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Journal articles on the topic 'Oka manifold'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

LÁRUSSON, FINNUR. "EXCISION FOR SIMPLICIAL SHEAVES ON THE STEIN SITE AND GROMOV'S OKA PRINCIPLE." International Journal of Mathematics 14, no. 02 (March 2003): 191–209. http://dx.doi.org/10.1142/s0129167x03001727.

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A complex manifold X is said to satisfy the Oka–Grauert property if the inclusion [Formula: see text] is a weak equivalence for every Stein manifold S, where the spaces of holomorphic and continuous maps from S to X are given the compact-open topology. Gromov's Oka principle states that if X has a spray, then it has the Oka–Grauert property. The purpose of this paper is to investigate the Oka–Grauert property using homotopical algebra. We embed the category of complex manifolds into the model category of simplicial sheaves on the site of Stein manifolds. Our main result is that the Oka–Grauert property is equivalent to X representing a finite homotopy sheaf on the Stein site. This expresses the Oka–Grauert property in purely holomorphic terms, without reference to continuous maps.

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2

TRIVEDI, SAURABH. "STRATIFIED TRANSVERSALITY OF HOLOMORPHIC MAPS." International Journal of Mathematics 24, no. 13 (December 2013): 1350106. http://dx.doi.org/10.1142/s0129167x13501061.

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We discuss genericity and stability of transversality of holomorphic maps to complex analytic stratifications. We prove that the set of maps between Stein manifolds and Oka manifolds transverse to a countable collection of submanifolds in the target is dense in the space of holomorphic maps with the weak topology. This greatly generalizes earlier results on the genericity of transverse maps by Forstnerič and by Kaliman and Zaidenberg. As an application we show that the Whitney (a)-regularity of a complex analytic stratification is necessary and sufficient for the stability of transverse holomorphic maps between a Stein manifold and an Oka manifold. This gives an analogue of a theorem in the real case due to Trotman.

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3

Kusakabe, Yuta. "An implicit function theorem for sprays and applications to Oka theory." International Journal of Mathematics 31, no. 09 (July 17, 2020): 2050071. http://dx.doi.org/10.1142/s0129167x20500718.

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We solve fundamental problems in Oka theory by establishing an implicit function theorem for sprays. As the first application of our implicit function theorem, we obtain an elementary proof of the fact that approximation yields interpolation. This proof and Lárusson’s elementary proof of the converse give an elementary proof of the equivalence between approximation and interpolation. The second application concerns the Oka property of a blowup. We prove that the blowup of an algebraically Oka manifold along a smooth algebraic center is Oka. In the appendix, equivariantly Oka manifolds are characterized by the equivariant version of Gromov’s condition [Formula: see text], and the equivariant localization principle is also given.

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4

Kusakabe, Yuta. "Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps." International Journal of Mathematics 28, no. 04 (April 2017): 1750028. http://dx.doi.org/10.1142/s0129167x17500288.

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We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. We first show that for any bounded convex domain [Formula: see text] and any connected complex manifold [Formula: see text], the space [Formula: see text] contains a dense holomorphic disc. Our second result states that [Formula: see text] is an Oka manifold if and only if for any Stein space [Formula: see text] there exists a dense entire curve in every path component of [Formula: see text]. In the second half of this paper, we apply the above results to the theory of universal functions. It is proved that for any bounded convex domain [Formula: see text], any fixed-point-free automorphism of [Formula: see text] and any connected complex manifold [Formula: see text], there exists a universal map [Formula: see text]. We also characterize Oka manifolds by the existence of universal maps.

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5

Ramos-Peon, Alexandre, and Riccardo Ugolini. "Parametric jet interpolation for Stein manifolds with the density property." International Journal of Mathematics 30, no. 08 (July 2019): 1950046. http://dx.doi.org/10.1142/s0129167x19500460.

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Given a Stein manifold with the density property, we show that under a suitable topological condition it is possible to prescribe derivatives at a finite number of points to automorphisms depending holomorphically on a Stein parameter. This is an Oka property of the manifold and is related to its holomorphic flexibility.

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6

STOPAR, KRIS. "APPROXIMATION OF HOLOMORPHIC MAPPINGS ON 1-CONVEX DOMAINS." International Journal of Mathematics 24, no. 14 (December 2013): 1350108. http://dx.doi.org/10.1142/s0129167x13501085.

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Let π : Z → X be a holomorphic submersion of a complex manifold Z onto a complex manifold X and D ⋐ X a 1-convex domain with strongly pseudoconvex boundary. We prove that under certain conditions there always exists a spray of π-sections over [Formula: see text] which has prescribed core, it fixes the exceptional set E of D, and is dominating on [Formula: see text]. Each section in this spray is of class [Formula: see text] and holomorphic on D. As a consequence we obtain several approximation results for π-sections. In particular, we prove that π-sections which are of class [Formula: see text] and holomorphic on D can be approximated in the [Formula: see text] topology by π-sections that are holomorphic in open neighborhoods of [Formula: see text]. Under additional assumptions on the submersion we also get approximation by global holomorphic π-sections and the Oka principle over 1-convex manifolds. We include an application to the construction of proper holomorphic maps of 1-convex domains into q-convex manifolds.

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7

Lutterodt, C. H. "A meromorphic extension of oka-weil approximation in a stein manifold." Complex Variables, Theory and Application: An International Journal 16, no. 2-3 (April 1991): 153–62. http://dx.doi.org/10.1080/17476939108814477.

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8

Tereshina, Maria, Oxana Erina, Dmitriy Sokolov, Lyudmila Efimova, and Nikolay Kasimov. "Nutrient dynamics along the Moskva River under heavy pollution and limited self-purification capacity." E3S Web of Conferences 163 (2020): 05014. http://dx.doi.org/10.1051/e3sconf/202016305014.

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An extensive study conducted during the dry summer of 2019 provided a detailed picture of the nutrient content dynamics along the Moskva River. Water sampling at 38 locations on the main river and at 17 of its tributaries revealed a manifold increase in phosphorus and nitrogen concentrations as the river crosses the Moscow metropolitan area, which can be attributed to both direct discharge of poorly treated sewage and nonpoint urban pollution. Even at the Moskva River lower reaches, where the anthropogenic pressure on the river and its tributaries is less pronounced, the inorganic nitrogen and phosphorus content remains consistently high and exceeds the environmental guidelines by up to almost 10 times. This indicates increased vulnerability of the Moskva River ecosystem during periods of low flow, which can be a major factor of eutrophication in the entire Moskva-Oka-Volga system. Comparison of our data with some archive records shows no significant improve in the nutrient pollution of the river since the 1990s, which raises further concern about the effectiveness of water quality management in Moscow urban region.

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9

Forstnerič, Franc. "Oka manifolds." Comptes Rendus Mathematique 347, no. 17-18 (September 2009): 1017–20. http://dx.doi.org/10.1016/j.crma.2009.07.005.

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10

Lárusson, Finnur, and Tuyen Trung Truong. "Approximation and interpolation of regular maps from affine varieties to algebraic manifolds." MATHEMATICA SCANDINAVICA 125, no. 2 (October 19, 2019): 199–209. http://dx.doi.org/10.7146/math.scand.a-114893.

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We consider the analogue for regular maps from affine varieties to suitable algebraic manifolds of Oka theory for holomorphic maps from Stein spaces to suitable complex manifolds. The goal is to understand when the obstructions to approximation or interpolation are purely topological. We propose a definition of an algebraic Oka property, which is stronger than the analytic Oka property. We review the known examples of algebraic manifolds satisfying the algebraic Oka property and add a new class of examples: smooth nondegenerate toric varieties. On the other hand, we show that the algebraic analogues of three of the central properties of analytic Oka theory fail for all compact manifolds and manifolds with a rational curve; in particular, for projective manifolds.

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11

Lárusson, Finnur. "Deformations of Oka manifolds." Mathematische Zeitschrift 272, no. 3-4 (December 11, 2011): 1051–58. http://dx.doi.org/10.1007/s00209-011-0973-9.

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12

Forstnerič, Franc. "Oka manifolds: From Oka to Stein and back." Annales de la faculté des sciences de Toulouse Mathématiques 22, no. 4 (2013): 747–809. http://dx.doi.org/10.5802/afst.1388.

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13

Kusakabe, Yuta. "Oka complements of countable sets and nonelliptic Oka manifolds." Proceedings of the American Mathematical Society 148, no. 3 (November 6, 2019): 1233–38. http://dx.doi.org/10.1090/proc/14832.

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14

Lárusson, Finnur. "Affine simplices in Oka manifolds." Documenta Mathematica 14 (2009): 691–97. http://dx.doi.org/10.4171/dm/286.

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15

Mongodi, Samuele, and Giuseppe Tomassini. "Oka principle for Levi flat manifolds." Bollettino dell'Unione Matematica Italiana 12, no. 1-2 (October 8, 2018): 177–96. http://dx.doi.org/10.1007/s40574-018-0174-0.

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16

Kusakabe, Yuta. "Elliptic characterization and localization of Oka manifolds." Indiana University Mathematics Journal 70, no. 3 (2021): 1039–54. http://dx.doi.org/10.1512/iumj.2021.70.8454.

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17

Schwarz, Gerald. "An Oka principle for Stein G-manifolds." Indiana University Mathematics Journal 67, no. 5 (2018): 2045–60. http://dx.doi.org/10.1512/iumj.2018.67.7448.

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18

Chenoweth, Brett. "Carleman approximation of maps into Oka manifolds." Proceedings of the American Mathematical Society 147, no. 11 (May 29, 2019): 4847–61. http://dx.doi.org/10.1090/proc/14595.

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19

Arosio, Leandro, and Finnur Lárusson. "Dynamics of generic endomorphisms of Oka–Stein manifolds." Mathematische Zeitschrift 300, no. 3 (October 5, 2021): 2467–84. http://dx.doi.org/10.1007/s00209-021-02874-9.

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20

Prezelj, Jasna, and Marko Slapar. "The generalized Oka-Grauert principle for 1-convex manifolds." Michigan Mathematical Journal 60, no. 3 (November 2011): 495–506. http://dx.doi.org/10.1307/mmj/1320763045.

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21

Coltoiu, Mihnea. "On the Oka-Grauert principle for 1-convex manifolds." Mathematische Annalen 310, no. 3 (March 1, 1998): 561–69. http://dx.doi.org/10.1007/s002080050160.

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22

Lárusson, Finnur. "Absolute neighbourhood retracts and spaces of holomorphic maps from Stein manifolds to Oka manifolds." Proceedings of the American Mathematical Society 143, no. 3 (October 16, 2014): 1159–67. http://dx.doi.org/10.1090/s0002-9939-2014-12335-5.

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23

Forstnerič, Franc, and Erlend Fornæss Wold. "Holomorphic families of Fatou–Bieberbach domains and applications to Oka manifolds." Mathematical Research Letters 27, no. 6 (2020): 1697–706. http://dx.doi.org/10.4310/mrl.2020.v27.n6.a5.

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24

Patyi, Imre. "A converse to the Oka principle over certain complex Banach manifolds." Bulletin des Sciences Mathématiques 133, no. 5 (July 2009): 484–92. http://dx.doi.org/10.1016/j.bulsci.2008.10.004.

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25

Fogarasi, Barbara, and Andrea Dúll. "Inside the Mind and Heart of Homo Aedificator •." Építés - Építészettudomány 49, no. 1-2 (March 15, 2021): 267–87. http://dx.doi.org/10.1556/096.2021.00009.

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While the reasons that lead to the current crisis of the heritage preservation sector in Hungary are manifold, it is worth looking into what might be done to draw attention to some issues that may help consolidate the ground of common values; the foundation, upon which a meaningful dialogue can be constructed, leading to the appreciation of and willingness to care for the historic environment by all actors. There seems to be a hidden conflict between the values of conservation experts and those of laypeople. Possessing thorough knowledge about the nature of historical and architectural values and trained to easily identify these, we are bound to focus more on people, their meanings and values. Much can be learned from pervious, human-centred architectural theory and practice, some of which are reviewed in the study, with special attention to the work of Gyula Hajnóczi. Referring to his space theory and ideas about the perception of space, we are especially grateful for his term homo aedificator suggesting that architecture satisfies material and spiritual needs universal to all human beings. Recognizing the challenges that stem from the differences between architects and non-architects, and likewise, heritage professionals and laypeople, the concepts of environmental psychology can help us show the way to universal values. We look into the method of the semantic differential scale to identify the affective meanings of built historic environments. The first steps of an empirical psychological research allow us to see into the minds and hearts of heritage professionals by assessing how they qualify the subject of their daily expertise. While these preliminary results are definitely intriguing, shedding light on how professionals tend to give meaning, our research continues with the aim to reveal the attitudes and meanings people associate with built historic heritage and find viable tools to mitigate the discrepancies between the profession and the general public.Miközben a magyarországi műemlékvédelem jelenlegi válságának számos oka lehet, érdemes figyelmet fordítanunk arra, hogy mit tehetünk azért, hogy megerősítsük a közös értékek talaját; azt az alapot, amire olyan értelmes párbeszédeket építhetünk, melyek a történeti környezet értékelése és törődése iránti hajlandósághoz vezetnek. Egyre gyakrabban üti fel a fejét az a rejtett ellentét, ami a műemlékes szakértők és a laikusok értékei között feszül. Szakértőként, átfogó ismerettel a történeti és építészeti értékekről, melyeket megtanultunk könnyen azonosítani, hasznos lehet a figyelmünket az emberekre, az ő jelentésadásaikra és értékeikre fordítanunk. Sokat okulhatunk a korábbi, ember- központú építészetelméleti és gyakorlati példákból, melyek közül néhányat tanulmányunkban átte- kintünk, kiemelve Hajnóczi Gyula munkásságát. Térelméletére és térészlelési gondolataira hivat- kozva, különösen hálásak vagyunk a homo aedificator fogalmáért, utalva arra, hogy az építészet minden emberi lény anyagi és szellemi igényeit kielégíti. Felismerve az építész–nemépítész és ehhez hasonlóan a műemlékes szakember–laikus közötti különbözőségek kihívásait, a környezetpszicholó- gia segíthet az univerzális értékek felé vezető út megtalálásában. A szemantikus differenciál módsze- rét hívjuk segítségül az épített történeti környezet érzelmi jelentésének feltárására. Empirikus kutatá- sunk első lépéseivel betekintést nyerünk a műemlékes szakemberek vélekedéseibe, pontosabban abba, hogy hogyan minősítik szakértelmük tárgyát. Bár már ezek az előzetes eredmények is – melyek rávilágítanak arra, hogy a szakemberek hogyan értelmezik a műemlékeket – érdekesek lehetnek, kuta- tásunk azzal a céllal folytatódik, hogy általánosságban feltárjuk az emberek vélekedéseit és a történeti épületeknek tulajdonított jelentéseket. Eredményeinkkel használható eszközöket kívánunk nyújtani a szakmabeliek és a laikusok közötti ellentétek feloldására.

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26

Brudnyi, Alexander, and Damir Kinzebulatov. "Towards Oka–Cartan theory for algebras of holomorphic functions on coverings of Stein manifolds I." Revista Matemática Iberoamericana 31, no. 3 (2015): 989–1032. http://dx.doi.org/10.4171/rmi/861.

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27

Brudnyi, Alexander, and Damir Kinzebulatov. "Towards Oka–Cartan theory for algebras of holomorphic functions on coverings of Stein manifolds. II." Revista Matemática Iberoamericana 31, no. 4 (2015): 1167–230. http://dx.doi.org/10.4171/rmi/866.

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28

Hamenstädt, Ursula. "Time-preserving conjugacies of geodesic flows." Ergodic Theory and Dynamical Systems 12, no. 1 (March 1992): 67–74. http://dx.doi.org/10.1017/s0143385700006581.

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AbstractIn this note we study Borel-probability measures on the unit tangent bundle ofa compact negatively curved manifold M that are invariant under the geodesic flow. We interpret the entropy of such a measure as a Hausdorff dimension with respect to a natural family of distances on the ideal boundary of the universal covering of M. This in term yields necessary and sufficient conditions for the existence of time preserving conjugacies of geodesic flows.

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29

Naeve, Ambjörn. "Opportunistic (L)earning in the Mobile Knowledge Society." International Journal of Mobile and Blended Learning 2, no. 4 (October 2010): 29–46. http://dx.doi.org/10.4018/jmbl.2010100103.

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This paper discusses the concept of opportunistic collaboration within the emerging mobile knowledge society. The paper illustrates how opportunistic collaboration can be applied to the areas of learning and earning by demonstrating how to transform a traditional unemployment agency into an Opportunistic Collaboration Agency based on an entrepreneurial supply-support network structured in the form of a prosumer manifold. The OCA pattern provides ways to capture the dynamics of entrepreneurial work-relations in the emerging ’work-portfolio society’, increase the transparency of the entire value chain of economic activities, and create prosumer value loops that can support multi-dimensional bartering and increase the opportunities for marginalized groups of people to create value together. The paper ends by demonstrating how to use the OCA pattern to transform a traditional educational institution into an Opportunistic Learning Activity Broker that could help to bridge the gap between formal and informal learning.

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30

Grines, V. Z. "Structural stability and asymptotic behavior of invariant manifolds ofA-diffeomorphisms of surfaces." Journal of Dynamical and Control Systems 3, no. 1 (January 1997): 91–110. http://dx.doi.org/10.1007/bf02471763.

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31

Kai, Tatsuya. "Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part I: Fundamental Properties and Integrability/Nonintegrability Conditions." Mathematical Problems in Engineering 2012 (2012): 1–32. http://dx.doi.org/10.1155/2012/543098.

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We analyze a class of rheonomous affine constraints defined on configuration manifolds from the viewpoint of integrability/nonintegrability. First, we give the definition ofA-rheonomous affine constraints and introduce, geometric representation their. Some fundamental properties of theA-rheonomous affine constrains are also derived. We next define the rheonomous bracket and derive some necessary and sufficient conditions on the respective three cases: complete integrability, partial integrability, and complete nonintegrability for theA-rheonomous affine constrains. Then, we apply the integrability/nonintegrability conditions to some physical examples in order to confirm the effectiveness of our new results.

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32

Mikulski, W. M. "The natural operators lifting 1-forms on manifolds to the bundles ofA-velocities." Monatshefte f�r Mathematik 119, no. 1-2 (March 1995): 63–77. http://dx.doi.org/10.1007/bf01292769.

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33

Liu, Xing Hua, Dao Jing Wang, and Fu Shui Liu. "Experimental Study on Effect of Hot EGR on Combustion Characteristic of HICE under High Load Conditions." Advanced Materials Research 562-564 (August 2012): 1024–27. http://dx.doi.org/10.4028/www.scientific.net/amr.562-564.1024.

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In order to study the effect of hot EGR on combustion characteristic of hydrogen internal combustion engine (HICE), experimental study was taken on a 4 cylinder, 2.0L HICE. The speed was 3000rpm, and the throttle was fully open, the load was adjusted through quality regulation. When the hydrogen flow ratio was 2.79kg /h, the ignition advanced angle was optimized as maximum brake torque (MBT) timing, then the EGR valve was opened, and EGR valve was adjusted to control the flow of exhaust gas that back into the intake manifold. The test results show that: as the EGR ratio changing from 0(the EGR valve is fully closed) to 43.8%(the EGR valve is fully opened), the in-cylinder pressure is decreasing with the EGR ratio increasing; the coefficient of variation in indicated mean effective pressure (imepCOV) is not changing significantly at high load conditions, changing range is less than 1%; CA50 is postponed from 11.8oCAto15.2 oCA with EGR ratio increasing.

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34

Hall, T. J., and Curt Leben. "A new method for evaluating decay: the effect of oxygen on Polyporuscompactus in red oak." Canadian Journal of Forest Research 15, no. 6 (December 1, 1985): 1021–24. http://dx.doi.org/10.1139/x85-165.

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The effects of oxygen decay (weight loss) incited by Polyporuscompactus Overh. was studied using small fresh and dried wood blocks containing both sapwood and heartwood of similar radial position and age. A manifold was used to deliver hydrated gas mixtures of 1.0, 4.2, or 21% (ambient air) oxygen at constant pressure and continuous flow to jars containing inoculated or noninoculated blocks. Means (P = 0.05) for dry weight losses in inoculated blocks at 1.0, 4.2, and 21% oxygen were 3.3, 8.9, and 21.4%, respectively; losses may be comparable to decay by other white rot fungi using the soil-block procedure. Losses in noninoculated blocks at the above oxygen levels were 2.0, 4.6, and 7.0%, respectively. Differences in dry weight losses between fresh and dry blocks were found. In particular, losses in inoculated fresh blocks were significantly less than losses in inoculated dry blocks in ambient air. Native inhabitants occurring in fresh wood appear to interfere with the decay processes of P. compactus. Losses in noninoculated fresh blocks were significantly greater than in noninoculated dry blocks at 21% oxygen but not at 1.0 or 4.2% oxygen; losses were attributed to natural inhabitants in fresh wood.

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35

Dobrovolný, P., M. Rybníček, T. Kolář, R. Brázdil, M. Trnka, and U. Büntgen. "A tree-ring perspective on temporal changes in the frequency and intensity of hydroclimatic extremes in the territory of the Czech Republic since 761 AD." Climate of the Past Discussions 11, no. 4 (July 16, 2015): 3109–42. http://dx.doi.org/10.5194/cpd-11-3109-2015.

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Abstract. It is generally accepted that anthropogenic-induced climate change may affect the frequency and intensity of hydrological extremes, together with a variety of subsequent impacts on ecosystems and human society. Proxy records that are absolutely dated and annually resolved are indispensable to a better understanding of temporal changes in the occurrence of floods and droughts. This contribution presents a new dataset of 3194 oak (Quercus spp.) ring width samples from living trees and historical timbers, collected across the Czech Republic. A composite tree-ring width (TRW) chronology is developed that best captures the high-frequency extremes over the past 1250 years. The temporal distribution of negative and positive extremes is regular with no indication of clustering. The highest number of negative extremes was found in the 19th century, while positive extremes were most frequent in the 12th century. The lowest number of negative and positive extremes occurred in the 18th and 13th centuries respectively. Negative and positive TRW extremes were compared with the instrumental measurements back to 1805 AD, with documentary-based temperature and precipitation reconstructions from 1804 to 1500, and with documentary evidence before 1500 AD. Negative TRW extremes coincided with above-average March–May and June–August temperature means and below-average precipitation totals. Positive extremes coincided with higher summer precipitation, while temperatures were mostly normal. Mean sea level pressure (SLP) over the European/North Atlantic sector suggested drought for the negative oak TRW extremes, whereas the positive extremes corresponded to wetter conditions overall. More consistent patterns of synoptic SLP were found for negative rather than for positive extremes. Reasons for the possible offset between the oak-based hydroclimatic extremes and their counterparts from meteorological observations and documentary evidence may be manifold and emphasize the need for multi-proxy approaches and proxy-model comparisons.

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36

Dobrovolný, P., M. Rybníček, T. Kolář, R. Brázdil, M. Trnka, and U. Büntgen. "A tree-ring perspective on temporal changes in the frequency and intensity of hydroclimatic extremes in the territory of the Czech Republic since 761 AD." Climate of the Past 11, no. 10 (October 23, 2015): 1453–66. http://dx.doi.org/10.5194/cp-11-1453-2015.

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Abstract. It is generally accepted that anthropogenic-induced climate change may affect the frequency and intensity of hydrological extremes, together with a variety of subsequent impacts on ecosystems and human society. Proxy records that are absolutely dated and annually resolved are indispensable to a better understanding of temporal changes in the occurrence of floods and droughts. This contribution presents a new data set of 3194 oak (Quercus spp.) ring width samples from living trees and historical timbers, collected across the Czech Republic. A composite tree-ring width (TRW) chronology is developed that best captures the high-frequency extremes over the past 1250 years. The temporal distribution of negative and positive extremes is regular with no indication of clustering. The highest number of negative extremes was found in the 19th century, while positive extremes were most frequent in the 12th century. The lowest number of negative and positive extremes occurred in the 18th and 13th centuries respectively. Negative and positive TRW extremes were compared with the instrumental measurements back to 1805 AD, with documentary-based temperature and precipitation reconstructions from 1804 to 1500, and with documentary evidence before 1500 AD. Negative TRW extremes coincided with above-average March–May and June–August temperature means and below-average precipitation totals. Positive extremes coincided with higher summer precipitation, while temperatures were mostly normal. Mean sea level pressure (SLP) over the European/North Atlantic sector suggested drought for the negative oak TRW extremes, whereas the positive extremes corresponded to wetter conditions overall. More consistent patterns of synoptic SLP were found for negative rather than for positive extremes. Reasons for the possible offset between the oak-based hydroclimatic extremes and their counterparts from meteorological observations and documentary evidence may be manifold and emphasize the need for multi-proxy approaches.

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37

Mikulski, W. M. "The geometrical constructions lifting tensor fields of type (0,2) on manifolds to the bundles ofA-velocities." Nagoya Mathematical Journal 140 (December 1995): 117–37. http://dx.doi.org/10.1017/s0027763000005444.

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LetAbe a Weil algebra. The fibre bundleTAMofA-velocities over a manifoldMwas described by A. Morimoto [15] as another description of the bundle of nearA-points by Weil [17]. In [4] for any tensor fieldτof type (0,2) onMand any functionalλ ∈ A*we have defined the so calledλ-lift of τ toTAM. We recall this construction in Example 1.3. Theλ-lift of τ is a naturally induced tensor field of type (0,2) onTAM.

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38

Головин, Ю. И., А. И. Тюрин, А. А. Гусев, С. М. Матвеев, Д. Ю. Головин, А. А. Самодуров, И. А. Васюкова, М. А. Юнак, Е. А. Колесников, and О. В. Захарова. "Локальные механические свойства и кольцевая структура древесины, исследованные методом сканирующего наноиндентирования." Журнал технической физики 92, no. 4 (2022): 575. http://dx.doi.org/10.21883/jtf.2022.04.52245.297-21.

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The paper presents the results of scanning of mechanical properties of coniferous (common pine Pinus sylvestris) and deciduous (small-leaved lime Tilia cordata and common oak Quercus robur) trees wood using nanoindentation on crosscut face. Manifold increase in microhardness H and Young’s modulus E has been observed between early and late wood in every annual growth ring. Significant differences in intraring radial dependencies of H and E have been found among studied species. For all studied species the average values of E and H of early wood in each annual ring are found to be independent from ring width, while such dependence for late wood is weak at most. The ring widths measured by nanoindentation coincide with the ones measured by standard optical method within 2-3%. The developed technique and obtained results can be useful 1) to amend the understanding the origins of macromechanical properties of various wood species and their dependence upon microstructural characteristics and growth conditions, 2) to optimize the technologies of growing, reinforcement and subsequent usage of the wood, 3) to develop new independent high resolution methods in dendrochronology.

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Golovin Yu. I., Tyurin A. I., Gusev A. A., Matveev S. M., Golovin D. Yu., Samodurov A. A., Vasyukova I. A., Yunak M.A., Kolesnikov E. A., and Zakharova O. V. "Scanning naation as an instrument of studying local mechanical properties distribution in wood and a new technique for dendrochronology." Technical Physics 92, no. 4 (2022): 484. http://dx.doi.org/10.21883/tp.2022.04.53605.297-21.

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Abstract:

The paper presents the results of scanning of mechanical properties of coniferous (common pine Pinus sylvestris) and deciduous (small-leaved lime Tilia cordata and common oak Quercus robur) trees wood using naation on crosscut face. Manifold increase in microhardness H and Young's modulus E has been observed between early and late wood in every annual growth ring. Significant differences in intraring radial dependencies of H and E have been found among studied species. For all studied species the average values of E and H of early wood in each annual ring are found to be independent from ring width, while such dependence for late wood is weak at most. The ring widths measured by naation coincide with the ones measured by standard optical method within 2-3%. The developed technique and obtained results can be useful 1) to amend the understanding the origins of macromechanical properties of various wood species and their dependence upon microstructural characteristics and growth conditions, 2) to optimize the technologies of growing, reinforcement and subsequent usage of the wood, 3) to develop new independent high resolution methods in dendrochronology. Keywords: naation, nano-/microhardness and Young's modulus scanning, tree annual growth rings, dendrochronology.

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Finkelberg, Aryeh. "On the Unity of Orphic and Milesian Thought." Harvard Theological Review 79, no. 4 (October 1986): 321–35. http://dx.doi.org/10.1017/s0017816000020137.

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In the first volume ofA History of Greek PhilosophyW. K. C. Guthrie points out that “the promulgators ofteletaiin the name of Orpheus were concerned in the religious sphere with the same problem of the relation between the One and the Many which in a different form was the problem of the Milesian philosophers.” Elsewhere Guthrie provides a more detailed explanation of the similarities and differences between the Orphic and the Milesian treatment of the One-Many problem:Sixth-century religious and philosophical thought … was dominated by one central problem, the problem of the One and the Many. This appeared in two forms, one referring to the macrocosm, the other to the microcosm. In its first form it was the problem of the Milesian natural philosophers, who asked: “What is the relation between the manifold variety of the world in which we live and the one primary substance out of which, as we are convinced, it must in the first place have arisen?” In its second form it was the problem of the religious minds of the age. Their question was: “What is the relation of each individual man to the divine, to which we feel we are akin, and how can we best realize and actualize the potential unity which underlies the two?”

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Kutzschebauch, Frank, Finnur Lárusson, and Gerald W. Schwarz. "Equivariant Oka theory: survey of recent progress." Complex Analysis and its Synergies 8, no. 3 (August 24, 2022). http://dx.doi.org/10.1007/s40627-022-00103-5.

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AbstractWe survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles for equivariant isomorphisms of Stein manifolds on which a reductive complex Lie group G acts. Applications to the linearisation problem. A parametric Oka principle for sections of a bundle E of homogeneous spaces for a group bundle $${{\mathscr {G}}}$$ G , all over a reduced Stein space X with compatible actions of a reductive complex group on E, $${{\mathscr {G}}}$$ G , and X. Application to the classification of generalised principal bundles with a group action. Finally, an equivariant version of Gromov’s Oka principle based on a notion of a G-manifold being G-Oka.

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Nair, Arvind N., and Ankit Rai. "AUTOMORPHIC LEFSCHETZ PROPERTIES FOR NONCOMPACT ARITHMETIC MANIFOLDS." Journal of the Institute of Mathematics of Jussieu, October 18, 2021, 1–48. http://dx.doi.org/10.1017/s1474748021000499.

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Abstract We prove the injectivity of Oda-type restriction maps for the cohomology of noncompact congruence quotients of symmetric spaces. This includes results for restriction between (1) congruence real hyperbolic manifolds, (2) congruence complex hyperbolic manifolds, and (3) orthogonal Shimura varieties. These results generalize results for compact congruence quotients by Bergeron and Clozel [Quelques conséquences des travaux d’Arthur pour le spectre et la topologie des variétés hyperboliques, Invent. Math.192 (2013), 505–532] and Venkataramana [Cohomology of compact locally symmetric spaces, Compos. Math.125 (2001), 221–253]. The proofs combine techniques of mixed Hodge theory and methods involving automorphic forms.

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