Homomorphism and Isomorphism of Regular Power Ring

The upgrade of all kinds of algebraic structures has been emphasized with the development of fuzzy mathematics.The concept of hypergroup was raised first by Prof.LI Hong_xing in [1]and HX ring was done in [2].In this paper ,some properties of power ring and quasi_quotient ring are further studied based on paper [3～6].Especially,several theorems of homomorphism and isomorphism of regular power ring are established.

Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings

Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.

Weak M-Armendariz rings

For a monoid M, this paper introduces the weak M- Armendariz rings which are a common generalization of the M- Armendariz rings and the weak Armendariz rings, and investigates their properties. Moreover, this paper proves that： a ring R is weak M-Armendariz if and only if for any n, the n-by-n upper triangular matrix ring Tn （R） over R is weak M- Armendariz; if I is a semicommutative ideal of ring R such that R/I is weak M-Armendariz, then R is weak M-Armendariz, where M is a strictly totally ordered monoid; if a ring R is semicommutative and M-Armendariz, then R is weak M × N- Armendariz, where N is a strictly totally ordered monoid; a finitely generated Abelian group G is torsion-free if and only if there exists a ring R such that R is weak G-Armendariz.

On GP-V-rings and Characterizations of Strongly Regular Rings

The purpose of this paper is to characterize strongly regular rings via MERT rings and weakly one-sided ideals. Many important equivalent conditions on strongly regular rings are shown.

Enhancing efficiency and stability of organic solar cells through a simplified four-step synthesis of fully non-fused ring electron acceptor

Design and synthesis of superior cost-effective non-fullerene acceptors(NFAs)are still big challenges for facilitating the commercialization of organic solar cells(OSCs),yet to be realized.Herein,two medium bandgap fully non-fused ring electron acceptors(NFREAs,medium bandgap,i,e.,1,3-1,8 eV),namely PTR-2Cl and PTR-4Cl are synthesized with only four steps by using intramolecular noncovalent interaction central core,structured alkyl side chain orientation linking units and flanking with different electron-withdrawing end group.Among them,PTR-4C1 exhibits increased average electrostatic potential(ESP)difference with polymer donor,enhanced crystallinity and compactπ-πstacking compared with the control molecule PTR-2CI.As a result,the PTR-4Cl-based OSC achieved an impressive power conversion efficiency(PCE)of 14.72%,with a much higher open-circuit voltage(V_(OC))of 0.953 V and significantly improved fill factor(FF)of 0.758,demonstrating one of the best acceptor material in the top-performing fully NFREA-based OSCs with both high PCE and V_(OC).Notably,PTR-4Cl-based cells maintain a good T_80lifetime of its initial PCE after over 936 h under a continuous thermal annealing treatment and over1300 h T_(80)lifetime without encapsulation.This work provides a cost-effective design strategy for NFREAs on obtaining high V_(OC),efficient exciton dissociation,and ordered molecular packing and thus high-efficiency and stable OSCs.

MATRICES OVER A REDUCED RING AS SUMS OF THREE TRIPOTENTS

In this paper,we study reduced rings in which every element is a sum of three tripotents that commute,and determine the integral domains over which every n£n matrix is a sum of three tripotents.It is proved that for an integral domain R,every matrix in M_(n)(R)is a sum of three tripotents if and only if R■Zp with p=2,3,5 or 7.

Developing a novel big dataset and a deep neural network to predict the bearing capacity of a ring footing

The accurate prediction of the bearing capacity of ring footings,which is crucial for civil engineering projects,has historically posed significant challenges.Previous research in this area has been constrained by considering only a limited number of parameters or utilizing relatively small datasets.To overcome these limitations,a comprehensive finite element limit analysis(FELA)was conducted to predict the bearing capacity of ring footings.The study considered a range of effective parameters,including clay undrained shear strength,heterogeneity factor of clay,soil friction angle of the sand layer,radius ratio of the ring footing,sand layer thickness,and the interface between the ring footing and the soil.An extensive dataset comprising 80,000 samples was assembled,exceeding the limitations of previous research.The availability of this dataset enabled more robust and statistically significant analyses and predictions of ring footing bearing capacity.In light of the time-intensive nature of gathering a substantial dataset,a customized deep neural network(DNN)was developed specifically to predict the bearing capacity of the dataset rapidly.Both computational and comparative results indicate that the proposed DNN(i.e.DNN-4)can accurately predict the bearing capacity of a soil with an R2 value greater than 0.99 and a mean squared error(MSE)below 0.009 in a fraction of 1 s,reflecting the effectiveness and efficiency of the proposed method.

The Some Properties of Skew Polynomial Rings

This paper mainly studies some properties of skew polynomial ring related to Morita invariance, Armendariz and (quasi)-Baer. First, we show that skew polynomial ring has no Morita invariance by the counterexample. Then we prove a necessary condition that skew polynomial ring constitutes Armendariz ring. We lastly investigate that condition of skew polynomial ring is a (quasi)-Baer ring, and verify that the conditions is necessary, but not sufficient by example and counterexample.

Rising utilization of stable isotopes in tree rings for climate change and forest ecology

Analyses of stable isotopes(C,O,H)in tree rings are increasingly important cross-disciplinary programs.The rapid development in this field documented in an increasing number of publications requires a comprehensive review.This study includes a bibliometric analysis-based review to better understand research trends in tree ring stable isotope research.Overall,1475 publications were selected from the Web of Science Core Collection for 1974-2023.The findings are that:(1)numbers of annual publications and citations increased since 1974.From 1974 to 1980,there were around two relevant publications per year.However,from 2020 to 2022,this rose sharply to 109 publications per year.Likewise,average article citations were less than four per year before 1990,but were around four per article per year after 2000;(2)the major subjects using tree ring stable isotopes include forestry,geosciences,and environmental sciences,contributing to 42.5%of the total during 1974-2023;(3)the top three most productive institutions are the Chinese Academy of Sciences(423),the Swiss Federal Institute for Forest,Snow and Landscape Research(227),and the University of Arizona(204).These achievements result from strong collaborations;(4)review papers,for example,(Dawson et al.,Annu Rev Ecol Syst 33:507-559,2002)and(McCarroll and Loader,Quat Sci Rev 23:771-801,2004),are among the most cited,with more than 1000 citations;(5)tree ring stable isotope studies mainly focus on climatology and ecology,with atmospheric CO_(2) one of the most popular topics.Since 2010,precipitation and drought have received increasing attention.Based on this analysis,the research stages,key findings,debated issues,limitations and direc-tions for future research are summarized.This study serves as an important attempt to understand the progress on the use of stable isotopes in tree rings,providing scientific guid-ance for young researchers in this field.

On Weakly Semicommutative Rings

A ring R is said to be weakly semicommutative if for any a,b∈R, ab=0 implies aRb（？）Nil（R）,where Nil（R） is the set of all nilpotent elements in R. In this note,we clarify the relationship between weakly semicommutative rings and NI-rings by proving that the notion of a weakly semicommutative ring is a proper generalization of NI-rings.We say that a ring R is weakly 2-primal if the set of nilpotent elements in R coincides with its Levitzki radical,and prove that if R is a weakly 2-primal ring which satisfiesα-condition for an endomorphismαof R（that is,ab=0（？）aα（b）=0 where a,b∈R） then the skew polynomial ring R[x;α] is a weakly 2-primal ring,and that if R is a ring and I is an ideal of R such that I and R/I are both weakly semicommutative then R is weakly semicommutative. Those extend the main results of Liang et al.2007（Taiwan Residents J.Math.,11（5）（2007）, 1359-1368） considerably.Moreover,several new results about weakly semicommutative rings and NI-rings are included.

Extensions of McCoy Rings

A ring R is said to be right McCoy if the equation f（x）g（x） = 0, where y（x） and g（x） are nonzero polynomials of R[x], implies that there exists nonzero s E R such that f（x）s = 0. It is proven that no proper （triangular） matrix ring is one-sided McCoy. It is shown that for many polynomial extensions, a ring R is right Mccoy if and only if the polynomial extension over R is right Mccoy.

Supersemiprime Rings and Supersemiprime Radical

In this paper,supersemiprime ring is introduced,relations among the supersemiprime rings and the some rings around it are discussed,supersemiprime radical and its properties are studied.

Special Properties of Formal Triangular Matrix Rings

We consider the sufficient and necessary conditions for the formal triangular matrix ring being right minsymmetric, right DS, semicommutative, respectively.

Ore Extensions over Weakly 2-primal Rings

A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.

Some Characterizations of GVNL Rings

A ring R is called a GVNL-ring if a or 1-a is π-regular for every a∈R,as a common generalization of local and π-regular rings.It is proved that if R is a GVNL ring,then either(1-e)R(1-e) or eRe is a π-regular ring for every idempotent e of R.We prove that the center of a GVNL ring is also GVNL and every abelian GVNL ring is SGVNL.The formal power series ring R[x] is GVNL if and only if R is a local ring.

Generalized fuzzy ideals of near-rings

The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（∈,∈∨ q）-fuzzy subnear-rings（ideals） and（∈,∈∨q）-fuzzy subnear-rings（ideals） of near-rings are described.Finally,some characterization of [μ]t is given by means of（∈,∈∨ q）-fuzzy ideals.

Redefined generalized fuzzy ideals of near-rings

With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings, and discuss the relationship between strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals and prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings.

深水采油树Spring-Seal密封圈接触模型构建与实验测试

为提高深水采油树在高压、高温、低温等工况下长时间工作的稳定性,对采油树密封圈进行重新设计,提出Spring-Seal密封圈(以下简称S密封圈);基于赫兹接触理论、填料密封接触理论,重新构建S密封圈接触力学模型;建立有限元仿真分析模型,分析不同条件下S密封圈的密封性能,同时验证新建接触模型的合理性;利用实验测试S密封圈的实际密封效果。研究结果表明:S密封圈在高压、高温、低温等工况下能够长时间稳定工作且密封性能良好。研究结果可为S密封圈的接触研究及工程运用提供理论参考。

Dynamics of a rotating ring-stiffened sandwich conical shell with an auxetic honeycomb core

The free vibration analysis of a rotating sandwich conical shell with a reentrant auxetic honeycomb core and homogenous isotropic face layers reinforced with a ring support is studied.The shell is modeled utilizing the first-order shear deformation theory(FSDT)incorporating the relative,centripetal,and Coriolis accelerations alongside the initial hoop tension created by the rotation.The governing equations,compatibility conditions,and boundary conditions are attained using Hamilton’s principle.Utilizing trigonometric functions,an analytical solution is derived in the circumferential direction,and a numerical one is presented in the meridional direction via the differential quadrature method(DQM).The effects of various factors on the critical rotational speeds and forward and backward frequencies of the shell are studied.The present work is the first theoretical work regarding the dynamic analysis of a rotating sandwich conical shell with an auxetic honeycomb core strengthened with a ring support.

Winter-spring minimum temperature variations inferred from tree-ring δ^(13)C in southeastern China

Long-term temperature variations inferred from high-resolution proxies provide an important context to evaluate the intensity of current warming.However,tem-perature reconstructions in humid southeastern China are scarce and particularly lack long-term data,limiting us to obtain a complete picture of regional temperature evolution.In this study,we present a well-verified reconstruction of winter-spring(January–April)minimum temperatures over southeastern China based on stable carbon isotopic(δ^(13)C)records of tree rings from Taxus wallichiana var.mairei from 1860 to 2014.This reconstruction accounted for 56.4%of the total observed variance.Cold periods occurred during the 1860s–1910s and 1960s–1970s.Although temperatures have had an upward trend since the 1920s,most of the cold extremes were in recent decades.The El Niño-Southern Oscillation(ENSO)variance acted as a key modulator of regional winter-spring minimum temperature variability.However,teleconnections between them were a nonlinear process,i.e.,a reduced or enhanced ENSO variance may result in a weakened or intensified temperature-ENSO relationship.