On a generalization of principal weak (po-)flatness of S-posets

In [H. Rashidi, A. Golchin and H. Mohammadzadeh saany, On [Formula: see text]-flat acts, Categ. Gen. Algebr. Struct. Appl. 12(1) (2020) 175–197], the study of [Formula: see text]-flatness property of right acts [Formula: see text] over a monoid [Formula: see text] that can be described by means of when the functor [Formula: see text]-preserves some pullbacks is initiated. In this paper, we extend these results to [Formula: see text]-posets and present equivalent description of [Formula: see text]-po-flatness of [Formula: see text]-posets. We show that [Formula: see text]-flatness does not imply torsion freeness in [Formula: see text]-posets and give some general properties and a characterization of pomonoids for which some other properties of their posets imply this condition.

On a generalization of weak flatness

Laan in Pullbacks and flatness properties of acts I, [Commun. Algebra 29(2) (2001) 829–850] introduced Condition [Formula: see text], a generalization of Condition [Formula: see text]. Golchin and Mohammadzadeh in [On Condition ([Formula: see text]), Semigroup Forum 86(2) (2012) 413–430] introduced Condition [Formula: see text], a generalization of Condition [Formula: see text]. In this paper similarly, we introduce a generalization of weak flatness property, called [Formula: see text], and will classify monoids by this property of their acts. We also characterize [Formula: see text] coherent monoids in general and monoids coming from some special classes.

Directed colimits of some flatness properties and purity of epimorphisms in S-posets

Let S be a pomonoid. In this paper, we introduce some new types of epimorphisms with certain purity conditions, and obtain equivalent descriptions of various flatness properties of S-posets, such as strong flatness, Conditions (E), (E′), (P), (Pw), (WP), (WP)w, (PWP) and (PWP)w. Thereby, we present other equivalent conditions in the Stenström-Govorov-Lazard theorem for S-posets. Furthermore, we prove that these new epimorphisms are closed under directed colimits. Meantime, this implies that by a new approach we can show that most of flatness properties of S-posets can be transferred to their directed colimit. Finally, we prove that every class of S-posets having a flatness property is closed under directed colimits.

On classification of pomonoids by properties of generators

In this paper, we attempt to collect the knowledge on generators in the category Pos-[Formula: see text] and to apply this to proceed on the questions of homological classification of ordered monoids, that is results of the type: all generators in the category Pos-[Formula: see text], have a flatness property if and only if [Formula: see text] has a certain property.

On homological classification of pomonoids by GP-po-flatness of S-posets

In this paper, we introduce GP-po-flatness property of S-posets over a pomonoid S, which lies strictly between principal weak po-flatness and po-torsion freeness. Furthermore, we investigate the homological classification problems of pomonoids by using this new property. Finally, we consider direct products of GP-po-flat S-posets. As an application, characterizations of pomonoids over which direct products of nonempty families of principally weakly po-flat S-posets are principally weakly po-flat are obtained, and some results of Khosravi, R. in a certain extent are generalized.

Two-Stage Control Design of a Buck Converter/DC Motor System without Velocity Measurements via aΣ−Δ-Modulator

This paper presents a two-stage control design for the “Buck power converter/DC motor” system, which allows to perform the sensorless angular velocity trajectory tracking task. The differential flatness property of the DC-motor model is exploited in order to propose a first-stage controller, which is designed to achieve the desired angular velocity trajectory. This controller provides the voltage profiles that must be tracked by the Buck converter. Then, a second-stage controller is meant to assure the aforementioned. This controller is based on flatness property of the Buck power converter model, which provides the input voltage to the DC motor. Due to the fact that the two-stage controller proposed uses the average model of the system, as a practical and effective implementation of this controller, aΣ − Δ-modulator is employed. Finally, in order to verify the control performance of this approach, numerical simulations are included.