Graded Ring Research Articles

Study on Abnormal Heat of Polymeric Insulators on Coastal Power Transmission Line

Heating at the high-voltage end has become one of the most frequent defects on polymeric insulators in service, particularly in humid and hot regions. Recent case surveys show that some highly overheated sample insulators survive almost all the standardized lab tests, which could not be fully explained by common related heating factors, including the fracture defects, superficial wet pollution, water absorption and moisture of polymeric housing, uneven sunlight, etc. In this paper, we try to find an alternative perspective to explain the temperature rise in the order of 10°C by studying the relationship between the heat at the high-voltage end and the degree of corrosion on a cast aluminum grading ring.

Integrally Closed Ideals of Reduction Number Three

In a Cohen-Macaulay local ring [Formula: see text], we study the Hilbert function of an integrally closed [Formula: see text]-primary ideal [Formula: see text] whose reduction number is three. With a mild assumption we give an inequalityi [Formula: see text], where [Formula: see text] denotes the [Formula: see text]th Hilbert coefficient and [Formula: see text] denotes a minimal reduction of [Formula: see text]. The inequality is located between inequalities of Itoh and Elias-Valla. Furthermore, this inequality becomes an equality if and only if the depth of the associated graded ring of [Formula: see text] is larger than or equal to [Formula: see text]. We also study the Cohen-Macaulayness of the associated graded rings of determinantal rings.

On the associated graded ring of semigroup algebras

In this paper, we give a necessary and sufficient condition for the Cohen-Macaulayness of the associated graded ring of a simplicial affine semigroup using Gröbner basis. We generalize the concept of homogeneous numerical semigroup for the simplicial affine semigroup and show that the Betti numbers of the corresponding semigroup ring matches with the Betti numbers of the associated graded ring. We also discuss nice extensions for simplicial affine semigroups, a concept which is motivated by nice extensions of numerical semigroups.

When does a perturbation of the equations preserve the normal cone?

Let ( R , m ) (R,\frak {m}) be a local ring and I , J I, J two arbitrary ideals of R R . Let g r J ( R / I ) gr_J(R/I) denote the associated graded ring of R / I R/I with respect to J J , which corresponds to the normal cone in algebraic geometry. With regards to the finite determinacy of singularity with respect to the Jacobian ideal we study the problem for which ideal I = ( f 1 , … , f r ) I = (f_1,\dots ,f_r) does there exist a number N N such that if f i ′ ≡ f i mod J N f_i’ \equiv f_i \mod J^N , i = 1 , … , r i = 1,\dots ,r , and I ′ = ( f 1 ′ , … , f r ′ ) I’ = (f_1’,\dots ,f_r’) , then g r J ( R / I ) ≅ g r J ( R / I ′ ) gr_J(R/I) \cong gr_J(R/I’) . This problem arises from a recent result of Ma, Quy and Smirnov in the case J J is an m \frak {m} -primary ideal, which solves a long standing conjecture of Srinivas and Trivedi on the invariance of Hilbert functions under small perturbations. Their approach involves Hilbert functions and cannot be used to study the above general problem. Our main result shows that such a number N N exists if f 1 , … , f r f_1,\dots ,f_r is locally a regular sequence outside the locus of J J . It has interesting applications to a range of related problems.

Abstract 2141: Claudin 18.2 (CLDN18.2) expression prevalence, prognostication and clinical variables in gastric and gastroesophageal junction adenocarcinoma patient samples

Abstract Introduction: CLDN18.2 is an isoform of CLDN18, a member of the Claudin family of proteins with expression that is highly restricted to the gastric epithelium of normal gastric tissue. In tumor tissue from patients with gastric (G) and gastroesophageal junction (GEJ) adenocarcinoma, CLDN18.2 expression has been found to be frequently expressed as determined by gene expression and immunohistochemistry (IHC). Based on its expression pattern in malignant tissues and past clinical studies, CLDN18.2 has emerged as a target of interest for new therapeutics. The goal of this study was to obtain a deeper understanding of CLDN18.2 expression, prevalence, as well as its prognostic implications, clinical characteristics, and relationship with select biomarkers in G and GEJ adenocarcinoma patient samples. Methods: Formalin-Fixed Paraffin-Embedded tissue samples of G and GEJ adenocarcinoma patients (n=304) from a tissue biorepository at MD Anderson Cancer Center were retrospectively studied for CLDN18.2 expression by IHC (antibody clone 43-14A). Tissue samples included primary G and GEJ adenocarcinoma tissues, matched pre- and post- metastatic samples and matched naïve versus chemotherapy treated patients. Interpretation of CLDN18.2 expression was conducted by clinical pathologists to score samples based on staining intensity (≥2+) as well as the percentage of positively stained CLDN18.2 tumor cells (≥75% and ≥50%). CLDN18.2 expression was analyzed for its association with prognosis, clinical and demographic data and its relationship with other variables (e.g. sex, age, histology, HER2, PD-L1, EBV). Results: Prevalence of CLDN18.2 expression at the >75% cutoff was observed in 51% and 35% of samples from G and GEJ adenocarcinoma patients, respectively, with a combined prevalence of 44%. At the >50% cutoff, CLDN18.2 was expressed in 64% and 45% of G and GEJ adenocarcinoma samples, respectively, with a combined prevalence of 56%. CLDN18.2 expression did not appear to associate with prognosis at either CLDN18.2 expression cutoff. Associations between CLDN18.2 expression based upon sex, tumor grade, histology, peritoneal metastasis and signet ring morphology were observed. When evaluating the relationship between CLDN18.2 expression (at either cutoff) and other select biomarkers (MSI, PD-L1, HER2 and EBV), data suggests there is limited overlap. Conclusion: Based upon the data from this study, CLDN18.2 appears to be a highly prevalent, but not prognostically associated biomarker in G and GEJ adenocarcinoma patients. Additionally, CLDN18.2 expression appears independent of other biomarkers, however further research is warranted. These data are consistent with prior reports and support CLDN18.2 as a promising molecular target for therapeutics to treat G and GEJ adenocarcinoma patients. Citation Format: Matheus Sewastjanow, Kohei Yamashita, Kenneth K. Iwata, Diarmuid Moran, Dina Elsouda, Melissa Pizzi, Ernesto Rosa Vicentini, Namita Shanbhag, Anh Ta, Rebecca Waters, Deyali Chatterjee, Jaffer Ajani. Claudin 18.2 (CLDN18.2) expression prevalence, prognostication and clinical variables in gastric and gastroesophageal junction adenocarcinoma patient samples [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 2141.

A Study on Electric Potential and Electric Field Distribution for Optimal Design of Lightning Rod Using Finite Element Method

In this paper, we present an electric field analysis for the optimal structural design of lightning rods for high performance with a charge transfer system (CTS). In the case of a conventional rod that is produced with an empirical design and structure without quantitative data because the design is structurally very simple, only the materials and radius of curvature of the lightning rod to concentrate the electric field at the tip part of the rod are considered. Recently, the development of new types of lightning rods, such as early streamer emission (ESE) and charge transfer system (CTS), has been introduced through simulation analysis and experiments, but detailed specifications and information about the optimal design and structure have not been fully reported. In this paper, we performed an electric field analysis of the structures and materials for the optimal structural design of lightning rods with a function of CTS through computer software analysis with consideration for the radius of curvature, the size of corona ring, and optimal position (X-axis and Y-axis) of the floating electrode. For optimal structural design of lightning rods based on electric field analysis, we used a source of lightning voltage with 1.2/50 µs based on a double exponential equation. The results revealed that the electric field on the relaxation part decreases as the radius of curvature and corona ring increases. For the radius of curvature, the electric field first decreases and then increases with increasing radius of curvature and reaches a minimum at 7 mm and a maximum above 8 mm. For the case of the corona ring, the electric field decreases with increasing corona ring, and the optimal size of the corona ring was selected as 4 mm; the size of the 4 mm corona ring uniformly formed the electric field both at the tip part of the ground current collector and the corona ring. For the electric field concentration part, we found that the optimal X-axis position of the floating electrode and the Y-axis position between the ionizer conductor and floating electrode are 7 mm and 0.1 mm, respectively. These simulation results in this paper are expected to provide useful information for the design of optimized CTS-type lightning rods.

Graded amalgamated algebras along an ideal

Let [Formula: see text] and [Formula: see text] be two commutative rings graded by an arbitrary commutative monoid [Formula: see text], let [Formula: see text] be a homogeneous ideal of [Formula: see text] and [Formula: see text] a graded ring homomorphism. In this paper, we introduce a new graded ring construction called “the graded amalgamation of [Formula: see text] with [Formula: see text] along [Formula: see text] with respect to [Formula: see text]” (denoted by [Formula: see text]). Then we investigate, through the properties of the homogeneous components that build the body of this “graded” study, the transfer of the property of graded-coherence to the graded amalgamation [Formula: see text].

Investigation of the Effect of Corona Ring Design Parameters on Electric Field Distribution by Finite Element Method

Investigation of the Effect of Corona Ring Design Parameters on Electric Field Distribution by Finite Element Method

Quadratically presented grade three Gorenstein ideals

Let J be a quadratically presented grade three Gorenstein ideal in the standard graded polynomial ring R=k[x,y,z], where k is a field. Assume that R/J satisfies the weak Lefschetz property. We give the presentation matrix for J in terms of the coefficients of a Macaulay inverse system for J. (This presentation matrix is an alternating matrix and J is generated by the maximal order Pfaffians of the presentation matrix.) Our formulas are computer friendly; they involve only matrix multiplication; they do not involve multilinear algebra or complicated summations. As an application, we give the presentation matrix for J1=(xn+1,yn+1,zn+1):(x+y+z)n+1, when n is even and the characteristic of k is zero. Generators for J1 had been identified previously; but the presentation matrix for J1 had not previously been known. The first step in our proof is to give improved formulas for the presentation matrix of a linearly presented grade three Gorenstein ideal I in terms of the coefficients of the Macaulay inverse system for I.

Analysis of Influencing Factors on Electric Field Distribution of 500 kV Porcelain Insulators

With the upsurge of the digital twin power grid, it is very necessary to carry out a three-dimensional model and simulation analysis of the power grid system. Insulators are one of the important components in the power system, and the appropriate simplification of the simulation model is of great significance. In this paper, the finite element software is used to calculate the three-dimensional model, and the influence of the length of the conductor, the tower, the yoke plate, the grading ring, and the arrangement of the insulators on the axial electric field distribution (EFD) is analyzed. The results show that: the length of the conductor will affect the uniformity of the axial electric field; compared with the grading ring, the yoke plate will cause serious distortion of the electric field intensity curve; the integrity of the tower has different effects; the arrangement of the insulators will affect the magnitude of the electric field and even the shape of the curve. Therefore, in the simulation analysis of the axial electric field, the above factors should be considered when simplifying the insulator model, which will promote the development of relevant digital twin technology.

Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories

Khovanov and Sazdanovic recently introduced symmetric monoidal categories parameterized by rational functions and given by quotients of categories of two-dimensional cobordisms. These categoriesgeneralizeDeligne'sinterpolation categories of representations of symmetric groups. In this paper, we classify indecomposable objects and identify the associated graded Grothendieck rings of Khovanov–Sazdanovic's categories through sums of representation categories over crossed products of polynomial rings over a general field. To obtain these results, we introduce associated graded categories for Krull–Schmidt categories with filtrations as a categorification of the associated graded Grothendieck ring, and study field extensions and Galois descent for Krull–Schmidt categories.

The indecomposable objects in the center of Deligne's category Re̲pSt$\protect\underline{{\rm Re}}\!\operatorname{p}S_t$

AbstractWe classify the indecomposable objects in the monoidal center of Deligne's interpolation category by viewing as a model‐theoretic limit in rank and characteristic. We further prove that the center of is semisimple if and only if is not a non‐negative integer. In addition, we identify the associated graded Grothendieck ring of this monoidal center with that of the graded sum of the centers of representation categories of finite symmetric groups with an induction product. We prove analogous statements for the abelian envelope.

Graded (quasi-)Frobenius rings

In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations of such objects. We need to revisit graded simple graded left Artinian rings, graded semisimple rings, and to provide graded versions of certain results concerning the Jacobson radical, the singular radical, and their connection to finiteness conditions and injectivity. We prove a structure result for (shift-)graded Frobenius rings.

Optimal Design of Corona Ring for 132 kV Insulator at High Voltage Transmission Lines Based on Optimisation Techniques

The installation of a corona ring on an insulator string on a transmission line is one of the solutions to reduce the electric field stress surrounding the energised end of the insulator string. However, installing a corona ring with an optimum design to reduce the electric field magnitude on an insulator string is a challenging task. Therefore, in this work, a method to achieve the optimum design of a corona ring for 132 kV composite non-ceramic insulator string was proposed using two optimisation methods: the Imperialist Competitive Algorithm (ICA) and Grey Wolf Optimisation (GWO). A composite non-ceramic insulator string geometry with and without a corona ring was modelled in finite element analysis and used to obtain the electric field distribution in the model geometry. The electric field distribution was evaluated using a variation in the corona ring’s dimensions, i.e., the ring diameter, the ring tube diameter and the vertical position of the ring along the insulator string. From the results achieved, a comparison of the minimum electric field magnitude along the insulator string with a corona ring design shows that the minimum electric field magnitude is found to be lower using optimisation techniques compared to without using optimisation techniques by between 3.724% and 3.827%. Hence, this indicates the capability and effectiveness of the proposed methods in achieving the optimum design of a corona ring on an insulator string.

Graded Rings with Finiteness Conditions

This paper is devoted to quotient rings of graded rings with finiteness conditions for ideals. The analogs of Goldie, Shock, and Small theorems are proved. We find criteria for a graded ring R to admit a gr-semisimple and gr-Artinian (the Goldie theorem) and gr-Artinian (the Small theorem) classical graded quotient ring.

On Properties of Graded Rings with respect to Group Homomorphisms

Let G be a group and R be a G‐graded ring with non‐zero unity. The goal of our article is reconsidering some well‐known concepts on graded rings using a group homomorphism α : G⟶G. Next is to examine the new concepts compared to the known concepts. For example, it is known that (R, G) is weak if whenever g ∈ G such that Rg = 0, then . In this article, we also introduce the concept of α‐weakly graded rings, where (R, G) is said to be α‐weak whenever g ∈ G such that Rg = 0, and Rα(g) = 0. Note that if G is abelian, then the concepts of weakly and α‐weakly graded rings coincide with respect to the group homomorphism α(g) = g−1. We introduce an example of non‐weakly graded ring that is α‐weak for some α. Similarly, we establish and examine the concepts of α‐non‐degenerate, α‐regular, α‐strongly, α‐first strongly graded rings, and α‐weakly crossed product.

Graded modules with Noetherian graded second spectrum

<abstract><p>Let $ R $ be a $ G $ graded commutative ring and $ M $ be a $ G $-graded $ R $-module. The set of all graded second submodules of $ M $ is denoted by $ Spec_G^s(M), $ and it is called the graded second spectrum of $ M $. We discuss graded rings with Noetherian graded prime spectrum. In addition, we introduce the notion of the graded Zariski socle of graded submodules and explore their properties. We also investigate $ Spec^s_G(M) $ with the Zariski topology from the viewpoint of being a Noetherian space.</p></abstract>

Corona Ring Improvement to Surface Electric Field Stress Mitigation of 400 kV Composite Insulator

Corona Ring Improvement to Surface Electric Field Stress Mitigation of 400 kV Composite Insulator

500kV급 HVDC 폴리머 애자의 전계 완화에 관한 연구

An HVDC(high voltage direct current) is economical owing to its excellent power transmission efficiency and a low insulation class compared with HVAC(high voltage alternative current). In addition, HVDC is known as a high efficiency green technology because power systems with different frequencies can be connected asynchronously. Therefore, research on the HVDC is being actively conducted. In order to develop HVDC transmission lines, it is necessary to secure insulation design technology for DC insulators. DC has different properties from AC due to the presence of space charge and the temperature dependence of conductivity. However, until now, there is no standard for the insulation design of DC insulators. In this study, the difference in insulation design was verified through AC electric field and DC electric field analysis, and a corona ring design was derived to improve the electrical stability of the 500kV DC insulator.

Generalized Koszul algebra and Koszul duality

We define generalized Koszul modules and rings and develop a generalized Koszul theory for N-graded rings with the degree zero part noetherian semiperfect. This theory specializes to the classical Koszul theory for graded rings with degree zero part artinian semisimple developed by Beilinson-Ginzburg-Soergel and the ungraded Koszul theory for noetherian semiperfect rings developed by Green and Martinéz-Villa. Let A be a left finite N-graded ring generated in degree 1 with A0 noetherian semiperfect, J be its graded Jacobson radical. By the Koszul dual of A we mean the Yoneda Ext ring Ext_A•(A/J,A/J). If A is a generalized Koszul ring and M is a generalized Koszul module, then it is proved that the Koszul dual of the Koszul dual of A is the associated graded ring GrJA and the Koszul dual of the Koszul dual of M is the associated graded module GrJM. If A is a locally finite algebra, then the following statements are proved to be equivalent: A is generalized Koszul; the Koszul dual Ext_A•(A/J,A/J) of A is (classically) Koszul; GrJA is (classically) Koszul; the opposite ring Aop of A is generalized Koszul. As an application, it is proved that if A is generalized Koszul with finite global dimension then A is generalized AS regular if and only if the Koszul dual of A is self-injective.