WEAK and CO-WEAK BAER MODULES: موديلات بيير الضعيفة والضعيفة المرافقة

The object of this paper is study the notions of weak Baer and weak Rickart rings and modules. We obtained many characterizations of weak Rickart rings and provide their properties. Relations ship between a weak Rickart (weak Baer) module and its endomorphism ring are studied. We proved that a weak Baer module with no infinite set of nonzero orthogonal idempotent elements in its endomorphism ring is precisely a Baer module. In addition, the endomorphism ring of a semi-projective weak Rickart module is semi-potent and the endomorphism ring of a semi-injective coweak Rickart module is semi-potent. Furthermore, we show that a free module is weak Baer if and only if its endomorphism ring is left weak Baer.

Krull modules and completely integrally closed modules

Let [Formula: see text] be a torsion-free module over an integral domain [Formula: see text] with quotient field [Formula: see text]. We define a concept of completely integrally closed modules in order to study Krull modules. It is shown that a Krull module [Formula: see text] is a [Formula: see text]-multiplication module if and only if [Formula: see text] is a maximal [Formula: see text]-submodule and [Formula: see text] for every minimal prime ideal [Formula: see text] of [Formula: see text]. If [Formula: see text] is a finitely generated Krull module, then [Formula: see text] is a Krull module and [Formula: see text]-multiplication module. It is also shown that the following three conditions are equivalent: [Formula: see text] is completely integrally closed, [Formula: see text] is completely integrally closed, and [Formula: see text] is completely integrally closed.

Cointegration, Root Functions and Minimal Bases

This paper discusses the notion of cointegrating space for linear processes integrated of any order. It first shows that the notions of (polynomial) cointegrating vectors and of root functions coincide. Second, it discusses how the cointegrating space can be defined (i) as a vector space of polynomial vectors over complex scalars, (ii) as a free module of polynomial vectors over scalar polynomials, or finally (iii) as a vector space of rational vectors over rational scalars. Third, it shows that a canonical set of root functions can be used as a basis of the various notions of cointegrating space. Fourth, it reviews results on how to reduce polynomial bases to minimal order—i.e., minimal bases. The application of these results to Vector AutoRegressive processes integrated of order 2 is found to imply the separation of polynomial cointegrating vectors from non-polynomial ones.

On strongly coseparable modules

A module M is called $$\mathfrak {s}$$ s -coseparable if for every nonzero submodule U of M such that M/U is finitely generated, there exists a nonzero direct summand V of M such that $$V \subseteq U$$ V ⊆ U and M/V is finitely generated. It is shown that every non-finitely generated free module is $$\mathfrak {s}$$ s -coseparable but a finitely generated free module is not, in general, $$\mathfrak {s}$$ s -coseparable. We prove that the class of $$\mathfrak {s}$$ s -coseparable modules over a right noetherian ring is closed under finite direct sums. We show that the class of commutative rings R for which every cyclic R-module is $$\mathfrak {s}$$ s -coseparable is exactly that of von Neumann regular rings. Some examples of modules M for which every direct summand of M is $$\mathfrak {s}$$ s -coseparable are provided.

Free Counseling Chatbot in a Communication Application For Improving Patient Satisfaction with Indwelling Ureteric Stents After Ureterorenoscopic Lithotripsy: A Retrospective Study (Preprint)

BACKGROUND Health education is important for improving patients’ adherence to treatment, thereby reducing morbidity. Face-to-face communication is not sufficient nowadays, and online interaction can improve patient–physician communication and education. OBJECTIVE We designed a chatbot for patients who received indwelling double-J ureteric stents (DJs) after ureterorenoscopic lithotripsy (URSL) and evaluated the efficacy of this chatbot in improving patient satisfaction in clinical practice. METHODS We designed a chatbot, based on the free module provided by the communication application Line©, which described the associated symptoms with DJs and the self-care of DJs after discharge and emphasized the importance of timely DJ removal. Patients could interact with the chatbot for any concerns regarding their DJs after discharge. We prospectively included patients who received indwelling DJs after URSL at our hospital from August 1st, 2019 to November 30th, 2019. Patient education on DJ-related information was conducted either by medical staff before discharge or by using the chatbot, based on patients’ preference. Patients were asked to rate the severity of their DJ-related symptoms and their satisfaction with using the free chatbot on a five-point scale before DJ removal. Fisher’s exact test was used to evaluate the effect of the chatbot on the severity of DJ-related symptoms and the possible factors associated with the satisfaction with this chatbot. RESULTS A total of 70 patients were included. Twenty patients received routine education by medical staff while 50 patients elected to have additional interaction through the chatbot. The patients in the chatbot group were significantly younger (age <60 years: 74% versus 15%, P < .001), had a higher education level (40% versus 5%, P = .004), and reported more severe gross hematuria (66% versus 15%, P < .001) than those in the medical-staff group. No differences were observed for other DJ-associated symptoms. On multivariate analysis, severe gross hematuria was significantly associated with age younger than 60 years (odds ratio 6.704, P = .003, 95% CI 1.898–23.673) and the use of the chatbot (odds ratio 6.63, P = .02, 95% 1.374–31.989). All 50 patients in the chatbot group reported being satisfied (32%) or very satisfied (68%) with the chatbot tool. Patients older than 60 years were significantly more satisfied with the chatbot (35.5% versus 6.3%, P = .04). Education level, the severity of DJ-associated symptoms, and the recognition of the necessity of DJ removal were not significantly associated with the degree of satisfaction. CONCLUSIONS The use of a chatbot resulted in high satisfaction of the patients, especially elderly patients. Younger patients with higher education levels were more likely to adopt this new form of communication, which helped improve their knowledge of DJ-associated symptoms.

Novel Joint Object Detection Algorithm Using Cascading Parallel Detectors

Object detection is an essential computer vision task that aims to detect target objects from an image. The traditional models are insufficient to generate a high-quality anchor box. To solve the problem, we propose a novel joint model called guided anchoring Region proposal networks and Cascading Grid Region Convolutional Neural Networks (RCGrid R-CNN), enhancing the ability of object detection. Our proposed model design is a joint object detection algorithm containing an anchor-based and an anchor-free branch in parallel and symmetry. In the anchor-based, we use nine-point spatial information fusion to obtain better anchor box location and introduce the shape prediction method of Guided Anchoring Region Proposal Networks (GA-RPN) to enhance the accuracy of the predicted anchor box. In the anchor-free branch, we introduce the Feature Selective Anchor-Free module (FSAF) to reduce the overlapping anchor boxes to obtain a more accurate anchor box. Furthermore, inspired by cascading theory, we cascade the new-designed detectors to improve the ability of object detection by setting a gradually increasing Intersection over Union (IoU) threshold. Compared with typical baseline models, we comprehensively evaluated our model by conducting experiments on two open datasets: Pascal VOC2007 and COCO2017. The experimental results demonstrate the effectiveness of RCGrid R-CNN in producing a high-quality anchor box.

Arithmetic modules over generalized Dedekind domains

Let [Formula: see text] be a finitely generated torsion-free module over a generalized Dedekind domain [Formula: see text]. It is shown that if [Formula: see text] is a projective [Formula: see text]-module, then it is a generalized Dedekind module and [Formula: see text]-multiplication module. In case [Formula: see text] is Noetherian it is shown that [Formula: see text] is either a generalized Dedekind module or a Krull module. Furthermore, the polynomial module [Formula: see text] is a generalized Dedekind [Formula: see text]-module (a Krull [Formula: see text]-module) if [Formula: see text] is a generalized Dedekind module (a Krull module), respectively.

On the Structure of Affine Flat Group Schemes Over Discrete Valuation Rings, II

In the first part of this work [ 12], we studied affine group schemes over a discrete valuation ring (DVR) by means of Neron blowups. We also showed how to apply these findings to throw light on the group schemes coming from Tannakian categories of $\mathcal{D}$-modules. In the present work, we follow up this theme. We show that a certain class of affine group schemes of “infinite type,” Neron blowups of formal subgroups, are quite typical. We also explain how these group schemes appear naturally in Tannakian categories of $\mathcal{D}$-modules. To conclude, we isolate a Tannakian property of affine group schemes, named prudence, which allows one to verify if the underlying ring of functions is a free module over the base ring. This is then successfully applied to obtain a general result on the structure of differential Galois groups over complete DVRs.

A Study of The Density Property in Module Theory

In this paper, there are two main objectives. The first objective is to study the relationship between the density property and some modules in detail, for instance; semisimple and divisible modules. The Addition complement has a good relationship with the density property of the modules as this importance is highlighted by any submodule N of M has an addition complement with Rad(M)=0. The second objective is to clarify the relationship between the density property and the essential submodules with some examples. As an example of this relationship, we studied the torsion-free module and its relationship with the essential submodules in module M.