Zero Module Research Articles

Módulo Cero y su Impacto positivo en el Aprendizaje del Idioma Inglés como Lengua Extranjera en los Alumnos del Primer Semestre de la Universidad Estatal de Milagro

The English language has become one of the greatest opportunities and weaknesses of people worldwide, since not everyone can develop the different skills of this foreign language, which has caused uncertainty at the moment of understanding it, rejecting the subject and therefore, avoiding the acquisition of it as a basic tool in this globalized world. This research work arose from the need to demonstrate the importance of having the Zero Module addressed to students who enter to the State University of Milagro; this work was done considering the quantitative and qualitative methods which were developed taking as a sample 65 students who approved The Zero Module in the First Semester 2015. The authors reiterate the importance of this English Starter Module, since the results demonstrated that the students acquired the necessary knowledge according to their level to continue to Module 1 of English. The progressive learning of English as a foreign language will serve to strengthen ties of trust and adaptation between students and teachers making it more enjoyable to acquire this language, besides learners will achieve proficiency and ease of communicating in English in the different academic spheres.

Identification of technical problems affecting performance of DustTrak DRX aerosol monitors.

The TSI DustTrak Aerosol Monitor is a portable real-time instrument widely used for particulate matter (PM) mass concentrations monitoring. The aim of this work is to report on issues that have arisen from the use of the latest generation models DustTrak DRX (8533 and 8534) in the BREATHE, UPTECH and IMPROVE projects that can compromise data quality. The main issue we encountered was the occurrence of sudden artefact jumps in PM concentration, which can involve an increase from a few to some hundreds of μg·m-3. These artefact jumps can sometimes be easily recognised ("obvious jump"), while others can be difficult to identify because the difference in the concentrations before and after the jump might be just few μg·m-3 ("possible jump") or because the jump is sustained over the whole monitoring period and only detectable if PM concentrations are simultaneously measured by other instruments ("hidden jump"). Moreover, in areas of relatively low PM levels, the unit reported concentration of 0μg·m-3 for ambient PM concentration or even negative concentration values which may seriously compromise the dataset. These data suggest issues with the detection of low PM concentrations, which could be due to an incorrect instrument offset or the factory calibration setting being inadequate for these PM concentrations. The upward and downward artefact jumps were not related to especially dusty or clean conditions, since they have been observed in many kinds of environments: indoor and outdoor school environments, subway stations and in ambient urban background air. Therefore, PM concentration data obtained with the TSI DustTrak DRX models should be handled with care and meticulously revised before being considered valid. To prevent these issues the use of auto zero module is recommended, so the DustTrak monitor is automatic re-zeroed without requiring the presence of any user.

Coupling operators, wedderburn-forney spaces, and generalized inverses

The pole-zero structure of a transfer function has been analyzed by two distinct approaches: module-theoretic (coordinate-free) and analytic (basis-dependent). The former (the Wyman-Sain-Conte-Perdon school) emphasizes pole modules, zero modules, exact sequences of maps, and abstract realization theory; applications developed include the model-matching problem, zero structure of one-sided inverses, and connections with geometric systems theory. The latter (the Gohberg school) works with pole chains, zero chains, matrix equations, and concrete factorization theory (minimal, Wiener-Hopf, inner-outer) and interpolation (zero-pole, Lagrange- Sylvester, Nevanlinna-Pick). In this paper we make explicit the connection between the two approaches. In particular, we describe the zero-pole exact sequence of a transfer function without a pole or zero at infinity in the coordinate system provided by a global left null-pole triple. An important tool for us, and an object of interest in its own right, is a generalized inverse G × of a transfer function G. We relate the poles of G × with the zeros of G. We also show that if the pole module of G × is isomorphic to the zero module of G, then left (right) pole pairs of G × are left (right) null pairs of G.

Extended Zeros and Model Matching

The model matching equation $T(z) = P(z)M(z)$ induces constraints upon the multivariate zero structures of $P(z)$ and $M(z)$; the nature of the constraint is best explained by extending the usual notion of zero. In particular, the extended $\Gamma $-zero module of $P(z)$ must contain as a submodule the module $Z_\Gamma $ of matching $\Gamma $-zeros, which depends only upon $T(z)$ and $M(z)$; and the extended $\Omega $-zero module of $M(z)$ must contain as a factor module the module $Z_\Omega $ of matching $\Omega $-zeros, which depends only upon $T(z)$ and $P(z)$. Essential solutions, in which the constraint is by module isomorphism, are possible if and only if the nullity of $P(z)$ does not exceed the nullity of $T(z)$, on the one hand, or the co-nullity of $M(z)$ does not exceed the co-nullity of $T(z)$, on the other. Both the matching zero modules and their finitely generated, torsion parts—which have state-space interpretation—can be given concrete, intuitive interpretation in terms of short exact sequences, though the former is less involved than the latter. Moreover, in the case of the latter, a natural notion of essential solution is not available, in marked contrast to the situation for poles.

Module Theoretic Zero Structures for System Matrices

The foundation for a coordinate-free theory of the poles of a linear dynamical system was laid in 1965 by the module-theoretic work of Kalman. However, although the theoretical and application importance of transfer function zeros for feedback system design was widely known for single input, single output systems by 1955, it remained for Rosenbrock in 1970 to propose the ideas of transmission zeros, input-decoupling zeros, and output-decoupling zeros for multi-input, multi-output systems, by means of matrix theoretic methods. A coordinate-free, module-theoretic treatment of transmission zeros for a multi-input, mufti-output transfer function was given in 1981 by Wyman and Sain. This paper extends these coordinate-free, module-theoretic studies to include systems which need not be controllable or observable. Interpretation of the Rosenbrock system matrix is given on three levels: rational, finitely generated free-modular, and torsion divisible. On the second level, an $\Omega $-Zero Module$Z_\Omega $ is defined and imbedded in a short exact sequence showing that the input-decoupling zero module is contained as a factor module in $Z_\Omega $. On the third level, a $\Gamma $-Zero Module$Z_\Gamma $ is defined and imbedded in a short exact sequence showing that the output-decoupling zero module is contained as a submodule in $Z_\Gamma $. Both structures are studied further in regard to transmission zero module information with emphasis on lumped zeros, and the cases of right and left invertible transfer functions are given in detail. Not surprisingly, these investigations can support considerable fine detail, which is in accord with the widely held belief that questions on the nature of multivariable zeros must be broadly based.

On the design of pole modules for inverse systems

When a linear dynamical system admits more than one inverse, it is known that the pole module of any inverse must contain, either as a submodule or as a factor module, a module of fixed poles isomorphic to the zero module of the original system. Design of the pole module for such an inverse system is resolved by introducing a variable pole module for the inverse, by determining necessary and sufficient conditions for a desired module to be a variable pole module, and by studying the manner in which the fixed and variable modules assemble into the pole module of the inverse. If the fixed and variable pole spectra are disjoint, the pole module of the inverse system is a direct sum of the fixedand variable-pole modules; if not, procedures for addressing the Jordan structure are presented. Subject only to mild necessary conditions, design of inverse systems with specified characteristic polynomial (and, therefore, specified state-space dimension) is possible even in the latter case. For pedagogical reasons, most of the paper is cast over polynomial rings. However, one section discusses generalizations to a wider class of useful rings. Examples are provided for three types of rings.

On the causal factorization problem

In this note the formalism of the infinite zero module and of the infinite pole module is used to analyze the causal factorization problem. This allows us to express its solutions in terms of zeros and poles at infinity and to have a better understanding of both the problem and the techniques previously proposed by various authors to solve it. Moreover, we obtain a characterization, in terms of the existence of certain causal factorizations, of the transfer functions having no infinite zeros.

A unified pole-zero module for linear transfer functions

A new module-theoretic tool is presented for the study of linear time-invariant input/output maps (‘transfer functions’). For suitable subrings 0 of the field k(s) of rational functions, an O-module called the structure module can be attached to each transfer function. This structure module naturally contains the classical (Kalman) pole module as a submodule which gives the (Wyman-Sain) multivariable zero module as the corresponding factor module. A posteriori the resulting exact sequence splits, and the structure module is isomorphic to the direct sum of the pole module and the zero module. Calculations over local rings echo valuation-theoretic results obtained by Kung and Kailath.

On the zeros of a minimal realization

In an earlier work, the authors have introduced a coordinate-free, module-theoretic definition of zeros for the transfer function G( s) of a linear multivariable system ( A, B, C). The first contribution of this paper is the construction of an explicit k[ z]-module isomorphism from that zero module, Z( G), to V ∗/ R ∗, where V ∗ is the supremal ( A, B)-invariant subspace contained in ker C and R ∗ is the supremal ( A, B)-controllable subspace contained in ker C, and where ( A, B, C) constitutes a minimal realization of G( s). The isomorphism is developed from an exact commutative diagram of k-vector spaces. The second contribution is the introduction of a zero-signal generator and the establishment of a relation between this generator and the classic notion of blocked signal transmissions.