Journal articles on the topic 'Derivators'

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1

Groth, Moritz. "Derivators, pointed derivators and stable derivators." Algebraic & Geometric Topology 13, no. 1 (February 25, 2013): 313–74. http://dx.doi.org/10.2140/agt.2013.13.313.

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2

Groth, Moritz, Kate Ponto, and Michael Shulman. "The additivity of traces in monoidal derivators." Journal of K-theory 14, no. 3 (July 14, 2014): 422–94. http://dx.doi.org/10.1017/is014005011jkt262.

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AbstractMotivated by traces of matrices and Euler characteristics of topological spaces, we expect abstract traces in a symmetric monoidal category to be “additive”. When the category is “stable” in some sense, additivity along cofiber sequences is a question about the interaction of stability and the monoidal structure.May proved such an additivity theorem when the stable structure is a triangulation, based on new axioms for monoidal triangulated categories. in this paper we use stable derivators instead, which are a different model for “stable homotopy theories”. We define and study monoidal structures on derivators, providing a context to describe the interplay between stability and monoidal structure using only ordinary category theory and universal properties. We can then perform May's proof of the additivity of traces in a closed monoidal stable derivator without needing extra axioms, as all the needed compatibility is automatic.
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3

Hörmann, Fritz. "Enlargement of (fibered) derivators." Journal of Pure and Applied Algebra 224, no. 3 (March 2020): 1023–63. http://dx.doi.org/10.1016/j.jpaa.2019.07.001.

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4

Coley, Ian. "Stabilization of derivators revisited." Journal of Homotopy and Related Structures 14, no. 2 (November 10, 2018): 525–77. http://dx.doi.org/10.1007/s40062-018-0224-4.

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5

Muro, Fernando, and Georgios Raptis. "K-theory of derivators revisited." Annals of K-Theory 2, no. 2 (January 1, 2017): 303–40. http://dx.doi.org/10.2140/akt.2017.2.303.

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6

Coley, Ian. "The theory of half derivators." Documenta Mathematica 27 (2022): 655–98. http://dx.doi.org/10.4171/dm/881.

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7

Groth, Moritz, Kate Ponto, and Michael Shulman. "Mayer-Vietoris sequences in stable derivators." Homology, Homotopy and Applications 16, no. 1 (2014): 265–94. http://dx.doi.org/10.4310/hha.2014.v16.n1.a15.

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8

Gallauer Alves de Souza, Martin. "Traces in monoidal derivators, and homotopy colimits." Advances in Mathematics 261 (August 2014): 26–84. http://dx.doi.org/10.1016/j.aim.2014.03.029.

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9

Lenz, Tobias. "Homotopy (pre)derivators of cofibration categories and quasicategories." Algebraic & Geometric Topology 18, no. 6 (October 18, 2018): 3601–46. http://dx.doi.org/10.2140/agt.2018.18.3601.

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10

Muro, Fernando, and George Raptis. "A note on K-theory and triangulated derivators." Advances in Mathematics 227, no. 5 (August 2011): 1827–45. http://dx.doi.org/10.1016/j.aim.2011.04.005.

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11

Lagkas-Nikolos, Ioannis. "Levelwise modules over separable monads on stable derivators." Journal of Pure and Applied Algebra 222, no. 7 (July 2018): 1704–26. http://dx.doi.org/10.1016/j.jpaa.2017.08.001.

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12

CISINSKI, DENIS–CHARLES. "Locally constant functors." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 3 (June 10, 2009): 593–614. http://dx.doi.org/10.1017/s030500410900262x.

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AbstractWe study locally constant coefficients. We first study the theory of homotopy Kan extensions with locally constant coefficients in model categories, and explain how it characterizes the homotopy theory of small categories. We explain how to interpret this in terms of left Bousfield localization of categories of diagrams with values in a combinatorial model category. Finally, we explain how the theory of homotopy Kan extensions in derivators can be used to understand locally constant functors.
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13

Nakaoka, Hiroyuki. "Biset Functors as Module Mackey Functors and its Relation to Derivators." Communications in Algebra 44, no. 12 (July 6, 2016): 5105–48. http://dx.doi.org/10.1080/00927872.2016.1147572.

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14

Balmer, Paul, and John Zhang. "Affine space over triangulated categories: A further invitation to Grothendieck derivators." Journal of Pure and Applied Algebra 221, no. 7 (July 2017): 1560–64. http://dx.doi.org/10.1016/j.jpaa.2016.12.016.

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15

Laking, Rosanna. "Purity in compactly generated derivators and t-structures with Grothendieck hearts." Mathematische Zeitschrift 295, no. 3-4 (November 7, 2019): 1615–41. http://dx.doi.org/10.1007/s00209-019-02411-9.

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16

Fernández, Francisco J., and F. Adrián F. Tojo. "Numerical Solution of Stieltjes Differential Equations." Mathematics 8, no. 9 (September 11, 2020): 1571. http://dx.doi.org/10.3390/math8091571.

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This work is devoted to the obtaining of a new numerical scheme based on quadrature formulae for the Lebesgue–Stieltjes integral for the approximation of Stieltjes ordinary differential equations. This novel method allows us to numerically approximate models based on Stieltjes ordinary differential equations for which no explicit solution is known. We prove several theoretical results related to the consistency, convergence, and stability of the numerical method. We also obtain the explicit solution of the Stieltjes linear ordinary differential equation and use it to validate the numerical method. Finally, we present some numerical results that we have obtained for a realistic population model based on a Stieltjes differential equation and a system of Stieltjes differential equations with several derivators.
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17

Patrik, Grosinger, and Šolek Peter. "Application of Analogue Derivators for Obtaining Direct Non-Measurable Components of the State Vector in Crane Control." Strojnícky časopis - Journal of Mechanical Engineering 69, no. 4 (December 1, 2019): 33–44. http://dx.doi.org/10.2478/scjme-2019-0041.

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AbstractThis paper presents a simple-to-use system for estimating non-measurable components of crane state vector considering parameter changes. To obtain them, it is possible to use a numerical derivative, where the measurement noise causes great inaccuracies, or the Luenberger observer and Kalman filter, which require knowledge of the dynamics of the controlled system, which is constantly changing with the crane.
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18

Alekseev, Aleksandr, and Andronick Arutyunov. "DERIVATIONS IN SEMIGROUP ALGEBRAS." Eurasian Mathematical Journal 11, no. 2 (2020): 9–18. http://dx.doi.org/10.32523/2077-9879-2020-11-2-09-18.

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19

Borisavljevi, Mirjana. "NORMAL DERIVATIONS AND SEQUENT DERIVATIONS." Journal of Philosophical Logic 37, no. 6 (May 29, 2008): 521–48. http://dx.doi.org/10.1007/s10992-008-9084-4.

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20

Brzdęk, Janusz, and Ajda Fošner. "On approximate generalized Lie derivations." Glasnik Matematicki 50, no. 1 (June 22, 2015): 77–99. http://dx.doi.org/10.3336/gm.50.1.07.

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21

Putri Syafriani, Adek, Sri Gemawati, and Sya msudhuha. "T-DERIVATIONS IN BF-ALGEBRAS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 10, no. 12 (December 26, 2022): 3064–67. http://dx.doi.org/10.47191/ijmcr/v10i12.11.

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In this paper, we define the concept of (ℓ,ꭉ)-t-derivation and (ꭉ,ℓ)-t-derivation in BF-algebras. Then, we investigate some properties of (ℓ,ꭉ) and (ꭉ,ℓ)-t-derivation in BF-algebras. Also, we obtain some properties of regular of t-derivation in BF-algebra. Finally, we investigate the properties of the concept in BF1-algebras.
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22

NABIEL, Hesham. "Derivations, generalized derivations, and *-derivations of period 2 in rings." TURKISH JOURNAL OF MATHEMATICS 42, no. 5 (September 9, 2018): 2664–71. http://dx.doi.org/10.3906/mat-1805-111.

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23

Mitra and Mukhopadhyay. "DERIVATES, APPROXIMATE DERIVATES AND POROSITY DERIVATES OF n-CONVEX FUNCTIONS." Real Analysis Exchange 27, no. 1 (2001): 249. http://dx.doi.org/10.2307/44154121.

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24

AL-NOFAYEE, S., and S. K. NAUMAN. "DERIVATIONS ON MORITA RINGS AND GENERALIZED DERIVATIONS." Journal of Algebra and Its Applications 10, no. 02 (April 2011): 191–200. http://dx.doi.org/10.1142/s0219498811004525.

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25

Johnson, B. E. "Local derivations on $C^*$-algebras are derivations." Transactions of the American Mathematical Society 353, no. 1 (September 18, 2000): 313–25. http://dx.doi.org/10.1090/s0002-9947-00-02688-x.

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26

Samman, M., and N. Alyamani. "Derivations and reverse derivations in semiprime rings." International Mathematical Forum 2 (2007): 1895–902. http://dx.doi.org/10.12988/imf.2007.07168.

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27

Fošner, Ajda, and Maja Fošner. "On ε-derivations and local ε-derivations." Acta Mathematica Sinica, English Series 26, no. 8 (July 15, 2010): 1555–66. http://dx.doi.org/10.1007/s10114-010-7650-5.

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28

de León, Manuel, and Modesto Salgado. "Lifts of derivations to the frame bundle." Czechoslovak Mathematical Journal 37, no. 1 (1987): 42–50. http://dx.doi.org/10.21136/cmj.1987.102133.

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29

Vanžura, Jiří. "Derivations on the Nijenhuis-Schouten bracket algebra." Czechoslovak Mathematical Journal 40, no. 4 (1990): 671–89. http://dx.doi.org/10.21136/cmj.1990.102420.

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30

Molnár, Lajos. "Locally inner derivations of standard operator algebras." Mathematica Bohemica 121, no. 1 (1996): 1–7. http://dx.doi.org/10.21136/mb.1996.125942.

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31

Kosi-Ulbl, Irena, and Joso Vukman. "On certain identity related to Jordan *-derivations." Glasnik Matematicki 50, no. 2 (December 30, 2015): 363–71. http://dx.doi.org/10.3336/gm.50.2.07.

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32

Redondo, María Julia, and Andrea Solotar. "α-Derivations." Canadian Mathematical Bulletin 38, no. 4 (December 1, 1995): 481–89. http://dx.doi.org/10.4153/cmb-1995-070-2.

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AbstractLet A be a commutative k-algebra with 1. We present a characterization of α-derivations, for α: A →> A a morphism of algebras, using α-Taylor series. When S = C[x,x-1,ξ] and α(x) = qx, α(ξ) = qξ, we compare the q-de Rham cohomology of the C-algebra S with the Hochschild homology of Dq, the algebra of q-difference operators on C[x,x-1], for q ∊ C, q ≠ 0,1.
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33

Burzio, Luigi. "Zero Derivations." Linguistic Inquiry 32, no. 4 (October 2001): 658–77. http://dx.doi.org/10.1162/002438901753373032.

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Rubach (2000) proposes a modified version of Optimality Theory (OT) that features derivations. While Prince and Smolensky's (1993) original formulation requires some modification, argue here that, rather than reintroducing derivations, the correct approach is to take fuller advantage of OT's inherent parallelism. I propose that outputs must be related not only to inputs, but to other, “neighboring” representations as well—a feature that is shared by both the output-to-output faithfulness approach and the theory of targeted constraints developed by Wilson (2000, to appear). I show that all the cases cited by Rubach that seem to support derivations are in fact handled by the latter two related theories, and that both ofthese have significant advantages over derivations.
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34

Doubek, Martin, and Tom Lada. "Homotopy derivations." Journal of Homotopy and Related Structures 11, no. 3 (September 9, 2015): 599–630. http://dx.doi.org/10.1007/s40062-015-0118-7.

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35

Pedersen, Steen. "Anticommuting derivations." Proceedings of the American Mathematical Society 127, no. 4 (1999): 1103–8. http://dx.doi.org/10.1090/s0002-9939-99-04642-0.

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36

Nowicki, Andrzej. "Integral derivations." Journal of Algebra 110, no. 1 (October 1987): 262–76. http://dx.doi.org/10.1016/0021-8693(87)90045-7.

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37

Morrison, Sally D. "Continuous derivations." Journal of Algebra 110, no. 2 (October 1987): 468–79. http://dx.doi.org/10.1016/0021-8693(87)90058-5.

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38

Kadison, Richard V. "Local derivations." Journal of Algebra 130, no. 2 (May 1990): 494–509. http://dx.doi.org/10.1016/0021-8693(90)90095-6.

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39

Reinhart, Tanya. "Experiencing Derivations." Semantics and Linguistic Theory 11 (October 3, 2001): 365. http://dx.doi.org/10.3765/salt.v11i0.2845.

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40

Ollagnier, Jean Moulin, and Andrzej Nowicki. "Monomial Derivations." Communications in Algebra 39, no. 9 (September 2011): 3138–50. http://dx.doi.org/10.1080/00927872.2010.496750.

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41

Chuang, C. L. "Hypercentral Derivations." Journal of Algebra 166, no. 1 (May 1994): 34–71. http://dx.doi.org/10.1006/jabr.1994.1140.

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42

Chung, L. O. "Nil derivations." Journal of Algebra 95, no. 1 (July 1985): 20–30. http://dx.doi.org/10.1016/0021-8693(85)90089-4.

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43

Chuang, Chen-Lian, and Tsiu-Kwen Lee. "Nilpotent derivations." Journal of Algebra 287, no. 2 (May 2005): 381–401. http://dx.doi.org/10.1016/j.jalgebra.2005.02.010.

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44

Kishimoto, Akitaka, and Hideki Nakamura. "Super-derivations." Communications in Mathematical Physics 159, no. 1 (January 1994): 15–27. http://dx.doi.org/10.1007/bf02100483.

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45

Achinstein, Peter. "Theoretical derivations." Studies in History and Philosophy of Science Part A 17, no. 4 (December 1986): 375–414. http://dx.doi.org/10.1016/0039-3681(86)90001-4.

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46

Mirzavaziri. "Generalized Higher Derivations are Sequences of Generalized Derivations." Journal of Advanced Research in Pure Mathematics 3, no. 1 (January 1, 2011): 75–86. http://dx.doi.org/10.5373/jarpm.445.052610.

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47

Yon, Yong, and Şule Özbal. "On derivations and generalized derivations of bitonic algebras." Applicable Analysis and Discrete Mathematics 12, no. 1 (2018): 110–25. http://dx.doi.org/10.2298/aadm1801110y.

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We introduce the notion of bitonic algebras as a generalization of dual BCCalgebras, and define the notion of (r,l)-derivations, (l,r)-derivations and generalized (r,l) and (l,r)-derivations on the bitonic algebras. Then we study the properties of the derivations and the generalized derivations on the bitonic algebras and the commutative bitonic algebras. Finally, we show that every generalized derivation of commutative bitonic algebras is a derivation.
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48

Hosseinia, Amin. "Identities related to generalized derivations and jordan (*,*)-derivations." Filomat 35, no. 7 (2021): 2349–60. http://dx.doi.org/10.2298/fil2107349h.

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The main purpose of this research is to characterize generalized (left) derivations and Jordan (*,*)-derivations on Banach algebras and rings using some functional identities. Let A be a unital semiprime Banach algebra and let F,G : A ? A be linear mappings satisfying F(x) =-x2G(x-1) for all x ? Inv(A), where Inv(A) denotes the set of all invertible elements of A. Then both F and G are generalized derivations on A. Another result in this regard is as follows. Let A be a unital semiprime algebra and let n > 1 be an integer. Let f,g : A ? A be linear mappings satisfying f (an) = nan-1g(a) = ng(a)an-1 for all a ? A. If g(e) ? Z(A), then f and g are generalized derivations associated with the same derivation on A. In particular, if A is a unital semisimple Banach algebra, then both f and 1 are continuous linear mappings. Moreover, we define a (*,*)-ring and a Jordan (*,*)-derivation. A characterization of Jordan (*,*)-derivations is presented as follows. Let R be an n!-torsion free (*,*)-ring, let n > 1 be an integer and let d : R ? R be an additive mapping satisfying d(an) = ?nj =1 a*n-jd(a)a* j-1 for all a ? R. Then d is a Jordan (*,*)-derivation on R. Some other functional identities are also investigated.
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49

Çeven, Yılmaz. "n-Derivations and (n,m)-Derivations of Lattices." Mathematics 6, no. 12 (December 6, 2018): 307. http://dx.doi.org/10.3390/math6120307.

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In this paper, firstly, as a generalization of derivations on a lattice, the notion of n-derivation is introduced and some fundamental properties are investigated. Secondly, the concept of (n,m)-derivation-homomorphism on lattices is described and important and characteristic properties are given.
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50

BAVULA, V. V. "DERIVATIONS AND SKEW DERIVATIONS OF THE GRASSMANN ALGEBRAS." Journal of Algebra and Its Applications 08, no. 06 (December 2009): 805–27. http://dx.doi.org/10.1142/s0219498809003655.

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Surprisingly, skew derivations rather than ordinary derivations are more basic (important) object in study of the Grassmann algebras. Let Λn = K ⌊x1, …, xn⌋ be the Grassmann algebra over a commutative ring K with ½ ∈ K, and δ be a skew K-derivation of Λn. It is proved that δ is a unique sum δ = δ ev + δ od of an even and odd skew derivation. Explicit formulae are given for δev and δod via the elements δ (x1), …, δ (xn). It is proved that the set of all even skew derivations of Λn coincides with the set of all the inner skew derivations. Similar results are proved for derivations of Λn. In particular, Der K(Λn) is a faithful but not simple Aut K(Λn)-module (where K is reduced and n ≥ 2). All differential and skew differential ideals of Λn are found. It is proved that the set of generic normal elements of Λn that are not units forms a single Aut K(Λn)-orbit (namely, Aut K(Λn)x1) if n is even and two orbits (namely, Aut K(Λn)x1 and Aut K(Λn)(x1 + x2 ⋯ xn)) if n is odd.
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