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Статті в журналах з теми "Torsion pairs"

Автор: Grafiati

Опубліковано: 11 березня 2023

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1

Bravo, Daniel, and Carlos E. Parra. "tCG torsion pairs." Journal of Algebra and Its Applications 18, no. 07 (July 2019): 1950127. http://dx.doi.org/10.1142/s0219498819501275.

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Анотація:

We investigate conditions when the [Formula: see text]-structure of Happel–Reiten–Smalø associated to a torsion pair is a compactly generated [Formula: see text]-structure. The concept of a [Formula: see text]CG torsion pair is introduced and for any ring [Formula: see text], we prove that [Formula: see text] is a [Formula: see text]CG torsion pair in [Formula: see text] if, and only if, there exists, [Formula: see text] a set of finitely presented [Formula: see text]-modules in [Formula: see text], such that [Formula: see text]. We also show that every [Formula: see text]CG torsion pair is of finite type, and show that the reciprocal is not true. Finally, we give a precise description of the [Formula: see text]CG torsion pairs over Noetherian rings and von Neumman regular rings.

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2

Kerner, Otto. "Reduced torsion pairs." Journal of Pure and Applied Algebra 220, no. 2 (February 2016): 802–9. http://dx.doi.org/10.1016/j.jpaa.2015.07.017.

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3

Assem, Ibrahim, and Otto Kerner. "Constructing Torsion Pairs." Journal of Algebra 185, no. 1 (October 1996): 19–41. http://dx.doi.org/10.1006/jabr.1996.0310.

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4

Fan, Chunyan, and Hailou Yao. "Torsion Pairs in Triangulated Categories." Advances in Pure Mathematics 03, no. 03 (2013): 374–79. http://dx.doi.org/10.4236/apm.2013.33054.

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5

Zhou, Panyue, Jinde Xu, and Baiyu Ouyang. "Torsion Pairs in Stable Categories." Communications in Algebra 43, no. 8 (June 4, 2015): 3498–514. http://dx.doi.org/10.1080/00927872.2014.927686.

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6

Angeleri Hügel, Lidia, Frederik Marks, and Jorge Vitória. "Torsion pairs in silting theory." Pacific Journal of Mathematics 291, no. 2 (September 14, 2017): 257–78. http://dx.doi.org/10.2140/pjm.2017.291.257.

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7

Holm, Thorsten, Peter Jørgensen, and Martin Rubey. "Torsion pairs in cluster tubes." Journal of Algebraic Combinatorics 39, no. 3 (June 14, 2013): 587–605. http://dx.doi.org/10.1007/s10801-013-0457-6.

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8

Banerjee, Abhishek. "On Auslander’s formula and cohereditary torsion pairs." Communications in Contemporary Mathematics 20, no. 06 (August 27, 2018): 1750071. http://dx.doi.org/10.1142/s0219199717500717.

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Анотація:

For a small abelian category [Formula: see text], Auslander’s formula allows us to express [Formula: see text] as a quotient of the category [Formula: see text] of coherent functors on [Formula: see text]. We consider an abelian category with the added structure of a cohereditary torsion pair [Formula: see text]. We prove versions of Auslander’s formula for the torsion-free class [Formula: see text] of [Formula: see text], for the derived torsion-free class [Formula: see text] of the triangulated category [Formula: see text] as well as the induced torsion-free class in the ind-category [Formula: see text] of [Formula: see text]. Further, for a given regular cardinal [Formula: see text], we also consider the category [Formula: see text] of [Formula: see text]-presentable objects in the functor category [Formula: see text]. Then, under certain conditions, we show that the torsion-free class [Formula: see text] can be recovered as a subquotient of [Formula: see text].

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9

Angeleri Hügel, Lidia, and Michal Hrbek. "Parametrizing torsion pairs in derived categories." Representation Theory of the American Mathematical Society 25, no. 23 (July 30, 2021): 679–731. http://dx.doi.org/10.1090/ert/579.

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We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D ( M o d - A ) \mathrm {D}({\mathrm {Mod}}\text {-}A) of a ring A A . To this end, we provide a construction of t-structures from chains in the lattice of ring epimorphisms starting in A A , which is a natural extension of the construction of compactly generated t-structures from chains of subsets of the Zariski spectrum known for the commutative noetherian case. We also provide constructions of silting and cosilting objects in D ( M o d - A ) \mathrm {D}({\mathrm {Mod}}\text {-}A) . This leads us to classification results over some classes of commutative rings and over finite dimensional hereditary algebras.

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10

Bravo, Daniel, and Carlos E. Parra. "Torsion pairs over n-hereditary rings." Communications in Algebra 47, no. 5 (February 22, 2019): 1892–907. http://dx.doi.org/10.1080/00927872.2018.1524005.

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11

Colpi, Riccardo, Francesca Mantese та Alberto Tonolo. "Cotorsion pairs, torsion pairs, and Σ-pure-injective cotilting modules". Journal of Pure and Applied Algebra 214, № 5 (травень 2010): 519–25. http://dx.doi.org/10.1016/j.jpaa.2009.06.003.

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12

He, Jian, Yonggang Hu, and Panyue Zhou. "Torsion pairs and recollements of extriangulated categories." Communications in Algebra 50, no. 5 (November 10, 2021): 2018–36. http://dx.doi.org/10.1080/00927872.2021.1996585.

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13

Baur, Karin, and Rosanna Laking. "Torsion pairs and cosilting in type A˜." Journal of Pure and Applied Algebra 226, no. 10 (October 2022): 107057. http://dx.doi.org/10.1016/j.jpaa.2022.107057.

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14

Dung, Nguyen Viet, and José Luis García. "Splitting torsion pairs over pure semisimple rings." Journal of Pure and Applied Algebra 219, no. 7 (July 2015): 2637–57. http://dx.doi.org/10.1016/j.jpaa.2014.09.020.

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15

Baur, Karin, Aslak Bakke Buan, and Robert J. Marsh. "Torsion Pairs and Rigid Objects in Tubes." Algebras and Representation Theory 17, no. 2 (March 20, 2013): 565–91. http://dx.doi.org/10.1007/s10468-013-9410-6.

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16

Ma, Xin, and Zhaoyong Huang. "Torsion pairs in recollements of abelian categories." Frontiers of Mathematics in China 13, no. 4 (July 23, 2018): 875–92. http://dx.doi.org/10.1007/s11464-018-0712-1.

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17

Kong, Fan, Keyan Song, and Pu Zhang. "Decomposition of torsion pairs on module categories." Journal of Algebra 388 (August 2013): 248–67. http://dx.doi.org/10.1016/j.jalgebra.2013.03.034.

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18

Yan, Hangyu. "STRONGLY COTORSION (TORSION-FREE) MODULES AND COTORSION PAIRS." Bulletin of the Korean Mathematical Society 47, no. 5 (September 30, 2010): 1041–52. http://dx.doi.org/10.4134/bkms.2010.47.5.1041.

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19

Jasso, Gustavo. "Reduction of τ-Tilting Modules and Torsion Pairs". International Mathematics Research Notices 2015, № 16 (26 вересня 2014): 7190–237. http://dx.doi.org/10.1093/imrn/rnu163.

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20

AZAK, AYŞE ZEYNEP. "INVOLUTE-EVOLUTE CURVES ACCORDING TO MODIFIED ORTHOGONAL FRAME." Journal of Science and Arts 21, no. 2 (June 30, 2021): 385–94. http://dx.doi.org/10.46939/j.sci.arts-21.2-a06.

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Анотація:

In this paper, the involute-evolute curve concept has been deﬁned according to two type modiﬁed orthogonal frames at non-zero points of curvature and torsion in the Euclidean space E^3 , respectively. Later, the characteristic theorems related to the distance between the corresponding points of these curves have been given. Besides, the relations have been found between the curvatures and also torsions of the two type the involute-evolute modiﬁed orthogonal pairs.

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21

Ivanov, S. V., and Roman Mikhailov. "On Zero-divisors in Group Rings of Groups with Torsion." Canadian Mathematical Bulletin 57, no. 2 (June 14, 2014): 326–34. http://dx.doi.org/10.4153/cmb-2012-036-6.

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AbstractNontrivial pairs of zero-divisors in group rings are introduced and discussed. A problem on the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of odd exponent n ≫ 1 is solved in the affirmative. Nontrivial pairs of zero-divisors are also found in group rings of free products of groups with torsion.

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22

Assem, Ibrahim, María José Souto-Salorio, and Sonia Trepode. "Split t-structures and torsion pairs in hereditary categories." Journal of Algebra and Its Applications 17, no. 11 (November 2018): 1850218. http://dx.doi.org/10.1142/s0219498818502183.

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Анотація:

We construct a bijection between split torsion pairs in the module category of a tilted algebra having a complete slice in the preinjective component with corresponding [Formula: see text]-structures. We also classify split [Formula: see text]-structures in the derived category of a hereditary algebra.

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23

Šťovíček, Jan, Otto Kerner, and Jan Trlifaj. "Tilting via torsion pairs and almost hereditary noetherian rings." Journal of Pure and Applied Algebra 215, no. 9 (September 2011): 2072–85. http://dx.doi.org/10.1016/j.jpaa.2010.11.016.

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24

Dugas, Alex. "Torsion Pairs and Simple-Minded Systems in Triangulated Categories." Applied Categorical Structures 23, no. 3 (February 11, 2014): 507–26. http://dx.doi.org/10.1007/s10485-014-9365-8.

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25

Fiorot, Luisa. "$n$-quasi-abelian categories vs $n$-tilting torsion pairs." Documenta Mathematica 26 (2021): 149–97. http://dx.doi.org/10.4171/dm/812.

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26

NAJMAN, FILIP. "EXCEPTIONAL ELLIPTIC CURVES OVER QUARTIC FIELDS." International Journal of Number Theory 08, no. 05 (July 6, 2012): 1231–46. http://dx.doi.org/10.1142/s1793042112500716.

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Анотація:

We study the number of elliptic curves, up to isomorphism, over a fixed quartic field K having a prescribed torsion group T as a subgroup. Let T = ℤ/mℤ⊕ℤ/nℤ, where m|n, be a torsion group such that the modular curve X1(m, n) is an elliptic curve. Let K be a number field such that there is a positive and finite number of elliptic curves E over K having T as a subgroup. We call such pairs (T, K)exceptional. It is known that there are only finitely many exceptional pairs when K varies through all quadratic or cubic fields. We prove that when K varies through all quartic fields, there exist infinitely many exceptional pairs when T = ℤ/14ℤ or ℤ/15ℤ and finitely many otherwise.

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27

Perez, Mireya, Mohammad Hossain, Edward Silverman, Randall Fitch, Ryan Wicker, and Michelle Meyer. "Effect of headless compression screw on construct stability for centre of rotation and angulation-based levelling osteotomy." Veterinary and Comparative Orthopaedics and Traumatology 30, no. 04 (2017): 1–5. http://dx.doi.org/10.3415/vcot-16-09-0136.

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Summary Objective: To compare the biomechanical properties of bone and implant constructs when used for the centre of rotation and angulation (CORA) based levelling osteotomy, with and without implantation of a trans-osteotomy headless compression screw tested under three-point flexural and torsional forces; thereby determining the contribution of a trans-osteotomy headless compression screw with regards to stability of the construct. Methods: Experimental biomechanical study utilizing 12 pairs of cadaveric canine tibias. Using the CORA based levelling osteotomy (CBLO) procedure, the osteotomy was stabilized with either a standard non-locking CBLO bone plate augmented with a headless compression screw (HCS) or a CBLO bone plate alone. Tibial constructs were mechanically tested in three-point craniocaudal flexural testing or in torsion. Results: In three-point flexural testing, the difference between the two constructs was not significant. In torsion, the difference in the angle of failure between constructs with a HCS (48.46°) and constructs without a HCS (81.65°) was significant (p = 0.036). Maximum torque achieved by constructs with a HCS (21.7 Nm) was greater than those without (18.7 Nm) (p = 0.056). Stiffness differences between both groups in torsion and bending were not significant. Use of a HCS did increase the stability of the CBLO construct in torsional testing, but not in flexural testing.

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28

DOBBS, DAVID E., and JAY SHAPIRO. "A GENERALIZATION OF PRÜFER'S ASCENT RESULT TO NORMAL PAIRS OF COMPLEMENTED RINGS." Journal of Algebra and Its Applications 10, no. 06 (December 2011): 1351–62. http://dx.doi.org/10.1142/s021949881100521x.

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Let R ⊆ T be a (unital) extension of (commutative) rings, such that the total quotient ring of R is a von Neumann regular ring and T is torsion-free as an R-module. Let T ⊆ B be a ring extension such that B is a reduced ring that is torsion-free as a T-module. Let R* (respectively, A) be the integral closure of R in T (respectively, in B). Then (R*, T) is a normal pair (i.e. S is integrally closed in T for each ring S such that R* ⊆ S ⊆ T) if and only if (A, AT) is a normal pair. This generalizes results of Prüfer and Heinzer on Prüfer domains to normal pairs of complemented rings.

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29

Lo, Jason. "Torsion pairs and filtrations in abelian categories with tilting objects." Journal of Algebra and Its Applications 14, no. 08 (April 27, 2015): 1550121. http://dx.doi.org/10.1142/s0219498815501212.

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Given a noetherian abelian k-category [Formula: see text] of finite homological dimension, with a tilting object T of projective dimension 2, the abelian category [Formula: see text] and the abelian category of modules over End (T) op are related by a sequence of two tilts; we give an explicit description of the torsion pairs involved. We then use our techniques to obtain a simplified proof of a theorem of Jensen–Madsen–Su, that [Formula: see text] has a three-step filtration by extension-closed subcategories. Finally, we generalize Jensen–Madsen–Su's filtration to the case where T has any finite projective dimension.

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30

Beligiannis, Apostolos. "Cohen–Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras." Journal of Algebra 288, no. 1 (June 2005): 137–211. http://dx.doi.org/10.1016/j.jalgebra.2005.02.022.

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31

Nakaoka, Hiroyuki. "General heart construction for twin torsion pairs on triangulated categories." Journal of Algebra 374 (January 2013): 195–215. http://dx.doi.org/10.1016/j.jalgebra.2012.10.027.

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32

Carlton, David. "Moduli for pairs of elliptic curves¶with isomorphic N -torsion." manuscripta mathematica 105, no. 2 (June 1, 2001): 201–34. http://dx.doi.org/10.1007/s002290170003.

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33

Pavon, Sergio, and Jorge Vitória. "Hearts for commutative Noetherian rings: torsion pairs and derived equivalences." Documenta Mathematica 26 (2021): 829–71. http://dx.doi.org/10.4171/dm/831.

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34

Dzhimak, Stepan, Alexandr Svidlov, Anna Elkina, Eugeny Gerasimenko, Mikhail Baryshev, and Mikhail Drobotenko. "Genesis of Open States Zones in a DNA Molecule Depends on the Localization and Value of the Torque." International Journal of Molecular Sciences 23, no. 8 (April 17, 2022): 4428. http://dx.doi.org/10.3390/ijms23084428.

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Анотація:

The formation and dynamics of the open states in a double-stranded DNA molecule are largely determined by its mechanical parameters. The main one is the torque. However, the experimental study of DNA dynamics and the occurrence of open states is limited by the spatial resolution of available biophysical instruments. Therefore, in this work, on the basis of a mechanical mathematical model of DNA, calculations of the torque effect on the process of occurrence and dynamics of open states were carried out for the interferon alpha 17 gene. It was shown that torsion action leads to the occurrence of rotational movements of nitrogenous bases. This influence is nonlinear, and an increase in the amplitude of the torsion action does not lead to an automatic increase in the amplitude of rotational movements and an increase in the zones’ open states. Calculations with a constant torsion moment demonstrate that open states zones are more often formed at the boundaries of the gen and in regions with a predominance of A–T pairs. It is shown, that for the occurrence of open states in the part of the gene that contains a small number of A–T pairs, a large amount of torque is required. When the torque is applied to a certain region of the gene, the probability of the formation of the open state depends on the content of A–T pairs in this region, the size of this region, and on the exposure time. For this mathematical model, open states zones can be closed when the torsion action stops. The simulation results showed that the values of the torsion moment required for the appearance of open states zones, in some cases, are close to experimentally measured (13–15 pN·nm).

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35

Тихонов, Д. А., and D. A. Tikhonov. "Analysis of the Torsion Angles between Helical Axes in Pairs of Helices in Protein Molecules." Mathematical Biology and Bioinformatics 12, no. 2 (November 27, 2017): 398–410. http://dx.doi.org/10.17537/2017.12.398.

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In this study, an analysis of distribution of the torsion angles Ω between helical axes in pairs of connected helices found in known proteins has been performed. The database for helical pairs was compiled using the Protein Data Bank taking into account the definite rules suggested earlier. The database was analyzed in order to elaborate its classification and find out novel structural features in helix packing. The database was subdivided into three subsets according to criterion of crossing helix projections on the parallel planes passing through the axes of the helices. It was shown that helical pairs not having crossing projections are distributed along whole range of angles Ω, although there are two maxima at Ω = 0° and Ω = 180°. Most of helical pairs of this subset are pairs formed by α-helices and 310- helices. It is shown that the distribution of all the helical pairs having the crossing helix projections has a maximum at 20° < Ω < 25°. In this subset, most helical pairs are formed by α-helices. The distribution of only α-helical pairs having crossing axes projections has three maxima, at –50° < Ω < –25°, 20° < Ω < 25°, and 70° < Ω < 110°.

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36

Zhou, Yu, and Bin Zhu. "Mutation of Torsion Pairs in Triangulated Categories and its Geometric Realization." Algebras and Representation Theory 21, no. 4 (October 6, 2017): 817–32. http://dx.doi.org/10.1007/s10468-017-9740-x.

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37

Coelho Simões, Raquel, and David Pauksztello. "Torsion pairs in a triangulated category generated by a spherical object." Journal of Algebra 448 (February 2016): 1–47. http://dx.doi.org/10.1016/j.jalgebra.2015.09.011.

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38

Gratz, Sira. "Mutation of Torsion Pairs in Cluster Categories of Dynkin Type D." Applied Categorical Structures 24, no. 1 (January 7, 2015): 79–104. http://dx.doi.org/10.1007/s10485-014-9387-2.

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39

Migler, Joseph. "Functional Calculus and Joint Torsion of Pairs of Almost Commuting Operators." Integral Equations and Operator Theory 85, no. 2 (May 20, 2016): 167–90. http://dx.doi.org/10.1007/s00020-016-2299-9.

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40

Bhandari, Avinash, Rajan Suwal, and Aakarsha Khawas. "Seismic Fragility Assessment of Irregular High Rise Buildings using Incremental Dynamic Analysis." Advances in Engineering and Technology: An International Journal 2, no. 01 (December 31, 2022): 69–76. http://dx.doi.org/10.3126/aet.v2i01.50446.

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Анотація:

The construction of high rise buildings is common in city areas. These buildings may be irregular because of aesthetics or other requirements. As Nepal lies in a seismically active region these irregular high rise buildings may not perform well during earthquakes. Two existing irregular high rise buildings are taken as case study buildings that had pre-existing torsion. Shear walls are added to the building at the required location to minimize torsion in the buildings. The objective of the study is to determine the performance of building with and without torsional irregularity. The seismic performance of all the buildings is carried out by taking seven pairs of ground motions using nonlinear time history analysis. These ground motions are scaled to the required intensity to develop incremental dynamic analysis (IDA) curve. These IDA curves are used to develop fragility curves to access the performance in the buildings. The result from the analysis showed that performance in one building improved by 35% and in another by 70% at the peak ground acceleration (PGA) of 0.35g.

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41

Vukman, Joso, and Irena Kosi-Ulbl. "On centralizers of semiprime rings with involution." Studia Scientiarum Mathematicarum Hungarica 43, no. 1 (February 1, 2006): 61–67. http://dx.doi.org/10.1556/sscmath.43.2006.1.4.

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42

Zhou, Yu, and Bin Zhu. "T -structures and torsion pairs in a 2-Calabi-Yau triangulated category." Journal of the London Mathematical Society 89, no. 1 (October 8, 2013): 213–34. http://dx.doi.org/10.1112/jlms/jdt059.

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43

Boutros, C. P., M. Kasra, M. D. Grynpas, and D. R. Trout. "The Effect of Repeated Freeze-thaw Cycles on the Biomechanical Properties of Canine Cortical Bone." Veterinary and Comparative Orthopaedics and Traumatology 13, no. 02 (2000): 59–64. http://dx.doi.org/10.1055/s-0038-1632632.

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SummaryAs orthopaedic investigations have become more intricate, bone specimens have sometimes undergone multiple freeze-thaw cycles prior to biomechanical testing. The purpose of this study was to determine if repeated freezing and thawing affected the mechanical properties of canine cortical bone. Six pairs of third-metacarpal bones were tested in three-point bending and six pairs of femurs were tested in torsion. At the time of collection, one member of each pair was tested destructively. The other member was tested nondestructively at the time of collection and after each of five freeze-thaw cycles, followed by destructive testing after the fifth cycle. For destructive tests, the material properties (modulus, maximum stress, maximum strain and absorbed energy) of a specimen at the time of collection were compared to those of the corresponding contralateral specimen that had undergone five freeze-thaw cycles. For repeated nondestructive tests, the modulus of a specimen at the time of collection was compared to modulus of the same specimen at each of the five thaw intervals. During destructive testing, there was a significant (p = 0.02) decrease (20%) in maximum torsional strain. Other changes in bending and torsional destructive properties were not statistically significant. During repeated nondestructive testing, there were solitary significant (p < 0.05) increases (8% and 9%, respectively) in both bending and torsional modulus. However, these isolated changes were not correlated to the number of freeze-thaw cycles. The pattern of alterations in destructive and non-destructive biomechanical properties was most consistent with varying specimen dehydration at each thaw interval. Despite using accepted methods to maintain specimen hydration, repeated freezing, thawing, handling and testing of cortical bone increased the risk of moisture loss. Unless stringent efforts are made to ensure proper hydration, the mechanical properties of canine cortical bone will be altered by repeated freezing and thawing, affecting the results of studies utilizing this technique.The effect of five freeze-thaw cycles on paired canine cortical bone specimens was evaluated using destructive and repeated non-destructive three-point bending and torsion tests. A significant decrease in destructive torsional strain and isolated significant increases in nondestructive bending and torsional modulus were most consistent with varying specimen dehydration at each thaw interval.

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44

Chandra, N. Srikantamurthy, Shamantha Kumar, B. H. Doreswamy, K. B. Umesha, and M. Mahendra. "N′-Benzoyl-5-methyl-1,3-diphenyl-1H-pyrazole-4-carbohydrazide." Acta Crystallographica Section E Structure Reports Online 69, no. 12 (November 13, 2013): o1769. http://dx.doi.org/10.1107/s1600536813029528.

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In the title compound, C24H20N4O2, the pyrazole ring makes dihedral angles of 47.57 (10)° and 30.56 (11)° with its N-bound and C-bound phenyl groups, respectively. The C—N—N—C group that links the two carbonyls has a torsion angle of 81.5 (2)°. The torsion angles between the carbonyl groups and their adjacent pyrazole and phenyl rings are 125.89 (19) and 164.22 (17)°, respectively. In the crystal, pairs of molecules are linked by N—H...O hydrogen bonds intoR22(10) ring motifs, which in turn link to form chains that propagate parallel to thec-axis direction.

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45

Poltev, Valeri, Victor M. Anisimov, Veronica Dominguez, Andrea Ruiz, Alexandra Deriabina, Eduardo Gonzalez, Dolores Garcia, and Francisco Rivas. "Understanding the Origin of Structural Diversity of DNA Double Helix." Computation 9, no. 9 (September 11, 2021): 98. http://dx.doi.org/10.3390/computation9090098.

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Deciphering the contribution of DNA subunits to the variability of its 3D structure represents an important step toward the elucidation of DNA functions at the atomic level. In the pursuit of that goal, our previous studies revealed that the essential conformational characteristics of the most populated “canonic” BI and AI conformational families of Watson–Crick duplexes, including the sequence dependence of their 3D structure, preexist in the local energy minima of the elemental single-chain fragments, deoxydinucleoside monophosphates (dDMPs). Those computations have uncovered important sequence-dependent regularity in the superposition of neighbor bases. The present work expands our studies to new minimal fragments of DNA with Watson–Crick nucleoside pairs that differ from canonic families in the torsion angles of the sugar-phosphate backbone (SPB). To address this objective, computations have been performed on dDMPs, cdDMPs (complementary dDMPs), and minimal fragments of SPBs of respective systems by using methods of molecular and quantum mechanics. These computations reveal that the conformations of dDMPs and cdDMPs having torsion angles of SPB corresponding to the local energy minima of separate minimal units of SPB exhibit sequence-dependent characteristics representative of canonic families. In contrast, conformations of dDMP and cdDMP with SPB torsions being far from the local minima of separate SPB units exhibit more complex sequence dependence.

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46

CHEN, ZEXIANG. "Families of elliptic curves with the same mod 8 representations." Mathematical Proceedings of the Cambridge Philosophical Society 165, no. 1 (April 19, 2017): 137–62. http://dx.doi.org/10.1017/s0305004117000354.

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AbstractWe compute certain twists of the classical modular curve X(8). Searching for rational points on these twists enables us to find non-trivial pairs non-isogenous elliptic curves over ℚ whose 8-torsion subgroups are isomorphic as Galois modules. We also show that there are infinitely many examples over ℚ.

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47

Chang, Huimin, and Bin Zhu. "Torsion pairs in finite 2-Calabi-Yau triangulated categories with maximal rigid objects." Communications in Algebra 47, no. 7 (January 24, 2019): 2810–32. http://dx.doi.org/10.1080/00927872.2018.1539741.

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48

Holm, Thorsten, Peter Jørgensen, and Martin Rubey. "Ptolemy diagrams and torsion pairs in the cluster categories of Dynkin type D." Advances in Applied Mathematics 51, no. 5 (October 2013): 583–605. http://dx.doi.org/10.1016/j.aam.2013.07.005.

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49

Begum, M. S., M. B. H. Howlader, R. Miyatake, E. Zangrando, and M. C. Sheikh. "Crystal structure ofS-hexyl (E)-3-(4-methoxybenzylidene)dithiocarbazate." Acta Crystallographica Section E Crystallographic Communications 71, no. 3 (February 25, 2015): o199. http://dx.doi.org/10.1107/s2056989015003199.

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In the title compound, C15H22N2OS2, the dithiocarbazate group adopts anEEconformation with respect to the C=N bond of the benzylidene moiety. The hexyl side chain adopts an extended conformation and the C—S—C—C torsion angle is −93.36 (13)°. In the crystal, inversion dimers linked by pairs of N—H...S hydrogen bonds generateR22(8) loops.

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50

Mughal, Shumaila Younas, Islam Ullah Khan, William T. A. Harrison, Muneeb Hayat Khan, and Muhammad Nadeem Arshad. "2,5-Dichloro-N-(3-methylphenyl)benzenesulfonamide." Acta Crystallographica Section E Structure Reports Online 68, no. 8 (July 18, 2012): o2476. http://dx.doi.org/10.1107/s1600536812032023.

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In the title compound, C13H11Cl2NO2S, the dihedral angle between the aromatic rings is 76.62 (10)° and the C—S—N—C linkage between the rings adopts agaucheconformation [torsion angle = −51.4 (2)°]. A weak intramolecular C—H...O interaction closes anS(6) ring. In the crystal, inversion dimers linked by pairs of N—H...O hydrogen bonds generateR22(8) loops.

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