AIM:To observe the effect of the plus power ring zone(PPRZ)area and distribution on myopia progression.METHODS:This retrospective study enrolled 137 pre-teens aged 8-12 at Taiyuan Aier Eye Hospital between 2019 and 20...AIM:To observe the effect of the plus power ring zone(PPRZ)area and distribution on myopia progression.METHODS:This retrospective study enrolled 137 pre-teens aged 8-12 at Taiyuan Aier Eye Hospital between 2019 and 2021.They were fitted with Ortho-K lenses for the first time due to refractive error,with a one-year follow-up period.To indicate the peripheral plus ring zone overlapping with the pupil zone(PPROPZ)accompanying PPRZ,participants were divided based on the PPROPZ to PPRZ ratio.The experimental group had 103 eyes with a PPROPZ to PPRZ ratio of≥0.2,and the control group had 103 eyes with a ratio of<0.2.Participants had a spherical diopter in the range of-6.00 D to-0.75 D,against-the-rule astigmatism less than 1.00 D,with-the-rule astigmatism less than 1.50 D,and corneal curvatures of 39.00 D to 46.00 D.They had a stable best corrected visual acuity of 0.10 LogMAR(20/25)or better when wearing orthokeratology(Ortho-K)lenses.PPRZ and PPROPZ were measured using ImageJ;corneal topography assessed corneal-related parameters,and an optical biometer measured the axial length of the eyes pre and post-one years of lens wear.RESULTS:Changes in axial length elongation were found to decrease when either the PPRZ(P<0.01)or PPROPZ(P<0.001)was increased significantly.The axial length growth was faster in the control group(0.37±0.2 mm)than in the experimental group(0.21±0.11 mm).Furthermore,we found that a larger horizontal visible iris diameter(HVID)corresponded to slower axial growth of the eye.In contrast,axial length growth showed no correlation with surface regularity index(SRI),surface asymmetry index(SAI),flat keratometry value(K_(f)),steep keratometry value(K_(s)).CONCLUSION:For orthokeratology,wearers with larger PPROPZ to PPRZ ratio usually experiences a reduction in axial length growth.The PPRZ and PPROPZ are negatively correlated with the axial length.Our findings provide a recommendation and methods for studying the myopia control mechanism through Ortho-K lenses.展开更多
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 thi...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.展开更多
In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power s...In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.展开更多
For a ring endomorphism α, in this paper we introduce the notion of s-power- serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this general...For a ring endomorphism α, in this paper we introduce the notion of s-power- serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this generalization are established, and the extensions of α- power-serieswise nil-Armendariz rings are investigated. Which generalizes the corresponding results of nil-Armendariz rings and power-serieswise nil-Armendariz rings.展开更多
Let R be a ring such that all left semicentral idempotents are central and （S, ≤） a strictly totally ordered monoid satisfying that 0 ≤s for all s ∈S. It is shown that [[R^S≤]], the ring of generalized power ser...Let R be a ring such that all left semicentral idempotents are central and （S, ≤） a strictly totally ordered monoid satisfying that 0 ≤s for all s ∈S. It is shown that [[R^S≤]], the ring of generalized power series with coefficients in R and exponents in S, is right p.q.Baer if and only if R is right p.q.Baer and any S-indexed subset of I（R） has a generalized join in I（R）, where I（R） is the set of all idempotents of R.展开更多
Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of genera...Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of generalized power series over M is a PS [[RS,≤]]-module.展开更多
Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]]...Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,（R） has a generalized join in S,（R）. Several known results follow as consequences of our results.展开更多
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 p...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.展开更多
随着人工智能大模型训练与推理业务的快速发展,智算中心面临算网协同调度的新挑战。为优化分布式智算Ring Allreduce业务的部署问题,首先,通过扩展传统波平面,开发了算力波平面技术,实现了算力与网络资源的一体化虚拟管理。然后,基于算...随着人工智能大模型训练与推理业务的快速发展,智算中心面临算网协同调度的新挑战。为优化分布式智算Ring Allreduce业务的部署问题,首先,通过扩展传统波平面,开发了算力波平面技术,实现了算力与网络资源的一体化虚拟管理。然后,基于算力波平面,提出了一种高效路由、波长、算力和时隙分配(routing,wavelength,computing power and time slot assignment,RWCTA)算法用于环规约(Ring Allreduce)业务部署。仿真结果表明,与传统基于波平面的部署算法相比,基于算力波平面的RWCTA算法能有效降低62.4%的总业务完成时间和54.5%的平均业务计算时间。展开更多
This paper demonstrated a high power and high beam quality diode-pumped 1319-nm Nd：YAG master oscillator-power amplifier laser system. A thermally near-unstable resonator with four-rod birefringence compensation fiat...This paper demonstrated a high power and high beam quality diode-pumped 1319-nm Nd：YAG master oscillator-power amplifier laser system. A thermally near-unstable resonator with four-rod birefringence compensation fiat-fiat cavity was adopted as the master oscillator. A solid etalon was inserted in the unidirectional ring resonator to compress the laser linewidth. Under a repetition rate of 500 Hz and pulse width of 160 μs, the master oscillator delivers an average output power of 16.8 W at 1319 nm with linear polarisation, beam quality factor M^2=1.16 and linewidth of 3.2 GHz. A double-pass power amplifier with two amplifier stages was employed for higher power scaling and the output power was amplified to be 25.9 W with M^2 = 1.43.展开更多
Let R be a finite chain ring with maximal ideal （7） and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = （C ： γ0） C_ （C： 7） C ... C_ （C： γ2） C_ ...Let R be a finite chain ring with maximal ideal （7） and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = （C ： γ0） C_ （C： 7） C ... C_ （C： γ2） C_ .-. C_ （C：γ^t-1） can be associated with C, where for any r C R, （C ： r） = {e C Rn I re E C}. Using generator elements of the projection of such a tower of codes to the residue field F, we characterize cyclic codes over R. This characterization turns the condition for codes over R to be cyclic into one for codes over the residue field F. Furthermore, we obtain a characterization of cyclic codes over the formal power series ring of a finite chain ring.展开更多
Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a an...Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs and such as connectivity, diameter, girth, clique numbers and planarity. We also study the cozero-divisor graphs of the direct products of two arbitrary commutative rings.展开更多
In this paper,the chaotic behaviors in an erbium-doped fiber（EDF） single-ring laser（EDFSRL） are investigated experimentally by using the loss modulation method.An electro-optic modulator（EOM） made of LiNbO 3 cry...In this paper,the chaotic behaviors in an erbium-doped fiber（EDF） single-ring laser（EDFSRL） are investigated experimentally by using the loss modulation method.An electro-optic modulator（EOM） made of LiNbO 3 crystal is added to the system.Thus,by changing the modulation voltage and the modulation frequency of the EOM,the freedom of the EDFSRL system is increased.The chaotic characteristics of the system are studied by observing the time series and the power spectra.The experimental results indicate that the erbium-doped fiber single-ring laser system can enter into chaos states through period-doubling bifurcation and intermittency routes.展开更多
文摘AIM:To observe the effect of the plus power ring zone(PPRZ)area and distribution on myopia progression.METHODS:This retrospective study enrolled 137 pre-teens aged 8-12 at Taiyuan Aier Eye Hospital between 2019 and 2021.They were fitted with Ortho-K lenses for the first time due to refractive error,with a one-year follow-up period.To indicate the peripheral plus ring zone overlapping with the pupil zone(PPROPZ)accompanying PPRZ,participants were divided based on the PPROPZ to PPRZ ratio.The experimental group had 103 eyes with a PPROPZ to PPRZ ratio of≥0.2,and the control group had 103 eyes with a ratio of<0.2.Participants had a spherical diopter in the range of-6.00 D to-0.75 D,against-the-rule astigmatism less than 1.00 D,with-the-rule astigmatism less than 1.50 D,and corneal curvatures of 39.00 D to 46.00 D.They had a stable best corrected visual acuity of 0.10 LogMAR(20/25)or better when wearing orthokeratology(Ortho-K)lenses.PPRZ and PPROPZ were measured using ImageJ;corneal topography assessed corneal-related parameters,and an optical biometer measured the axial length of the eyes pre and post-one years of lens wear.RESULTS:Changes in axial length elongation were found to decrease when either the PPRZ(P<0.01)or PPROPZ(P<0.001)was increased significantly.The axial length growth was faster in the control group(0.37±0.2 mm)than in the experimental group(0.21±0.11 mm).Furthermore,we found that a larger horizontal visible iris diameter(HVID)corresponded to slower axial growth of the eye.In contrast,axial length growth showed no correlation with surface regularity index(SRI),surface asymmetry index(SAI),flat keratometry value(K_(f)),steep keratometry value(K_(s)).CONCLUSION:For orthokeratology,wearers with larger PPROPZ to PPRZ ratio usually experiences a reduction in axial length growth.The PPRZ and PPROPZ are negatively correlated with the axial length.Our findings provide a recommendation and methods for studying the myopia control mechanism through Ortho-K lenses.
文摘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.
文摘In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.
文摘For a ring endomorphism α, in this paper we introduce the notion of s-power- serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this generalization are established, and the extensions of α- power-serieswise nil-Armendariz rings are investigated. Which generalizes the corresponding results of nil-Armendariz rings and power-serieswise nil-Armendariz rings.
基金TRAPOYT(200280)the Cultivation Fund(704004)of the Key Scientific and Technical Innovation Project,Ministry of Education of China
文摘Let R be a ring such that all left semicentral idempotents are central and （S, ≤） a strictly totally ordered monoid satisfying that 0 ≤s for all s ∈S. It is shown that [[R^S≤]], the ring of generalized power series with coefficients in R and exponents in S, is right p.q.Baer if and only if R is right p.q.Baer and any S-indexed subset of I（R） has a generalized join in I（R）, where I（R） is the set of all idempotents of R.
基金The NNSF (10171082) of China and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, P.R.C.
文摘Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of generalized power series over M is a PS [[RS,≤]]-module.
基金The Youth Foundation(QN2012-14)of Hexi University
文摘Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,（R） has a generalized join in S,（R）. Several known results follow as consequences of our results.
文摘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.
文摘随着人工智能大模型训练与推理业务的快速发展,智算中心面临算网协同调度的新挑战。为优化分布式智算Ring Allreduce业务的部署问题,首先,通过扩展传统波平面,开发了算力波平面技术,实现了算力与网络资源的一体化虚拟管理。然后,基于算力波平面,提出了一种高效路由、波长、算力和时隙分配(routing,wavelength,computing power and time slot assignment,RWCTA)算法用于环规约(Ring Allreduce)业务部署。仿真结果表明,与传统基于波平面的部署算法相比,基于算力波平面的RWCTA算法能有效降低62.4%的总业务完成时间和54.5%的平均业务计算时间。
基金Project supported by the National High Technology Research and Development Program and the National Natural Science Foundation of China (Grant No. 60508013)
文摘This paper demonstrated a high power and high beam quality diode-pumped 1319-nm Nd：YAG master oscillator-power amplifier laser system. A thermally near-unstable resonator with four-rod birefringence compensation fiat-fiat cavity was adopted as the master oscillator. A solid etalon was inserted in the unidirectional ring resonator to compress the laser linewidth. Under a repetition rate of 500 Hz and pulse width of 160 μs, the master oscillator delivers an average output power of 16.8 W at 1319 nm with linear polarisation, beam quality factor M^2=1.16 and linewidth of 3.2 GHz. A double-pass power amplifier with two amplifier stages was employed for higher power scaling and the output power was amplified to be 25.9 W with M^2 = 1.43.
基金supported by the Natural Science Foundation of Hubei Province (B20114410)the Natural Science Foundation of Hubei Polytechnic University (12xjz14A)
文摘Let R be a finite chain ring with maximal ideal （7） and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = （C ： γ0） C_ （C： 7） C ... C_ （C： γ2） C_ .-. C_ （C：γ^t-1） can be associated with C, where for any r C R, （C ： r） = {e C Rn I re E C}. Using generator elements of the projection of such a tower of codes to the residue field F, we characterize cyclic codes over R. This characterization turns the condition for codes over R to be cyclic into one for codes over the residue field F. Furthermore, we obtain a characterization of cyclic codes over the formal power series ring of a finite chain ring.
文摘Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs and such as connectivity, diameter, girth, clique numbers and planarity. We also study the cozero-divisor graphs of the direct products of two arbitrary commutative rings.
基金Project supported by the Science and Technology Development Program of Jilin Province,China (Grant No. 20090309)
文摘In this paper,the chaotic behaviors in an erbium-doped fiber（EDF） single-ring laser（EDFSRL） are investigated experimentally by using the loss modulation method.An electro-optic modulator（EOM） made of LiNbO 3 crystal is added to the system.Thus,by changing the modulation voltage and the modulation frequency of the EOM,the freedom of the EDFSRL system is increased.The chaotic characteristics of the system are studied by observing the time series and the power spectra.The experimental results indicate that the erbium-doped fiber single-ring laser system can enter into chaos states through period-doubling bifurcation and intermittency routes.
