scholarly journals Duo property for rings by the quasinilpotent perspective

2021 ◽  
Vol 13 (2) ◽  
pp. 485-500
Author(s):  
A. Harmanci ◽  
Y. Kurtulmaz ◽  
B. Ungor
Keyword(s):  
Stable Range ◽  
Exchange Ring ◽  
Series Ring

In this paper, we focus on the duo ring property via quasinilpotent elements, which gives a new kind of generalizations of commutativity. We call this kind of rings qnil-duo. Firstly, some properties of quasinilpotents in a ring are provided. Then the set of quasinilpotents is applied to the duo property of rings, in this perspective, we introduce and study right (resp., left) qnil-duo rings. We show that this concept is not left-right symmetric. Among others, it is proved that if the Hurwitz series ring $H(R; \alpha)$ is right qnil-duo, then $R$ is right qnil-duo. Every right qnil-duo ring is abelian. A right qnil-duo exchange ring has stable range 1.

scholarly journals Exchange rings having stable range one

2001 ◽  
Vol 25 (12) ◽  
pp. 763-770 ◽  
Author(s):  
Huanyin Chen
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Stable Range ◽  
Exchange Ring ◽  
Stable Range One ◽  
Exchange Rings

We investigate the sufficient conditions and the necessary conditions on an exchange ringRunder whichRhas stable range one. These give nontrivial generalizations of Theorem 3 of V. P. Camillo and H.-P. Yu (1995), Theorem 4.19 of K. R. Goodearl (1979, 1991), Theorem 2 of R. E. Hartwig (1982), and Theorem 9 of H.-P. Yu (1995).

Special properties of differential inverse power series rings

2016 ◽  
Vol 15 (10) ◽  
pp. 1650181 ◽  
Author(s):  
K. Paykan ◽  
A. Moussavi
Keyword(s):  
Power Series ◽  
Triangular Matrix ◽  
Inverse Power ◽  
Stable Range ◽  
Power Series Ring ◽  
Series Ring ◽  
Stable Range One ◽  
Derivation Formula ◽  
Power Series Rings ◽  
Generalized Triangular Matrix Representation

In this paper, we continue to study the differential inverse power series ring [Formula: see text], where [Formula: see text] is a ring equipped with a derivation [Formula: see text]. We characterize when [Formula: see text] is a local, semilocal, semiperfect, semiregular, left quasi-duo, (uniquely) clean, exchange, right stable range one, abelian, projective-free, [Formula: see text]-ring, respectively. Furthermore, we prove that [Formula: see text] is a domain satisfying the [Formula: see text] on principal left ideals if and only if so does [Formula: see text]. Also, for a piecewise prime ring (PWP) [Formula: see text] we determine a large class of the differential inverse power series ring [Formula: see text] which have a generalized triangular matrix representation for which the diagonal rings are prime. In particular, it is proved that, under suitable conditions, if [Formula: see text] has a (flat) projective socle, then so does [Formula: see text]. Our results extend and unify many existing results.

scholarly journals When is a power series ring n-root closed?

1997 ◽  
Vol 114 (2) ◽  
pp. 111-131 ◽  
Author(s):  
David F. Anderson ◽  
David E. Dobbs ◽  
Moshe Roitman
Keyword(s):  
Power Series ◽  
Power Series Ring ◽  
Series Ring

Evaluation of Non-Vibrating Utility Burner/Furnace Systems for Resistance to Thermoacoustic Oscillations

2006 ◽  
Author(s):  
Frantisek L. Eisinger ◽  
Robert E. Sullivan
Keyword(s):  
Design Process ◽  
Axial Direction ◽  
Stability Diagram ◽  
Stable Range ◽  
Design Engineers ◽  
Secondary Role ◽  
The Stability ◽  
Thermoacoustic Oscillations

Six burner/furnace systems which operated successfully without vibration are evaluated for resistance to thermoacoustic oscillations. The evaluation is based on the Rijke and Sondhauss models representing the combined burner/furnace (cold/hot) thermoacoustic systems. Frequency differences between the lowest vulnerable furnace acoustic frequencies in the burner axial direction and those of the systems’ Rijke and Sondhauss frequencies are evaluated to check for resonances. Most importantly, the stability of the Rijke and Sondhauss models is checked against the published design stability diagram of Eisinger [1] and Eisinger and Sullivan [2]. It is shown that the resistance to thermoacoustic oscillations is adequately defined by the published design stability diagram to which the evaluated cases generally adhere. Once the system falls into the stable range, the frequency differences or resonances appear to play only a secondary role. It is concluded, however, that in conjunction with stability, the primary criterion, sufficient frequency separations shall also be maintained in the design process to preclude resonances. The paper provides sufficient details to aid the design engineers.

Constraining Neoproterozoic subtropical low-level clouds to assess the plausibility of near-Snowball Earth states

2021 ◽  
Author(s):  
Christoph Braun ◽  
Aiko Voigt ◽  
Johannes Hörner ◽  
Joaquim G. Pinto
Keyword(s):  
Sea Ice ◽  
Climate Models ◽  
Global Climate ◽  
Global Climate Models ◽  
Mixed Phase ◽  
Snowball Earth ◽  
Stable Range ◽  
Climate Regime ◽  
Low Level ◽  
Mixed Phase Clouds

<p>Stable waterbelt climate states with close to global ice cover challenge the classical Snowball Earth hypothesis because they provide a robust explanation for the survival of advanced marine species during the Neoproterozoic glaciations (1000 – 541 Million years ago). Whether Earth’s climate stabilizes in a waterbelt state or rushes towards a Snowball state is determined by the magnitude of the ice-albedo feedback in the subtropics, where dark, bare sea ice instead of snow-covered sea ice prevails. For a given bare sea-ice albedo, the subtropical ice-albedo feedback and thus the stable range of the waterbelt climate regime is sensitive to the albedo over ice-free ocean, which is largely determined by shortwave cloud-radiative effects (CRE). In the present-day climate, CRE are known to dominate the spread of climate sensitivity across global climate models. We here study the impact of uncertainty associated with CRE on the existence of geologically relevant waterbelt climate regimes using two global climate models and an idealized energy balance model. We find that the stable range of the waterbelt climate regime is very sensitive to the abundance of subtropical low-level mixed-phase clouds. If subtropical cloud cover is low, climate sensitivity becomes so high as to inhibit stable waterbelt states.</p><p>The treatment of mixed-phase clouds is highly uncertain in global climate models. Therefore we aim to constrain the uncertainty associated with their CRE by means of a hierarchy of global and regional simulations that span horizontal grid resolutions from 160 km to 300m, and in particular include large eddy simulations of subtropical mixed-phase clouds located over a low-latitude ice edge. In the cold waterbelt climate subtropical CRE arise from convective events caused by strong meridional temperature gradients and stratocumulus decks located in areas of large-scale descending motion. We identify the latter to dominate subtropical CRE and therefore focus our large eddy simulations on subtropical stratocumulus clouds. By conducting simulations with two extreme scenarios for the abundance of atmospheric mineral dust, which serves as ice-nucleating particles and therefore can control mixed-phase cloud physics, we aim to estimate the possible spread of CRE associated with subtropical mixed-phase clouds. From this estimate we may assess whether Neoproterozoic low-level cloud abundance may have been high enough to sustain a stable waterbelt climate regime.</p>

Arithmetic of matrices over rings

2021 ◽  
Author(s):  
V.P. Shchedryk ◽  
Keyword(s):  
Graduate Students ◽  
Normal Form ◽  
Matrix Factorization ◽  
Ring Theory ◽  
Stable Range ◽  
Matrix Rings ◽  
Principal Ideals ◽  
Factorization Theory ◽  
Close Relationship ◽  
The Matrix

The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals do- mains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a close relationship between the matrix factorization and specific properties of subgroups of the complete linear group and the special normal form of matrices with respect to unilateral equivalence. The properties of matrices over rings of stable range 1.5 are thoroughly studied. The book is intended for experts in the ring theory and linear algebra, senior and post-graduate students.

scholarly journals Accommodative Haptics Study Based on Flexible Amplification Mechanism

2020 ◽  
pp. 1-7
Author(s):  
Wenjing Wang ◽  
Qiuyue Du ◽  
Wenjing Chen ◽  
Bin Tian ◽  
Wenjing Wang
Keyword(s):  
Measurement Data ◽  
Theoretical Method ◽  
Structural Features ◽  
Stable Range ◽  
Element Analysis ◽  
Output Displacement ◽  
Amplification Ratio ◽  
Motion Trajectories ◽  
Bridge Type ◽  
Lens Power

In this study, we take the effect of the anterior movement of the optic into account and propose a novel haptic based on lever-type and bridge-type flexible amplification mechanisms. Based on the consideration of the offset of the rotation center of the flexible hinge, we have deduced the formula for calculating the amplification ratio of the proposed four-stage amplifier. The geometric parameters and the material property parameters, in terms of the clinical measurement data of the human eye, are assumed to restrain the structural features and motion trajectories for the amplifier. As the ciliary muscle achieves the contraction limit, the output displacement and amplification ratio reach the highest and lowest values, separately, and gradually approach a stable range. The amplification ratio of formula calculation and FEA (Finite Element Analysis) are around 18.86 and 17.79, respectively, with the input displacement ranging from 0.115mm to 0.127mm. The error of the amplification ratio between theoretical method and FEA is less than 5%. The presented haptic acting as a four-stage displacement amplifier, enables an improved lens power of 3.80 diopters to obtain much more focus shift to achieve a better near visual performance for patients.

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