Projective Dimension Research Articles

Crisis times and school education: is teacher agency changing?

ABSTRACT This article explores how educators dealt with an unprecedented educational crisis using remote teaching and delve into the characteristics of teacher agency in crisis situations. Employing a multiple case study design, the study explores diverse school experiences in the Metropolitan Region of Santiago, Chile. Data were gathered from three schools, comprising 24 interviews (18 teachers and six administrators) and analysed using grounded theory. Findings suggest that teachers demonstrate the ability to reconstruct the affected dimensions when faced with a lack of pedagogical resources for emergency remote teaching (fracture in the iterative dimension) and uncertainty about the future (fracture in the projective dimension). Moreover, the agentic transition can explain the practical-evaluative dimension in crises. Across three stages, agentic transition outlines a journey for teachers, from grappling with an unprecedented crisis with limited resources to normalising their practices with technical expertise in the context of new remote teaching scenarios. The present article introduces key concepts and models and delves into implications and future projections.

Decomposition and equivalence of general nonlinear dynamical control systems

AbstractProjection and equivalence concepts have been widely studied in the literature. In the present paper two nonlinear systems with the same number of inputs, but not the same number of state variables, are considered. Under mild assumptions, necessary and sufficient conditions are given for the existence of a submersion such that the higher dimensional system projects locally onto the other one. The solution to this problem has relevant applications, for instance in robotics. It includes as a special case the equivalence of nonlinear systems with no particular structure.

Mapping free resolutions of length three II - Module formats

Let M be a perfect module of projective dimension 3 over a Gorenstein, local or graded ring R. We denote by F the minimal free resolution of M. Using the generic ring associated to the format of F we define higher structure maps, according to the theory developed by Weyman in [26]. We introduce a generalization of classical linkage for R-module using the Buchsbaum–Rim complex, and study the behavior of structure maps under this Buchsbaum–Rim linkage. In particular, for certain formats we obtain criteria for these R-modules to lie in the Buchsbaum–Rim linkage class of a Buchsbaum–Rim complex of length 3.

Triviality criteria for unbounded complexes

We study properties of modules that appear as syzygies of acyclic complexes of projective, injective, flat or flat-cotorsion modules and obtain criteria for these complexes to be contractible or totally acyclic. Our results illustrate the importance of strongly fp-injective modules in the study of these properties. We examine implications of the existence of complete resolutions (in a certain weak sense) and the finiteness of the Gorenstein projective dimension of pure-projective modules. We also use the orthogonality in the homotopy category between complexes of flat modules and pure acyclic complexes of cotorsion modules, in order to study the syzygies of acyclic complexes of flat modules. Finally, we present some applications of our results to group rings, regarding complete resolutions and cohomological periodicity.

On the subadditivity condition of edge ideal

Let S=K[x1,…,xn]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S=K[x_1,\\ldots ,x_n]$$\\end{document}, where K is a field, and ti(S/I)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t_i(S/I)$$\\end{document} denotes the maximal shift in the minimal graded free S-resolution of the graded algebra S/I at degree i, where I is an edge ideal. In this paper, we prove that if tb(S/I)≥⌈3b2⌉\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t_b(S/I)\\ge \\lceil \\frac{3b}{2} \\rceil $$\\end{document} for some b≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b\\ge 0$$\\end{document}, then the subadditivity condition ta+b(S/I)≤ta(S/I)+tb(S/I)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t_{a+b}(S/I)\\le t_a(S/I)+t_b(S/I)$$\\end{document} holds for all a≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a\\ge 0$$\\end{document}. In addition, we prove that ta+4(S/I)≤ta(S/I)+t4(S/I)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t_{a+4}(S/I)\\le t_a(S/I)+t_4(S/I)$$\\end{document} for all a≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a\\ge 0$$\\end{document} (the case b=0,1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b=0,1,2,3$$\\end{document} is known). We conclude that if the projective dimension of S/I is at most 9, then I satisfies the subadditivity condition.

Supporting kindergarten staff’s agency in inclusion through long-term in-service training

ABSTRACT Supporting teachers’ agency is essential for implementing inclusive education, as agentic teachers tend to take more responsibility for making a change and focus more on activities that benefit the children they teach. Lack of teacher agency might be one of the reasons why inclusive education has not been applied successfully in kindergartens. In our study, we focused on supporting teacher agency for inclusive education according to the ecological model of agency. Our approach to inclusive education was drawn from the holistic model of inclusive education. We developed an in-service training program to support the three dimensions of agency across different levels outlined in the model of the implementation of inclusive education. The aim of this study was to explore the improvement in participants’ agency during the in-service training program. We applied pre- and post-questionnaires to explore the agency of kindergarten staff members who attended the in-service training program. The results showed statistically significant changes in kindergarten staff’s agency in the iterational and projective dimensions of agency in implementing inclusion. Therefore, we can conclude that a long-term team-based in-service course is effective in supporting teacher agency related to inclusion.

Cofiniteness of generalized local cohomology modules over local rings

Let [Formula: see text] be a local commutative Noetherian ring and [Formula: see text] an ideal of [Formula: see text] Assume that [Formula: see text] is a finitely generated [Formula: see text]-module of finite projective dimension [Formula: see text] and [Formula: see text] is a finitely generated [Formula: see text]-module of dimension [Formula: see text] We prove that [Formula: see text] is Artinian. Moreover, if [Formula: see text] is finitely generated, then [Formula: see text] is an [Formula: see text]-cofinite [Formula: see text]-module.

On the Lowey length of modules of finite projective dimension—II

On the Lowey length of modules of finite projective dimension—II

Investigation of the dimension of the spectral projection of a self-adjoint second order quasidifferential operator

Investigation of the dimension of the spectral projection of a self-adjoint second order quasidifferential operator

Lombardo Radice’s serene school as his link to idealism

ABSTRACT The contribution intends to illustrate Lombardo Radice’s ties with idealism and specifically with the Gentile heritage, starting from the reflection on didactics carried out by the Sicilian educationist. In this way, the 1923 reform isn’t a simple legislative update, but takes on the dimension of a broader educational project and at the same time certifies a considerable depth of thought. The reform becomes the application of a peculiar Italian way to New Education, of which Lombardo Radice is specifically the author. This Italian way to New Education, while dialoguing with international suggestions, draws its roots from a different terrain, the one that goes from Vico to Croce and Gentile. The analysis of the Lombardo Radice’s didactics in this view allows us to understand similarities and differences between the Italian way to New Education and the international movement, shedding more light on the figure of Lombardo Radice as one of Italy’s leading educational theorists.

Projective dimensions of hyperplane arrangements

We establish a general theory for projective dimensions of the logarithmic derivation modules of hyperplane arrangements. This includes an addition-deletion and a restriction theorem, a Yoshinaga type result, and a division theorem for projective dimensions of hyperplane arrangements. These new theorems are all generalizations of classical results for free arrangements, which is the special case of projective dimension zero. To prove these results, we introduce several new methods to determine the surjectivity of the Euler and the Ziegler restriction maps, which is combinatorially determined when the projective dimension is not maximal for all localizations. Also, we introduce a new class of arrangements in which the projective dimension is combinatorially determined.

Developing community energy systems to facilitate Ethiopia's transition to sustainable energy

In Ethiopia, renewable energy offers people an affordable, dependable, and eco-friendly power supply while decreasing the carbon footprint. However, delivering a renewable future for the country requires a massive change in social practices and systems of provision. The slow progress of renewable development is hindering the transition to a cleaner energy future. Over 80 % of people live in rural areas where it is expensive to reach them via grid networks in Ethiopia, requiring off-grid alternatives.Community energy systems, which are off-grid energy systems in which communities play a key role, offer alternative strategies to close the country's energy access gap. However, community energy systems remain underdeveloped in Ethiopia. There is a need to understand the opportunities for community energy and the barriers that hinder its development in Ethiopia, and their role in energy transitions.This paper adopts an experimental lens to understand the diverse dimensions of community energy projects through how they are made, maintained, and lived. Using a comparative analysis of three multi-method, qualitative case studies, this paper argues that the political context poses the biggest obstacle to the development of community energy in Ethiopia despite these projects' tangible benefits.The analysis indicates that community energy projects allow communities to be involved in all stages of project development. In every project, communities assume project management responsibilities after commissioning. However, these projects encounter challenges in resourcing capital, managing supply chains, and building necessary skills among community members to understand business models to ensure sustained operation of the systems.

Technologically mediated encounters with ‘nature’

Despite well-founded critiques on the concept of nature and even claims that the concept is decidedly obsolete, evidence would suggest that nature continues to play a pivotal role in orienting people towards environmental practices and advocacy. Given nature’s unyielding relevance, this paper takes inspiration from Sally Haslanger’s project of conceptual amelioration to examine how meanings ascribed to nature can lead to the actualization of desired sociomaterial realities. By building on posthumanist political ecology and Michel Callon’s notion of performation, I illustrate a dynamic in which meanings of nature emerge through the engagement in practices with the environment which are, more often than not, mediated by different technologies. After exploring this proposal through the lens of different environmentalisms, I argue that technologies can play a significant role in mediating conceptualizations of nature. To support this argument, I introduce a few elements of mediation theory and examine the meaning of nature that may emerge when social media users interact with online content of climate and ecological collapse. Overall, this approach advances a postphenomenological contribution to the scholarly trend of examining how technologies may disrupt fundamental concepts with which we respond to ethical issues. This approach underscores the role of technologically mediated practices in processes of conceptualization, as well as the significant political dimension of conceptual engineering projects.

One Resolution of the Conjecture between the Projective Dimension of a Simple Module S of an Artinian Ring on Zero Radical’s Cube and the First Bifunctor Extension on S

Through concepts from non-commutative algebra and homology, this paper resolves the conjecture that lets the first bifunctor extension to be zero when the projective dimension is finite, for a simple module S of an Artinian ring whose cube of its Jacobson radical is zero and under the condition that any simple module over this ring of finite projective dimension has aradical square zero of the cover projective of its first syzygy. For that, we use a property of the simple module which realizes the minimum of the finite projective dimensions of simple modules. Our main result is presented in the form of a corollary in the case of an Artinian ring with radical cubed zero such that the projective cover of its radical is of Loewy length two and its supremumbeing finite. In the part of discussions, we succeed to show the no loop conjecture through two examples. The first one is about its weak version by taking a quiver algebra A verifying J3 = 0 and without considering that rad2 (P(Ω(S))) = 0 for every simple module, while the second one shows that if the extension quiver has a loop in a simple module then its projective dimension is infinite for every nilpotence index of the Jacobson radical. More importantly, we finally provide a practical third example for our special case.

Ethical committee frameworks and processes used to evaluate humanities research require reform: Findings from a UK-wide network consultation

ABSTRACT Background Qualitative Humanities research is perturbed by ethical review processes that routinely invoke epistemological assumptions skewed towards positivistic or deductive research, giving rise to several concerns, including increased risk aversion by University Research Ethics Committees (URECs) and the evaluation of qualitative research designs according to STEM standards. Methods/Materials This paper presents findings from an AHRC-funded research network built to better understand how research ethics frameworks and processes might be reformed to more appropriately fit ethically challenging qualitative methodologies. Results There remains dissatisfaction with the current processes for awarding ethical approval and the subsequent management of ethical dimensions of projects. In spite of recent developments, UREC frameworks remain seriously flawed, with a wide divergence in the quality of expertise, procedures, and practices, leading to inconsistency in ethical approval awards. Conclusions These factors downgrade UK Higher Education research power in the Humanities and undermine our commitments to the researched. We propose a series of recommendations for reform.

IMPLEMENTASI PROJEK PENGUATAN PROFIL PELAJAR PANCASILA KEARIFAN LOKAL DI SMP GEMA 45 SURABAYA

This study aims to describe the implementation of the project to strengthen Pancasila student profile of local wisdom at SMP Gema 45 Surabaya. The focuses of this research are: project implementation, project supporting factors, project inhibiting factors, and solutions to project inhibiting factors. This research is a descriptive qualitativeresearch. The results of this study describe that the implementation of the project to strengthen the Pancasila student profile of local wisdom at SMP Gema 45 Surabaya was carried out through a process of planning, managing and reporting project results. Project planning is carried out through the stages of: forming a project facilitator team, identifying the stages of education unit readiness in carrying out the project, determining project dimensions and themes, designing project time allocations, compiling project modules, determining project learning objectives, and developing topics, activity flow, and project assessment. Management of the project to strengthen the Pancasila student profile of local wisdom is carried out by initiating project activities, optimizing project implementation, closing a series of project activities, and optimizing partner involvement. The report on the results of the project to strengthen the Pancasila student profile of local wisdom is carried out by collecting and processing the results of the assessment, and compiling a project report card.

LANGUAGE TEACHER AGENCY IN FACING FREEDOM-TO-LEARN CURRICULUM IN TWO TOWNS IN JAVA

Teacher agency in facing new national curriculum shifts has been a topic discussed widely around the world, as many nations implement curriculum shifts and transitions. Indonesia has also in its early years implemented the new national curriculum called Freedom-to-Learn Curriculum. This study is aimed at exploring the agency of language teachers of public junior high schools in two different towns in Java Island, Indonesia. Employing the ecological approach by Priestley, Biesta, and Robinson (2015) which supported the interplay and dynamics of iterative, practical-evaluative, and projective dimensions, this qualitative study brings into play the semi-structured and focus group discussion data-gathering techniques. Six teachers participated in this study. The finding showed that the level of agency was diverse ranging from high (demonstrated by three research participants), emerging (demonstrated by one participant), and low (participated by two participants). Future researchers might examine the teacher agency by involving more participants as well as capture the robust study of language teacher agencies from other parts of Indonesia.

Dose assessment by TL dosimetry according to parameters used in treatment plans for obsessive compulsive disorder using the Gamma Knife@ Perfexion™ device

The objective of this work was to assess the response of TLDs inserted in an anthropomorphic phantom for an OCD treatment considering the planning methodologies, dimensions of an isodose projection in a plan, detector dimensions, uncertainty of mechanical movement of the patient positioning system, dose calculation algorithms and dose rate in Gamma Knife Perfexion™ equipment. The doses to the brainstem were evaluated as well as the possibility of alopecia occurrence. Considering the dosimetry of the internal capsule region, differences seen were within the error of the method. The measured doses to the brainstem, due to the treatment of OCD, were lower than the limits considered relevant. However, for the scalp region, dose values, higher than the desirable limiting ones to determine alopecia were observed. Results showed that it is possible to establish a methodology that allows characterizing a treatment plan of OCD using TLDs.

Dimension of complexes related to special Gorenstein projective precovers (III)

We show that a commutative Noetherian ring R with finite Krull dimension is a Gorenstein ring if and only if Gppd ( X ) = Gpd ( X ) for any complex X of R-modules, where Gpd ( X ) is the Gorenstein projective dimension of X and Gppd ( X ) is the dimension of the complex X related to special Gorenstein projective precovers. In order to do this, the notion of DG-Gorenstein projective resolutions of complexes is introduced and a characterization of Gorenstein projective dimension of complexes is given via DG-Gorenstein projective resolutions.

Asymptotic behavior of homological invariants of localizations of modules

Let R be a commutative noetherian ring, I an ideal of R, and M a finitely generated R-module. We consider the asymptotic injective dimensions, projective dimensions, Bass numbers, and Betti numbers of localizations of M/InM at prime ideals of R and prove that these invariants are stable or have polynomial growth for large integers n that do not depend on the prime ideals.