A graded subring of an inverse limit of polynomial rings

We study the power series ring R= K[[x1,x2,x3,...]]on countably infinitely many variables, over a field K, and two particular K-subalgebras of it: the ring S, which is isomorphic to an inverse limit of the polynomial rings in finitely many variables over K, and the ring R', which is the largest graded subalgebra of R. Of particular interest are the homogeneous, finitely generated ideals in R', among them the generic ideals. The definition of S as an inverse limit yields a set of truncation homomorphisms from S to K[x1,...,xn] which restrict to R'. We have that the truncation of a generic I in R' is a generic ideal in K[x1,...,xn]. It is shown in Initial ideals of Truncated Homogeneous Ideals that the initial ideal of such an ideal converge to the initial ideal of the corresponding ideal in R'. This initial ideal need no longer be finitely generated, but it is always locally finitely generated: this is proved in Gröbner Bases in R'. We show in Reverse lexicographic initial ideals of generic ideals are finitely generated that the initial ideal of a generic ideal in R' is finitely generated. This contrast to the lexicographic term order. If I in R' is a homogeneous, locally finitely generated ideal, and if we write the Hilbert series of the truncated algebras K[x1,...,xn] module the truncation of I as qn(t)/(1-t)n, then we show in Generalized Hilbert Numerators that the qn's converge to a power series in t which we call the generalized Hilbert numerator of the algebra R'/I. In Gröbner bases for non-homogeneous ideals in R' we show that the calculations of Gröbner bases and initial ideals in R' can be done also for some non-homogeneous ideals, namely those which have an associated homogeneous ideal which is locally finitely generated. The fact that S is an inverse limit of polynomial rings, which are naturally endowed with the discrete topology, provides S with a topology which makes it into a complete Hausdorff topological ring. The ring R', with the subspace topology, is dense in R, and the latter ring is the Cauchy completion of the former. In Topological properties of R' we show that with respect to this topology, locally finitely generated ideals in R'are closed.

El impacto del enfoque léxico sobre la adquisición de la competencia léxica en aprendices de español como lengua extranjera

Este estudio presenta los resultados de una investigación que examina la efectividad del enfoque léxico como forma de instrucción explícita sobre la adquisición de la competencia léxica en aprendices de español como lengua extranjera. El estudio esta guiado por dos preguntas de investigación. La primera pregunta de investigación (PI 1) examina el impacto del enfoque léxico sobre la adquisición de la competencia léxica. La segunda pregunta de investigación (PI 2) examina si la efectividad del enfoque léxico en el grupo de alumnos examinados viene condicionada por las creencias de los participantes acerca de las estrategias empleadas en dicho método. La aplicación del enfoque léxico se basó en una propuesta pedagógica consistente en una unidad didáctica de creación propia. Se analizaron los datos obtenidos tanto de forma cuantitativa como cualitativa. Los resultados confirmaron empíricamente la validez del enfoque léxico como principio metodológico para adquirir la competencia léxica. Del mismo modo, se encontró una relación entre las creencias de los participantes y las estrategias de aprendizaje empleadas.

Tech Fashion : Fashion Institutionalization in Digital Technology

This thesis explores aesthetization in general and fashion in particular in digital technology design and how we can design digital technology to account for the extended influences of fashion. The thesis applies a combination of methods to explore the new design space at the intersection of fashion and technology. First, it contributes to theoretical understandings of aesthetization and fashion institutionalization that influence digital technology design. We show that there is an unstable aesthetization in mobile design and the increased aesthetization is closely related to the fashion industry. Fashion emerged through shared institutional activities, which are usually in the form of action nets in the design of digital devices. “Tech Fashion” is proposed to interpret such dynamic action nets of institutional arrangements that make digital technology fashionable and desirable. Second, through associative design research, we have designed and developed two prototypes that account for institutionalized fashion values, such as the concept “outfit-centric accessory.” We call for a more extensive collaboration between fashion design and interaction design.