Projective Modules Research Articles

On projectivity of finitely generated modules

In a recent paper of Holston, López-Permouth, Mastromatteo and Simental-Rodriguez, a ring R is defined to have no subprojective middle class if the subprojectivity domain of any R-module is the smallest or largest possible. In this work, we continue to use this idea of restricting the class of subprojectivity domains to classify rings. A finitely generated (resp., cyclic) module is called fingp-indigent (resp., singp-indigent), if its subprojectivity domain consists of only finitely projective (resp., singly projective) modules. We give a characterization of rings over which finitely generated (resp., cyclic) modules are either projective or fingp-indigent (resp., singp-indigent).

Lifting recollements of abelian categories and model structures

We use Quillen model structures to show a systematic method to lift recollements of hereditary abelian model categories to recollements of their associated homotopy categories. To that end, we use the notion of Quillen adjoint triples and we investigate transfers of abelian model structures along adjoint pairs. Applications include liftings of recollements of module categories to their derived counterpart, liftings to homotopy categories that provide models for stable categories of Gorenstein projective and injective modules and liftings to homotopy categories of n-morphism categories over Iwanaga-Gorenstein rings.

SS-TMNet: Spatial–Spectral Transformer Network with Multi-Scale Convolution for Hyperspectral Image Classification

Hyperspectral image (HSI) classification is a significant foundation for remote sensing image analysis, widely used in biology, aerospace, and other applications. Convolution neural networks (CNNs) and attention mechanisms have shown outstanding ability in HSI classification and have been widely studied in recent years. However, the existing CNN-based and attention mechanism-based methods cannot fully use spatial–spectral information, which is not conducive to further improving HSI classification accuracy. This paper proposes a new spatial–spectral Transformer network with multi-scale convolution (SS-TMNet), which can effectively extract local and global spatial–spectral information. SS-TMNet includes two key modules, i.e., multi-scale 3D convolution projection module (MSCP) and spatial–spectral attention module (SSAM). The MSCP uses multi-scale 3D convolutions with different depths to extract the fused spatial–spectral features. The spatial–spectral attention module includes three branches: height spatial attention, width spatial attention, and spectral attention, which can extract the fusion information of spatial and spectral features. The proposed SS-TMNet was tested on three widely used HSI datasets: Pavia University, IndianPines, and Houston2013. The experimental results show that the proposed SS-TMNet is superior to the existing methods.

Pendampingan Kepala Sekolah Dan Guru SD Pada Lokakarya Kurikulum 2 Projek Penguatan “Profil Pelajar Pancasila” Tahun Kedua Di Kabupaten Soppeng

The project to strengthen the profile of Pancasila students is essential because it can provide a deeper understanding of what strengthening Pancasila values is like for students in schools that apply the independent curriculum. The purpose of implementing the assistance is to strengthen further the knowledge of school principals and teachers regarding the implementation of projects to strengthen Pancasila student profiles and to design ideas for modifying project modules that are by the context of the situation and needs of the school. The method in mentoring workshop 2 was a participatory learning committee, namely the principal and 2 teacher representatives for each school, which consisted of 4 levels of elementary school, namely SD Negeri 5 Mattiropole. SD Negeri 238 Laempa, SD Negeri 118 Ujung, and SD Negeri 100 Dare Bunga-Bungae, which are in the Soppeng Regency area, were held on December 10, 2022, by involving participants directly during the activity. The final result of the curriculum 2 workshop activities is in the form of product design ideas for project modifications to strengthen the profile of Pancasila students. Thus, project assistance to strengthen Pancasila student profiles can positively impact schools in the Mobilizing School Program, strengthening various skills, competencies, and characters from curricular activities in schools.

An enhanced text classification model by the inverted attention orthogonal projection module

ABSTRACT The orthogonal projection method has made significant progress in text classification, especially in generating discriminative features. This method obtains more pure and suitable for classification features by projecting text features onto the orthogonal direction of common features (which are not helpful for classification and actually confuse performance). However, this approach requires an additional branch network to generate these common features, which reduces the flexibility of this method compared to representation optimisation methods such as self-attention mechanisms, as it requires significant modification of the base network structure to use. To address this issue, this paper proposes the Inversed Attention Orthogonal Projection Module (IAOPM). IAOPM uses inversed attention (IA) to iteratively reverse the attention map on text features, encouraging the network to remove discriminating features from the text features and obtain potential common features. Unlike the original orthogonal projection method, IAOPM can extract common features within a single network without any branch networks, increasing the flexibility of the orthogonal projection method. We also use an orthogonal loss to ensure the quality of the common features during training, so IAOPM also has better purity performance than the original method. Experiments show that text classification models based on IAOPM outperform the baseline models, self-attention mechanisms, and the original orthogonal projection method on multiple text classification datasets with an average accuracy increase of 1.02%, 0.44%, and 0.52%, respectively.

The Implementation of P5 Local Wisdom Themes in the Independent Curriculum in Elementary Schools

The pancasila student profile strengthening project was created to optimize students' abilities by strengthening the pancasila student profile, which was develop based on a theme. However it is not introduced directly in every educational institution, but rather gradually and is not limited to the content basis. This research aims to analyse students' enthusiasm for implementing P5 in the implementation of the new curriculum by focusing on the theme of local wisdom that develops through project-based learning. The qualitative description method was applied in this study. This study is based on primary and secondary data. This study's principal data sources are fourth-grade teachers and fourth-grade learners, while the secondary data are the results of observation and documentation in the form of project modules and the results of P5 implementation activities on the theme of local wisdom. Data analysis technique used is interactive, and it consists of four components of the analysis process: data collection, data reduction, data presentation, and drawing conclusions. The study's findings revealed that learners were highly enthusiastic about the application of P5. Although it was relatively new in the implementation of the independent curriculum, it was able to become a new value for students and teachers so that the projects carried out did not hinder the learning process by determining the choice of themes by the teacher. in accordance with the facilities and capabilities of the school. Improving the character values of students according to the profile of Pancasila students.

Research on Defect Inspection Technology for Bump Height in Wafer-Level Packaging Based on the Triangulation Method

With the advent of the era of big data and the vigorous development of consumer electronics, the demand for higher-speed processing capacity for gigantic amounts of data is increasing; this requires finer and far more numerous connections between dies as an essential component for connection and electronic communication between layers. The coplanarity of the height of micro bumps is crucial to ensure the reliability of the chip. The triangulation method has been widely used in various types of visual inspection applications over the past several years due to its high measurement accuracy and fast detection speed. In this paper, the application of triangulation technology is analyzed and used in micro bump height measurement. The measurement system proposed consists of a delicate design, a linearly arranged light projection module and a high-quality imaging module. Along the light stripe, multiple-height data of micro bumps are collected in a frame, and the full-field measurement is realized as the wafer is driven by the high-precision motional stage, following the optimal measurement route planned previously. In the scanning process, the images of the light strip projected on the top and bottom of the micro bumps are simultaneously acquired by the sophisticated micro vision system, and then the heights of micro bumps are calculated from a simple formula based on the geometry of the specimen and the system configuration. The experimental results demonstrate that the measuring deviation of the micro bump height has an accuracy of 1.5 μm.

A Generalization of Projective Module

Let $V$ be a submodule of a direct sum of some elements in $\mathcal{U}$, and $X$ be a submodule of a direct sum of some elements in $\mathcal{N}$, where $\mathcal{U}$ and $\mathcal{N}$ are families of $R$-modules. A $\mathcal{U}$-free module is a generalization of a free module. According to the definition of $\mathcal{U}$-free module, we define three kinds of projective$_{\mathcal{U}}$ in this research, i.e., projective$_{\underline{\mathcal{U}}}$, projective$_{\mathcal{U}}$ module, and strictly projective$_{\mathcal{U}}$ module. The notion of strictly projective$_{\mathcal{U}}$ is a generalization of the projective module. In this research, we discuss the relationship between projective modules and the three types of modules. Furthermore, we show that the properties of $\mathcal{U}$ impact the properties of the projective$_{\mathcal{U}}$ module so that we can determine some properties of the projective$_{\mathcal{U}}$ module based on the properties of the family of $\mathcal{U}$ of $R$-modules.

M-Periodic Gorenstein objects

We present and study the concept of m-periodic Gorenstein objects relative to a pair (A,B) of classes of objects in an abelian category, as a generalization of m-strongly Gorenstein projective modules over associative rings. We prove several properties when (A,B) satisfies certain homological conditions, like for instance when (A,B) is a GP-admissible pair. Connections to Gorenstein objects and Gorenstein homological dimensions relative to these pairs are also established.

FEA based opto-mechanisms design and thermal analysis of a dynamic SFS with an ultra-long exit pupil distance

The dynamic star field simulator (SFS) reproduces the actual operating conditions for the star tracker (STR) to assess its performance along with the flight motion simulator (FMS) in the hard-ware-in-the-loop (HWIL) simulation. The exit pupil distance of a traditional SFS is extremely short, which limits its application to large FMSs. To project the liquid crystal on silicon (LCoS) output to the STR entrance pupil, a 1250 mm ultra-long exit pupil distance SFS, operating in the broad waveband of 450–900 nm, is designed and implemented. In this study, the opto-mechanisms design and thermal analysis of the SFS are evaluated. The detailed design for key assemblies is specifically addressed to suppress negative heat effects. From the finite element analysis (FEA) results under different thermal conditions, the Zernike coefficients of 16 deformed optical surfaces in the projection module are solved using singular value decomposition (SVD), and the temperature adaptability is verified using a ray-tracing software. The preliminary SFS assessment confirms the simplicity of manufacture and excellent performance. The closed-loop opto-mechanisms design significantly improves the SFS reliability and enhances its suitability for large FMS use.

Virtually Gorenstein rings and relative homology of complexes

We extend the notion of virtually Gorenstein rings to the setting of arbitrary rings, and prove that all rings R of finite Gorenstein weak global dimension are virtually Gorenstein such that all Gorenstein projective R -modules are Gorenstein flat. For such a ring R , we introduce the notion of relative homology functors of complexes with respect to Gorenstein projective (resp., flat) modules, and establish a balanced and a vanishing result for the homology functor.

Projective class rings of a kind of category of Yetter-Drinfeld modules

<abstract><p>In this paper, all simple Yetter-Drinfeld modules and indecomposable projective Yetter-Drinfeld modules over a family of non-pointed $ 8m $-dimension Hopf algebras of tame type with rank two, are construted and classified. The technique is Radford's method of constructing Yetter-Drinfeld modules over a Hopf algebra. Furthermore, the projective class rings of the category of Yetter-Drinfeld modules over this class of Hopf algebras are described explicitly by generators and relations.</p></abstract>

The reform of the training mode of building intelligent engineering technology professionals based on the Internet of Things smart home 1 + X certificate

As the third batch of “1+X” certificate pilots, the integration and application of the Internet of Things smart home system is of great significance to the reform of talent training programs for building intelligent engineering technology majors in higher vocational colleges. Integrate the standard of “educational certificate + vocational skill certificate” into the training plan for building intelligent engineering technology professionals, and reform the teaching of “project penetration and module progression” by reconstructing the “platform foundation + course certificate integration” curriculum Methods and methods such as building a “trinity” functional teaching team, to achieve the integration of courses and certificates , and to cultivate compound talents majoring in building intelligent engineering technology.

A Semi-Fragile Reversible Watermarking for Authenticating 3D Models Based on Virtual Polygon Projection and Double Modulation Strategy

A Semi-Fragile Reversible Watermarking for Authenticating 3D Models Based on Virtual Polygon Projection and Double Modulation Strategy

MOPDDI: Predicting Drug-Drug Interaction Events Based on Multimodal Mutual Orthogonal Projection and Intermodal Consistency Loss.

Predicting accurately the mechanisms of drug-drug interaction (DDI) events is crucial in drug research and development. Existing methods used to predict these events are primarily based on deep learning and have achieved satisfactory results. However, they rarely consider the presence of redundant co-information between the multimodal data of a drug and the need for consistency in the predicted features of each drug modality. Herein, we propose a new method for drug interaction event prediction based on multimodal mutual orthogonal projection and intermodal consistency loss. Our method obtains the features of each modality through a multimodal mutual orthogonal projection module, which eliminates redundant common information with other modalities. In addition, we use the consistency loss between modalities and make the predicted features of each modality more similar. In comparative experiments, our proposed method achieves a prediction accuracy of 0.9500, and an area under the precision-recall (AUPR) curve is 0.9833 for known DDIs. This method outperforms existing methods. The results show that the proposed method is capable of accurately predicting DDIs. The source code is available at https://github.com/xiaqixiaqi/MOPDDI.

A note on $ss$-supplement submodules

In this paper, we describe $ss$-supplement submodules in terms of a special class of endomorphisms. Let $R$ be a ring with semisimple radical and $P$ be a projective $R-$module. We show that there is a bijection between ss-supplement submodules of $P$ and ss-supplement submodules of $End_{R}(P)$. Moreover, we define radical-s-projective modules as a generalization of projective modules. We prove that every $ss$-supplement submodule of a projective $R-$module is radical-s-projective over the ring $R$ with semisimple radical. We show that over $SSI$-ring $R$, every radical-s-projective $R-$module is projective. We provide that over a ring $R$ with semisimple radical, every $ss$-supplement submodule of a projective $R-$module is a direct summand if and only if every radical-s-projective $R-$module is projective.

Projective class ring of a restricted quantum group $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $

<abstract><p>In this paper, we compute the projective class ring of the new type restricted quantum group $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $. First, we describe the principal indecomposable projective $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $-modules and study their radicals, composition series, Cartan matrix of $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $ and so on. Then, we deconstruct the tensor products between two simple modules, two indecomposable projective modules and a simple module and an indecomposable projective module, into direct sum of some indecomposable representations. At last, we characterize the projective class ring by generators and relations explicitly.</p></abstract>

Filtration games and potentially projective modules

The notion of a $\mathcal C$-<em>filtered</em> object, where $\mathcal C$ is some (typically small) collection of objects in a Grothendieck category, has become ubiquitous since the solution of the Flat Cover Conjecture around the year 2000. We introduce

Flexible modules and graded rings

A G−graded R−module is called flexible if Mg = RgMe for every g ∈ G. In this paper, we study the relationship between a flexible module and the graded ring R through different aspects. On one hand, we distinguish the flexible modules from other graded modules by characterizing the influence of the e-component of a flexiblemodule on the graded module itself. On the other hand, we extend the class covered by flexible graded modules to include free and projective modules in a comparatively simple manner.

Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition

We study many-body localization (MBL) in a spin-chain model mimicking the Rydberg-blockade quantum simulator with infinite-strength projection and moderate quasiperiodic modulation. Employing exact diagonalization, Krylov-typicality technique, and time-evolving block decimation, we identify evidence for a constrained MBL phase stabilized by a pure quasirandom transverse field. Intriguingly, the constrained MBL transition may embody a discontinuous eigenstate phase transition, whose discontinuity nature significantly suppresses finite-size drifts that plague most numerical studies of conventional MBL transition. Through quantum dynamics, we find that rotating the modulated field from parallel toward perpendicular to the projection axis induces an eigenstate transition between diagonal and constrained MBL phases. The entanglement-entropy growth in constrained MBL follows a double-log form, whereas it changes to a power law in approaching the diagonal limit. By unveiling confined nonlocal effects in integrals of motion of constrained MBL, we show this insulating state is not a many-body Anderson insulator. Our predictions are testable in Rydberg experiments.