Projective Modules Research Articles

Character formulas in category O for exceptional Lie superalgebra G(3)

We classify the blocks and compute the Verma flags of tilting and projective modules in the BGG category O for the exceptional Lie superalgebra G(3). The projective injective modules in O are classified. We also compute the Jordan–Hölder multiplicities of the Verma modules in O.

Generalized Gorenstein Modules

We introduce a generalization of the Gorenstein injective modules: the Gorenstein [Formula: see text]-injective modules (denoted by [Formula: see text]). They are the cycles of the exact complexes of injective modules that remain exact when we apply a functor [Formula: see text], with [Formula: see text] any [Formula: see text]-injective module. Thus, [Formula: see text] is the class of classical Gorenstein injective modules, and [Formula: see text] is the class of Ding injective modules. We prove that over any ring [Formula: see text], for any [Formula: see text], the class [Formula: see text] is the right half of a perfect cotorsion pair, and therefore it is an enveloping class. For [Formula: see text] we show that [Formula: see text] (i.e., the Ding injectives) forms the right half of a hereditary cotorsion pair. If moreover the ring [Formula: see text] is coherent, then the Ding injective modules form an enveloping class. We also define the dual notion, that of Gorenstein [Formula: see text]-projectives (denoted by [Formula: see text]). They generalize the Ding projective modules, and so, the Gorenstein projective modules. We prove that for any[Formula: see text] the class [Formula: see text] is the left half of a complete hereditary cotorsion pair, and therefore it is special precovering.

Geometry-Guided Street-View Panorama Synthesis From Satellite Imagery.

This paper presents a new approach for synthesizing a novel street-view panorama given a satellite image, as if captured from the geographical location at the center of the satellite image. Existing works approach this as an image generation problem, adopting generative adversarial networks to implicitly learn the cross-view transformations, but ignore the geometric constraints. In this paper, we make the geometric correspondences between the satellite and street-view images explicit so as to facilitate the transfer of information between domains. Specifically, we observe that when a 3D point is visible in both views, and the height of the point relative to the camera is known, there is a deterministic mapping between the projected points in the images. Motivated by this, we develop a novel satellite to street-view projection (S2SP) module which learns the height map and projects the satellite image to the ground-level viewpoint, explicitly connecting corresponding pixels. With these projected satellite images as input, we next employ a generator to synthesize realistic street-view panoramas that are geometrically consistent with the satellite images. Our S2SP module is differentiable and the whole framework is trained in an end-to-end manner. Extensive experimental results on two cross-view benchmark datasets demonstrate that our method generates more accurate and consistent images than existing approaches.

Unimodular rows over monoid extensions of overrings of polynomial rings

Let R be a commutative Noetherian ring of dimension d and M a commutative cancellative torsion-free seminormal monoid. Then: (1) Let A be a ring of type R[d,m,n] and P be a projective A[M]-module of rank r≥max {2,d+1}. Then the action of E(A[M]⊕P) on (A[M]⊕P) is transitive and (2) Assume (R,m,K) is a regular local ring containing a field k such that either char k=0 or char k=p and tr-deg K∕𝔽p≥1. Let A be a ring of type R[d,m,n]∗ and f∈R be a regular parameter. Then all finitely generated projective modules over A[M], A[M]f and A[M]⊗RR(T) are free. When M is free both results are due to Keshari and Lokhande (2014).

Notes on Super Projective Modules

Projective modules are a link between geometry and algebra as established by the theorem of Serre-Swan. In this paper, we define the super analog of projective modules and explore this link in the case of some particular super geometric objects. We consider the tangent bundle over the supersphere and show that the module of vector field over a supersphere is a super projective module over the ring of supersmooth functions. Also, we discuss a class of super projective modules that can be constructed from a projection map on modules defined over the ring of supersmooth functions over superspheres.

M-CBN: Manifold constrained joint image dehazing and super-resolution based on chord boosting network

This paper proposes a Manifold Constrained Chord Boosting Network (M-CBN), which incorporates the super-resolution principle to achieve image dehazing. M-CBN is a task-specific image restoration network that explicitly learns the mapping from Low-resolution (LR) hazy images to High-resolution (HR) haze-free images. Hence, we design a preliminary image degradation to imitate super-resolution training on hazy images. In M-CBN, a plug-and-play Cross-linked Dual Projection Module (CDPM) for skip connections is developed. In CDPM, back-projections for HR encoder features and LR decoder features are cross-linked for better recovery of spatial information, and a cross-resolution spatial attention is designed to enhance fusion features. Then, to boost the generation of image details and textures, we propose a Chord Residual Module (CRM), which can separately process High-frequency (HF) and Low-frequency (LF) features by progressive inner-frequency updating and dense inter-frequency cross-collaboration to enhance decoding features. Finally, a manifold constraint dual discriminator is established. The static discriminator explicitly constrains dehazed images in the expected manifold to unify the joint learning of image dehazing and super-resolution. And the dynamic discriminator implicitly optimizes the network by adversarial training. Extensive experiments on general, dense and non-homogeneous haze datasets and cross-domain dehazing tasks show the proposed M-CBN presents high-quality dehazed results with natural colors and clear details.

Quasi-Gorenstein projective and quasi-Gorenstein injective modules

In this paper, we introduce quasi-Gorenstein projective and quasi-Gorenstein injective modules, study some of their properties and investigate their behavior with respect to short exact sequences. Also, we give homological descriptions of quasi-Gorenstein homological dimensions of modules when they are finite and in this case, we prove that quasi-Gorenstein projective precover and quasi-Gorenstein injective preenvelope exist.

Generalized lattices over one-dimensional noetherian domains

We study direct sum decompositions of pure projective torsion free modules over one-dimensional commutative noetherian domains. Drawing inspiration from the representation theory of orders in separable algebras, we study when every pure projective torsion free module is a direct sum of finitely generated modules. A satisfactory criterion is given for analytically unramified reduced local rings and for Bass domains.

On functors between categories of modules over trusses

Categorical aspects of the theory of modules over trusses are studied. Tensor product of modules over trusses is defined and its existence established. In particular, it is shown that bimodules over trusses form a monoidal category. Truss versions of the Eilenberg-Watts theorem and Morita equivalence are formulated. Projective and small-projective modules over trusses are defined and their properties studied.

Hardware Implementation of Euclidean Projection Module Based on Simplified LSA for ADMM Decoding

The Euclidean projection operation is the most complex and time-consuming of the alternating direction method of multipliers (ADMM) decoding algorithms, resulting in a large number of resources when deployed on hardware platforms. We propose a simplified line segment projection algorithm (SLSA) and present the hardware design and the quantization scheme of the SLSA. In simulation results, the proposed SLSA module has a better performance than the original algorithm with the same fixed bitwidths due to the centrosymmetric structure of SLSA. Furthermore, the proposed SLSA module with a simpler structure without hypercube projection can reduce time consuming by up to 72.2% and reduce hardware resource usage by more than 87% compared to other Euclidean projection modules in the experiments.

A study of [formula omitted]-projective QTAG-modules

In this paper, we define a new class of ω1-(ω+n)-projective module and study their basic properties. We proved that a module M is almost ω1-(ω+n)- projective if and only if there exists a countably generated nice submodule K which satisfies the inequalities Hω+n(M)⊆K⊆Hω(M) such that M/K is almost (ω+n)-projective.

EMBEDDING A GROUP PROJECT INTO INTERMEDIATE ACCOUNTING TO TEACH THE ETHICS OF EARNINGS MANAGEMENT

We propose a novel pedagogic design to integrate teaching earnings management and accounting ethics at the undergraduate level. Earnings management is an extensive topic related to almost every topic in collegiate accounting education. Generally Accepted Accounting Principles (GAAP) give accountants discretion to exercise professional judgment on how to report earnings. The ethicality of earnings management has its profound pedagogical challenges. This flexibility exposes many ethical dimensions for professional training. The interaction of earnings management and accounting ethics offers a particular perspective to design a course project module to integrate the detection of earnings management schema and its ethicality. We follow the accounting ethics pedagogic framework (Apostolou & Schleifer, 2013) to demonstrate and validate our course design: (1) assess the need to embed the ethicality of earnings management in the curriculum; (2) articulate learning objectives; (3) identify the nature of the content; (4) select suitable delivery modes; and (5) conduct learning assessment. The paper has three contributions to accounting ethics education. First, the proposed course module offers a solution to relieve the limited space in the curriculum to train accounting ethics. Second, the ethicality of earnings management can act as a bridge to integrating ethical accounting decision-making and professional judgment. Third, the course design offers a virtual platform to engage the instructor and students in exploring the boundary of positive and fraudulent earnings management.

Frobenius functors, stable equivalences and K-theory of Gorenstein projective modules

Owing to the difference in K-theory, an example by Dugger and Shipley implies that the equivalence of stable categories of Gorenstein projective modules should not be a Quillen equivalence. We give a sufficient and necessary condition for the Frobenius pair of faithful functors between two abelian categories to be a Quillen equivalence, which is also equivalent to that the Frobenius functors induce mutually inverse equivalences between stable categories of Gorenstein projective objects.We show that the category of Gorenstein projective objects is a Waldhausen category, then Gorenstein K-groups are introduced and characterized. As applications, we show that stable equivalences of Morita type preserve Gorenstein K-groups, CM-finiteness and CM-freeness. Two specific examples of path algebras are presented to illustrate the results, for which the Gorenstein K0 and K1-groups are calculated.

SelfNet: A semi-supervised local Fisher discriminant network for few-shot learning

Few-shot learning, employing small-scale labeled samples to recognize new objects, has received substantial research interest. The prototypical network (ProtoNet) is a simple yet effective meta-learning method to solve this problem. In the few-shot scenario, however, the scarcity of data usually has a negative impact on the representational ability of prototypes. In this paper, a unique semi-supervised few-shot learning architecture, referred to as Semi-supervised local Fisher discriminant network (SelfNet), which integrates few-shot learning with subspace learning, is proposed. Using the union of the support set and the additional unlabeled set, a feature projection module is constructed to achieve the subspace projection. Additionally, a pseudo-labeling strategy, which adds the unlabeled samples with high prediction confidence to the support set, is employed to refine the original prototypes. Experimental results on two few-shot classification benchmarks demonstrate that SelfNet can achieve superior performance to the state-of-the-arts, indicating the benefits of utilizing unlabeled samples for feature projection.

Upper topology and its relation with the projective modules

In this article, first we obtain a number of new results on projective modules and on the upper topology of an ordinal number. Then it is shown that the rank map of a locally finite type projective module is continuous with respect to the upper topology (by contrast, it is well known that this map is not necessarily continuous with respect to the discrete topology).

Cancellation of vector bundles of rank 3 with trivial Chern classes on smooth affine fourfolds

If n ≡ 0 , 1 m o d 4 , we prove a sum formula V θ 0 ( a 0 , a R n ) = n ⋅ V θ 0 ( a 0 , a R ) for the generalized Vaserstein symbol whenever R is a smooth affine algebra over a perfect field k with c h a r ( k ) ≠ 2 such that − 1 ∈ k × 2 . This enables us to generalize a result of Fasel-Rao-Swan on transformations of unimodular rows via elementary matrices over normal affine algebras of dimension d ≥ 4 over algebraically closed fields of characteristic ≠2. As a consequence, we prove that any projective module of rank 3 with trivial Chern classes over a smooth affine algebra of dimension 4 over an algebraically closed field k with c h a r ( k ) ≠ 2 , 3 is cancellative.

3D‐FEGNet: A feature enhanced point cloud generation network from a single image

Deep learning-based single view 3D reconstruction is a hot topic in computer vision. However, predicting a more realistic 3D point cloud from a single image is an ill-posed problem. In recent years, most of the 3D point cloud prediction methods based on single view are straight-through structure, which will cause the loss of part of feature information and the loss of part of detail information of the resulting point clouds, which will lead to the unsatisfactory visual effect of reconstructed point clouds. In this paper, a Feature-Enhanced 3D point clouds generation Network (3D-FENet) from a single image is proposed. In order to enhance the feature information of RGB image, edge extraction module is adopted. In the process of point cloud generation, a point cloud pyramid is designed, which combines low resolution point cloud with high resolution point cloud to enhance the local details of the generated point clouds. In the fine-tuning stage, the differential projection module is used to fine-tune the whole network by 2D projection of reconstructed point clouds. Experimental results show that the performance of the authors’ proposed method is better than the state-of-the-art studies.

Semihollow-Lifting Modules and Projectivity

Throughout this paper, T is a ring with identity and F is a unitary left module over T. This paper study the relation between semihollow-lifting modules and semiprojective covers. proposition 5 shows that If T is semihollow-lifting, then every semilocal T-module has semiprojective cover. Also, give a condition under which a quotient of a semihollow-lifting module having a semiprojective cover. proposition 2 shows that if K is a projective module. K is semihollow-lifting if and only if For every submodule A of K with K/( A) is hollow, then K/( A) has a semiprojective cover.

Bi-level scheduling in high-end equipment R&D: when more algorithm strategies may not be better

Motivated by the practical research and development (R&D) process in high-end equipment manufacturing, this study investigates a bi-level scheduling problem in a complex R&D project network, where each project contains multiple modules with a complete task network. In the bi-level scheduling problem, the upper-level problem is that the R&D project leader makes the decision on allocating all R&D project modules to limited R&D researchers and the objective is to minimise the total penalty cost of all projects, and the lower-level problem is that the researchers schedule and sort the assigned tasks to minimise their minimum makespan. The different capacity of researchers is considered, and some structural properties are derived based on the capacity analytics. To tackle this complex scheduling problem, an effective Variable Neighborhood Search algorithm based on the ‘less is more' concept is proposed, where a Multi-Greedy Heuristic is incorporated. Interestingly, we observe that simpler algorithmic strategies may lead to better algorithmic performance. Computational experiments are carried out to demonstrate that the performance of the proposed algorithm is efficient and stable.

N-stability of a support on a ring and application to projective modules

n-stability of a support on a ring and application to projective modules