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Journal articles on the topic 'N extension'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Xu, Lei, Mingxiang Ju, Wentai Guo, and Shengrui Yu. "Extensional Rheology of Poly(vinylidene fluoride)/N,N-dimethylformamide Solutions." Polymers 15, no. 5 (2023): 1119. http://dx.doi.org/10.3390/polym15051119.

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Typical extension flow occurs in electrospinning process of Poly(vinylidene fluoride) (PVDF) solutions such that researchers focus on extensional rheological behaviors of PVDF solutions. The extensional viscosity of PVDF solutions is measured to know the fluidic deformation in extension flows. The solutions are prepared by dissolving PVDF powder into N,N-dimethylformamide (DMF) solvent. A homemade extensional viscometric device is used to produce uniaxial extension flows and the feasibility of the viscometric device is verified by applying the glycerol as a test fluid. Experimental results sho

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2

Faul, Peter F. "Baer sums for a natural class of monoid extensions." Semigroup Forum 102, no. 3 (2021): 655–73. http://dx.doi.org/10.1007/s00233-020-10156-9.

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AbstractIt is well known that the set of isomorphism classes of extensions of groups with abelian kernel is characterized by the second cohomology group. In this paper we generalise this characterization of extensions to a natural class of extensions of monoids, the cosetal extensions. An extension "Equation missing" is cosetal if for all $$g,g' \in G$$ g , g ′ ∈ G in which $$e(g) = e(g')$$ e ( g ) = e ( g ′ ) , there exists a (not necessarily unique) $$n \in N$$ n ∈ N such that $$g = k(n)g'$$ g = k ( n ) g ′ . These extensions generalise the notion of special Schreier extensions, which are th

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3

Lindenstrauss, Ayelet, Birgit Richter, and Foling Zou. "Examples of étale extensions of Green functors." Proceedings of the American Mathematical Society, Series B 11, no. 27 (2024): 287–303. http://dx.doi.org/10.1090/bproc/189.

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We provide new examples of étale extensions of Green functors by transferring classical examples of étale extensions to the equivariant setting. Our examples are Tambara functors, and we prove Green étaleness for them, which implies Tambara étaleness. We show that every C 2 C_2 -Galois extensions of fields gives rise to an étale extension of C 2 C_2 -Green functors. Here we associate the constant Tambara functor to the base field and the fix-Tambara functor to the extension. We also prove that all C n C_n -Kummer extensions give rise to étale extensions for arbitrary finite n n . Étale extensi

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4

Bai, Ruipu, та Ying Li. "Tθ∗-Extensions of n-Lie Algebras". ISRN Algebra 2011 (11 вересня 2011): 1–11. http://dx.doi.org/10.5402/2011/381875.

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The paper is mainly concerned with Tθ∗-extensions of n-Lie algebras. The Tθ∗-extension Lθ(L∗) of an n-Lie algebra L by a cocycle θ is defined, and a class of cocycles is constructed by means of linear mappings from an n-Lie algebra on to its dual space. Finally all Tθ∗-extensions of (n+1)-dimensional n-Lie algebras are classified, and the explicit multiplications are given.

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Sarkis, Maretta. "A Short Contribution to the Extension of the Group C(n)." Galoitica: Journal of Mathematical Structures and Applications 1, no. 2 (2022): 11–12. http://dx.doi.org/10.54216/gjmsa.010202.

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In this work, we study the extension problem of a group with type C(n)=∑_(i∈I) C_P^∞ by using a cyclic group of order p. Also, we prove the following two results: 1-) The group C(n) has only one extension which is compatible with R_3. 2-) The group C(n) has two extensions which are compatible with R_2.

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6

OTT, B., N. MCDANIEL, and E. HUMPHREY. "Fourteen new species of demosponges (Porifera) from three coastal fjords in southern British Columbia, Canada." Zootaxa 5463, no. 2 (2024): 151–200. http://dx.doi.org/10.11646/zootaxa.5463.2.1.

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Collections of encrusting sponges from the shallow subtidal zone of three southern fjords in British Columbia, Canada, and adjacent waters provided the material for the description of 14 new species. Species represent 5 orders, 8 families and 11 genera providing a cross section of British Columbia shallow water fjord Demospongiae. New species include Eurypon reiswigi n. sp., E. scruposus n. sp., E. microtuberculatum n. sp., Hymeraphia pacifica n. sp., Hamigera bakusi n. sp., Hymedesmia (Hymedesmia) anvilensis n. sp., Hymetrochota austini n. sp., Discorhabdella atypica n. sp., Antho (Acarnia) f

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Amaral, M. M., Y. E. Chifarelli, and V. E. R. Lemes. "N= 1 Gribov superfield extension." Journal of Physics A: Mathematical and Theoretical 47, no. 7 (2014): 075401. http://dx.doi.org/10.1088/1751-8113/47/7/075401.

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8

Brodskii, N. B. "Extension ofUV n -valued mappings." Mathematical Notes 66, no. 3 (1999): 283–91. http://dx.doi.org/10.1007/bf02676435.

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9

Tomás, Marco Aragón. "La máquina como extensión musical." Música Oral del Sur, no. 4 (March 8, 1999): 85–95. https://doi.org/10.5281/zenodo.4626977.

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Cuando se abordan las relaciones entre la música y las máquinas, lo habitual es elegir entre una de dos direcciones posibles, una de ellas con una conocida subdivisión. Son, por supuesto, por un lado la consideración de las máquinas mecánicas musicales como relojes, autómatas y otros mecanismos que hacen referencia a la robótica mecánica, y por otro a las aplicaciones de los circuitos electrónicos a la música que tiene la doble variante de la producción de sonido y la de reproducción del mismo sea por me

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10

Fahmy, M. H., A. M. Hassanein, and S. M. Abdelwahab. "Two extensions of right G-semilocal and right N-semilocal rings." Journal of Algebra and Its Applications 18, no. 01 (2019): 1950012. http://dx.doi.org/10.1142/s0219498819500129.

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The paper studies the transfer of the property of being right G-semilocal and right N-semilocal from a ring [Formula: see text] to its extensions and vice versa. We will focus on two extensions, namely finite normalizing extension [Formula: see text] of [Formula: see text] and the ring of polynomials [Formula: see text].

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11

Boukhetouta, M. N., M. Krachni, F. Yazid, and F. S. Djeradi. "HOLOMORPHIC EXTENSION." Advances in Mathematics: Scientific Journal 12, no. 1 (2023): 217–24. http://dx.doi.org/10.37418/amsj.12.1.14.

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In this paper, we prove that if there exists a holomorphic, proper, surjective map defined on a complex manifold $ X $ into a smooth algebraic curve with parallelizable fibers, then any holomorphic mappings defined on the Hartogs domain $ T $ of $\mathbb{C}^n$ can be extended holomorphically (resp. meromorphically) from $ \Delta ^n \setminus Z $ into $ X $, where $ Z $ is an analytic subset of $\Delta^n $ such that codimension of $ Z $ at least 2.

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12

Zhou, Panyue. "n-extension closed subcategories of $$(n+2)$$-angulated categories." Archiv der Mathematik 118, no. 4 (2022): 375–82. http://dx.doi.org/10.1007/s00013-022-01705-5.

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13

Luukkainen, Jouni. "Respectful quasiconformal extension from dimension n−1 to n." Arkiv för Matematik 31, no. 2 (1993): 355–76. http://dx.doi.org/10.1007/bf02559491.

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14

Alkam, Osama, and Mehpare Bilhan. "Class number of (v, n, M)-extensions." Bulletin of the Australian Mathematical Society 63, no. 1 (2001): 21–34. http://dx.doi.org/10.1017/s0004972700019080.

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An analogue of cyclotomic number fields for function fields over the finite field q, was investigated by L. Carlitz in 1935 and has been studied recently by D. Hayes, M. Rosen, S. Galovich and others. For each nonzero polynomial M in q [T], we denote by k (ΛM) the cyclotomic function field associated with M, where k = q(T). Replacing T by 1/T in k and considering the cyclotomic function field Fv that corresponds to (1/T)v+1 gets us an extension of k, denoted by Lv, which is the fixed field of Fv modulo . We define a (v, n, M)-extension to be the composite N = knk (Λm) Lv where kn is the con

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15

FAHIM, Kistosil. "The extension of step-N signatures." TURKISH JOURNAL OF MATHEMATICS 45, no. 3 (2021): 1345–67. http://dx.doi.org/10.3906/mat-2010-82.

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16

Mecheri, Salah. "Analytic extension of n-normal operators." Operators and Matrices, no. 2 (2021): 615–26. http://dx.doi.org/10.7153/oam-2021-15-41.

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17

DOOLEY, A. H., and V. YA GOLODETS. "The geometric dimension of an equivalence relation and finite extensions of countable groups." Ergodic Theory and Dynamical Systems 29, no. 6 (2009): 1789–814. http://dx.doi.org/10.1017/s014338570800093x.

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AbstractWe say that the geometric dimension of a countable group G is equal to n if any free Borel action of G on a standard Borel probability space (X,μ), induces an equivalence relation of geometric dimension n on (X,μ) in the sense of Gaboriau. Let ℬ be the set of all finitely generated amenable groups all of whose subgroups are also finitely generated, and let 𝒜 be the subset of ℬ consisting of finite groups, torsion-free groups and their finite extensions. In this paper we study finite free products K of groups in 𝒜. The geometric dimension of any such group K is one: we prove that also g

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18

Casas, J. M. "Ganea Term for Homology of Leibniz n-Algebras." Algebra Colloquium 12, no. 04 (2005): 629–34. http://dx.doi.org/10.1142/s1005386705000593.

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We extend the five-term exact sequence of homology with trivial coefficients of Leibniz n-algebras [Formula: see text] associated to a central extension of Leibniz n-algebras [Formula: see text] by means of a sixth term which is a generalization of the Ganea term for homology of Leibniz algebras. We use this sequence in order to analyze several questions related with the centre and central extensions of a Leibniz n-algebra.

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19

Lobov, Alexander A., and Mikhail B. Abrosimov. "About uniqueness of the minimal 1-edge extension of hypercube Q4." Prikladnaya Diskretnaya Matematika, no. 58 (2023): 84–93. http://dx.doi.org/10.17223/20710410/58/8.

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One of the important properties of reliable computing systems is their fault tolerance. To study fault tolerance, you can use the apparatus of graph theory. Minimal edge extensions of a graph are considered, which are a model for studying the failure of links in a computing system. A graph G* = (V*,α*) with n vertices is called a minimal k-edge extension of an n-vertex graph G = (V, α) if the graph G is embedded in every graph obtained from G* by deleting any of its k edges and has the minimum possible number of edges. The hypercube Qn is a regular 2n-vertex graph of order n, which is the Cart

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20

Pąk, Karol. "Tietze Extension Theorem for n-dimensional Spaces." Formalized Mathematics 22, no. 1 (2014): 11–19. http://dx.doi.org/10.2478/forma-2014-0002.

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Summary In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic with a convex compact subset of En with a non-empty interior. This article is based on [20]; [23] and

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21

Hoxha, Ilmi, and Naim L. Braha. "Algebraic extension of $\mathcal{A}^{*}_{n}$ operator." Boletim da Sociedade Paranaense de Matemática 40 (December 17, 2021): 1–7. http://dx.doi.org/10.5269/bspm.43345.

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$T\in L(H_{1}\oplus H_{2})$ is said to be an algebraic extension of a $\mathcal{A}^{*}_{n}$ operator if $$ T = \begin{pmatrix} T_{1} & T_{2} \\O & T_{3} \end{pmatrix} $$ is an operator matrix on $H_{1}\oplus H_{2}$, where $T_{1}$ is a $\mathcal{A}^{*}_{n}$ operator and $T_{3}$ is a algebraic.In this paper, we study basic and spectral properties of an algebraic extension of a $\mathcal{A}^{*}_{n}$ operator. We show that every algebraic extension of a $\mathcal{A}^{*}_{n}$ operator has SVEP, is polaroid and satisfies Weyl's theorem.

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22

Maciaszek, Krzysztof. "On Polynomial Extension Property in N-Disc." Complex Analysis and Operator Theory 13, no. 6 (2019): 2771–80. http://dx.doi.org/10.1007/s11785-019-00912-3.

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23

Willeboordse, Frederick H. "Time-Delayed Map extension to n-dimensions." Chaos, Solitons & Fractals 2, no. 4 (1992): 411–20. http://dx.doi.org/10.1016/0960-0779(92)90016-g.

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24

Knauf, Andreas. "Regularisation by Hamiltonian extension." Nonlinearity 38, no. 7 (2025): 075033. https://doi.org/10.1088/1361-6544/adf0d8.

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Abstract We consider the Kepler potential and its relatives q ↦ − ‖ q ‖ − 2 ( 1 − 1 / n ) , n ∈ N in arbitrary dimension d. We derive a unique real-analytic symplectic extension of phase space on which the Hamiltonian flow is complete and still real-analytic.

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25

Miginiac-Maslow, Myroslawa, Emmanuelle Issakidis, Martine Lemaire, Eric Ruelland, Jean-Pierre Jacquot, and Paulette Decottignies. "Light-dependent Activation of NADP-Malate Dehydrogenase: a Complex Process." Functional Plant Biology 24, no. 4 (1997): 529. http://dx.doi.org/10.1071/pp97004.

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After the discovery of the light-activation properties of the chloroplastic NADP-dependent malate dehydrogenase in 1970, the elements of the activation pathway were identified and shown to consist of the stromal proteins of the ferredoxin/thioredoxin system. It was further demonstrated that the activation was a reductive process during which disulfides were reduced into dithiols by reduced thioredoxin. Sequence alignments with the permanently active NAD-malate dehydrogenases revealed N- and C-terminal extensions specific for the light-regulated form. A regulatory disulfide was identified in th

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26

Würfel, Tilmann. "Dimension-Preserving Extensions of Pro-p-Groups." Canadian Mathematical Bulletin 34, no. 1 (1991): 136–40. http://dx.doi.org/10.4153/cmb-1991-022-3.

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AbstractWe investigate extensions of pro-p-groups 1 —> N —> G —> Γ —> 1 where N is pro-p-free and Nab, is a free Zp[Γ]-module. In case Γ is finite we show that such an extension splits modulo the second derived group N".

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27

Dougherty, Steven T., Joe Gildea, and Adrian Korban. "Extending an established isomorphism between group rings and a subring of the n × n matrices." International Journal of Algebra and Computation 31, no. 03 (2021): 471–90. http://dx.doi.org/10.1142/s0218196721500223.

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In this work, we extend an established isomorphism between group rings and a subring of the [Formula: see text] matrices. This extension allows us to construct more complex matrices over the ring [Formula: see text] We present many interesting examples of complex matrices constructed directly from our extension. We also show that some of the matrices used in the literature before can be obtained by a direct application of our extended isomorphism.

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Agunga, Robert, Ruth Sleshi, and Rahwa Hassen. "Towards a Professionalism of Agricultural Extension: Key to Promoting Extension Effectiveness in Africa." Sustainable Agriculture Research 6, no. 2 (2017): 81. http://dx.doi.org/10.5539/sar.v6n2p81.

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A survey of a small sample of 123 extension workers in Ghana and Ethiopia may have revealed the key issue facing extension ineffectiveness in Africa—the paucity of extension training. Questions on job satisfaction showed that respondents were highly satisfied with: a) an opportunity to work in an area they are trained (N=88, 57%), b) level of education (N=75 (61%), c) enthusiasm towards their work (N=72 (58.5%), and d) opportunity to work with local farmers. However, they were highly dissatisfied with: a) their salaries (N=108 (87.8%), b) the process of decentralization (N=83 (75.6%), c) coope

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BOYLE, MIKE, and SCOTT SCHMIEDING. "Finite group extensions of shifts of finite type: -theory, Parry and Livšic." Ergodic Theory and Dynamical Systems 37, no. 4 (2016): 1026–59. http://dx.doi.org/10.1017/etds.2015.87.

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This paper extends and applies algebraic invariants and constructions for mixing finite group extensions of shifts of finite type. For a finite abelian group$G$, Parry showed how to define a$G$-extension$S_{A}$from a square matrix over$\mathbb{Z}_{+}G$, and classified the extensions up to topological conjugacy by the strong shift equivalence class of$A$over$\mathbb{Z}_{+}G$. Parry asked, in this case, if the dynamical zeta function$\det (I-tA)^{-1}$(which captures the ‘periodic data’ of the extension) would classify the extensions by$G$of a fixed mixing shift of finite type up to a finite numb

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30

Goodearl, K. R., and D. A. Jordan. "Localizations of essential extensions." Proceedings of the Edinburgh Mathematical Society 31, no. 2 (1988): 243–47. http://dx.doi.org/10.1017/s0013091500003369.

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In an earlier paper [4] we considered the question of whether an injective module E over a noncommutative ring R remains injective after localization with respect to a denominator set X in R. A related question is whether, given an essential extension N of an R-module M, the localization N[X–1] must be an essential extension of M[X–1]. In [1] it is shown that if R is left noetherian and X is central in R, then localization at X preserves both injectivity and essential extensions of left R-modules and, hence, preserves injective hulls and minimal injective resolutions.

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31

Krukowski, Rebecca A., Loneke T. Blackman Carr, and Danielle Arigo. "Pandemic-Related Tenure Timeline Extensions in Higher Education in the United States: Prevalence and Associated Characteristics." Challenges 13, no. 2 (2022): 34. http://dx.doi.org/10.3390/challe13020034.

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Many universities implemented pandemic-related tenure timeline extensions in response to productivity disruptions. However, little is known about the availability, nature, or uptake of these extensions, including which faculty were most likely to extend their timeline. Tenure-track faculty in the United States (n = 385, 64.4% women, 35.3% identifying with a National Institutes of Health-designated racial/ethnic minority group, 73.0% with children, 33.8% with non-child caregiving) completed a survey about their personal/career/institution characteristics, their institution’s pandemic extension

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32

Samet, Dov. "An Extension of Ceva’s Theorem to n-Simplices." American Mathematical Monthly 128, no. 5 (2021): 435–45. http://dx.doi.org/10.1080/00029890.2021.1896292.

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33

Ageev, Sergei M., Dusan Repovs, and Evgenij V. Scepin. "The extension problem for complete $UV^{n}$-preimages." Tsukuba Journal of Mathematics 23, no. 1 (1999): 97–111. http://dx.doi.org/10.21099/tkbjm/1496163778.

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34

Bar-Itzhack, I. Y. "Extension of Euler's theorem to n-dimensional spaces." IEEE Transactions on Aerospace and Electronic Systems 25, no. 6 (1989): 903–9. http://dx.doi.org/10.1109/7.40731.

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BARCELÓ, J. A., J. M. BENNETT, and A. CARBERY. "A MULTILINEAR EXTENSION INEQUALITY IN $\mathbb{R}^{n}$." Bulletin of the London Mathematical Society 36, no. 03 (2004): 407–12. http://dx.doi.org/10.1112/s0024609304003091.

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36

Bodaghi, Abasalt, and Hülya İnceboz. "Extension of Zelazko’s theorem to n-Jordan homomorphisms." Advances in Pure and Applied Mathematics 10, no. 2 (2019): 165–70. http://dx.doi.org/10.1515/apam-2016-0075.

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Abstract In this article, we correct the proof of the main theorem of Gordji’s paper [M. Eshaghi Gordji, n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 2009, 1, 159–164] by a different method and generalize Zelazko’s theorem to 4-Jordan homomorphisms by considering an extra condition.

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Martynchuk, N. N. "Transfinite extension of dimension function(m,n)-dim." Topology and its Applications 160, no. 18 (2013): 2514–22. http://dx.doi.org/10.1016/j.topol.2013.07.045.

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Mosic, Dijana, Honglin Zou, and Long Wang. "Extension of the generalized n-strong Drazin inverse." Filomat 37, no. 23 (2023): 7781–90. http://dx.doi.org/10.2298/fil2323781m.

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The aim of this paper is to present an extension of the generalized n-strong Drazin inverse for Banach algebra elements using a g-Drazin invertible element rather than a quasinilpotent element in the definition of the generalized n-strong Drazin inverse. Thus, we introduce a new class of generalized inverses which is a wider class than the classes of the generalized n-strong Drazin inverse and the extended generalized strong Drazin inverses. We prove a number of characterizations for this new inverse and some of them are based on idempotents and tripotents. Several generalizations of Cline?s f

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39

Barbarosie, Cristian. "Extension Operators." Mathematische Nachrichten 218, no. 1 (2000): 5–17. http://dx.doi.org/10.1002/1522-2616(200010)218:1<5::aid-mana5>3.0.co;2-n.

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Petrie, C. J. S. "Some asymptotic results for planar extension." Journal of Non-Newtonian Fluid Mechanics 34, no. 1 (1990): 37–62. http://dx.doi.org/10.1016/0377-0257(90)80011-n.

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41

Miller, David. "An extension of Milnor's \̄gm-invariants." Topology and its Applications 65, no. 1 (1995): 69–82. http://dx.doi.org/10.1016/0166-8641(94)00098-n.

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Feng, William W., Tin-Kan Hung, and Guan-Liang Chang. "Extension and torsion of hyperviscoelastic cylinders." International Journal of Non-Linear Mechanics 27, no. 3 (1992): 329–35. http://dx.doi.org/10.1016/0020-7462(92)90001-n.

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43

Deveney, James K., and Nickolas Heerema. "Higher Derivations and Distinguished Subfields." Canadian Journal of Mathematics 40, no. 1 (1988): 131–41. http://dx.doi.org/10.4153/cjm-1988-006-6.

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Let L be a finitely generated extension of a field K having characteristic p ≠ 0. A rank t higher derivation on L over K is a sequenceof additive maps of K into K such thatd0 is the identity map and dt(x) = 0, i > 0, x ∊ K. [6] contains the relevant background material on higher derivations. By Zorn's Lemma, there are maximal separable extensions of K in L. A maximal separable extension D of K in L is called distinguished ifDieudonné [4] established that any finitely generated extension always has distinguished subfields. L has the same dimension over any distinguished subfield [5], and thi

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Armaselu, Bogdan. "Extensions of the Maximum Bichromatic Separating Rectangle Problem." Information 13, no. 10 (2022): 476. http://dx.doi.org/10.3390/info13100476.

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An important topic in the field of geometric optimization is finding the largest rectangle separating two different points sets, which has significant applications in circuit design and data science. We consider some extensions of the maximum bichromatic separating rectangle (MBSR) problem. In one of the extensions, the optimal rectangle may include up to k outliers, where k is given as part of the input. This extension and is called MBSR with outliers or MBSR-O. In this paper, we improve the current known time bounds for MBSR-O from O(k7mlogm+n) to O(k3m+kmlogm+n) using a clever staircase swe

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Doria, Renato, and M. J. Neves. "A non-abelian model SU(N) Ã— SU(N)." JOURNAL OF ADVANCES IN PHYSICS 8, no. 1 (2015): 1988–2004. http://dx.doi.org/10.24297/jap.v8i1.1528.

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A composite non-abelian model SU(N) Ã— SU(N) is proposed as possible extension of the Yang-Mills symmetry. We obtainÂ the corresponding gauge symmetry of the model and the most general lagrangian invariant by SU(N) Ã— SU(N). The correspondingÂ Feynman rules of the model are studied. Propagators and vertices are derived in the momentum space. As physical application, insteadÂ of considering the color symmetry SUc(3) for QCD, we substitute it by the combination SUc(3) Ã— SUc(3). It yields a possibility to goÂ beyond QCD symmetry in the sense that quarks are preserved with three colors. This exte

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Androulakis, George, and Ryan McGaha. "A variational quantum algorithm for approximating convex roofs." Quantum Information and Computation 22, no. 13&14 (2022): 1081–109. http://dx.doi.org/10.26421/qic22.13-14-1.

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Many entanglement measures are first defined for pure states of a bipartite Hilbert space, and then extended to mixed states via the convex roof extension. In this article we alter the convex roof extension of an entanglement measure, to produce a sequence of extensions that we call $f$-$d$ extensions, for $d \in \mathbb{N}$, where $f:[0,1]\to [0, \infty)$ is a fixed continuous function which vanishes only at zero. We prove that for any such function $f$, and any continuous, faithful, non-negative function, (such as an entanglement measure), $\mu$ on the set of pure states of a finite dimensio

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47

Chen, Qinghua, and Min Zheng. "K-Groups of Trivial Extensions and Gluings of Abelian Categories." Mathematics 9, no. 16 (2021): 1864. http://dx.doi.org/10.3390/math9161864.

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This paper focuses on the Ki-groups of two types of extensions of abelian categories, which are the trivial extension and the gluing of abelian categories. We prove that, under some conditions, Ki-groups of a certian subcategory of the trivial extension category is isomorphic to Ki-groups of the similar subcategory of the original category. Moreover, under some conditions, we show that the Ki-groups of a left (right) gluing of two abelian categories are isomorphic to the direct sum of Ki-groups of two abelian categories. As their applications, we obtain some results of the Ki-groups of the tri

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48

Benkhadra, Dirar, Driss Bennis, and J. R. García Rozas. "The Category of Modules on an n-Trivial Extension: the Basic Properties." Algebra Colloquium 27, no. 03 (2020): 607–20. http://dx.doi.org/10.1142/s1005386720000504.

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In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules. Namely, we introduce the right (resp., left) n-trivial extension of a category by a family of endofunctors. Among other results, projective, injective and flat objects of this category are characterized, and two applications are presented at the end of this paper. We characterize when an n-trivial extension ring is k-perfect and establish a result on the self-injective dimension of an n-trivial extension ring.

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Mkochi, Winfred. "Encoding the plural-honorific suffix -ani and the imperfective anga in Malawian CiTonga (N.15)." Studies in African Linguistics 48, no. 2 (2019): 356–69. http://dx.doi.org/10.32473/sal.v48i2.118043.

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Many Bantu languages have the plural-honorific suffix *-Vni and the imperfective morpheme *-a(n)g-. In most of these languages, *-Vni is reported to be clearly encoded at POST-FINAL position. On the other hand, *-a(n)g- is said to be ambiguously encoded, either at EXT (extension) in one language or FV (final vowel) in another language. Still in others it coexists at both EXT and FV; there has also been a suggestion that it is encoded at POST-FINAL in several others. This article argues that the status of both the plural-honorific suffix -ani (*-Vni) and the imperfective -anga (*-a(n)g)- in CiT

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Frič, Roman, Peter Eliaš, and Martin Papčo. "Divisible extension of probability." Mathematica Slovaca 70, no. 6 (2020): 1445–56. http://dx.doi.org/10.1515/ms-2017-0441.

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AbstractWe outline the transition from classical probability space (Ω, A, p) to its "divisible" extension, where (as proposed by L. A. Zadeh) the σ-field A of Boolean random events is extended to the class 𝓜(A) of all measurable functions into [0,1] and the σ-additive probability measure p on A is extended to the probability integral ∫(·) dp on 𝓜(A). The resulting extension of (Ω, A,p) can be described as an epireflection reflecting A to 𝓜(A) and p to ∫(·) dp.The transition from A to 𝓜(A), resembling the transition from whole numbers to real numbers, is characterized by the extension of two-va

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