Graded Ring Research Articles

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.

Graded rings associated to valuations and direct limits

In this paper, we study the structure of the graded ring associated to a limit key polynomial Qn in terms of the key polynomials that define Qn. In order to do that, we use direct limits. In general, we describe the direct limit of a family of graded rings associated to a totally ordered set of valuations. As an example, we describe the graded ring associated to a valuation-algebraic valuation as a direct limit of graded rings associated to residue-transcendental valuations.

On properties of graded rings and graded modules

Let R be a G-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded rings. Also, we study the concept of weakly crossed products and study some properties defined on weakly crossed product and give the relationship between this new concept and several properties of graded rings. Moreover, in this article, we give a generalization for the concept of graded essential submodules, and introduce the concept of graded semi-uniform modules which is a generalization for the concept of graded uniform modules.

The Varchenko-Gel'fand ring of a cone

For a hyperplane arrangement in a real vector space, the coefficients of its Poincaré polynomial have many interpretations. An interesting one is provided by the Varchenko-Gel'fand ring, which is the ring of functions from the chambers of the arrangement to the integers with pointwise addition and multiplication. Varchenko and Gel'fand gave a simple presentation for this ring, along with a filtration and associated graded ring whose Hilbert series is the Poincaré polynomial. We generalize these results to cones defined by intersections of halfspaces of some of the hyperplanes and prove a novel result for the Varchenko-Gel'fand ring of an arrangement: when the arrangement is supersolvable the associated graded ring of the arrangement is Koszul.

The reduction number of stretched ideals

The homological property of the associated graded ring of an ideal is an important problem in commutative algebra and algebraic geometry. In this paper we explore the almost Cohen–Macaulayness of the associated graded ring of stretched $\mathfrak{m}$-primary ideals in the case where the reduction number attains almost minimal value in a Cohen–Macaulay local ring $(A,\mathfrak{m})$. As an application, we present complete descriptions of the associated graded ring of stretched $\mathfrak{m}$-primary ideals with small reduction number.

MR Imaging Findings of Carcinoma Ex Pleomorphic Adenoma Related to Extracapsular Invasion and Prognosis.

MR imaging can reflect the pathologic progression of carcinoma ex pleomorphic adenoma (CXPA). This study aimed to identify the imaging findings related to extracapsular invasion of CXPA. Additionally, the pathologic background of these findings was investigated. This retrospective study included 37 patients with histologically confirmed CXPA. Three radiologists independently evaluated whether the CXPA showed the following characteristic MR imaging findings: border, capsule, the corona sign on fat-saturated T2WI and contrast-enhanced fat-saturated T1WI, and the black ring sign. The corona sign appeared larger on fat-saturated and/or contrast-enhanced fat-saturated T1WI than on T1WI. The black ring sign was defined as an intratumoral nodule with a thick low-intensity rim on T2WI. Interreader agreement of the visual assessment was performed using κ analysis, and MR imaging and histopathologic findings were also correlated. Kaplan-Meier survival and the log-rank test were used to estimate the 3-year disease-free survival. MR imaging findings, especially peritumoral findings, showed a significant difference between invasive and noninvasive CXPA. The reliability was poor for the border and capsule. In contrast, it was good for the corona sign on fat-saturated and contrast-enhanced fat-saturated T1WI and the black ring sign. Pathologically, the corona sign reflected the invasiveness of the tumor and inflammatory cells, while the black ring sign reflected hyalinization or fibrosis. The corona sign also showed a significant difference in the 3-year disease-free survival. MR imaging findings, including the corona and black ring signs, reliably differentiated invasive and noninvasive CXPA. The corona sign can be used as a prognostic factor for CXPA.

Optimal design configuration of corona rings for 1200 KV bus post insulators

Estimation and regulation of the electric field stresses at ultra-high voltage levels are vital to achieve the reliable power system operation. Designing of the sustainable ultra-high potential equipment’s are the major challenge for the design engineers to satisfy the modified power demand scenario. The substation bus post insulator is the one of the key devices supports to achieve the sustainable and reliable power system operation. The severe problem in designing of the station post insulator at ultra-high potential ratings is its field stresses. To control these severe field stresses, significant electrodes like bus conductors, toroid rings, grading rings and corona rings are essential. The appropriate selection of these high potential electrode dimensions supports the optimal economic power system operation: failure reports the catastrophic behaviour of the station bus post insulators. Hence, the significant research knowledge on optimal size of high potential electrodes of substation bus post insulators at Extra and ultra-high potential levels is necessary before designing of these high voltage electrodes. Usually, it is a tedious process to attain the optimal design dimensions and its positions of the high potential electrodes in the actual field. Thus, the sophisticated numerical analysis-based simulation studies provide significant support to obtain the optimal size of high potential electrodes of bus post insulators at ultra- high potential ratings. Therefore, this paper aims to present the numerical based simulation design and its study of the high potential electrodes of the 1200 kV substation bus post insulator. Multiple design configurations of the electrodes like various corona ring, grading ring, bus conductor diameters and its positions are considered and compared to analyse the effect of the electrical stress, potential distribution variation of the 1200 kV bus post insulator. Therefore, from the simulation investigations, the optimal design data configuration of high potential electrodes for 1200 kV substation bus post insulator was suggested. Also, the high voltage electrode design configuration of proposed 1200 kV insulator followed by the one of the manufacturing industries is tested and compared.

Finite generation for valuations computing stability thresholds and applications to K-stability

We prove that on any log Fano pair of dimension $n$ whose stability threshold is less than $\frac{n+1}{n}$, any valuation computing the stability threshold has a finitely generated associated graded ring. Together with earlier works, this implies that (a) a log Fano pair is uniformly K-stable (resp. reduced uniformly K-stable) if and only if it is K-stable (resp. K-polystable); (b) the K-moduli spaces are proper and projective; and combining with the previously known equivalence between the existence of Kähler-Einstein metric and reduced uniform K-stability proved by the variational approach, (c) the Yau-Tian-Donaldson conjecture holds for general (possibly singular) log Fano pairs.

Cohen-Macaulay local rings with e2 = e1 − e + 1

In this paper we study Cohen-Macaulay local rings of dimension d, multiplicity e and second Hilbert coefficient e2 in the case e2=e1−e+1. Let h=μ(m)−d. If e2≠0 then in our case we can prove that type(A)≥e−h−1. If type(A)=e−h−1 then we show that the associated graded ring G(A) is Cohen-Macaulay. In the next case when type(A)=e−h we determine all possible Hilbert series of A. In this case we show that depthG(A) completely determines the Hilbert Series of A.

Lim Ulrich sequences and Lech’s conjecture

The long standing Lech’s conjecture in commutative algebra states that for a flat local extension \((R,\mathfrak {m})\rightarrow (S,\mathfrak {n})\) of Noetherian local rings, we have an inequality on the Hilbert–Samuel multiplicities: \(e(R)\le e(S)\). In general the conjecture is wide open when \(\dim R>3\), even in equal characteristic. In this paper, we prove Lech’s conjecture in all dimensions, provided \((R,\mathfrak {m})\) is a standard graded ring over a perfect field localized at the homogeneous maximal ideal. We introduce the notions of lim Ulrich and weakly lim Ulrich sequences. Roughly speaking these are sequences of finitely generated modules that are not necessarily Cohen–Macaulay, but asymptotically behave like Ulrich modules. We prove that the existence of these sequences imply Lech’s conjecture. Though the existence of Ulrich modules is known in very limited cases, we construct weakly lim Ulrich sequences for all standard graded domains over perfect fields of positive characteristic.

Commutative graded-$n$-coherent and graded valuation rings

Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading commutative monoid $G$. For each positive integer, the notions of a graded-n-coherent module and a graded-n-coherent ring are introduced. In this paper many results are generalized from $n$-coherent rings to graded-$n$-coherent rings. In the last section, we provide necessary and sufficient conditions for the graded trivial extension ring to be a graded-valuation ring.

A generalization of graded prime hyperideals over graded multiplicative hyperrings

Let [Formula: see text] be a group with identity [Formula: see text] and [Formula: see text] be a graded multiplicative hyperring. In this paper, we introduce and study the notion of graded [Formula: see text]-absorbing hyperideals of [Formula: see text] as a generalization of prime hyperideals. Many properties, examples and characterizations of graded [Formula: see text]-absorbing hyperideals of [Formula: see text] are introduced. Moreover, we investigate the behavior of this structure under homogeneous components, graded hyperring homomorphisms, Cartesian product and fundamental relations. We consider the fundamental relation [Formula: see text] on [Formula: see text] as the smallest equivalence relation such that the quotient [Formula: see text] is a ring. Also, we show that if [Formula: see text] is a graded hyperring, then [Formula: see text] is a graded ring.

Graded Weakly 2-Absorbing Ideals over Non-Commutative Graded Rings

Let G be a group and R be a G-graded ring. In this paper, we present and examine the concept of graded weakly 2-absorbing ideals as in generality of graded weakly prime ideals in a graded ring which is not commutative, and demonstrates that the symmetry is obtained as a lot of the outcomes in commutative graded rings remain in graded rings that are not commutative.

K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories

We build on previous work on multirings ([17]) that providesgeneralizations of the available abstract quadratic forms theories (specialgroups and real semigroups) to the context of multirings ([10], [14]). Herewe raise one step in this generalization, introducing the concept of pre-specialhyperfields and expand a fundamental tool in quadratic forms theory to themore general multivalued setting: the K-theory. We introduce and developthe K-theory of hyperbolic hyperfields that generalize simultaneously Milnor’sK-theory ([11]) and Special Groups K-theory, developed by Dickmann-Miraglia ([5]). We develop some properties of this generalized K-theory, thatcan be seen as a free inductive graded ring, a concept introduced in [2] inorder to provide a solution of Marshall’s Signature Conjecture.

Dimension Theory in Iterated Local Skew Power Series Rings

Many well-known local rings, including soluble Iwasawa algebras and certain completed quantum algebras, arise naturally as iterated skew power series rings. We calculate their Krull and global dimensions, obtaining lower bounds to complement the upper bounds obtained by Wang. In fact, we show that many common such rings obey a stronger property, which we call triangularity, and which allows us also to calculate their classical Krull dimension (prime length). Finally, we correct an error in the literature regarding the associated graded rings of general iterated skew power series rings, but show that triangularity is enough to recover this result.

Transmission Line Object Detection Method Based on Label Adaptive Allocation

Inspection of the integrality of components and connecting parts is an important task to maintain safe and stable operation of transmission lines. In view of the fact that the scale difference of the auxiliary component in a connecting part is large and the background environment of the object is complex, a one-stage object detection method based on the enhanced real feature information and the label adaptive allocation is proposed in this study. Based on the anchor-free detection algorithm FCOS, this method is optimized by expanding the real feature information of the adjacent feature layer fusion and the semantic information of the deep feature layer, as well as adaptively assigning the label through the idea of pixel-by-pixel detection. In addition, the grading ring image is sliced in original data to improve the proportion of bolts in the dataset, which can clear the appearance features of small objects and reduce the difficulty of detection. Experimental results show that this method can eliminate the background interference in the GT (ground truth) as much as possible in object detection process, and improve the detection accuracy for objects with a narrow shape and small size. The evaluation index AP (average precision) increased by 4.1%. Further improvement of detection accuracy lays a foundation for the realization of efficient real-time patrol inspection.

Topology optimization for a station class surge arrester model

AbstractHigh‐voltage stress can cause partial discharges, which in turn result in deterioration of high‐voltage equipment, and hence, in increased maintenance costs. To this end, corona rings are used as means to capacitive field‐grading. In this work, topology optimization is employed for designing alternative layouts for capacitive field‐grading in a station class surge arrester. The objective of the formulated optimization problem is to homogenize the electric field strength along the axis of symmetry of the considered surge arrester. The resulting layout exhibits an improved electric field strength homogeneity profile, when compared to the standard IEC60099‐4:2004 design.

Preclinical safety study of a fully implantable, sub-scalp ring electrode array for long-term EEG recordings

Objective. Long-term electroencephalogram (EEG) recordings can aid diagnosis and management of various neurological conditions such as epilepsy. In this study we characterize the safety and stability of a clinical grade ring electrode arrays by analyzing EEG recordings, fluoroscopy, and computed tomography (CT) imaging with long-term implantation and histopathological tissue response. Approach. Seven animals were chronically implanted with EEG recording array consisting of four electrode contacts. Recordings were made bilaterally using a bipolar longitudinal montage. The array was connected to a fully implantable micro-processor controlled electronic device with two low-noise differential amplifiers and a transmitter-receiver coil. An external wearable was used to power, communicate with the implant via an inductive coil, and store the data. The sub-scalp electrode arrays were made using medical grade silicone and platinum. The electrode arrays were tunneled in the subgaleal cleavage plane between the periosteum and the overlying dermis. These were implanted for 3–7 months before euthanasia and histopathological assessment. EEG and impedance were recorded throughout the study. Main results. Impedance measurements remained low throughout the study for 11 of 12 channels over the recording period ranged from 3 to 5 months. There was also a steady amplitude of slow-wave EEG and chewing artifact (noise). The post-mortem CT and histopathology showed the electrodes remained in the subgaleal plane in 6 of 7 sheep. There was minimal inflammation with a thin fibrotic capsule that ranged from 4 to 101 μm. There was a variable fibrosis in the subgaleal plane extending from 210 to 3617 μm (S3–S7) due to surgical cleavage. One sheep had an inflammatory reaction due to electrode extrusion. The passive electrode array extraction force was around 1 N. Significance. Results show sub-scalp electrode placement was safe and stable for long term implantation. This is advantageous for diagnosis and management of neurological conditions where long-term, EEG monitoring is required.