Geometric Interpretation of Fröberg-iarrobino Conjectures on Infinitesimal Neighbourhoods of Points in Projective Space

The study of infinitesimal deformations of a variety embedded in projective space requires, at ground level, that of deformation of a collection of points, as specified by a zero-dimensional scheme. Further, basic problems in infinitesimal interpolation correspond directly to the analysis of such schemes. An optimal Hilbert function of a collection of infinitesimal neighbourhoods of points in p...