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Статті в журналах з теми "Extension bases"

Автор: Grafiati

Опубліковано: 28 вересня 2024

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1

Chen, Yuqun. "Gröbner–Shirshov Bases for Extensions of Algebras." Algebra Colloquium 16, no. 02 (June 2009): 283–92. http://dx.doi.org/10.1142/s1005386709000285.

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Анотація:

An algebra [Formula: see text] is called an extension of the algebra M by B if M2 = 0, M is an ideal of [Formula: see text] and [Formula: see text] as algebras. In this paper, by using Gröbner–Shirshov bases, we characterize completely the extensions of M by B. An algorithm to find the conditions of an algebra A to be an extension of M by B is obtained.

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2

Hantash, Ra’edOmar Abu, and Mohammed H. AbuH Abu Yunis. "Distal extension bases: Removable partial dentures." Journal of Indian Prosthodontic Society 9, no. 4 (2009): 186. http://dx.doi.org/10.4103/0972-4052.206949.

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3

Antoniou, G., and C. K. MacNish. "Conservative extension concepts for nonmonotonic knowledge bases." International Journal of Intelligent Systems 15, no. 9 (2000): 859–77. http://dx.doi.org/10.1002/1098-111x(200009)15:9<859::aid-int3>3.0.co;2-e.

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4

Zhang, Aixian, and Keqin Feng. "Normal Bases on Galois Ring Extensions." Symmetry 10, no. 12 (December 3, 2018): 702. http://dx.doi.org/10.3390/sym10120702.

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Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension.

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5

Boveda, Eugenia. "Reseña / Comunicación y Chagas. Bases para un diálogo urgente." +E: Revista de Extensión Universitaria, no. 16.Ene-Jun (June 9, 2022): e0004. http://dx.doi.org/10.14409/extension.2022.16.ene-jun.e0004.

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Анотація:

Se trata de una recopilación de reflexiones y recomendaciones que surgieron, desde Argentina, a partir de la organización del 1° Conversatorio sobre Comunicación y Chagas (14 de abril de 2020), entre integrantes del grupo ¿De qué hablamos cuando hablamos de Chagas?, el Programa Nacional de Chagas del Ministerio de Salud de la Nación Argentina y la Universidad Nacional del Litoral, junto a una diversidad de actores sociales de distintos puntos del país y del exterior.Este libro pretende ser una herramienta clave para lograr un cambio en la percepción social del Chagas, con el propósito de que cada vez sean más las voces que hablen del tema desde perspectivas críticas, contextualizadas y multidimensionales. Asimismo, constituye un material de consulta para todas aquellas personas interesadas y/o vinculadas con esta problemática, cualquiera sea el ámbito o disciplina de abordaje y el contexto donde este vínculo tenga lugar. En particular, la extensión universitaria resulta un escenario clave por los diálogos que la misma habilita entre actores y saberes diversos.

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6

PICKETT, ERIK JARL. "CONSTRUCTION OF SELF-DUAL INTEGRAL NORMAL BASES IN ABELIAN EXTENSIONS OF FINITE AND LOCAL FIELDS." International Journal of Number Theory 06, no. 07 (November 2010): 1565–88. http://dx.doi.org/10.1142/s1793042110003654.

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Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that Tr F/E(g(x), h(x)) = δg, h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char (E) ≠ 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char (E) = 2, then F admits a self-dual normal basis if and only if the exponent of Γ is not divisible by 4. In this paper, we construct self-dual normal basis generators for finite extensions of finite fields whenever they exist. Now let K be a finite extension of ℚp, let L/K be a finite abelian Galois extension of odd degree and let [Formula: see text] be the valuation ring of L. We define AL/K to be the unique fractional [Formula: see text]-ideal with square equal to the inverse different of L/K. It is known that a self-dual integral normal basis exists for AL/K if and only if L/K is weakly ramified. Assuming p ≠ 2, we construct such bases whenever they exist.

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7

KOO, JA KYUNG, DONG HWA SHIN, and DONG SUNG YOON. "NORMAL BASES FOR MODULAR FUNCTION FIELDS." Bulletin of the Australian Mathematical Society 95, no. 3 (March 2, 2017): 384–92. http://dx.doi.org/10.1017/s0004972716001362.

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Анотація:

We provide a concrete example of a normal basis for a finite Galois extension which is not abelian. More precisely, let $\mathbb{C}(X(N))$ be the field of meromorphic functions on the modular curve $X(N)$ of level $N$. We construct a completely free element in the extension $\mathbb{C}(X(N))/\mathbb{C}(X(1))$ by means of Siegel functions.

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8

Mehta, Ritu, and Sanket Agrawal. "Embracing the organic way: is consumer preference the same for all brands?" International Journal of Retail & Distribution Management 48, no. 5 (April 13, 2020): 453–64. http://dx.doi.org/10.1108/ijrdm-09-2019-0311.

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Анотація:

PurposeThe growing market for organic products presents a tremendous opportunity for marketers to extend their existing brands. However, there is hardly any research that investigates the factors extension from an organic parent brand is preferred over extension into same product category for success of such brand extensions. This paper investigates the role of two different bases consumers may use to evaluate the extension into organic product – organic status of the parent brand and its similarity to the extended product category.Design/methodology/approachThe study involved a 2 × 2 (organic versus regular parent brand and same versus different product category) between-subjects factorial design. Data collected from 164 postgraduate students presented with one of the four scenarios were analysed using ANOVA.FindingsThe results reveal that extensions from organic parent brand versus regular brand, and in the same product category versus different category, are evaluated more favourably. Moreover, extension from an organic parent brand is preferred over extension into same product category.Originality/valueThe research contributes to the extant literature on branding and retailing by building on categorisation theory to explain consumer preference for brand extension when launching a new organic product. The findings provide valuable insights to practitioners to launch a new organic product using brand extension.

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9

Capps, Richard H. "Extension and replacement bases for semisimple Lie algebras." Journal of Mathematical Physics 27, no. 4 (April 1986): 914–23. http://dx.doi.org/10.1063/1.527164.

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10

Jouini, Abdellatif, and Khalifa Trimèche. "Biorthogonal multiresolution analyses and decompositions of Sobolev spaces." International Journal of Mathematics and Mathematical Sciences 28, no. 9 (2001): 517–34. http://dx.doi.org/10.1155/s0161171201010936.

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Анотація:

The object of this paper is to construct extension operators in the Sobolev spacesHk(]−∞,0])andHk([0,+∞[)(k≥0). Then we use these extensions to get biorthogonal wavelet bases inHk(ℝ). We also give a construction inL2([−1,1])to see how to obtain boundaries functions.

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11

Georg, Klein, and Zargeh Chia. "Operadic approach to HNN-extensions of Leibniz algebras." Quasigroups and Related Systems 30, no. 1(47) (May 2022): 101–14. http://dx.doi.org/10.56415/qrs.v30.08.

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We construct HNN-extensions of Lie di-algebras in the variety of di-algebras and provide a presentation for the replicated HNN-extension of a Lie di-algebras. Then, by applying the method of Gröbner-Shirshov bases for replicated algebras, we obtain a linear basis. As an application of HNN-extensions, we prove that Lie di-algebras are embedded in their HNNextension.

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12

Pickett, Erik Jarl, and Stéphane Vinatier. "Self-dual integral normal bases and Galois module structure." Compositio Mathematica 149, no. 7 (May 10, 2013): 1175–202. http://dx.doi.org/10.1112/s0010437x12000851.

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AbstractLet $N/ F$ be an odd-degree Galois extension of number fields with Galois group $G$ and rings of integers ${\mathfrak{O}}_{N} $ and ${\mathfrak{O}}_{F} = \mathfrak{O}$. Let $ \mathcal{A} $ be the unique fractional ${\mathfrak{O}}_{N} $-ideal with square equal to the inverse different of $N/ F$. B. Erez showed that $ \mathcal{A} $ is a locally free $\mathfrak{O}[G] $-module if and only if $N/ F$ is a so-called weakly ramified extension. Although a number of results have been proved regarding the freeness of $ \mathcal{A} $ as a $ \mathbb{Z} [G] $-module, the question remains open. In this paper we prove that $ \mathcal{A} $ is free as a $ \mathbb{Z} [G] $-module provided that $N/ F$ is weakly ramified and under the hypothesis that for every prime $\wp $ of $\mathfrak{O}$ which ramifies wildly in $N/ F$, the decomposition group is abelian, the ramification group is cyclic and $\wp $ is unramified in $F/ \mathbb{Q} $. We make crucial use of a construction due to the first author which uses Dwork’s exponential power series to describe self-dual integral normal bases in Lubin–Tate extensions of local fields. This yields a new and striking relationship between the local norm-resolvent and the Galois Gauss sum involved. Our results generalise work of the second author concerning the case of base field $ \mathbb{Q} $.

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13

Nguyen, Van, and Patrice Lassere. "Bases communes holomorphes: nouvelle extension du théorème de Whittaker." Annales Polonici Mathematici 58, no. 3 (1993): 311–18. http://dx.doi.org/10.4064/ap-58-3-311-318.

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14

Kocapinar, Canan, Eylem Güzel Karpuz, Firat Ateş, and A. Sinan Çevik. "Gröbner-Shirshov Bases of the Generalized Bruck-Reilly ∗-Extension." Algebra Colloquium 19, spec01 (October 31, 2012): 813–20. http://dx.doi.org/10.1142/s1005386712000703.

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15

Fonf, V. P. "On the extension of operator bases in Banach spaces." Journal of Soviet Mathematics 58, no. 4 (February 1992): 319–22. http://dx.doi.org/10.1007/bf01097281.

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16

Ono, Tomoaki. "On the Existence ofp-Bases and -Adicp-Bases of a Semi-Local Ring Extension." Communications in Algebra 34, no. 5 (June 2006): 1897–907. http://dx.doi.org/10.1080/00927870500542887.

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17

Azanchiler, Habib. "Γ-Extension of Binary Matroids". ISRN Discrete Mathematics 2011 (3 листопада 2011): 1–8. http://dx.doi.org/10.5402/2011/629707.

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We extend the notion of a point-addition operation from graphs to binary matroids. This operation can be expressed in terms of element-addition operation and splitting operation. We consider a special case of this construction and study its properties. We call the resulting matroid of this special case a Γ-extension of the given matroid. We characterize circuits and bases of the resulting matroids and explore the effect of this operation on the connectivity of the matroids.

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18

Bartel, D. P., J. A. Doudna, N. Usman, and J. W. Szostak. "Template-directed primer extension catalyzed by the Tetrahymena ribozyme." Molecular and Cellular Biology 11, no. 6 (June 1991): 3390–94. http://dx.doi.org/10.1128/mcb.11.6.3390-3394.1991.

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The Tetrahymena ribozyme has been shown to catalyze an RNA polymerase-like reaction in which an RNA primer is extended by the sequential addition of pN nucleotides derived from GpN dinucleotides, where N = A, C, or U. Here, we show that this reaction is influenced by the presence of a template; bases that can form Watson-Crick base pairs with a template add as much as 25-fold more efficiently than mismatched bases. A mutant enzyme with an altered guanosine binding site can catalyze template-directed primer extension with all four bases when supplied with dinucleotides of the form 2-aminopurine-pN.

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19

Bartel, D. P., J. A. Doudna, N. Usman, and J. W. Szostak. "Template-directed primer extension catalyzed by the Tetrahymena ribozyme." Molecular and Cellular Biology 11, no. 6 (June 1991): 3390–94. http://dx.doi.org/10.1128/mcb.11.6.3390.

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Анотація:

The Tetrahymena ribozyme has been shown to catalyze an RNA polymerase-like reaction in which an RNA primer is extended by the sequential addition of pN nucleotides derived from GpN dinucleotides, where N = A, C, or U. Here, we show that this reaction is influenced by the presence of a template; bases that can form Watson-Crick base pairs with a template add as much as 25-fold more efficiently than mismatched bases. A mutant enzyme with an altered guanosine binding site can catalyze template-directed primer extension with all four bases when supplied with dinucleotides of the form 2-aminopurine-pN.

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20

BOKUT, L. A., YUQUN CHEN, and CIHUA LIU. "GRÖBNER–SHIRSHOV BASES FOR DIALGEBRAS." International Journal of Algebra and Computation 20, no. 03 (May 2010): 391–415. http://dx.doi.org/10.1142/s0218196710005753.

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In this paper, we define the Gröbner–Shirshov basis for a dialgebra. The Composition–Diamond lemma for dialgebras is given then. As a result, we give Gröbner–Shirshov bases for the universal enveloping algebra of a Leibniz algebra, the bar extension of a dialgebra, the free product of two dialgebras, and Clifford dialgebra. We obtain some normal forms for algebras mentioned the above.

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21

HASHEMI, AMIR, and BENYAMIN M.-ALIZADEH. "USING GRÖBNER BASES FOR FACTORING POLYNOMIALS OVER ALGEBRAIC EXTENSION FIELDS." Journal of Algebra and Its Applications 11, no. 01 (February 2012): 1250003. http://dx.doi.org/10.1142/s0219498811005270.

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Анотація:

In this paper, we present a simple and efficient algorithm for factoring an arbitrary univariate polynomial over algebraic extension fields, using Gröbner bases. We have implemented our algorithm in MAPLE and we evaluate its performance via some examples.

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22

Kanai, N., and T. Ono. "The module of differentials andp-bases of a ring extension." Communications in Algebra 28, no. 11 (January 2000): 5369–82. http://dx.doi.org/10.1080/00927870008827162.

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23

Li, Dongmei, and Licui Zheng. "The Extension of the GVW Algorithm to Valuation Domains." Complexity 2021 (June 4, 2021): 1–8. http://dx.doi.org/10.1155/2021/7010413.

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Анотація:

The GVW algorithm is an effective algorithm to compute Gröbner bases for polynomial ideals over a field. Combined with properties of valuation domains and the idea of the GVW algorithm, we propose a new algorithm to compute Gröbner bases for polynomial ideals over valuation domains in this study. Furthermore, we use an example to demonstrate the improvement of our algorithm.

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24

Haghighi, Mahmood. "Computation of relative integral bases for algebraic number fields." International Journal of Mathematics and Mathematical Sciences 11, no. 3 (1988): 523–26. http://dx.doi.org/10.1155/s0161171288000626.

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At first we are given conditions for existence of relative integral bases for extension(K;k)=n. Then we will construct relative integral bases for extensionsOK6(−36)/Ok2(−3),OK6(−36)/Ok3(−33),OK6(−36)/Z.

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25

Błażej, Paweł, Małgorzata Wnetrzak, Dorota Mackiewicz, and Paweł Mackiewicz. "Basic principles of the genetic code extension." Royal Society Open Science 7, no. 2 (February 2020): 191384. http://dx.doi.org/10.1098/rsos.191384.

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Compounds including non-canonical amino acids (ncAAs) or other artificially designed molecules can find a lot of applications in medicine, industry and biotechnology. They can be produced thanks to the modification or extension of the standard genetic code (SGC). Such peptides or proteins including the ncAAs can be constantly delivered in a stable way by organisms with the customized genetic code. Among several methods of engineering the code, using non-canonical base pairs is especially promising, because it enables generating many new codons, which can be used to encode any new amino acid. Since even one pair of new bases can extend the SGC up to 216 codons generated by a six-letter nucleotide alphabet, the extension of the SGC can be achieved in many ways. Here, we proposed a stepwise procedure of the SGC extension with one pair of non-canonical bases to minimize the consequences of point mutations. We reported relationships between codons in the framework of graph theory. All 216 codons were represented as nodes of the graph, whereas its edges were induced by all possible single nucleotide mutations occurring between codons. Therefore, every set of canonical and newly added codons induces a specific subgraph. We characterized the properties of the induced subgraphs generated by selected sets of codons. Thanks to that, we were able to describe a procedure for incremental addition of the set of meaningful codons up to the full coding system consisting of three pairs of bases. The procedure of gradual extension of the SGC makes the whole system robust to changing genetic information due to mutations and is compatible with the views assuming that codons and amino acids were added successively to the primordial SGC, which evolved minimizing harmful consequences of mutations or mistranslations of encoded proteins.

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26

YAACOV, ITAÏ BEN, and ARTEM CHERNIKOV. "AN INDEPENDENCE THEOREM FOR NTP2 THEORIES." Journal of Symbolic Logic 79, no. 01 (March 2014): 135–53. http://dx.doi.org/10.1017/jsl.2013.22.

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Анотація:

Abstract We establish several results regarding dividing and forking in NTP2 theories. We show that dividing is the same as array-dividing. Combining it with existence of strictly invariant sequences we deduce that forking satisfies the chain condition over extension bases (namely, the forking ideal is S1, in Hrushovski’s terminology). Using it we prove an independence theorem over extension bases (which, in the case of simple theories, specializes to the ordinary independence theorem). As an application we show that Lascar strong type and compact strong type coincide over extension bases in an NTP2 theory. We also define the dividing order of a theory—a generalization of Poizat’s fundamental order from stable theories—and give some equivalent characterizations under the assumption of NTP2. The last section is devoted to a refinement of the class of strong theories and its place in the classification hierarchy.

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27

Ono, Tomoaki. "A note on $p$-bases of a regular affine domain extension." Proceedings of the American Mathematical Society 136, no. 09 (April 30, 2008): 3079–87. http://dx.doi.org/10.1090/s0002-9939-08-09338-6.

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28

LI, AI-JUN, GUANGTING WANG, and GANGSONG LENG. "AN EXTENDED LOOMIS–WHITNEY INEQUALITY FOR POSITIVE DOUBLE JOHN BASES." Glasgow Mathematical Journal 53, no. 3 (March 10, 2011): 451–62. http://dx.doi.org/10.1017/s0017089511000061.

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AbstractIn this paper, we establish an extended Loomis–Whitney inequality for positive double John bases, which generalises Ball's result [1]. Moreover, a different extension of the Loomis–Whitney inequality is deduced.

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29

Kosmatka, J. B., H. C. Lin, and S. B. Dong. "On Saint-Venant’s Problem for an Inhomogeneous, Anisotropic Cylinder—Part II: Cross-Sectional Properties." Journal of Applied Mechanics 68, no. 3 (July 21, 2000): 382–91. http://dx.doi.org/10.1115/1.1365152.

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Анотація:

Cross-sectional properties of a prismatic inhomogeneous, anisotropic cylinder are determined from Saint-Venant solutions for extension-bending-torsion and flexure, whose method of construction was presented in a previous paper. The coupling of extensional, bending, and twisting deformations due to anisotropy and inhomogeneity leads to some very interesting features. Herein, it is shown that for an inhomogeneous, anisotropic cylinder whose cross-sectional plane is not a material symmetry plane, distinct modulus-weighted and compliance-weighted centroids and distinct principal bending axes are possible. A line of extension-bending centers is given on which an axial force causes extension and bending only but no twist. Two shear centers are given, one using the Griffith-Taylor definition that ignores cross-sectional warpages and the other by stipulating a zero mean rotation over the cross section. The center of twist is discussed, and this property depends on root end fixity conditions that are prescribed in terms of their mean values based on integrals over the cross section rather than by a pointwise specification. While these shear center and center of twist definitions have some rational bases, it is recognized that other definitions are possible, for example those based on modulus or compliance-weighted integrals. Two examples, an angle and a channel, both composed of a two-layer ±30 deg angle-ply composite material, illustrate the procedures for determining these cross-sectional properties.

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30

Perry, John. "An extension of Buchberger’s criteria for Gröbner basis decision." LMS Journal of Computation and Mathematics 13 (April 22, 2010): 111–29. http://dx.doi.org/10.1112/s1461157008000193.

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Анотація:

AbstractTwo fundamental questions in the theory of Gröbner bases are decision (‘Is a basisGof a polynomial ideal a Gröbner basis?’) and transformation (‘If it is not, how do we transform it into a Gröbner basis?’) This paper considers the first question. It is well known thatGis a Gröbner basis if and only if a certain set of polynomials (theS-polynomials) satisfy a certain property. In general there arem(m−1)/2 of these, wheremis the number of polynomials inG, but criteria due to Buchberger and others often allow one to consider a smaller number. This paper presents two original results. The first is a new characterization theorem for Gröbner bases that makes use of a new criterion that extends Buchberger’s criteria. The second is the identification of a class of polynomial systemsGfor which the new criterion has dramatic impact, reducing the worst-case scenario fromm(m−1)/2 S-polynomials tom−1.

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31

Cardozo, Laura Cecilia, and Gilda Cecilia Chosco Diaz. "Reseña / El pensamiento ambiental del Sur. Complejidad, recursos y ecología política latinoamericana." +E: Revista de Extensión Universitaria, no. 13.Jul-Dic (August 23, 2020): e0003. http://dx.doi.org/10.14409/extension.2020.13.jul-dic.e0003.

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Анотація:

En esta obra, referentes de la problemática ambiental latinoamericana y mundial describen y analizan: ¿cuáles son las bases del pensamiento ambiental del Sur? ¿Cómo surgió? ¿En qué contexto? ¿Quiénes contribuyeron a este saber emancipador? Los autores aportan al pensamiento ambiental regional y global desde América Latina. Adoptan una postura crítica, situada e histórica al mismo tiempo, y realizan novedosas propuestas en el contexto de la ciencia, la tecnología y la innovación. El libro invita a recorrer las páginas de los trece capítulos de manera amena y llevadera. Significa que cualquiera puede leer y reflexionar sobre diversas realidades y problemáticas de una ciudad, de una comunidad, de un barrio, de las familias y de las organizaciones.

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32

Marchenkov, Sergey Seraphimovich. "The implicatively implicit bases in implicatively closed classes of three-valued logic." Mathematical Problems of Cybernetics, no. 21 (2023): 156–67. http://dx.doi.org/10.20948/mvk-2023-156.

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It is proved that for any k ≥ 3, any implicatively implicit extension in P<sub>k</sub> contains a class of H<sub>k</sub> homogeneous functions. In each of the 17 implicatively closed classes in P<sub>3</sub>, an implicatively implicitly generating system of functions is constructed. With the exception of the H<sub>3</sub> class, each of the systems consists of one or two no more than two-place functions. A one-place function is specified, the implicatively implicit extension of which is different from any implicatively closed class in P<sub>3</sub>.

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33

Kawasha, Boniface. "Imbrication Patterns of Lunda." Studies in African Linguistics 50, no. 1 (April 23, 2021): 59–81. http://dx.doi.org/10.32473/sal.v50i1.128779.

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This paper examines the imbrication process in Lunda. It is widely acknowledged in the literature that imbrication in Bantu languages is mainly triggered by the perfective or past tense suffix (Bastin 1983). In Lunda, however, this morphophonological process is not only conditioned by the remote past tense inflectional suffix but also caused by derivational extensions that include the applicative, the causative, and to a lesser extent the reciprocal affix when they are attached to a large number of verb bases. Imbrication typically occurs with verb bases containing what is known as an extension, whether productive or frozen. Unlike many Bantu languages, this phenomenon always results in the deletion of the base final consonant and the consonant of the suffix survives. This segmental loss leads to either vowel coalescence between the two adjacent vowels or gliding

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34

Agunga, Robert, and R. Ahmad Romadhoni Surya Putra. "Training Needs of Indonesian Agricultural Extension Workers for the 21st Century: A Recommendation Based on a Field Study." Asian Journal of Agriculture and Development 12, no. 2 (December 15, 2015): 45–57. http://dx.doi.org/10.37801/ajad2015.12.2.4.

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Agricultural extension in Indonesia has undergone major policy changes, depending on the government in power. In particular, since 1998, the government passed Law No 16/2006, aimed at making the extension system more democratic and participatory, especially for smallholder farmers. Law No. 16/2006 is in line with the “pluralistic and demand-driven extension approach” adopted by many developing countries since 2000, which allowed public and private extension systems to exist side-byside. Success of the new extension approach rests on the degree to which extension workers are able to mobilize smallholder farmers for "demand-driven" development that bases extension on smallholder farmers’ needs. This survey of 78 public extension workers in Yogyakarta Province, Indonesia examined challenges in implementing the pluralistic and demand-driven extension approach, including training needed to help extension workers deal more effectively with these challenges. The study found that the challenges relate to agreeing on extension goals; eliciting collaboration with non-government agencies and other development partners; and using ICTs to narrow the farmers-to-agent ratio. In general, the study found that extension workers need training in communication and development, also known as communication for development (C4D) to effectively facilitate development and navigate the increasing complexity of development programming in the 21st century. Thus, we recommend C4D training for extension workers as a way of enhancing their effectiveness. Fortunately, the World Bank and the Food and Agriculture Organization of the United Nations are promoting this strategy. Therefore, we urge the government of Indonesia to explore C4D as a strategy for strengthening extension in the country.

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35

Danchev, Peter. "An Extension of Nice Bases on Ulm Subgroups of Primary Abelian Groups." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 3 (December 1, 2012): 33–36. http://dx.doi.org/10.2478/v10309-012-053-0.

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Abstract Suppose A is an Abelian p-group and is an ordinal such that A/pα A is a direct sum of countable groups. It is shown that A has a nice basis if, and only if, pα A has a nice basis. This strengthens an earlier result of ours in Bull. Allah. Math. Soc. (2011) proved when α< ω2.

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36

Warman, Harry, Louie Slocombe, and Marco Sacchi. "How proton transfer impacts hachimoji DNA." RSC Advances 13, no. 20 (2023): 13384–96. http://dx.doi.org/10.1039/d3ra00983a.

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Анотація:

Hachimoji DNA is a synthetic nucleic acid extension of DNA formed by an additional four bases that can encode information. We examine the possibility of proton transfer between the hachimoji bases, which can result in base mismatch under replication.

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37

Li, Min, Yumeng Zhang, Delong Han, and Mingle Zhou. "Meta-IP: An Imbalanced Processing Model Based on Meta-Learning for IT Project Extension Forecasts." Mathematical Problems in Engineering 2022 (September 20, 2022): 1–11. http://dx.doi.org/10.1155/2022/3140301.

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With increasing developments in information technology, IT projects have received widespread attention. However, the success rate of large information technology projects is extremely low. Most current extension forecast models are designed based on a balanced number of samples and require a large amount of training data to achieve an acceptable prediction result. Constructing an effective extension forecast model with a small number of actual training samples and imbalanced data remains a challenge. This paper proposes a Meta-IP model based on transferable knowledge bases with few-shot learning and a model-agnostic meta-learning improvement algorithm to solve the problems of sample scarcity and data imbalance. The experimental results show that Meta-IP not only outperforms many current imbalance processing strategies but also resolves the problem of having too few samples. This provides a new direction for IT project extension forecasts.

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38

Sahmoudi, Mohammed, and Soullami Abderazak. "On sextic integral bases using relative quadratic extention." Boletim da Sociedade Paranaense de Matemática 38, no. 4 (March 10, 2019): 175–80. http://dx.doi.org/10.5269/bspm.v38i4.40042.

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Let $K=\mathbb{Q}(\theta)$ be a cubic number filed and $P(X)=X^3-aX-b$ ($a,b$ in $\ZZ$), the monic irreducible polynomial of $\theta$. In this paper we give a sufficient conditions on $a$,$b$ which ensure that $\theta$ is a power basis generator, also we give conditions on relative quadratic extension to be monogenic. As a consequence of this theoretical result we can reach an integral basis of some sextic fields which Neither algebraically split nor arithmetically split.

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39

Avila, Andrea Alejandra, Carla Vanezza Rueda, Marta Patricia Rueda, and Adriana Teresita Gómez. "Puentes entre la universidad y el territorio: herramientas al servicio de productores en transición agroecológica en el departamento Banda, Santiago del Estero." +E: Revista de Extensión Universitaria, no. 15.Jul-Dic (December 22, 2021): e0012. http://dx.doi.org/10.14409/extension.2021.15.jul-dic.e0012.

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Este trabajo describe la experiencia de articulación entre el Proyecto de Extensión Certificación Participativa Agroecológica y una Práctica Profesional Supervisada de la Universidad Nacional de Santiago del Estero (UNSE), Argentina, desde un enfoque de vinculación y aprendizaje participativo. Tuvo 3 etapas: 1) desarrollo del marco conceptual, 2) construcción del sistema agroecológico, y 3) obtención de mapa preliminar de actores claves. Mediante el marco conceptual, se decidió continuar con sistemas participativos de garantía como espacio de trabajo más eficaz para la transición agroecológica. El enfoque de sistemas con técnicas participativas permite conocer el modelo y cuantificar las entradas y salidas del sistema y aporta las bases para el protocolo de garantía de la producción agroecológica. Se construyó la red de actores para la construcción de la identidad agroecológica. Los resultados se publicaron en informes, trabajo a congresos, divulgación y talleres de devolución a la comunidad. Las herramientas metodológicas y los nuevos marcos teóricos apropiados a la realidad del territorio de vinculación enriquecieron la experiencia de aprendizaje.

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40

Goh, Say Song, and K. M. Teo. "An algorithm for constructing multidimensional biorthogonal periodic multiwavelets." Proceedings of the Edinburgh Mathematical Society 43, no. 3 (October 2000): 633–49. http://dx.doi.org/10.1017/s0013091500021246.

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AbstractThis paper deals with the problem of constructing multidimensional biorthogonal periodic multiwavelets from a given pair of biorthogonal periodic multiresolutions. Biorthogonal polyphase splines introduced to reduce the problem to a matrix extension problem, and an algorithm for solving the matrix extension problem is derived. Sufficient conditions for collections of periodic multiwavelets to form a pair of biorthogonal Riesz bases of the entire function space are also obtained.

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41

BĚLOHLÁVEK, RADIM, and VILEM VYCHODIL. "BASIC ALGORITHM FOR ATTRIBUTE IMPLICATIONS AND FUNCTIONAL DEPENDENCIES IN GRADED SETTING." International Journal of Foundations of Computer Science 19, no. 02 (April 2008): 297–317. http://dx.doi.org/10.1142/s0129054108005693.

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We present GLINCLOSURE, a graded extension of the well-known LINCLOSURE algorithm. GLINCLOSURE can be used to compute degrees of semantic entailment from sets of fuzzy attribute implications. It can also be used together with graded extension of Ganter's NEXTCLOSURE algorithm to compute non-redundant bases of data tables with fuzzy attributes. We present foundations, the algorithm, analysis of its complexity, implementation details, and illustrative examples.

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42

Wood, Christine T., Roger L. McCarthy, Jeya Padmanaban, and Roman R. Beyer. "Analysis of Accident Data and Fatal Risk for Occupational Use of Extension Ladders." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 38, no. 14 (October 1994): 806–10. http://dx.doi.org/10.1177/154193129403801402.

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This paper presents the results of analyses of injury and fatality accidents associated with the occupational use of metal extension ladders. Data contained in seven different data bases differing in geographic representation and level of severity of injury were analyzed to identify the type of accidents that occur and their frequency. In addition, the risks of fatality and of electrocution fatality associated with occupational use of extension ladders were estimated and compared with the fatal risk for various occupations. The overall fatal risk for extension ladder use by workers is less than the overall fatality risk for the construction industry.

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43

Lassoie, J. P., W. S. Teel, and K. M. Davies Jr. "Agroforestry Research and Extension Needs For Northeastern North America." Forestry Chronicle 67, no. 3 (June 1, 1991): 219–26. http://dx.doi.org/10.5558/tfc67219-3.

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Most farms in the Northeast include wooded areas that exist either as woodlots, plantations, or fence rows. However, the degree to which these areas support a particular farm is highly variable — some being largely ignored, others contributing significantly to the farm's economic well-being. The current economic plight and ecological problems facing the agricultural sector across North America are forcing many farmers to look for alternatives to traditional farming and forestry practices. One possibility is the greater integration of trees directly into the farming system through the adoption of various agroforestry principles and practices. Promoting the adoption of agroforestry by farmers in the Northeast, however, will require developing new research data bases and modifying current extension delivery systems. Suggestions for accomplishing both are provided in this paper based on an assessment of the potential for agroforestry in New York State. Key words: Agroforestry, tree crops, nut trees, technology transfer, Cooperative Extension, marginal lands

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44

Al-Rimawi, Ahmad, Mohammad Tabieh, and Hussein Al-Qudah. "Assessing Growers’ Perceptions of Effective Extension Methods and Information Communication Technologies for Training Vegetable Growers in Jordan." International Journal of Economics and Finance 8, no. 8 (July 20, 2016): 229. http://dx.doi.org/10.5539/ijef.v8n8p229.

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<p class="p4">The study examined the effectiveness of agricultural extension education methods as perceived by vegetable growers in Jordan to meet their assessed needs in areas of production, marketing and management. A random sample of 98 vegetable growers in two governorates in Jordan was used. Four point Likert-type scales were used as instruments to gather primary data. Cronbach’s alpha coefficients ranged from 0.88 to 0.91 indicated high internal consistency for the scales. Nonparametric methods were used to analyze the data based on approximations to normal distribution. The results showed that aged people with basic education and who are very largely dependent on farm income are still the ones most engaged in vegetable farming. The most preferred extension methods by farmers were farm visit, meeting groups of farmers, result demonstrations and farm tours. Low rated methods include information and communications technologies (ICTs). The method to be chosen depends on the goal and adoption stage, i.e. whether we wish to change knowledge, attitude, skills or behavior. Extension staff needs to be trained on how to use ICT tools as an extension method to enable them to train farmers on how they can use them in extension. The involvement of public extension staff in the survey contributes to the selection of extension delivery method on the bases of its ability to deliver the appropriate information to the targeted farmers in the right time.</p>

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45

Štohl, J., and V. Porubčan. "Dynamical Aspects of the Taurid Meteor Complex." Symposium - International Astronomical Union 152 (1992): 315–24. http://dx.doi.org/10.1017/s0074180900091324.

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Unusually long activity of the Taurid meteor complex, extending over 3-5 months according to new estimations based on various orbital similarity criteria, has been evoking controversies about the possible origin and dynamical evolution of this unique complex of meteor streams. It even casts doubts on the reality of the extension of the complex. In the present paper orbital elements and the extension of the Taurid meteor complex are re-examined on the bases of the most precise photographic meteor orbits available from the IAU Meteor Data Center in Lund. The results are evaluated and discussed from the viewpoint of various proposals on the origin and dynamical evolution of the complex.

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46

Choe, Young Chan. "The Research and Extension System with Agro-Food industry Development: To Strengthen The Regional R&D and On-Farm Bases Extension." Journal of Agricultural Extension & Community Development 20, no. 4 (December 30, 2013): 839–69. http://dx.doi.org/10.12653/jecd.2013.20.4.0839.

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47

Mackey, D. Steven. "Minimal indices and minimal bases via filtrations." Electronic Journal of Linear Algebra 37 (April 29, 2021): 276–94. http://dx.doi.org/10.13001/ela.2021.5971.

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A new way to formulate the notions of minimal basis and minimal indices is developed in this paper, based on the concept of a filtration of a vector space. The goal is to provide useful new tools for working with these important concepts, as well as to gain deeper insight into their fundamental nature. This approach also readily reveals a strong minimality property of minimal indices, from which follows a characterization of the vector polynomial bases in rational vector spaces. The effectiveness of this new formulation is further illustrated by proving several fundamental properties: the invariance of the minimal indices of a matrix polynomial under field extension, the direct sum property of minimal indices, the polynomial linear combination property, and the predictable degree property.

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48

Zhao, Zhonghua, and Lijuan Fan. "On Degenerate Ringel-Hall Algebras of Types A and G2." Algebra Colloquium 21, no. 01 (January 20, 2014): 67–80. http://dx.doi.org/10.1142/s1005386714000054.

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49

Wang, Yajun, Nicole Ng, Erkai Liu, Curtis H. Lam, and David M. Perrin. "Systematic study of constraints imposed by modified nucleoside triphosphates with protein-like side chains for use in in vitro selection." Organic & Biomolecular Chemistry 15, no. 3 (2017): 610–18. http://dx.doi.org/10.1039/c6ob02335e.

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To select modified DNAzymes and aptamers, modified nucleoside triphosphates (dNTPs) must replace their unmodified counterparts in enzyme-catalyzed primer extension reactions and, once incorporated, serve as template bases in enzyme-catalyzed recopying.

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50

Zein, Sara A., Marie-Claude Bordage, Ziad Francis, Giovanni Macetti, Alessandro Genoni, Claude Dal Cappello, Wook-Geun Shin, and Sebastien Incerti. "Electron transport in DNA bases: An extension of the Geant4-DNA Monte Carlo toolkit." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 488 (February 2021): 70–82. http://dx.doi.org/10.1016/j.nimb.2020.11.021.

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