Relevant bibliographies by topics / Almost split sequence

Academic literature on the topic 'Almost split sequence'

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Published: 11 March 2023

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Journal articles on the topic "Almost split sequence"

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ESHRAGHI, HOSSEIN. "EXISTENCE OF ALMOST SPLIT SEQUENCES VIA REGULAR SEQUENCES." Bulletin of the Australian Mathematical Society 88, no. 2 (March 18, 2013): 218–31. http://dx.doi.org/10.1017/s0004972713000099.

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AbstractLet $(R, \mathfrak{m})$ be a Cohen–Macaulay complete local ring. We will apply an inductive argument to show that for every nonprojective locally projective maximal Cohen–Macaulay object $ \mathcal{X} $ of the morphism category of $R$ with local endomorphism ring, there exists an almost split sequence ending in $ \mathcal{X} $. Regular sequences are exploited to reduce the Krull dimension of $R$ on which the inductive argument is established. Moreover, the Auslander–Reiten translate of certain objects is described.
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Brenner, Sheila. "The almost split sequence starting with a simple module." Archiv der Mathematik 62, no. 3 (March 1994): 203–6. http://dx.doi.org/10.1007/bf01261359.

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Razzaque, Asima, and Inayatur Rehman. "Some Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings." Journal of Mathematics 2022 (August 31, 2022): 1–8. http://dx.doi.org/10.1155/2022/2792450.

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The LA-module is a nonassociative structure that extends modules over a nonassociative ring known as left almost rings (LA-rings). Because of peculiar characteristics of LA-ring and its inception into noncommutative and nonassociative theory, drew the attention of many researchers over the last decade. In this study, the ideas of projective and injective LA-modules, LA-vector space, as well as examples and findings, are discussed. We construct a nontrivial example in which it is proved that if the LA-module is not free, then it cannot be a projective LA-module. We also construct free LA-modules, create a split sequence in LA-modules, and show several outcomes that are connected to them. We have proved the projective basis theorem for LA-modules. Also, split sequences in projective and injective LA-modules are discussed with the help of various propositions and theorems.
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Fedele, Francesca. "d-Auslander–Reiten sequences in subcategories." Proceedings of the Edinburgh Mathematical Society 63, no. 2 (January 15, 2020): 342–73. http://dx.doi.org/10.1017/s0013091519000312.

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AbstractLet Φ be a finite-dimensional algebra over a field k. Kleiner described the Auslander–Reiten sequences in a precovering extension closed subcategory ${\rm {\cal X}}\subseteq {\rm mod }\,\Phi $. If $X\in \mathcal {X}$ is an indecomposable such that ${\rm Ext}_\Phi ^1 (X,{\rm {\cal X}})\ne 0$ and $\zeta X$ is the unique indecomposable direct summand of the $\mathcal {X}$-cover $g:Y\to D\,{\rm Tr}\,X$ such that ${\rm Ext}_\Phi ^1 (X,\zeta X)\ne 0$, then there is an Auslander–Reiten sequence in $\mathcal {X}$ of the form $${\rm \epsilon }:0\to \zeta X\to {X}^{\prime}\to X\to 0.$$Moreover, when ${\rm En}{\rm d}_\Phi (X)$ modulo the morphisms factoring through a projective is a division ring, Kleiner proved that each non-split short exact sequence of the form $$\delta :0\to Y\to {Y}^{\prime}\buildrel \eta \over \longrightarrow X\to 0$$is such that η is right almost split in $\mathcal {X}$, and the pushout of δ along g gives an Auslander–Reiten sequence in ${\rm mod}\,\Phi $ ending at X.In this paper, we give higher-dimensional generalizations of this. Let $d\geq 1$ be an integer. A d-cluster tilting subcategory ${\rm {\cal F}}\subseteq {\rm mod}\,\Phi $ plays the role of a higher ${\rm mod}\,\Phi $. Such an $\mathcal {F}$ is a d-abelian category, where kernels and cokernels are replaced by complexes of d objects and short exact sequences by complexes of d + 2 objects. We give higher versions of the above results for an additive ‘d-extension closed’ subcategory $\mathcal {X}$ of $\mathcal {F}$.
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Ericson, Per G. P., Cajsa L. Anderson, Tom Britton, Andrzej Elzanowski, Ulf S. Johansson, Mari Källersjö, Jan I. Ohlson, Thomas J. Parsons, Dario Zuccon, and Gerald Mayr. "Diversification of Neoaves: integration of molecular sequence data and fossils." Biology Letters 2, no. 4 (August 9, 2006): 543–47. http://dx.doi.org/10.1098/rsbl.2006.0523.

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Patterns of diversification and timing of evolution within Neoaves, which includes almost 95% of all bird species, are virtually unknown. On the other hand, molecular data consistently indicate a Cretaceous origin of many neoavian lineages and the fossil record seems to support an Early Tertiary diversification. Here, we present the first well-resolved molecular phylogeny for Neoaves, together with divergence time estimates calibrated with a large number of stratigraphically and phylogenetically well-documented fossils. Our study defines several well-supported clades within Neoaves. The calibration results suggest that Neoaves, after an initial split from Galloanseres in Mid-Cretaceous, diversified around or soon after the K/T boundary. Our results thus do not contradict palaeontological data and show that there is no solid molecular evidence for an extensive pre-Tertiary radiation of Neoaves.
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Kowalski, Jakub, Maksymilian Mika, Wojciech Pawlik, Jakub Sutowicz, Marek Szykuła, and Mark H. M. Winands. "Split Moves for Monte-Carlo Tree Search." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (June 28, 2022): 10247–55. http://dx.doi.org/10.1609/aaai.v36i9.21265.

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In many games, moves consist of several decisions made by the player. These decisions can be viewed as separate moves, which is already a common practice in multi-action games for efficiency reasons. Such division of a player move into a sequence of simpler / lower level moves is called splitting. So far, split moves have been applied only in forementioned straightforward cases, and furthermore, there was almost no study revealing its impact on agents' playing strength. Taking the knowledge-free perspective, we aim to answer how to effectively use split moves within Monte-Carlo Tree Search (MCTS) and what is the practical impact of split design on agents' strength. This paper proposes a generalization of MCTS that works with arbitrarily split moves. We design several variations of the algorithm and try to measure the impact of split moves separately on efficiency, quality of MCTS, simulations, and action-based heuristics. The tests are carried out on a set of board games and performed using the Regular Boardgames General Game Playing formalism, where split strategies of different granularity can be automatically derived based on an abstract description of the game. The results give an overview of the behavior of agents using split design in different ways. We conclude that split design can be greatly beneficial for single- as well as multi-action games.
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Dyachenko, Elena A., Elena V. Semenova, and Elena Z. Kochieva. "Characterization of variability of the intergenic spacers cpDNA trnH–psbA, trnY–trnT AND rpoB–trnC in representatives of Pisum L. (Tribe Fabeae)." Ecological genetics 18, no. 4 (December 12, 2020): 445–56. http://dx.doi.org/10.17816/ecogen33959.

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Background. Plant chloroplast genome have conservative structure, but its nucleotide sequence is polymorphous due to which cpDNA fragments are often used in taxonomic and phylogenetic studies. Despite the widespread distribution and use of Fabeae species, mainly peas (Pisum), data on the intraspecific diversity of cpDNA fragments are almost absent. The aim of the work was to analyze the intraspecific variability of three cpDNA spacers in Pisum. Materials and methods. As a result of the work, intergenic spacers trnYtrnT, trnHpsbA and rpoBtrnC in 38 accessions of the Pisum and related Fabeae species were sequenced. Despite the fact that the selected chloroplast fragments are generally considered to be sufficiently variable in plants and are often used for phylogenetic studies, Pisum accessions have been found to have no intraspecific differences in two of the three spacers sequences analyzed. Results and conclusion. A total 97 SNPs were detected in Pisum accessions, seven of them distinguished P. sativum from P. fulvum. The most variable of the analyzed fragments was the intergenic spacer rpoBtrnC. Based on rpoBtrnC sequence 17 haplotypes in P. sativum and four haplotypes in P. fulvum were revealed. The cpDNA sequencing data were used for a phylogenetic analysis. On the obtained tree Vavilovia formosa accession formed a separate branch from pea accessions. All Pisum accessions fall in one cluster, split into distinct P. sativum and P. fulvum subclusters (BI = 99%).
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Brumley, Farrell, and Simon Marshall. "Lower bounds for Maass forms on semisimple groups." Compositio Mathematica 156, no. 5 (April 17, 2020): 959–1003. http://dx.doi.org/10.1112/s0010437x20007125.

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Let $G$ be an anisotropic semisimple group over a totally real number field $F$. Suppose that $G$ is compact at all but one infinite place $v_{0}$. In addition, suppose that $G_{v_{0}}$ is $\mathbb{R}$-almost simple, not split, and has a Cartan involution defined over $F$. If $Y$ is a congruence arithmetic manifold of non-positive curvature associated with $G$, we prove that there exists a sequence of Laplace eigenfunctions on $Y$ whose sup norms grow like a power of the eigenvalue.
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KAUR, ANUREET, K. S. SEKHON, S. THAMAN, A. S. SIDHU, and G. S. BUTTAR. "Evaluation of mustard (Brassica juncea) and barley (Hordeum vulgare) based cropping sequence under variable irrigation supplies." Indian Journal of Agricultural Sciences 88, no. 7 (July 19, 2018): 1129–36. http://dx.doi.org/10.56093/ijas.v88i7.81600.

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A field experiment was conducted at Regional Station, Bathinda during 2010-2013 to evaluate various crop sequences under variable irrigation regimes. The experiment was conducted in split plot design with six crop sequences, viz. barley-Bt cotton, barley-cluster bean, barley-green gram,mustard-Bt cotton, mustard-cluster bean and mustardgreen gram in main plots and three irrigation regimes [optimum (O), sub-optimum (SO) and sub-sub optimum (SSO) ] were kept in sub plots with three replications. The grain yield of barley reduced significantly where grown after cotton to the tune of 10.8 and 9.2% as compared to green gram and cluster bean, respectively. The barley grain equivalentyield (BGEY) was higher in mustard under all the preceding crops (cotton, green gram and cluster bean).Significant increase in cotton equivalent yield (CEY) was noticed in cotton sown after barley than mustard. Amongst the CEY of the system, barley-cotton crop sequence gave significantly highest CEY which was at par with mustard-clusterbean and mustard-cotton crop sequence. Significantly higher barley grain yield, mustard grain yield and cotton equivalent yield was recorded in optimum water regime, followed by SO and lowest in SSO regime. Water expense efficiency (WEE) of barley was higher preceding greengram followed by cluster bean and lowest in cotton system. Whereas,WEE was almost same under mustard succeeding cotton and greengram but was lowest in mustard-cluster bean crop sequence. The maximum water productivity (WP) was recorded in clusterbean- mustard followed by clusterbeanbarley crop sequence. The sub-sub-optimum irrigation regime recorded highest WP followed by SO and lowest in optimum. The highest organic carbon was observed under cluster bean-barley followed by cluster bean-mustard cropping system. The potassium content deceased in cotton based crop sequence as compared to cluster bean and greengram crop sequence. Whereas, increase in available N, and P was noticed in cluster bean and green gram based cropping systems than cotton based sequence. The highest cost of cultivation was recorded in cotton based cropping sequences and lowest in cluster bean based cropping sequences. Consequently, higher net returns, B: C ratio were obtained in clusterbean based crop sequence than cotton based sequence.The optimum water regime showed highest gross returns, net returns and benefit cost ratio.
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Sboras, Sotiris, Spyros Pavlides, Adamantios Kilias, Dimitris Galanakis, Athanasios Chatziioannou, and Alexandros Chatzipetros. "The Geological Structure and Tectonic Complexity of Northern Thessaly That Hosted the March 2021 Seismic Crisis." Geotechnics 2, no. 4 (November 4, 2022): 935–60. http://dx.doi.org/10.3390/geotechnics2040044.

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Knowing the rich presence of active faults in northern Thessaly and the lack of any significant seismic activity since at least the mid-1940s, the 2021 seismic sequence did not surprise us. What did surprise us was the fact that (i) despite the great knowledge of the neotectonic faults in the area, the causative faults were unknown, or almost unknown; (ii) the direction of the 2021 faulting was different than the expected, and given that the focal mechanisms showed almost pure normal dip-slip motion, the extensional main axis was also different than the one we thought we knew for this area; and (iii) besides the co-seismic ruptures that occurred within the Domeniko-Amouri basin and along the Titarissios River valley, there is evidence of rupturing in the alpine basement of Zarkos mountains. After thoroughly reviewing both the alpine and neotectonic structural setting and all the available literature concerning the seismotectonic data and interpretations of the 2021 sequence, including investigations of our own, we end up in a complex tectonic setting with older alpine structures now operating as inherited faults, and we also suggest the possible occurrence of a roughly N-dipping, low-angle, detachment-type fault. This fault runs below Mt Zarkos, reaching at least the Elassona Basin, with splay faults bifurcating upwards from the main fault zone. Following this complexity, rupture of the first mainshock must have chosen a split route reaching the surface through the gneiss rocks of Zarkos and almost (?) reaching the basinal sediments of the local tectonic depressions. This seismic sequence is a perfect case study to shed some light on the tectonic and rupture processes in the context of both geodynamics and seismic hazard assessment.
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Dissertations / Theses on the topic "Almost split sequence"

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Lian, Tea Sormbroen. "Computing Almost Split Sequences : An algorithm for computing almost split sequences of finitely generated modules over a finite dimensional algebra." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19355.

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An artin algebra $l$ over a commutative, local, artinian ring $R$ was fixed, and with this foundation some topics from representation theory were discussed. A series of functors of module categories were defined, and almost split sequences were introduced with some basic results. An isomorphism $omega_{delta,X} : D delta^* rightarrow delta_*(DTr(X))$ of $Gamma$-modules for an artin $R$-algebra $Gamma$ was constructed. The isomorphism $omega_{delta,X}$ was applied to a special case, yielding a deterministic algorithm for computing almost split sequences in the case that $R$ is a field.
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Stewart, David William. "Investigating the middle term of almost split sequences." Thesis, University of Liverpool, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241609.

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Nogueira, M. T. A. D. "On finitely presented functors, Auslander algebras, and almost split sequences." Thesis, University of Warwick, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377096.

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Trunkát, Marek. "Algoritmy v teorii reprezentací." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-328276.

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This thesis deals with an implementation of algorithm for computation of generator of almost split sequences ending at an indecomposable nonprojective module of path algebra over finite quiver. Algorithm is implemented in algebra system GAP (Groups, Algorithms, Programming) with additional package QPA (Quivers and Path Algebras). Powered by TCPDF (www.tcpdf.org)
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Books on the topic "Almost split sequence"

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Maria Teresa Anes Duarte Nogueira. On finitely presented functors, Auslander algebras and almost split sequences. [s.l.]: typescript, 1986.

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Igusa, Kiyoshi, 1949- editor of compilation, Martsinkovsky, A. (Alex), editor of compilation, and Todorov, G. (Gordana), editor of compilation, eds. Expository lectures on representation theory: Maurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA. Providence, Rhode Island: American Mathematical Society, 2014.

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1943-, Wiegand Roger, ed. Cohen-Macaulay representations. Providence, R.I: American Mathematical Society, 2012.

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Introduction to Quiver Representations. American Mathematical Society, 2018.

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Quiver Representations and Quiver Varieties. American Mathematical Society, 2016.

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Book chapters on the topic "Almost split sequence"

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Gabriel, P., and A. V. Roiter. "Almost Split Sequences." In Representations of Finite-Dimensional Algebras, 87–101. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-58097-0_9.

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Assem, Ibrahim, and Flávio U. Coelho. "Constructing almost split sequences." In Graduate Texts in Mathematics, 99–155. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35118-2_3.

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Assem, Ibrahim, and Flávio U. Coelho. "The radical and almost split sequences." In Graduate Texts in Mathematics, 41–98. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35118-2_2.

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Auslander, Maurice, and Idun Reiten. "Almost split sequences for ℤ-graded rings." In Lecture Notes in Mathematics, 232–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078847.

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Reiten, Idun. "Hereditary Abelian Categories and Almost Split Sequences." In Algebra — Representation Theory, 257–71. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0814-3_13.

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Auslander, Maurice, and Louise Unger. "Isolated singularities and existence of almost split sequences." In Representation Theory II Groups and Orders, 194–242. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075297.

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Arnold, D., and C. Vinsonhaler. "Almost Split Sequences and Representations of Finite Posets." In Abelian Groups, 79–95. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003071761-8.

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Roggenkamp, K. W. "Almost split sequences for some non-classical lattice categories." In Lecture Notes in Mathematics, 318–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078851.

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Drew, Richard A. I., and Meredith C. Romig. "Species and speciation." In The fruit fly fauna (Diptera: Tephritideae: Dacinae) of Papua New Guinea, Indonesian Papua, Associated Islands and Bougainville, 7–8. Wallingford: CABI, 2022. http://dx.doi.org/10.1079/9781789249514.0004.

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Abstract This chapter discusses two species models, which are diametrically opposed. The first, often called the 'biological species concept', defines species in terms of 'reproductive isolation', convinced that species arise when subsets of a population are split off and remain geographically isolated over evolutionary time. If and when such new species are reunited with their founder population, interbreeding does not occur, or if it does, infertile progeny result. Hence, from the biological species concept, natural selection is a primary agent of change and directly selects for new species. In this sense, species are the direct products of natural selection and they are therefore 'adaptive devices'. When applying this species concept, it has been impossible to separate some sibling species of fruit flies in the genus Bactrocera where distinct morphological species can be similar in molecular analyses of certain DNA sequences, while similar species morphologically are distinct in the same molecular characters. A radically different model, the 'recognition concept of species', relies heavily on a knowledge of species ecology and behaviour, particularly in their natural habitat. The principal points in this concept are given. In contrast to the now-outdated biological species concept that leads one to depend on laboratory-based research to define species, the recognition concept requires workers to undertake extensive field research in the habitat of the taxon under investigation. In translating this approach to research in the insect family Tephritidae, particularly the Dacinae, some 35 years of field surveys have been undertaken throughout the Indian subcontinent, South-east Asia and the South Pacific region. These surveys included trapping using male lure traps and host fruit collections of commercial/edible fruits. The results of this work have included the provision of specimens of almost all known species for morphological descriptions (c.800 species), material for male pheromone chemistry, and data on host fruit relationships and biogeographical studies.
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"Almost split sequences." In Representation Theory of Artin Algebras, 136–90. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511623608.006.

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