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1

DULGARIAN, ROBERT. "Richard Baxter, Thomas Barlow and the Advice to a Young Student in Theology, St John's College, Cambridge, MS K.38: A Preliminary Assessment." Journal of Ecclesiastical History 69, no. 2 (September 6, 2017): 345–66. http://dx.doi.org/10.1017/s0022046917000689.

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This article identifies as the work of Richard Baxter a set of ecclesiastical directions and reading recommendations contained in fos 180–208 of St John's College, Cambridge, MS K.38, once tentatively ascribed to Thomas Barlow, but demonstrably a close analogue of British Library, MS Harleian 6009, which is a copy of a lost Baxter original. Internal evidence of MS K.38 and comparison with MS 6009 and Baxter's Christian directory imply both an earlier date and a wider circulation of Baxter's archetype than hitherto suspected, suggesting a new direction of inquiry into Baxter's scholarly and ecclesiastical associations.
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2

Bouvel, Mathilde, Veronica Guerrini, Andrew Rechnitzer, and Simone Rinaldi. "Semi-Baxter and Strong-Baxter: Two Relatives of the Baxter Sequence." SIAM Journal on Discrete Mathematics 32, no. 4 (January 2018): 2795–819. http://dx.doi.org/10.1137/17m1126734.

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3

Ma, Tianshui, and Linlin Liu. "Rota–Baxter coalgebras and Rota–Baxter bialgebras." Linear and Multilinear Algebra 64, no. 5 (July 27, 2015): 968–79. http://dx.doi.org/10.1080/03081087.2015.1068269.

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4

Bäccman, Charlotte, Per Folkesson, and Torsten Norlander. "EXPECTATIONS OF ROMANTIC RELATIONSHIPS: A COMPARISON BETWEEN HOMOSEXUAL AND HETEROSEXUAL MEN WITH REGARD TO BAXTER'S CRITERIA." Social Behavior and Personality: an international journal 27, no. 4 (January 1, 1999): 363–74. http://dx.doi.org/10.2224/sbp.1999.27.4.363.

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According to Baxter (1986) every relationship has rules which must be followed. If at least one of these rules is broken, it gives the individual the right to breakup the relationship. Baxter identified eight such rules or criteria. The aim of the present study was to investigate whether or not the expectations of romantic relationships held by homosexual men can be linked to Baxter's criteria. Data were obtained through a questionnaire addressed to 31 homosexual men and 50 heterosexual men. Results indicated that Baxter's criteria can be linked to expectations of romantic relationships held by men regardless of sexual orientation, and that age and experience are more reliable predictors than is sexual orientation.
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5

CONDIE, KEITH. "SOME FURTHER CORRESPONDENCE BETWEEN RICHARD BAXTER AND KATHERINE GELL." Historical Journal 53, no. 1 (January 29, 2010): 165–76. http://dx.doi.org/10.1017/s0018246x0999046x.

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ABSTRACTThe puritan pastor and writer, Richard Baxter, and a member of a prominent Derbyshire family, Katherine Gell, exchanged a series of letters between 1655 and 1658. This article highlights the existence of three further items of correspondence in this exchange, located in the Derbyshire Record Office, hitherto believed not to be extant. The additional three letters are all penned by Baxter and include his replies to her first two epistles (dated 28 July 1655 and 4 September 1655) as well as a reply to a non-extant Gell letter (dated 31 July 1658). The correspondence provides valuable insights into Baxter's pastoral methods and the nature of puritan piety. The first two items draw attention to the importance of the dimension of duty within Baxter's pastoral agenda; while expressed in a context of warmth and encouragement, he believes that Gell will find a measure of resolution to her spiritual struggles by careful attention to the obligations of Christian living. The third letter, written some years later, after Baxter has discovered that Gell suffers from melancholia, is couched in a gentler tone and reveals a more reciprocal dimension to their relationship.
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6

Horling, Frank M., Christine Lenk, Rafi Uddin Ahmad, Markus Weiller, Maria Schuster, Hans Peter Schwarz, and Birgit M. Reipert. "Preclinical Immunogenicity Assessment of Baxter‘s Recombinant Factor VIIa,." Blood 118, no. 21 (November 18, 2011): 3327. http://dx.doi.org/10.1182/blood.v118.21.3327.3327.

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Abstract Abstract 3327 Baxter has developed a recombinant FVIIa (rFVIIa) product for the treatment of hemophilia patients with factor VIII or factor IX inhibitors. Before entering clinical development we assessed the immunogenic safety profile of the new product candidate BAX 817 using two novel mouse models that mimicked specific aspects of the situation in patients. Several comparative preclinical immunogenicity studies were conducted to assess the immunogenicity profile of Baxter`s rFVIIa BAX 817 in comparison to a licensed recombinant FVIIa product. Three different mouse models were used for this purpose. The first model expresses specific immune tolerance against human FVIIa and, therefore, mimics the situation in both hemophilia A and hemophilia B patients. Using this model, we asked if Baxter‘s rFVIIa is able to maintain immune tolerance to human FVIIa. The second model is a hemophilia A model that mimics the situation in an important fraction of hemophilia A patients with FVIII inhibitors. This model expresses a human MHC-class II haplotype (HLA-DRB1*1501) that was previously shown to be associated with an increased risk for the development of FVIII inhibitors. The third model represents a normal wildtype C57BL/6 mouse. All mice were treated with 8 weekly doses of either Baxter‘s rFVIIa BAX 817 or a licensed recombinant FVIIa product. Total anti-FVIIa antibodies were analyzed prior to the first dose as well as after the 4th and the 8th dose using ELISA assays. Baxter`s rFVIIa BAX 817 and a licensed recombinant FVIIa product induced similar titers of anti-FVIIa antibodies in C57BL/6 wildtype mice and in hemophilic HLA-DRB1*1501 mice. In addition, both Baxter`s rFVIIa BAX 817 and a licensed recombinant FVIIa product were able to maintain specific immune tolerance in a novel mouse model that is immunologically tolerant to human FVIIa. Based on the data obtained we conclude that both Baxter‘s rFVIIa BAX 817 and a licensed recombinant FVIIa product have a comparable immunogenic safety profile. Disclosures: Horling: Baxter Innovations GmbH: Employment. Lenk:Baxter BioScience: Employment. Ahmad:Baxter BioScience: Employment. Weiller:Baxter BioScience: Employment. Schuster:Baxter Innovation GmbH: Employment. Schwarz:Baxter Innovations GmbH: Employment. Reipert:Baxter Innovations GmbH: Employment.
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7

Adams, Anthony P. "FRED BAXTER." Survey of Anesthesiology 41, no. 6 (December 1997): 327. http://dx.doi.org/10.1097/00132586-199712000-00014.

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8

Dulucq, S., and O. Guibert. "Baxter permutations." Discrete Mathematics 180, no. 1-3 (February 1998): 143–56. http://dx.doi.org/10.1016/s0012-365x(97)00112-x.

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9

Baxter, Gordon. "Gordon Baxter." Interactions 27, no. 1 (December 26, 2019): 15. http://dx.doi.org/10.1145/3374233.

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10

Neachell, Emma, and Geoff Petts. "George Baxter." Progress in Physical Geography: Earth and Environment 41, no. 5 (October 2017): 686–97. http://dx.doi.org/10.1177/0309133317732922.

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This paper summarizes the innovative approach to setting environmental flows proposed by Baxter in 1961, describes its immediate impact across both engineering and fisheries disciplines and explores the reasons why his approach was not adopted in river flow regulation and management in the UK. Yet, the basic approach was to be used world-wide by the end of the century. Several barriers constrained innovation in flow regulation in England during the 1960s: the overwhelming pollution problems; serious concerns about water shortage and food security, not least in the context of the severe 1959 drought; the influence of the 1963 Water Resources Act and the legacy of previous legislation; the limited availability of both river flow data and biological data; and the lack of awareness of human impacts on the environment. The paper also provides lessons for promoting environmental science into policy and practice to advance the implementation of environmental flows.
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11

GUO, LI. "ASCENDING CHAIN CONDITIONS IN FREE BAXTER ALGEBRAS." International Journal of Algebra and Computation 12, no. 04 (August 2002): 601–22. http://dx.doi.org/10.1142/s0218196702001152.

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In this paper we study ascending chain conditions in a free Baxter algebra by making use of explicit constructions of free Baxter algebras that were obtained recently. We investigate ascending chain conditions both for ideals and for Baxter ideals. The free Baxter algebras under consideration include free Baxter algebras on sets and free Baxter algebras on algebras. We also consider complete free Baxter algebras.
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12

EBRAHIMI-FARD, KURUSCH, and LI GUO. "FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES." Journal of Algebra and Its Applications 07, no. 02 (April 2008): 167–94. http://dx.doi.org/10.1142/s0219498808002746.

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A Rota–Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota–Baxter relation, that generalizes the integration by parts formula. Most of the studies on Rota–Baxter algebras have been for commutative algebras. Two constructions of free commutative Rota–Baxter algebras were obtained by Rota and Cartier in the 1970s and a third one by Keigher and one of the authors in the 1990s in terms of mixable shuffles. Recently, noncommutative Rota–Baxter algebras have appeared both in physics in connection with the work of Connes and Kreimer on renormalization in perturbative quantum field theory, and in mathematics related to the work of Loday and Ronco on dendriform dialgebras and trialgebras. This paper uses rooted trees and forests to give explicit constructions of free noncommutative Rota–Baxter algebras on modules and sets. This highlights the combinatorial nature of Rota–Baxter algebras and facilitates their further study. As an application, we obtain the unitarization of Rota–Baxter algebras.
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13

Novak, Michael. "Liberal Ideology, An Eternal No; Liberal Institutions, A Temporal Yes? And Further Questions." Review of Politics 60, no. 4 (1998): 765–74. http://dx.doi.org/10.1017/s0034670500050889.

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Michael Baxter's long review provides an outline of David Schindler's useful first book; concentrates on its treatment of John Courtney Murray; gives a free pass to its lengthy ontological and theological speculations; and calls attention to its impracticality. Like Baxter, I share de Lubac's view of grace and nature (mediated to me by three Jesuits, Henry Bouillard, Juan Alfaro, and Bernard Lonergan), although I draw from it practical applications quite different from those of Schindler and Baxter. Further, I agree with the main thrust of Baxter's criticism: just where one wants to test Schindler's grand hypotheses about how grace ought to work in a “civilization of love,” particularly with regard to politics and economics, Schindler has almost nothing practical to say, and such few gestures as he offers seem lamely indistinguishable from those he criticizes, for example Murray (on the First Amendment) and Richard John Neuhaus (on the public square). His reading of my own work, too, is excessively polemical.
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14

Chen, Dan, Yan-Feng Luo, Yi Zhang, and Yuan-Yuan Zhang. "Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases." International Journal of Algebra and Computation 30, no. 07 (July 30, 2020): 1359–73. http://dx.doi.org/10.1142/s0218196720500447.

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Motivated by the formula of partial integration, we introduce the concept of [Formula: see text]-Rota–Baxter algebras, which generalizes the Rota–Baxter algebras introduced by Baxter. We then construct free objects in the category of [Formula: see text]-Rota–Baxter algebras, via a method of Gröbner–Shirshov bases.
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15

Zhang, Liangyun, Linhan Li, and Huihui Zheng. "Rota-Baxter Leibniz Algebras and Their Constructions." Advances in Mathematical Physics 2018 (December 2, 2018): 1–15. http://dx.doi.org/10.1155/2018/8540674.

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In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra. In the end, we give all Rota-Baxter operators of weight 0 and -1 on solvable and nilpotent Leibniz algebras of dimension ≤3, respectively.
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16

BAI, CHENGMING, LI GUO, and XIANG NI. "RELATIVE ROTA–BAXTER OPERATORS AND TRIDENDRIFORM ALGEBRAS." Journal of Algebra and Its Applications 12, no. 07 (May 16, 2013): 1350027. http://dx.doi.org/10.1142/s0219498813500278.

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A relative Rota–Baxter operator is a relative generalization of a Rota–Baxter operator on an associative algebra. In the Lie algebra context, it is called an [Formula: see text]-operator, originated from the operator form of the classical Yang–Baxter equation. We generalize the well-known construction of dendriform and tridendriform algebras from Rota–Baxter algebras to a construction from relative Rota–Baxter operators. In fact we give two such generalizations, on the domain and range of the operator respectively. We show that each of these generalized constructions recovers all dendriform and tridendriform algebras. Furthermore the construction on the range induces bijections between certain equivalence classes of invertible relative Rota–Baxter operators and tridendriform algebras.
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17

&NA;. "Factor VIII ??? Baxter." Drugs in R & D 4, no. 6 (2003): 366–68. http://dx.doi.org/10.2165/00126839-200304060-00007.

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18

Fee, Elizabeth, Theodore M. Brown, Jan Lazarus, and Paul Theerman. "Baxter Street Then." American Journal of Public Health 92, no. 5 (May 2002): 753. http://dx.doi.org/10.2105/ajph.92.5.753.

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19

Hodson, Hal. "Baxter breaks out." New Scientist 223, no. 2979 (July 2014): 19. http://dx.doi.org/10.1016/s0262-4079(14)61434-2.

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20

Lechevalier, Dominique, Lisa Bialé, Camille Glanowski, Isabelle Imbert, Evelyne Péroux, and Frédéric Banal. "Syndrome de Baxter." Revue du Rhumatisme 83, no. 3 (May 2016): 233. http://dx.doi.org/10.1016/j.rhum.2015.11.009.

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21

Marais, Ben J., Ronald Van Toorn, Tony Figaji, and Guy E. Thwaites. "Reply to Baxter." Clinical Infectious Diseases 69, no. 4 (January 14, 2019): 736. http://dx.doi.org/10.1093/cid/ciz026.

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22

Bray, Garth M., and Joseph B. Martin. "Donald W. Baxter." Annals of Neurology 73, no. 6 (June 2013): 685. http://dx.doi.org/10.1002/ana.23912.

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23

Schindler, David L. "Communio Ecclesiology and Liberalism." Review of Politics 60, no. 4 (1998): 775–86. http://dx.doi.org/10.1017/s0034670500050890.

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I. I begin with a discussion of Father Michael Baxter's reflections on my Heart of the World, Center of the Church (HWCC). I am deeply grateful for the evident care and thoroughness with which he read the book, and can suggest here only the beginning of a reply to his serious questions.Appropriately for the audience of the Review of Politics, Baxter develops his reflections mostly in terms of my argument regarding John Courtney Murray. Granting a basic validity to my critique of Murray, Baxter nonetheless argues that, in the end, my own constructive proposal “gets vague,” and he suspects that “it will turn out not to be substantially different from what has already been proposed by Murray and his successors.”
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24

Black, J. William. "From Martin Bucer to Richard Baxter: “Discipline” and Reformation in Sixteenthand Seventeenth-Century England." Church History 70, no. 4 (December 2001): 644–73. http://dx.doi.org/10.2307/3654544.

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Already famous for his best-selling books on Christian devotion and increasingly infamous for his attempts at a theological synthesis of Calvinist and Arminian perspectives on salvation—which (no surprise) pleased hardly anyone—Richard Baxter (1615–91) nearly succeeded in redefining English pastoral practice before the Restoration brought his experiment in pastor-led, parish-based reformation to a frustrating end. At the core of his efforts to bring reformation to Kidderminster lay his efforts to establish a parish-based system of church discipline that would preserve the integrity of the sacraments and thus rob separatists of one of their primary excuses for abandoning the parochial system. This article seeks to place Baxter's effort to develop a strategy for an effective church discipline in its historical context. In particular, I will first consider the precedents to the system which Richard Baxter developed for St. Mary's parish. Special attention will be given to Martin Bucer's Reformation-era prescription for reforming the discipline of the church and the intriguing possibility that Baxter's strategy was actually a recovery of Bucerian pastoral emphases. Second, I will trace the evolution of Baxter's own program for discipline. Finally, I will discuss the impact Baxter's discipline had on his wider goal of reformation, both in his parish and beyond.
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25

Liu, Ling, Abdenacer Makhlouf, Claudia Menini, and Florin Panaite. "-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation." Canadian Mathematical Bulletin 62, no. 02 (January 7, 2019): 355–72. http://dx.doi.org/10.4153/cmb-2018-028-8.

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AbstractWe introduce the concept of a $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator, as a twisted version of a Rota–Baxter operator of weight zero. We show how to obtain a certain $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator from a solution of the associative (Bi)Hom-Yang–Baxter equation, and, in a compatible way, a Hom-pre-Lie algebra from an infinitesimal Hom-bialgebra.
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26

Dimakis, Aristophanes, and Folkert Müller-Hoissen. "Tropical limit of matrix solitons and entwining Yang–Baxter maps." Letters in Mathematical Physics 110, no. 11 (August 11, 2020): 3015–51. http://dx.doi.org/10.1007/s11005-020-01322-9.

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Abstract We consider a matrix refactorization problem, i.e., a “Lax representation,” for the Yang–Baxter map that originated as the map of polarizations from the “pure” 2-soliton solution of a matrix KP equation. Using the Lax matrix and its inverse, a related refactorization problem determines another map, which is not a solution of the Yang–Baxter equation, but satisfies a mixed version of the Yang–Baxter equation together with the Yang–Baxter map. Such maps have been called “entwining Yang–Baxter maps” in recent work. In fact, the map of polarizations obtained from a pure 2-soliton solution of a matrix KP equation, and already for the matrix KdV reduction, is not in general a Yang–Baxter map, but it is described by one of the two maps or their inverses. We clarify why the weaker version of the Yang–Baxter equation holds, by exploring the pure 3-soliton solution in the “tropical limit,” where the 3-soliton interaction decomposes into 2-soliton interactions. Here, this is elaborated for pure soliton solutions, generated via a binary Darboux transformation, of matrix generalizations of the two-dimensional Toda lattice equation, where we meet the same entwining Yang–Baxter maps as in the KP case, indicating a kind of universality.
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27

Das, Apurba, and Satyendra Kumar Mishra. "The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators." Journal of Mathematical Physics 63, no. 5 (May 1, 2022): 051703. http://dx.doi.org/10.1063/5.0076566.

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A relative Rota–Baxter algebra is a triple ( A, M, T) consisting of an algebra A, an A-bimodule M, and a relative Rota–Baxter operator T. Using Voronov’s derived bracket and a recent work of Lazarev, Sheng, and Tang, we construct an L∞[1]-algebra whose Maurer–Cartan elements are precisely relative Rota–Baxter algebras. By a standard twisting, we define a new L∞[1]-algebra that controls Maurer–Cartan deformations of a relative Rota–Baxter algebra ( A, M, T). We introduce the cohomology of a relative Rota–Baxter algebra ( A, M, T) and study infinitesimal deformations in terms of this cohomology (in low dimensions). As an application, we deduce cohomology of triangular skew-symmetric infinitesimal bialgebras and discuss their infinitesimal deformations. Finally, we define homotopy relative Rota–Baxter operators and find their relationship with homotopy dendriform algebras and homotopy pre-Lie algebras.
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28

Zhang, Yi, Xiaosong Peng, and Yuanyuan Zhang. "Typed Angularly Decorated Planar Rooted Trees and Ω-Rota-Baxter Algebras." Mathematics 10, no. 2 (January 8, 2022): 190. http://dx.doi.org/10.3390/math10020190.

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As a generalization of Rota–Baxter algebras, the concept of an Ω-Rota–Baxter could also be regarded as an algebraic abstraction of the integral analysis. In this paper, we introduce the concept of an Ω-dendriform algebra and show the relationship between Ω-Rota–Baxter algebras and Ω-dendriform algebras. Then, we provide a multiplication recursion definition of typed, angularly decorated rooted trees. Finally, we construct the free Ω-Rota–Baxter algebra by typed, angularly decorated rooted trees.
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29

Gu, Yue, Shuanhong Wang, and Tianshui Ma. "Rota–Baxter (Co)algebra Equation Systems and Rota–Baxter Hopf Algebras." Mathematics 10, no. 3 (January 28, 2022): 426. http://dx.doi.org/10.3390/math10030426.

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30

Bardakov, Valeriy G., and Vsevolod Gubarev. "Rota—Baxter groups, skew left braces, and the Yang—Baxter equation." Journal of Algebra 596 (April 2022): 328–51. http://dx.doi.org/10.1016/j.jalgebra.2021.12.036.

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31

MATSUMOTO, Diogo Kendy, and Youichi SHIBUKAWA. "Quantum Yang-Baxter Equation, Braided Semigroups, and Dynamical Yang-Baxter Maps." Tokyo Journal of Mathematics 38, no. 1 (June 2015): 227–37. http://dx.doi.org/10.3836/tjm/1437506246.

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32

Babelon, Olivier, Karol K. Kozlowski, and Vincent Pasquier. "Baxter Operator and Baxter Equation for q-Toda and Toda2 Chains." Reviews in Mathematical Physics 30, no. 06 (July 2018): 1840003. http://dx.doi.org/10.1142/s0129055x18400032.

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We construct the Baxter operator [Formula: see text] for the [Formula: see text]-Toda chain and the Toda2 chain (the Toda chain in the second Hamiltonian structure). Our construction builds on the relation between the Baxter operator and Bäcklund transformations that were unravelled in [13]. We construct a number of quantum intertwiners ensuring the commutativity of [Formula: see text] with the transfer matrix of the models and of the [Formula: see text]’s between each other. Most importantly, [Formula: see text] is modular invariant in the sense of Faddeev. We derive the Baxter equation for the eigenvalues [Formula: see text] of [Formula: see text] and show that these are entire functions of [Formula: see text]. This last property will ultimately lead to the quantization of the spectrum for the considered Toda chains, in a subsequent publication [1]. This work is dedicated to the memory of L. D. Faddeev
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33

GUO, LI. "BAXTER ALGEBRAS, STIRLING NUMBERS AND PARTITIONS." Journal of Algebra and Its Applications 04, no. 02 (April 2005): 153–64. http://dx.doi.org/10.1142/s0219498805001083.

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Recent developments of Baxter algebras have led to applications to combinatorics, number theory and mathematical physics. We relate Baxter algebras to Stirling numbers of the first and the second kinds, partitions and multinomial coefficients. This allows us to apply congruences from number theory to obtain congruences in Baxter algebras.
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34

Guo, Qiaoling, Ling Liu, Jiafeng Lü, Bingliang Shen, and Xingting Wang. "Rota-Baxter Systems for BiHom-Type Algebras." Mathematics 10, no. 18 (September 6, 2022): 3222. http://dx.doi.org/10.3390/math10183222.

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The purpose of this paper is to study Rota–Baxter systems for BiHom-type algebras such as BiHom analogues of associative, dendriform, quadri algebras. It is shown that BiHom-dendriform structures of a particular kind are equivalent to Rota–Baxter systems. It is shown further that a Rota–Baxter system induces a weak BiHom-pseudotwistor which can be held responsible for the existence of a new product on the underlying BiHom-associative algebra. Moreover, we study the relationship between BiHom-quadri-algebras and Rota–Baxter systems for BiHom-dendriform algebras.
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35

Guo, Shuangjian, Shengxiang Wang, and Xiaohui Zhang. "The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras." Mathematics 10, no. 11 (June 3, 2022): 1920. http://dx.doi.org/10.3390/math10111920.

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In this paper, we first introduce the notion of Hom–Leibniz bialgebras, which is equivalent to matched pairs of Hom–Leibniz algebras and Manin triples of Hom–Leibniz algebras. Additionally, we extend the notion of relative Rota–Baxter operators to Hom–Leibniz algebras and prove that there is a Hom–pre-Leibniz algebra structure on Hom–Leibniz algebras that have a relative Rota–Baxter operator. Finally, we study the classical Hom–Leibniz Yang–Baxter equation on Hom–Leibniz algebras and present its connection with the relative Rota–Baxter operator.
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36

Wang, Zhongwei, Zhen Guan, Yi Zhang, and Liangyun Zhang. "Rota–Baxter Operators on Cocommutative Weak Hopf Algebras." Mathematics 10, no. 1 (December 28, 2021): 95. http://dx.doi.org/10.3390/math10010095.

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In this paper, we first introduce the concept of a Rota–Baxter operator on a cocommutative weak Hopf algebra H and give some examples. We then construct Rota–Baxter operators from the normalized integral, antipode, and target map of H. Moreover, we construct a new multiplication “∗” and an antipode SB from a Rota–Baxter operator B on H such that HB=(H,∗,η,Δ,ε,SB) becomes a new weak Hopf algebra. Finally, all Rota–Baxter operators on a weak Hopf algebra of a matrix algebra are given.
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37

Iantovics, Laszlo Barna, and Florin Felix Nichita. "On the Colored and the Set-Theoretical Yang–Baxter Equations." Axioms 10, no. 3 (July 2, 2021): 146. http://dx.doi.org/10.3390/axioms10030146.

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This paper is related to several articles published in AXIOMS, SCI, etc. The main concepts of the current paper are the colored Yang–Baxter equation and the set-theoretical Yang–Baxter equation. The Euler formula, colagebra structures, and means play an important role in our study. We show that some new solutions for a certain system of equations lead to colored Yang–Baxter operators, which are related to an Euler formula for matrices, and the set-theoretical solutions to the Yang–Baxter equation are related to means. A new coalgebra is obtained and studied.
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38

Dietrich, Barbara, Susan Kubik, Wilfried Auer, Kuno Wuersch, Birgit Reipert, Frank Horling, Martin Wolfsegger, et al. "Preclinical Safety of Baxter's Recombinant Factor IX." Blood 116, no. 21 (November 19, 2010): 4654. http://dx.doi.org/10.1182/blood.v116.21.4654.4654.

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Abstract Abstract 4654 Baxter has developed a rFIX product which is produced by a genetically engineered Chinese hamster ovary (CHO) cell line in a cell culture medium free from any animal or human proteins. The objective of this preclinical study-program was to evaluate the safety of Baxter's rFIX in different species. The preclinical program included studies on established models of general safety pharmacology (conscious, telemetered cynomolgus monkey), thrombogenicity (rabbit, Wessler test), single and repeated dose toxicity (mouse, rat, cynomolgus monkey), local tolerance (rabbit), and comparative immunogenicity (mouse, rat, cynomolgus monkey). Commercially available licensed rFIX and pdFIX served as active reference items. Thrombogenicity studies showed no thrombogenic potential of Baxter's rFIX. General safety pharmacology revealed no adverse effects on clinical signs, cardiovascular or respiratory variables. Single dose toxicity studies in mice, administered at doses of up to 7500 IU/kg BW, and repeated administration of Baxter's rFIX in rats and cynomolgus monkeys, administered doses of up to 750 IU/kg, confirmed the safety of the new product. Furthermore, Baxter's rFIX was well tolerated at the injection site after intravenous injection. No differences in immunogenicity between Baxter's rFIX and the reference items were revealed by comparative immunology studies. This good safety profile of Baxter's rFIX was the basis for proceeding with human trials, which have recently been initiated. Disclosures: Dietrich: Baxter Innovations GmbH: Employment. Kubik:Baxter Innovations GmbH: Employment. Auer:Baxter Innovations GmbH: Employment. Wuersch:Baxter Innovations GmbH: Employment. Reipert:Baxter Innovations GmbH: Employment. Horling:Baxter Innovations GmbH: Employment. Wolfsegger:Baxter Innovations GmbH: Employment. Ehrlich:Baxter Innovations GmbH: Employment. Scheiflinger:Baxter Innovations GmbH: Employment. Schwarz:Baxter Innovations GmbH: Employment. Muchitsch:Baxter Innovations GmbH: Employment.
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Dietrich, Barbara, Susan Kubik, Hartmut J. Ehrlich, Friedrich Scheiflinger, Hans Peter Schwarz, and Eva-Maria Muchitsch. "Preclinical Safety Pharmacology of Baxter’s Longer Acting rFVIII (BAX 855)." Blood 118, no. 21 (November 18, 2011): 4357. http://dx.doi.org/10.1182/blood.v118.21.4357.4357.

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Abstract Abstract 4357 Baxter has developed a PEGylated recombinant human factor VIII conjugate by modifying the FVIII molecule with polyethylene glycol (PEGylation). The product is derived from a CHO cell line using a plasma-protein-free method and a virus inactivation step. The objective of this preclinical study-program was to evaluate the safety of Baxter’s longer acting rFVIII in different species. The thrombogenic potential of Baxter’s longer acting rFVIII was evaluated in the rabbit stasis model developed by Wessler. Two lots of Baxter’s longer acting rFVIII were used to demonstrate consistent safety between different batches. Advate served as the control item. Baxter’s longer acting rFVIII was not thrombogenic in this preclinical model at a dose of 900 U/kg. There was no evidence of thrombogenic potential after intravenous treatment with either the test item or Advate, the active reference item. The effects of Baxter’s longer acting rFVIII on body temperature, heart rate, blood pressure, respiratory variables or QT, QTcf, PR and/or QRS intervals and respiratory system (intra-thoracic pressure) was evaluated in eight male, conscious telemetered cynomolgus monkeys. Baxter’s longer acting rFVIII was given at 150 and 600 U/kg/day to male monkeys by intravenous administration. Baxter’s longer acting rFVIII did not cause any adverse clinical, respiratory or cardiovascular effects and was very well tolerated at all dose levels tested. In conclusion, Baxter’s longer acting rFVIII did not cause any thrombocenic events or adverse clinical, respiratory or cardiovascular effects and was very well tolerated at all dose levels. Disclosures: Dietrich: Baxter Innovations GmbH: Employment. Kubik:Baxter Innovations GmbH: Employment. Ehrlich:Baxter Innovations GmbH: Employment. Scheiflinger:Baxter Innovations GmbH: Employment. Schwarz:Baxter Innovations GmbH: Employment. Muchitsch:Baxter Innovations GmbH: Employment.
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Gubarev, Vsevolod. "Rota-Baxter operators and Bernoulli polynomials." Communications in Mathematics 29, no. 1 (April 30, 2021): 1–14. http://dx.doi.org/10.2478/cm-2021-0001.

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Abstract We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and Bernoulli polynomials. We show how Rota-Baxter operators equalities rewritten in terms of Bernoulli polynomials generate identities for the latter.
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QIU, JIANJUN, and YUQUN CHEN. "COMPOSITION-DIAMOND LEMMA FOR λ-DIFFERENTIAL ASSOCIATIVE ALGEBRAS WITH MULTIPLE OPERATORS." Journal of Algebra and Its Applications 09, no. 02 (April 2010): 223–39. http://dx.doi.org/10.1142/s0219498810003859.

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In this paper, we establish the Composition-Diamond lemma for λ-differential associative algebras over a field K with multiple operators. As applications, we obtain Gröbner–Shirshov bases of free λ-differential Rota–Baxter algebras. In particular, linear bases of free λ-differential Rota–Baxter algebras are obtained and consequently, the free λ-differential Rota–Baxter algebras are constructed by words.
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42

Links, Jon. "The Yang–Baxter paradox." Journal of Physics A: Mathematical and Theoretical 54, no. 25 (May 31, 2021): 254001. http://dx.doi.org/10.1088/1751-8121/abfe48.

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43

Brzeziński, Tomasz. "Curved Rota-Baxter systems." Bulletin of the Belgian Mathematical Society - Simon Stevin 23, no. 5 (December 2016): 713–20. http://dx.doi.org/10.36045/bbms/1483671622.

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44

"Baxter." Analytical Chemistry 59, no. 17 (September 1987): 984A. http://dx.doi.org/10.1021/ac00144a702.

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"Baxter." Analytical Chemistry 59, no. 21 (November 1987): 1220A. http://dx.doi.org/10.1021/ac00148a702.

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"Baxter." Analytical Chemistry 60, no. 19 (October 1988): 1080A. http://dx.doi.org/10.1021/ac00170a711.

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"Baxter." Analytical Chemistry 60, no. 19 (October 1988): 1082A. http://dx.doi.org/10.1021/ac00170a715.

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48

"Baxter." Analytical Chemistry 60, no. 21 (November 1988): 1189A. http://dx.doi.org/10.1021/ac00172a708.

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"Baxter." Analytical Chemistry 60, no. 21 (November 1988): 1192A. http://dx.doi.org/10.1021/ac00172a711.

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"Baxter." Analytical Chemistry 60, no. 23 (December 1988): 1314A. http://dx.doi.org/10.1021/ac00174a708.

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