Graded Ring Research Articles

Improving the efficiency and reliability of India's power grid through targeted EHV transmission line investments: a case of UPPCL.

This study analyzes the optimization of Extra High Voltage (EHV) transmission line design parameters by Uttar Pradesh Power Corporation Limited (UPPCL) in India to improve power grid efficiency and reliability. UPPCL reduced insulation specifications for 400kV lines from 27 to 21 disc insulators and decreased live metal clearance from 2600 to 2400mm, resulting in 7-9% cost savings per line and reduced right-of-way requirements. While initial test lines performed satisfactorily for over 5years, longer lines experienced operational challenges related to insulator quality, bird activity, and design margins. Tripping issues emerged during adverse weather conditions, particularly in foggy winter periods. Root cause analysis revealed the need for stringent insulator quality control, regular cleaning to mitigate bird dropping contamination, and potential corona ring design improvements. This case study demonstrates how targeted EHV transmission line optimization can yield significant cost and environmental benefits, while highlighting the importance of balancing economic gains with reliability and safety considerations. The findings provide valuable insights for future EHV transmission line designs and upgrades across India's power grid.

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.

The Eisenbud-Green-Harris conjecture for fast-growing degree sequences

Let $S$ be a standard graded polynomial ring over a field, and $I$ be a homogeneous ideal that contains a regular sequence of degrees $d_1,\ldots,d_n$. We prove the Eisenbud-Green-Harris conjecture when the forms of the regular sequence satisfy $d_i \geqslant \sum_{j=1}^{i-1}(d_j-1)$, improving a result obtained in 2008 by the first author and Maclagan. Except for the sporadic case of a regular sequence of five quadrics, recently proved by Gunturkun and Hochster, the results of this article recover all known cases of the conjecture where only the degrees of the regular sequence are fixed, and include several additional ones.

Automated monitoring of insulation by ultraviolet imaging employing deep learning

The corona effect on the surface of electrical system equipment and components generally indicates undesirable phenomena that can lead to physical degradation of materials or even equipment failure. One of the most promising techniques for monitoring corona discharges is the use of specialized cameras for the detection of ultraviolet radiation. This paper introduces an innovative algorithm for classifying the criticality of insulation based on attributes extracted from videos recorded using an ultraviolet detection camera. The attributes extracted from each facula origin include maximum persistence, area, and the minimum distance between the facula origin and the insulation. To obtain this distance, a technique combining a deep convolutional neural network model with an adaptive segmentation thresholding method is proposed. To validate the proposed methodology, inspections were conducted at a 500 kV substation. A total of 96 videos were recorded, within which 99 facula origins were identified. The object detection model applied demonstrated an accuracy of 85.5 % in detecting insulation in images, based on a validation set comprising 1,985 images and 8,730 instances. The results of the classification showed that 72.7 % of the facula origins recorded originated from regions far from the insulation (mainly cables and corona rings). These results demonstrate that the distance between the insulation and the facula origin is an essential attribute for video analysis, providing context for recorded discharges and allowing differentiation between cases where ultraviolet radiation originates from insulation and those where discharge location is less critical.

Twists of graded Poisson algebras and related properties

We introduce a Poisson version of the graded twist of a graded associative algebra and prove that every graded Poisson structure on a connected graded polynomial ring A:=k[x1,…,xn] is a graded twist of a unimodular Poisson structure on A, namely, if π is a graded Poisson structure on A, then π has a decompositionπ=πunim+1∑i=1ndeg⁡xiE∧m where E is the Euler derivation, πunim is the unimodular graded Poisson structure on A corresponding to π, and m is the modular derivation of (A,π). This result is a generalization of the same one in the quadratic setting. The rigidity of graded twisting, PH1-minimality, and H-ozoneness are studied. As an application, we compute the Poisson cohomologies of the quadratic Poisson structures on the polynomial ring of three variables when the potential is irreducible, but not necessarily having an isolated singularity.

A note on Ratliff-Rush filtration, reduction number and postulation number of [formula omitted]-primary ideals

Let (R,m) be a Cohen-Macaulay local ring of dimension d≥2, and I an m-primary ideal. Let r(I) be the reduction number of I, n(I) the postulation number and ρ(I) the stability index of the Ratliff-Rush filtration with respect to I. We prove that for d=2, if n(I)=ρ(I)−1, then r(I)≤n(I)+2, and if n(I)≠ρ(I)−1, then r(I)≥n(I)+2. For d≥3, assuming I is integrally closed, depthgr(I)=d−2, and n(I)=−(d−3), we prove that r(I)≥n(I)+d. Our main result generalizes a result by Marley on the relation between the Hilbert-Samuel function and the Hilbert-Samuel polynomial by relaxing the condition on the depth of the associated graded ring to the good behavior of the Ratliff-Rush filtration with respect to I mod a superficial sequence. From this result, it follows that for Cohen-Macaulay local rings of dimension d≥2, if PI(k)=HI(k) for some k≥ρ(I), then PI(n)=HI(n) for all n≥k.

A Defect Detection Method for Grading Rings of Transmission Lines Based on Improved YOLOv8

Detecting defects in aerial images of grading rings collected by drones poses challenges due to the structural similarity between normal and defective samples. The small visual differences make it hard to distinguish defects and extract key features. Additionally, critical defect features often become lost during feature fusion. To address these issues, this paper uses YOLOv8 as the baseline model and proposes an improved YOLOv8-based method for detecting grading ring defects in transmission lines. Our approach first integrates the CloAttention and C2f modules into the feature extraction network, enhancing the model’s ability to capture and identify defect features in grading rings. Additionally, we incorporate CARAFE into the feature fusion network to replace the original upsampling module, effectively reducing the loss of critical defect information during the fusion process. Experimental results demonstrate that our method achieves an average detection accuracy of 67.6% for grading ring defects, marking a 6.8% improvement over the baseline model. This improvement significantly enhances the effectiveness of defect detection in transmission line grading rings.

Ore localisation for differential graded rings; towards Goldie's theorem for differential graded algebras

We study Ore localisation of differential graded algebras. Further we define dg-prime rings, dg-semiprime rings, and study the dg-nil radical of dg-rings. Then, we define dg-essential submodules, dg-uniform dimension, and apply all this to a dg-version of Goldie's theorem on prime dg-rings.

The eventual shape of the Betti table of 𝔪kM

Let [Formula: see text] be a standard graded polynomial ring over a field [Formula: see text] in a finite set of variables, and let [Formula: see text] be the graded maximal ideal of [Formula: see text]. It is known that for a finitely generated graded [Formula: see text]-module [Formula: see text] and all integers [Formula: see text], the module [Formula: see text] is componentwise linear. For large [Formula: see text] we describe the pattern of the Betti table of [Formula: see text] when [Formula: see text]. Moreover, we show that for any [Formula: see text], [Formula: see text] has linear quotients if [Formula: see text] is a monomial ideal.

Variation and Phenetic Relationship of Passiflora spp. in Yogyakarta Based on Morphological and Anatomical Characters

Passiflora spp. or passion fruit is a tropical plant that is often used as a food source. The large morphological variations of Passiflora cause difficulties in identifying the species. The objectives of the study are to identify the specific morphological and anatomical characters of Passiflora spp. in Yogyakarta and to determine their phenetic relationship for identification. A total of 15 samples of Passiflora were taken by purposive sampling technique from Bantul, Sleman, Kulon Progo, and Yogyakarta City, and then carried through the morphological and anatomical characterization. The morphological characters observed stems, leaves, and flowers, while the anatomical characters observed leaves. The results show that the observed samples are identified as four species, P. foetida, P. vitifolia, P. edulis, and P. quadrangularis. The P. edulis species consists of two forms, P. edulis f. flavicarpa and P. edulis f. edulis. The variation of morphological character lie in young stem shape, leaf shape, the texture of stem and leaf surface, bract shape and color, sepal and petal color, and the presence of a purple corona ring. While the variation of anatomical characters lie in the pattern of the vascular bundles, the shape of the upper and lower sides of the leaf veins, the shape and size of the palisade cells, as well as the type and density of stomata. Based on the phenetic analysis on the 0.8 phenon line, four main clusters were formed, P. foetida, P. vitifolia, P. edulis, and P. quadrangularis.

Coderived and contraderived categories of locally presentable abelian DG-categories

The concept of an abelian DG-category, introduced by the first-named author in Positselski (Exact DG-categories and fully faithful triangulated inclusion functors. arXiv:2110.08237 [math.CT]), unites the notions of abelian categories and (curved) DG-modules in a common framework. In this paper we consider coderived and contraderived categories in the sense of Becker. Generalizing some constructions and results from the preceding papers by Becker (Adv Math 254:187–232, 2014. arXiv:1205.4473 [math.CT]) and by the present authors (Positselski and Št’ovíček in J Pure Appl Algebra 226(#4):106883, 2022. arXiv:2101.10797 [math.CT]), we define the contraderived category of a locally presentable abelian DG-category B\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{B}$$\\end{document} with enough projective objects and the coderived category of a Grothendieck abelian DG-category A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{A}$$\\end{document}. We construct the related abelian model category structures and show that the resulting exotic derived categories are well-generated. Then we specialize to the case of a locally coherent Grothendieck abelian DG-category A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{A}$$\\end{document}, and prove that its coderived category is compactly generated by the absolute derived category of finitely presentable objects of A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{A}$$\\end{document}, thus generalizing a result from the second-named author’s preprint (Št’ovíček in On purity and applications to coderived and singularity categories. arXiv:1412.1615 [math.CT]). In particular, the homotopy category of graded-injective left DG-modules over a DG-ring with a left coherent underlying graded ring is compactly generated by the absolute derived category of DG-modules with finitely presentable underlying graded modules. We also describe compact generators of the coderived categories of quasi-coherent matrix factorizations over coherent schemes.

A novel application of artificial intelligence technology for outdoor high-voltage composite insulator

The distribution of the electric field plays a crucial role in evaluating the effectiveness of composite insulators. This research presents an innovative approach for optimizing the design of corona rings, aiming to decrease the electric field intensity in critical areas to satisfactory levels. The investigation examined the correlation among corona ring design variables and the intensity of the electric field close to the energized-end fitting in a 220 kV composite insulator equipped with a corona ring. Using design of experiment methods, the impact of three corona ring design parameters – corona ring diameter (R), ring tube diameter (Dr), and corona ring height (H) – was assessed. A novel nonlinear mathematical objective function was formulated, connecting the electric field magnitude to the structural parameters of the corona ring. Subsequently, the Bat algorithm, a bio-inspired optimization technique, was employed to enhance the initial corona ring design and mitigate the electric field intensity. Finally, the Finite Element Method (FEM) was utilized to simulate and evaluate the voltage distribution and electric field stress. The optimization process resulted in a substantial decrease in the highest electric field magnitude, by 58.6 % compared to the insulator with the threshold value, and 75 % when devoid of a corona ring. Additionally, the research highlighted the significant influence of ring tube thickness on the distribution of the electric field. The combination of experimental design and the Bat algorithm proved to be a powerful tool for optimizing the design of corona rings on transmission line composite insulators, providing precise solutions for optimizing corona discharge problems and enhancing the reliability of power transmission systems.

On graded-(m, n)-prime ideals of commutative graded rings

On graded-(m, n)-prime ideals of commutative graded rings

Improving electric field stress using grading ring devices for insulated cross-arm

Insulated cross-arms (ICA) allow for the compaction or enhancement of transmission lines. This study presents a comprehensive approach to designing and evaluating insulated cross-arm (ICA) grading devices to control electric fields for insulated cross-arms on a 132 kV lattice tower. A ring-shaped grading device is designed for the low voltage (LV) end of the insulator. A novel grading device is designed for the high voltage (HV) end—a single piece that controls the field for all four ICA members. Finite element analysis (FEA) simulations assess the electric field stress near the HV and LV ends of the ICAs, ensuring that it remains below the critical threshold of 18 kV/cm and effectively improves electric field stress at both ends of compression insulator by 70 % electric field stress at LV end and 80 % improved at HV end. The study outlines a thorough design methodology and provides valuable guidelines for utilising FEA in developing complex geometries. By adopting this approach, the researchers aim to enable the adequate compaction and upgrading of new and existing 132 kV overhead transmission lines, ultimately contributing to optimising power grid infrastructure. The findings of this study demonstrate the importance of integrating comprehensive design strategies and advanced simulation techniques to enhance the reliability and performance of ICA.

Risk factors of a positive resection margin in locoregional appendix cancer and its impact on survival: The national cancer database analysis

IntroductionThe impact of a positive resection margin (RM+) in appendiceal cancer (AC) remains unclear, with small studies suggesting it does not worsen survival in low-grade subtypes. We aimed to evaluate RM+ rates, its risk factors, and survival outcomes across different AC histologies. MethodsWe conducted a multicenter retrospective cohort study using the National Cancer Database (2004–2019) and including stage I-III AC cases. Surgical and survival outcomes were compared between RM+ and RM- groups, with logistic regression analyzing the association of RM+ and its predictors. Subgroup analysis was performed for low/high tumor grade (LG/HG), mucinous/non-mucinous pathology (MAC/NMAC), and signet ring cell carcinoma (SRC). ResultsAmong 6800 patients identified, 737 (10.8 %) had RM+, while 6063 (89.2 %) had RM-. RM+ rates varied across AC histologies: 10.9 % in LG-MAC, 17.0 % in HG-MAC, 7.8 % in LG-NMAC, 13.9 % in HG-NMAC, and 17.9 % in SRC. RM+ correlated with significantly worse survival in LG-MAC (HR 1.67), HG-MAC (HR 1.83), LG-NMAC (HR 2.04), and SRC (HR 2.37) but not in HG-NMAC after adjusting to other factors. Predictors of RM+ included pT stage, preoperative chemotherapy in LG tumors and pT stage and positive lymph nodes in HG tumors whereas more extensive resection was associated with RM- in both LG and HG. ConclusionRM+ worsens survival in most AC subtypes, highlighting the importance of achieving negative margins. Extensive resection, like right hemicolectomy, can improve RM- rate, but factors such as pT stage, lymph node status, and preoperative chemotherapy also affect RM+. Surgeons should prioritize achieving RM- in all AC histologies.

Quasi-pure resolutions and some lower bounds of Hilbert coefficients of Cohen-Macaulay modules

Let (A,m) be a Noetherian local ring and let M be a finitely generated Cohen Macaulay A module. Let G(A)=⨁n≥0mn/mn+1 be the associated graded ring of A and G(M)=⨁n≥0mnM/mn+1M be the associated graded module of M. If A is regular and if G(M) has a quasi-pure resolution then we show that G(M) is Cohen-Macaulay. If A is Gorenstein and G(A) is Cohen-Macaulay and if M has finite projective dimension then we give lower bounds on e0(M) and e1(M). Finally let A=Q/(f1,…,fc) be a strict complete intersection with ord(fi)=s for all i, where Q is a regular local ring. Let M be an Cohen-Macaulay module with complexity cxA(M)=r<c. We give lower bounds on e0(M) and e1(M).

Macaulay’s theorem for vector-spread algebras

Let [Formula: see text] be the standard graded polynomial ring, with K a field, and let [Formula: see text], [Formula: see text], be a [Formula: see text]-tuple whose entries are non-negative integers. To a t-spread ideal I in S, we associate a unique [Formula: see text]-vector and we prove that if I is t-spread strongly stable, then there exists a unique t-spread lex ideal which shares the same [Formula: see text]-vector of I via the combinatorics of the t-spread shadows of special sets of monomials of S. Moreover, we characterize the possible [Formula: see text]-vectors of t-vector spread strongly stable ideals generalizing the well-known theorems of Macaulay and Kruskal–Katona. Finally, we prove that among all t-spread strongly stable ideals with the same [Formula: see text]-vector, the t-spread lex ideals have the largest Betti numbers.

Hyperplane sections of non-standard graded rings

The purpose of this paper is to explain a method on the generalization of the Bertini-type theorem on standard graded rings to the non-standard graded case of certain type.

Combined Simulated annealing and Improved Binary PSO based Optimal Corona Ring Design for High Voltage Transmission Line

Combined Simulated annealing and Improved Binary PSO based Optimal Corona Ring Design for High Voltage Transmission Line

On graded pseudo 2-prime ideals

In this paper, we study graded pseudo 2-prime ideals of graded commutative rings with nonzero identities. Let G be a commutative additive monoid with an identity element 0, and R=⊕g∈G Rg be a commutative graded ring with a nonzero identity element. A proper graded ideal I of R is said to be a graded pseudo 2-prime ideal if whenever ab ∈ I for some homogeneous elements a,b ∈ R, then a²ⁿ ∈ Iⁿ or b²ⁿ ∈ Iⁿ for some n ∈ ℕ. Besides giving many properties of graded pseudo 2-prime ideals, we characterize graded almost valuation domains in terms of our new concept.