Graded Ring Research Articles

Cohen-Macaulayness of associated graded rings of Gorenstein monomial curves

Let C be a Gorenstein noncomplete intersection monomial curve in the 4-dimensional affine space with defining ideal I(C). In this article, we use the minimal generating set of I(C) to give a criterion for determining whether the tangent cone of C is Cohen-Macaulay. We also show that if the tangent cone of C is Cohen-Macaulay, then the minimal number of generators of the ideal I(C)⁎ is either 5 or an even integer of the form 2d+2, for a suitable integer d. Additionally, we provide a family of Gorenstein noncomplete intersection monomial curves C whose tangent cone is Cohen-Macaulay and the minimal number of generators of I(C)⁎ is large.

Parameters design optimization of grading ring based on electric field analysis through response surface methodology

This research delves into the primary cause of the ageing of insulated cross-arms in the field, which is attributed to the high electric stress experienced at the end fittings. To address this issue, a novel technique is introduced to meticulously analyse the influence of Grading rings on the electric field (E-field) stress, with the goal of regulating it within the prescribed limits on the surface of the insulated cross-arm. By employing advanced methodologies such as finite element analysis and design of experiment approaches, the impact of various geometrical characteristics of Grading rings on the E-field is comprehensively investigated. Through the application of the analysis of variance, the primary and interaction effects of these factors are carefully examined. Additionally, leveraging the power of the response surface technique, an optimal link between the E-field and the geometrical parameters is modelled and optimized. The results of this comprehensive study unequivocally reveal the profound influence of the geometrical parameters of Grading rings on the E-field. Furthermore, diligent efforts are made to estimate the Grading ring parameters that will effectively regulate the E-field within the suggested maximum threshold based on the derived model. The proposed technique not only significantly reduces the computational analysis time but also serves as an efficient and invaluable tool for investigating the intricate geometry of Grading rings without imposing any additional computing burden.According to the findings, the E-field is most impacted by the factors H, D, and T to optimise the shape of grading rings used in insulated cross-arms. The main objective was achieved by reducing the maximum E-field value by 65% compared to the E-field without a grading ring, which has been accomplished. The suggested technique provides a quick and easy way to analyse and improve the intricate geometry of grading rings. As a result, it lowers the cost and time related to computational analysis without needing an excessive amount of computing work to do this.

Optimal Design of Voltage Equalization Ring for the 1100 kV DC Voltage Proportional Standard Device Based on the Nation Standard Device Neural Network and Grey Wolf Optimization Algorithm

The DC voltage ratio standard device is an important tool for calibrating DC voltage transformers. At the 1100 kV voltage level, an increase in electric field intensity will increase the local heat generated inside the device, affecting the accuracy of its measurement. Using a suitable grading ring can even out the electric field intensity and reduce the maximum field strength to improve its measurement accuracy. This article mainly optimizes the design of the grading-ring structure of the 1100 kV DC voltage ratio standard device. First, a finite-element model of the 1100 kV DC voltage ratio standard device was built based on ANSYS; the electric field distribution around the voltage divider was calculated and analyzed, and a data set was constructed based on the calculation results. Secondly, for the optimization of electric field strength, this article presents the design of the nation standard device neural network, which learns the relationship between the structural parameters of the toroidal core and the field strength under the PyTorch 1.8 deep learning framework. Due to the strong convergence performance, few parameters, and ease of implementation of the grey wolf optimization algorithm, this study selected this algorithm to optimize the structural parameters of the grading ring. Finally, simulation examples are established in Python for validation. The experimental results indicate that the maximum field strength of the grading ring decreased from 12,161.1348 V/cm to 10,009.2881 V/cm, a reduction of 17.69%. The optimized structural parameters of the grading ring effectively reduced the electric field intensity around the 1100 kV DC voltage proportional standard device, providing a reliable and practical design approach for the selection of the DC voltage ratio standard device.

Artificial intelligence-based surrogate model for computation of the electric field of high voltage transmission line ceramic insulator with corona ring

Purpose The ionization of the air surrounding the phase conductor in high-voltage transmission lines results in a phenomenon known as the Corona effect. To avoid this, Corona rings are used to dampen the electric field imposed on the insulator. The purpose of this study is to present a fast and intelligent surrogate model for determination of the electric field imposed on the surface of a 120 kV composite insulator, in presence of the Corona ring. Design/methodology/approach Usually, the structural design parameters of the Corona ring are selected through an optimization procedure combined with some numerical simulations such as finite element method (FEM). These methods are slow and computationally expensive and thus, extremely reducing the speed of optimization problems. In this paper, a novel surrogate model was proposed that could calculate the maximum electric field imposed on a ceramic insulator in a 120 kV line. The surrogate model was created based on the different scenarios of height, radius and inner radius of the Corona ring, as the inputs of the model, while the maximum electric field on the body of the insulator was considered as the output. Findings The proposed model was based on artificial intelligence techniques that have high accuracy and low computational time. Three methods were used here to develop the AI-based surrogate model, namely, Cascade forward neural network (CFNN), support vector regression and K-nearest neighbors regression. The results indicated that the CFNN has the highest accuracy among these methods with 99.81% R-squared and only 0.045468 root mean squared error while the testing time is less than 10 ms. Originality/value To the best of the authors’ knowledge, for the first time, a surrogate method is proposed for the prediction of the maximum electric field imposed on the high voltage insulators in the presence Corona ring which is faster than any conventional finite element method.

Comparing generalized Gorenstein properties in semi-standard graded rings

Semi-standard graded rings are a generalized notion of standard graded rings. In this paper, we compare generalized notions of the Gorenstein property in semi-standard graded rings. We discuss the commonalities between standard graded rings and semi-standard graded rings, as well as elucidate distinctive phenomena present in semi-standard graded rings that are absent in standard graded rings.

Prime groupoid graded rings with applications to partial skew groupoid rings

In this paper, we investigate primeness of groupoid graded rings. We provide a set of necessary and sufficient conditions for primeness of a nearly-epsilon strongly groupoid graded ring. Furthermore, we apply our main result to get a characterization of prime partial skew groupoid rings, and in particular of prime groupoid rings, thereby generalizing a classical result by Connell and partially generalizing recent results by Steinberg.

Chain conditions for rings with enough idempotents with applications to category graded rings

We obtain criteria for when a ring with enough idempotents is left/right artinian or noetherian in terms of local criteria defined by the associated complete set of idempotents for the ring. We apply these criteria to object unital category graded rings in general and, in particular, to the class of skew category algebras. Thereby, we generalize results by Nastasescu-van Oystaeyen, Bell, Park, and Zelmanov from the group graded case to groupoid, and in some cases category, gradings.

Remarks on almost Gorenstein rings

This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once R is an almost Gorenstein graded ring, the localization RM of R at the graded maximal ideal M is almost Gorenstein as a local ring. The converse does not hold true in general ([7, Theorems 2.7, 2.8], [8, Example 8.8]). However, it does for one-dimensional graded domains with mild conditions, which we clarify in the present paper. We explore the defining ideals of almost Gorenstein numerical semigroup rings as well.

On graded co-multiplication-like modules over commutative graded rings

Let G be a group with identity e. Let wp be a G-graded commutative ring and Im a graded wp-module. In this paper, we will introduce the notion of graded co-multiplication-like modules over commutative graded rings and we obtain some related results. We say that a graded wp-module Im is a graded co-multiplication-like module if for each proper graded submodule U of Im, Ann_{wp}(Im)\subset Ann_{wp}(U).

The Koszulness of numerical semigroup rings of minimal multiplicity

Let R = k [H] be a numerical semigroup ring over a field k and grm (R) is the associated graded ring of R. In this paper, we show that grm (R) is a Cohen-Macaulay ring, provided H has minimal multiplicity. As a consequence, we conclude that the numerical semigroup ring R = k [H] of minimal multiplicity is a Koszul ring, i.e., the residue field k has a grm (R) – linear free resolution.

On some graded objects in graded module category

Let [Formula: see text] be a [Formula: see text]-graded ring and let [Formula: see text] be the category of [Formula: see text]-graded [Formula: see text]-modules and homogeneous homomorphisms. In this paper, we define and study some objects in this category. More precisely, we introduce the concepts of graded duo (weak and strong graded duo) modules and give some sources and an example for these types of modules. It is seen that, under some condition, graded duo property is a local property in this category. When the ring [Formula: see text] is a discrete graded valuation ring with unique [Formula: see text]maximal ideal [Formula: see text], we see that these three types of graded (duo) modules are identical and give an explicit characterization of them, so that any graded duo modules over such a ring is of the form [Formula: see text] or [Formula: see text] for some positive integer [Formula: see text] and some integers [Formula: see text]. The same task is done whenever [Formula: see text] is a graded Dedekind domain. Finally, by an example, that provides a wide variety of strong graded duo modules, it was shown that the given characterizations do not hold valid if the ground ring is not Dedekind.

On graded (1,r)-ideals

Let [Formula: see text] be a group with identity element [Formula: see text] and [Formula: see text] be a commutative [Formula: see text]-graded ring with nonzero unity [Formula: see text]. In this paper, we introduce the graded version of [Formula: see text]-ideals which is a generalization of graded [Formula: see text]-ideals. A proper graded ideal [Formula: see text] of [Formula: see text] is said to be a graded [Formula: see text]-ideal if whenever [Formula: see text] for some nonunits homogeneous elements [Formula: see text], then either [Formula: see text] or [Formula: see text]. We investigate some basic properties of graded [Formula: see text]-ideals. We show that if [Formula: see text] admits a graded [Formula: see text]-ideal that is not a graded [Formula: see text]-ideal, then [Formula: see text] is a [Formula: see text]-graded local ring. Also, we give a method to construct graded [Formula: see text]-ideals that are not graded [Formula: see text]-ideals. Furthermore, we prove that [Formula: see text] is a graded total quotient ring if and only if every proper graded ideal of [Formula: see text] is graded [Formula: see text]-ideal and also we present a counterpart of prime avoidance lemma for graded [Formula: see text]-ideals. Finally, an idea is given about some graded [Formula: see text]-ideals of the ring of fractions and the idealization.

Rees algebras and generalized depth‐like conditions in prime characteristic

AbstractIn this paper, we address a question concerning nilpotent Frobenius actions on Rees algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke for Cohen–Macaulay singularities. This is achieved by introducing a depth‐like invariant which captures as special cases Lyubeznik's F‐depth and the generalized F‐depth from Maddox–Miller and is related to the generalized depth with respect to an ideal. We also describe several properties of this new invariant and identify a class of regular elements for which weak F‐nilpotence deforms.

Computation of Electric Field and Potential Distribution of 110KV Polymer Insulator

The electric field (E-Field) and potential distribution are more important in deciding the lifetime of the insulator. Different climate conditions and several pollution conditions lead to the deterioration and degradation of the insulator's properties, increasing the electric stress and exceeding the threshold value during long working conditions, leading to the failure of the insulator. This project mainly focuses on improving the reduction of electric stress by using different side positions of the corona ring an optimizing corona ring placement on a 110 kV AC transmission line composite insulator. The Corona ring plays a significant role in the reduction of electric stress. Analyze the performance of three different positions of the corona ring: HV and LV side, LV side, and HV side, and implement the three different optimizations in the Bobyqa, Nelder-Mead, and Cobyla optimizations to achieve uniform distribution. The results show that HV-side corona ring placement significantly reduces electric stress, and Bobyqa optimization greatly reduces electrical stress compared to other optimization techniques.

Design Optimization and Flashover Probability Evaluation of a 3 MV, 3.4-m-Diameter Four-Level Axial Vacuum Insulator Stacks for a 15 MA Z-Pinch Accelerator

A four-level axial insulator stack is designed for a 15 MA Z-pinch accelerator. The height and diameter are 1.5 m and 3.4 m. The two upper levels operate at 2.5 MV, while the two bottom levels operate at 3.0 MV. The insulator ring stages in series, the vacuum flares, and water flares are optimized in details. By reiterative optimizations, the two upper levels consist of five 5-cm-thick insulator rings and four 0.8-cm-thick grading rings. While the two bottom levels consist of six insulator rings and five grading rings with the same individual insulator and grading ring. The inductance of each level is 14.02 nH, 15.48 nH, 18.71 nH, and 20.88 nH, respectively. The equivalent inductance is 4.21nH with the four levels in parallel. The voltage variations from average for the four levels are within ±4.9%, ±4.9%, ±2.1%, and ±2.2%, respectively. At the average operating electric field of 100 kV/cm, the predicted flashover probability for the two upper level and the two bottom level insulator stacks are about 0.29% and 0.53%, respectively.

Optimal design of high voltage composite insulators with grading rings in different configurations

Reliability of high voltage composite insulators depends on achieving an optimal electrical and geometrical design that produces the lowest electric field strength. This paper proposes a method to find the optimal geometrical design of composite insulators for different voltage levels. The design variables of the insulators include dimensions and locations of sheds and grading rings, as well as physical properties of the insulators. One composite insulator with single grading ring and two with double grading rings are considered and optimized. Considering the complexity of modifying composite insulator parameters to find the lowest electric field strength, five different optimization algorithms are applied and compared to find the optimal geometric design. The main objective of these optimization algorithms to be minimized is the maximum electric field strength, which is calculated using the finite element method-based COMSOL Multiphysics. The results for three different composite insulators under study show that the particle swarm optimization (PSO) algorithm produces the best results in terms of optimal geometrical design to minimize the electric field strength. In addition, the optimal design can reduce not only the electric field strength in clean, uniform pollution and water droplets environmental conditions but also the creepage distance of composite insulators. These improvements in optimized models are achieved without introducing any additional consideration besides the optimal dimensions.

Optimal design of corona ring in composite insulator considering the effects of tower structure, conductor, hardware and mutual phases

One of the key elements in lowering the electric field intensity (EFI) on the creepage distance of composite insulators is the usage of the corona ring and its ideal design. First, using the Finite Element Method (FEM) in the 3D COMSOL Multiphysics program, this paper investigated and calculated the changes in the EFI of the creepage distance of the 230-kV composite insulator with and without taking into account the effects of the corona ring, tower structure, conductor, hardware, and mutual phases. Next, the ideal goal function is chosen in order to minimize the insulator creepage distance's maximal EFI. Nelder-Mead (NM) and Bound Optimization by Quadratic Approximation (BOBYQA), two optimization techniques, are used for the best design of corona ring parameters on the 230 kV insulator. Finally, the diameter, thickness, and installation position of the ideal corona ring are determined using the suggested methodologies and different restrictions. The obtained results demonstrate that, in contrast to previous studies that have only focused on a few of the aforementioned constraints, taking into account the tower structure, conductor, hardware, and mutual phases will have a significant impact on the distribution of the EFI on the insulator creepage distance.

Case Study: Optimizing Grading Ring Design for High Voltage Polymeric Insulators in Power Transmission Systems for Enhanced Electric Field and Voltage Distribution by Using a Finite Element Method

This research paper aims to investigate the optimal design of grading rings for high-voltage polymeric insulators in an actual power transmission system, with a focus on improving the electrical representation of the insulator strings. One such subsidiary accessory commonly used with porcelain and polymer insulator strings is the grading ring, which is employed to improve the electric field and voltage distribution surrounding the insulator string. The efficiency of insulator strings can be enhanced by grading rings, as they facilitate a more linear potential division along the strings. The design parameters of grading rings significantly influence their performance on insulator strings. In this study, we examine the optimal design of the grading rings of high-voltage polymer insulators, since no uniform design methodology has been developed for high-voltage polymer insulators, and their optimization is currently the subject of many research studies. The electric field on an outdoor polymeric insulator is examined using finite element method (FEM) software and COMSOL Multi-Physics program. A 2D model is utilized to simulate a 220 kV polymeric insulator. The effectiveness of high-voltage polymeric insulators greatly depends on the dimensions and locations of the grading rings. Therefore, the impacts of the radius of the grading ring and that of its tube and the tube’s vertical position are thoroughly investigated, under dry and humid conditions. To achieve this objective, a search algorithm is employed to adjust the dimensions and locations of the grading ring. The optimization approach in this study is based on determining the maximum electric field across the insulator surface, while ensuring that it remains below the corona initiation level.

Identity and Phenotypic Variability of a Passion Fruit Cultivar in Lucban, Quezon Province, Philippines

The passion fruit cultivar in Lucban, Quezon, Philippines is poorly described. To address this knowledge gap, this study characterized the phenotypic features and variability that exists in the plantation of passion fruit in Lucban. A total of 68 morpho-agronomic descriptors (32 quantitative and 36 qualitative) were used for the characterization. The results showed that the distinguishing characteristics of the cultivar were light green branch color, long and wide leaf with trilobate division and nectaries on the petiole, campanulate hypanthium, wavy corona filament, nectaries on the sepal, white color of the perianth and corona ring filaments with deep purple color at the base, and yellow peel and pulp color. Based on these characteristics, this study confirmed that the identity of the passion fruit cultivar is Passiflora edulis f. flavicarpa Degener. Some notable variants were observed – including purplish green branches, scarce anthocyanin on the reproductive parts, and fruit with oval fruit shape and lenticels arranged in a striated pattern. The scaled principal component analysis identified nine principal components (PCs) that explain at least 80% of the total variation in quantitative characters, whereas three PCs explain about 78% of the total variation in qualitative characters. Further characterization using molecular markers could be done to supplement the results of this study. Nevertheless, the results are significant for reintroduction, pre-breeding, and ex situ conservation of passion fruit germplasm.

On coefficient ideals

Let be a Cohen-Macaulay local ring of dimension with infinite residue field and let I be an primary ideal. Let For let be the ith-coefficient ideal of I. Also let denote the Ratliff-Rush closure of A. Let be the associated graded ring of I. We show that if for then for all . In particular if G is generalized Cohen-Macaulay then for all . As a consequence we get that if A is an analytically unramified domain with G generalized Cohen-Macaulay, then the -ification of the Rees algebra A[It] is .