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Journal articles on the topic 'Base extension'

Author: Grafiati

Published: 17 May 2025

Last updated: 31 July 2025

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1

Pritee, Pritee, and Manjeet Singh Jakhar. "Arithmetic Progression and Binary Recurrence." International Journal of Applied and Behavioral Sciences 02, no. 01 (2025): 109–21. https://doi.org/10.70388/ijabs250111.

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When it comes to Galois theory, the idea of a field extension is considered to be one of the most fundamental concepts. In Galois theory, the field that is now being explored is used as an input, and the features of extension fields are investigated in relation to the field that is currently being investigated. It focuses on something called "Galois extensions," which are simply fields that possess specific symmetry features. These fields are referred to as "Galois extensions." Because of these features, we are now in a position to identify a relationship between the structure of the Galois gr

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2

Yu, Hefu, and Bo-Qiang Ma. "Origin of fermion generations from extended noncommutative geometry." International Journal of Modern Physics A 33, no. 29 (2018): 1850168. http://dx.doi.org/10.1142/s0217751x18501683.

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We propose a way to understand the three fermion generations by the algebraic structures of noncommutative geometry, which is a promising framework to unify the standard model and general relativity. We make the tensor product extension and the quaternion extension on the framework. Each of the two extensions alone keeps the action invariant, and we consider them as the almost trivial structures of the geometry. We combine the two extensions, and show the corresponding physical effects, i.e. the emergence of three fermion generations and the mass relationships among those generations. We defin

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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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Tikoo, Mohan. "On strict and simple type extensions." International Journal of Mathematics and Mathematical Sciences 21, no. 2 (1998): 239–47. http://dx.doi.org/10.1155/s0161171298000349.

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Let(Y,τ)be an extension of a space(X,τ′)⋅p∈Y, let𝒪yp={W∩X:W∈τ,p∈W}. ForU∈τ′, leto(U)={P∈Y:U∈𝒪yp}. In 1964, Banaschweski introduced the strict extensionY#, and the simple extensionY+ofX(induced by(Y,τ)) having base{o(U):U∈τ′}and{U∪{p}:p∈Y,and U∈Oyp}, respectively. The extensionsY#andY+have been extensively used since then. In this paper, the open filtersℒp={W∈τ′:W⫆intxclx(U)for someU∈𝒪yp}, and𝒰p={W∈τ′:intxclx(W)∈𝒪yp}={W∈τ′:intxclx(W)∈ℒp}=∩{𝒰:𝒰is an open ultrafilter onX,𝒪yp⊂𝒰}onXare used to define some new topologies onY. Some of these topologies produce nice extensions of(X,τ′). We study some i

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Snape, Simon, and Andrea Krott. "The role of inhibition in moving beyond perceptually focused noun extensions." First Language 38, no. 1 (2017): 95–108. http://dx.doi.org/10.1177/0142723717737195.

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When young children interpret novel nouns, they tend to be very much affected by the perceptual features of the referent objects, especially shape. This article investigates whether children might inhibit a prepotent tendency to base novel nouns on the shape of referent objects in order to base them on conceptual features (i.e. taxonomic object categories). The study tested 3- to 5-year old children on a noun extension task, alongside a test of their inhibition and more general executive control ability. Noun extensions were related to inhibition ability, independent of age. Noun extensions we

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6

DOMBI, E. R., N. D. GILBERT, and N. RUŠKUC. "FINITE PRESENTABILITY OF HNN EXTENSIONS OF INVERSE SEMIGROUPS." International Journal of Algebra and Computation 15, no. 03 (2005): 423–36. http://dx.doi.org/10.1142/s021819670500227x.

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HNN extensions of inverse semigroups, where the associated inverse subsemigroups are order ideals of the base, are defined by means of a construction based upon the isomorphism between the categories of inverse semigroups and inductive groupoids. The resulting HNN extension may conveniently be described by an inverse semigroup presentation, and we determine when an HNN extension with finitely generated or finitely presented base is again finitely generated or finitely presented. Our main results depend upon properties of the [Formula: see text]-preorder in the associated subsemigroups. Let S b

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7

Indyannara, Karyn Mendes Soares de Sousa, Beatriz Vasconcelos de Araújo Andreia, and Lima Ventura Patrícia. "A VISÃO DOS ACADÊMICOS DE FISIOTERAPIA NO IMPACTO DAS AÇÕES DO PROJETO DE EXTENSÃO PILATES DA GENTE." Revistaft 27, no. 127 (2023): 32. https://doi.org/10.5281/zenodo.10068832.

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A Extensão Universitária pode ser vista como um processo educativo, cultural  e científico que estimula o ensino e a pesquisa de forma indissociável. Nesse sentido,  a extensão nos cursos da saúde viabiliza uma formação integral capaz de motivar os  extensionistas a experimentarem o contato com a realidade coletiva em que estão  inseridos e a humanização desses futuros profissionais. <strong>Objetivo: </strong>O propósito deste  estudo é destacar a relevância do projeto de extensão "Pilates da Gente" na vida dos  estudantes do curso de fisioterapia, demonstrando o

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8

Scott, Brendan J. J., and Pauline Maillou. "The distal extension base denture." Dental Update 30, no. 3 (2003): 139–44. http://dx.doi.org/10.12968/denu.2003.30.3.139.

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9

Zwaan, Frank, Guido Schreurs, and Susanne J. H. Buiter. "A systematic comparison of experimental set-ups for modelling extensional tectonics." Solid Earth 10, no. 4 (2019): 1063–97. http://dx.doi.org/10.5194/se-10-1063-2019.

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Abstract. Analogue modellers investigating extensional tectonics often use different machines, set-ups and model materials, implying that direct comparisons of results from different studies can be challenging. Here we present a systematic comparison of crustal-scale analogue experiments using simple set-ups simulating extensional tectonics, involving either a foam base, a rubber base, rigid basal plates or a conveyor base system to deform overlying brittle-only or brittle-viscous models. We use X-ray computed tomography (CT) techniques for a detailed 3-D analysis of internal and external mode

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10

Hassett, Brendan, and Sándor J. Kovács. "Reflexive pull-backs and base extension." Journal of Algebraic Geometry 13, no. 2 (2004): 233–47. http://dx.doi.org/10.1090/s1056-3911-03-00331-x.

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11

Sade, Burak, Richard A. Prayson, and Joung H. Lee. "Gliosarcoma with infratemporal fossa extension." Journal of Neurosurgery 105, no. 6 (2006): 904–7. http://dx.doi.org/10.3171/jns.2006.105.6.904.

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✓ Gliosarcomas are bimorphic intraaxial tumors. Involvement of the skull base is highly unexpected. The authors present the case of a temporal lobe gliosarcoma with significant infratemporal fossa extension. This 55-year-old man presented with a 1-month history of severe progressive headache. Neurological examination was unremarkable except for bilateral papilledema. Magnetic resonance imaging revealed a 6-cm right temporal mass with extension into the infratemporal fossa. The patient underwent a right frontotemporal craniotomy together with drilling of the sphenoid ridge and middle fossa floo

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Huang, Q., M. R. Jacobson, and T. Pederson. "3' processing of human pre-U2 small nuclear RNA: a base-pairing interaction between the 3' extension of the precursor and an internal region." Molecular and Cellular Biology 17, no. 12 (1997): 7178–85. http://dx.doi.org/10.1128/mcb.17.12.7178.

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The spliceosomal small nuclear RNAs U1, U2, U4, and U5 are transcribed by RNA polymerase II as precursors with extensions at their 3' ends. The 3' processing of these pre-snRNAs is not understood in detail. Two pathways of pre-U2 RNA 3' processing in vitro were revealed in the present investigation by using a series of human wild-type and mutant pre-U2 RNAs. Substrates with wild-type 3' ends were initially shortened by three or four nucleotides (which is the first step in vivo), and the correct mature 3' end was then rapidly generated. In contrast, certain mutant pre-U2 RNAs displayed an aberr

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13

PÉREZ, EFRÉN. "ON SEMIGENERIC TAMENESS AND BASE FIELD EXTENSION." Glasgow Mathematical Journal 58, no. 1 (2015): 39–53. http://dx.doi.org/10.1017/s0017089515000051.

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AbstractThe notions of central endolength and semigeneric tameness are introduced, and their behaviour under base field extension for finite-dimensional algebras over perfect fields are analysed. Forka perfect field,Kan algebraic closure and Λ a finite-dimensionalk-algebra, here there is a proof that Λ is semigenerically tame if and only if Λ ⊗kKis tame.

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14

Ternovsky, Volodymyr. "ADVANTAGES AND DISADVANTAGES OF EXTENSION SERVICE ACTIVITY ON THE BASE OF THE STATE UNIVERSITY IN UKRAINE." sj-economics scientific journal 8 (June 30, 2011): 221–25. http://dx.doi.org/10.58246/sjeconomics.v8i.491.

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The article examines the importance of extension service work for agricultural development. The basic points of origin and development of extension service in the world showing the basic models of extension service. Advantages and disadvantages of extension service on the base of university are lighted.

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15

Аkhmedova, Dildora Bakhodirovna. "ETYMOLOGICAL DICTIONARY OF THE UZBEK LANGUAGE – INFORMATION BASE OF CORPUS SEMANTIC EXPANSION." International journal of word art 5, no. 6 (2022): 3. https://doi.org/10.5281/zenodo.7393777.

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In this article, the etymological dictionary of the Uzbek language serves as a source of information in the development of semantic extensions of the lexical units of the Uzbek language through several examples. Also, during the historical development of the language, the word does not change in content, but changes in sound, phenomena of homonymy are analyzed. Considering the wide public use of the "Etymological Dictionary of the Uzbek Language", it is noted that the comments are presented in a popular way, concisely, which facilitates the development of semantic extension comments.

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16

Chatzidakis, Zoé, and Ehud Hrushovski. "Difference fields and descent in algebraic dynamics. II." Journal of the Institute of Mathematics of Jussieu 7, no. 4 (2008): 687–704. http://dx.doi.org/10.1017/s1474748008000170.

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AbstractThis second part of the paper strengthens the descent theory described in the first part to rational maps and arbitrary base fields. We obtain in particular a decomposition of any difference field extension into a tower of finite, field-internal and one-based difference field extensions. This is needed in order to obtain the ‘dynamical Northcott’ Theorem 1.11 of Part I in sharp form.

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17

GUPTA, CHINMAYA. "Extreme-value distributions for some classes of non-uniformly partially hyperbolic dynamical systems." Ergodic Theory and Dynamical Systems 30, no. 3 (2009): 757–71. http://dx.doi.org/10.1017/s0143385709000406.

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AbstractIn this note, we obtain verifiable sufficient conditions for the extreme-value distribution for a certain class of skew-product extensions of non-uniformly hyperbolic base maps. We show that these conditions, formulated in terms of the decay of correlations on the product system and the measure of rapidly returning points on the base, lead to a distribution for the maximum of Φ(p)=−log(d(p,p0)) that is of the first type. In particular, we establish the type I distribution for S1 extensions of piecewise C2 uniformly expanding maps of the interval, non-uniformly expanding maps of the int

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18

Zou, Bingjie, Qinxin Song, Jianping Wang, Yunlong Liu, and Guohua Zhou. "Invasive reaction assisted strand-displacement signal amplification for sensitive DNA detection." Chem. Commun. 50, no. 89 (2014): 13722–24. http://dx.doi.org/10.1039/c4cc06079b.

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19

Cloyd, Raymond A. "Challenges to Extension Programming." HortTechnology 15, no. 1 (2005): 177–80. http://dx.doi.org/10.21273/horttech.15.1.0177.

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The way extension specialists and educators conduct programs, such as workshops, and transfer information to their designated clientele, including homeowners, professionals, and specialty groups, has changed within the last decade due to merging departments, budget cuts, reduced operating funds, and lack of refilling vacant positions. These factors have resulted in a number of driving forces that influence the way extension specialists and educators perform their duties, such as accountability, regionalization of extension, impact of technology, and expanding expertise. To be accountable under

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20

Baharoon, Asala H., Mohammed A. Al-mekhlafi, Reda A. Jamjoom, Talal A. Al-Khatib, Mazin A. Merdad, and Hani Z. Marzouki. "Carotid Body Tumor with Skull Base Extension." American Journal of Case Reports 18 (October 31, 2017): 1153–56. http://dx.doi.org/10.12659/ajcr.905526.

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21

Sandqvist, Tor. "Base-extension semantics for intuitionistic sentential logic." Logic Journal of IGPL 23, no. 5 (2015): 719–31. http://dx.doi.org/10.1093/jigpal/jzv021.

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22

Kasjan, Stanisław. "Auslander-Reiten sequences under base field extension." Proceedings of the American Mathematical Society 128, no. 10 (2000): 2885–97. http://dx.doi.org/10.1090/s0002-9939-00-05382-x.

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23

Seleem, Ashraf Salah. "Skull base tumors: assessment of intracranial extension." International Congress Series 1240 (October 2003): 437–44. http://dx.doi.org/10.1016/s0531-5131(03)00870-7.

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24

Wu, Quanshui. "Gelfand-Kirillov dimension under base field extension." Israel Journal of Mathematics 73, no. 3 (1991): 289–96. http://dx.doi.org/10.1007/bf02773842.

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25

Renshaw, J. "Extension and amalgamation in rings." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 102, no. 1-2 (1986): 103–15. http://dx.doi.org/10.1017/s0308210500014517.

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SynopsisIt is proved that if a ring R has the extension property in containing ringSi, then the amalgam [R; Si,] is strongly embeddable. Using a result of P. M. Cohn, a necessary and sufficient condition for a ring to be an amalgamation base is then given. It is also shown that R is a level subring of a ring S if and only if S/R is flat. From this, a classical result of P. M. Cohn on flat amalgams is proved.

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Wu, Han. "Non-invariance of Weak Approximation with Brauer–Manin Obstruction." Algebra Colloquium 31, no. 04 (2024): 595–608. http://dx.doi.org/10.1142/s1005386724000440.

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We study weak approximation with Brauer–Manin obstruction with respect to extensions of number fields. For any nontrivial extension [Formula: see text], assuming a conjecture of M. Stoll, we prove that there exists a [Formula: see text]-threefold satisfying weak approximation with Brauer–Manin obstruction off all archimedean places, while its base change to [Formula: see text] fails. Then we illustrate this construction with an explicit unconditional example.

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Schiere, J. B. "Research and extension in livestock development." BSAP Occasional Publication 16 (1993): 135–44. http://dx.doi.org/10.1017/s0263967x00031153.

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AbstractThis paper discusses results, justifications and definitions of research and extension in tropical animal production. The emphasis is on the applicability of new technologies and the interaction between research and extension. A description is given of the participants, the farming systems and of the research-extension interaction with attention to the fact that much extension is technology driven rather than problem orientated. Special issues in the livestock sector are highlighted. The diversity of farming systems implies that generalized solutions are hard to find because of technic

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Dooley, Tim P., Michael R. Hudec, Dan Carruthers, Martin P. A. Jackson, and G. Luo. "The effects of base-salt relief on salt flow and suprasalt deformation patterns — Part 1: Flow across simple steps in the base of salt." Interpretation 5, no. 1 (2017): SD1—SD23. http://dx.doi.org/10.1190/int-2016-0087.1.

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Passive margins underlain by a salt detachment are typically interpreted as kinematically linked zones of updip extension and downdip contraction separated by a zone of translation above a smoothly dipping base of salt. However, salt flow is affected by the base-of-salt geometry across which it flows, and early-stage gravity gliding induced by basin tilt may be complicated by the presence of salt-thickness changes caused by the pre-existing base-salt relief. We investigate these effects using physical models. Dip-parallel steps generate strike-slip fault zones separating domains of differentia

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DONG, Yuan-Yuan, Hai-Hui SHENG, Qian YANG, et al. "A new SNP microarray technology based on single base extension." Hereditas (Beijing) 31, no. 4 (2009): 439–44. http://dx.doi.org/10.3724/sp.j.1005.2009.00439.

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30

Cieza, Ramon, Griselda Sánchez Vallduví, Nora Tamagno, and Santiago Sarandón. "Estrategias de base agroecológica para y con agricultores familiares de la región Pampeana. Construyendo faros agroecológicos." +E: Revista de Extensión Universitaria, no. 14.Ene-Jun (June 18, 2021): e0005. http://dx.doi.org/10.14409/extension.2021.14.ene-jun.e0005.

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Este trabajo describe y analiza un proceso de intervención realizada por un equipo interdisciplinario de la Facultad de Ciencias Agrarias y Forestales de la Universidad Nacional de la Plata, Argentina, cuyo objetivo fue difundir, desarrollar y evaluar estrategias y tecnologías de base agroecológica apropiadas para y con productores familiares de la región Pampeana. Se describen los aportes que realizó el proyecto a partir del acompañamiento, intercambio de saberes y fortalecimiento de sistemas productivos agroecológicos en el territorio. Respecto del desarrollo de la experiencia, se analiza la

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Arun, Kumar Chaudhary, and Kumar Vijay. "Half Logistic Exponential Extension Distribution with Properties and Applications." International Journal of Recent Technology and Engineering (IJRTE) 9, no. 3 (2020): 506–12. https://doi.org/10.35940/ijrte.C4625.099320.

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In this article, we have introduced a new distribution based on type I half logistic-G family and exponential extension as a base distribution known as Half Logistic Exponential Extension (HLEE) distribution. The statistical properties of this model are also explored, such as the behavior of probability density, hazard rate, and quantile functions are investigated. The Maximum likelihood estimation (MLE) method is used to estimate model parameters. For the potentiality of the proposed model we have compared the goodness of fit with some others models. We have proven the importance and flexibil

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Jackson, C. Gary, Michael E. Glasscock, Kevin X. Mckennan, et al. "The Surgical Treatment of Skull-Base Tumors with Intracranial Extension." Otolaryngology–Head and Neck Surgery 96, no. 2 (1987): 175–85. http://dx.doi.org/10.1177/019459988709600211.

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As a discipline, skull-base surgery via the transtemporal route has matured since 1975. Previously considered unresectable, skull-base tumors with intracranial extension can now be successfully removed by means of modification of contemporary exposures with neurosurgical collaboration. Between September 1970 and February 1986, 126 skull-base tumors have been operated on by The Otology Group, P.C. Of these, 49 had intracranial extension. In this article, techniques for tumor removal and dural defect reconstruction are outlined. A single-staged procedure is advised. The advantages of and excepti

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Gerber, John M. "1039 THE NEW ENGLAND EXTENSION CONSORTIUM: INTEGRATING RESEARCH AND EXTENSION ACROSS A REGION." HortScience 29, no. 5 (1994): 577c—577. http://dx.doi.org/10.21273/hortsci.29.5.577c.

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There is a fundamental need for the land grant system to debate and rediscover its place in society as a learning organization founded upon enhanced internal and external connectivity. Two critical connections are the linkage between research and extension, and cooperation among the states. As with any system in which the component parts are no longer functionally integrated, the land grant system is declining in vitality. Poor cooperation among states and weak linkages between the research and extension functions have reduced the capacity of the system to serve the public good. The New Englan

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Tu, Shuai, and Ai Min Sha. "Influence on the Stress of Pavement with Crack in Base from Flexible Transition Layer under Dynamic Loading." Advanced Materials Research 602-604 (December 2012): 2189–92. http://dx.doi.org/10.4028/www.scientific.net/amr.602-604.2189.

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After cracks appear in the semi-rigid base layer, the stress mode of pavement structure transits from infinite continuum to limited size board, and the cracks become stress concentration areas. Based on the practical tire contact pressure and contact area, this paper establishes the C3D8R model by ABAQUS, to calculate and analyse the influence on the base cracks extension from graded gravel transition layer under half-sinusoid load. Analysis shows that the graded gravel has excellent stress dissipation ability. Whether there are cracks in the base, the graded gravel transition layer between as

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Hussain, Hasnain, and Nikson Fatt-Ming Chong. "Combined Overlap Extension PCR Method for Improved Site Directed Mutagenesis." BioMed Research International 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/8041532.

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The combined overlap extension PCR (COE-PCR) method developed in this work combines the strengths of the overlap extension PCR (OE-PCR) method with the speed and ease of the asymmetrical overlap extension (AOE-PCR) method. This combined method allows up to 6 base pairs to be mutated at a time and requires a total of 40–45 PCR cycles. A total of eight mutagenesis experiments were successfully carried out, with each experiment mutating between two to six base pairs. Up to four adjacent codons were changed in a single experiment. This method is especially useful for codon optimization, where doub

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Moffitt, L. Joe, Robert L. Christensen, and Kent D. Fleming. "Popular Informational Priorities in Agricultural Extension." Northeastern Journal of Agricultural and Resource Economics 19, no. 1 (1990): 17–23. http://dx.doi.org/10.1017/s0899367x00000131.

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Due to agriculture's increasingly complex technical and economic environment, the diversity of information required for competitive and profitable farming is growing as never before. With constant and, in some cases, reduced resources for agricultural programs, Extension must exercise special care in prioritizing informational efforts to best meet farm-client needs and retain an important base of public support. This paper presents a method of identifying popular informational priorities in Agricultural Extension. The method is illustrated by application to dairy programming in Massachusetts.

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Iwase, N. "Homotopy associativity of sphere extensions." Proceedings of the Edinburgh Mathematical Society 32, no. 3 (1989): 459–72. http://dx.doi.org/10.1017/s0013091500004703.

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Throughout this paper, we work in the category of (p-localized) spaces having the homotopy type of connected CW-complexes of finite type with base point. We consider a principal bundlewhereGn=SU(n),U(n) orSp(n) andd= 1, 1 or 2 respectively. In this case, the bundle is obtained as an induced bundle by a mappingfof base spaceS2dn−1from the classical group extension as follows:

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He, Gui-lu, Ye-hai Li, Jian-hao Lin, et al. "Bronchogenic Cyst: Skull Base Lesions with Extracranial Extension." World Neurosurgery 139 (July 2020): 182–85. http://dx.doi.org/10.1016/j.wneu.2020.04.010.

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39

Sobrino, B., M. Lareu, M. Brion, and A. Carracedo. "SNP genotyping with single base extension-tag microarrays." International Congress Series 1261 (April 2004): 331–33. http://dx.doi.org/10.1016/j.ics.2003.12.002.

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Allwood, Julia S., and Sally Ann Harbison. "“YFlag” - A Single-base Extension Primer Based Method for Gender Determination." Journal of Forensic Sciences 60, no. 1 (2014): 142–46. http://dx.doi.org/10.1111/1556-4029.12553.

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Jun, Jongho. "Metrical weight consistency in Korean partial reduplication." Phonology 11, no. 1 (1994): 69–88. http://dx.doi.org/10.1017/s0952675700001846.

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Korean possesses a rich onomatopoeic and mimetic vocabulary that may be augmented by partial reduplication and/or suffixation. This augmented category, which is referred to as partial extension in Jun (1993), is semantically characterised by a lengthening, or temporal extension of the base form:

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Del Basso De Caro, Maria Laura, Antonella Siciliano, Paolo Cappabianca, Alessandra Alfieri, and Enrico de Divitiis. "Intrasellar Paraganglioma with Suprasellar Extension: Case Report." Tumori Journal 84, no. 3 (1998): 408–11. http://dx.doi.org/10.1177/030089169808400319.

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Paragangliomas are usually benign tumors which can be found in many sites of the body, from the base of the skull down to the pelvic floor. In the central nervous system the sellar region is very rarely involved; only three well studied cases have been reported to date. We present the cytological, histological, histochemical, immunocytochemical and ultrastructural features of an intrasellar and suprasellar paraganglioma in an 84-year-old man.

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ČESNAVIČIUS, KĘSTUTIS. "The ℓ-parity conjecture over the constant quadratic extension". Mathematical Proceedings of the Cambridge Philosophical Society 165, № 3 (2017): 385–409. http://dx.doi.org/10.1017/s030500411700055x.

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AbstractFor a prime ℓ and an abelian varietyAover a global fieldK, the ℓ-parity conjecture predicts that, in accordance with the ideas of Birch and Swinnerton–Dyer, the ℤℓ-corank of the ℓ∞-Selmer group and the analytic rank agree modulo 2. Assuming that charK> 0, we prove that the ℓ-parity conjecture holds for the base change ofAto the constant quadratic extension if ℓ is odd, coprime to charK, and does not divide the degree of every polarisation ofA. The techniques involved in the proof include the étale cohomological interpretation of Selmer groups, the Grothendieck–Ogg–Shafarevich formul

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Thakar, Alok, Gaurav Gupta, and Mohnish Grover. "Successful Repair of Large Skull Base Defect Following JNA Excision." An International Journal Clinical Rhinology 3, no. 1 (2010): 49–52. http://dx.doi.org/10.5005/jp-journals-10013-1028.

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Abstract Juvenile nasopharyngeal angiofibroma (JNA) is a highly vascular tumor of young males. Surgical excision remains the principal modality of treatment. Tumors with intracranial extension may require major surgical resections which are not devoid of complications. We here present a case of JNA with massive intracranial extension with postsurgery huge skull base defect with resultant encephalocele which was repaired successfully using rectus abdominis free flap.

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Česnavičius, Kęstutis, and Naoki Imai. "The remaining cases of the Kramer–Tunnell conjecture." Compositio Mathematica 152, no. 11 (2016): 2255–68. http://dx.doi.org/10.1112/s0010437x16007624.

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For an elliptic curve $E$ over a local field $K$ and a separable quadratic extension of $K$, motivated by connections to the Birch and Swinnerton-Dyer conjecture, Kramer and Tunnell have conjectured a formula for computing the local root number of the base change of $E$ to the quadratic extension in terms of a certain norm index. The formula is known in all cases except some where $K$ is of characteristic $2$, and we complete its proof by reducing the positive characteristic case to characteristic $0$. For this reduction, we exploit the principle that local fields of characteristic $p$ can be

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Mao, Zhengyu, and Stephen Rallis. "Cubic Base Change for GL(2)." Canadian Journal of Mathematics 52, no. 1 (2000): 172–96. http://dx.doi.org/10.4153/cjm-2000-008-9.

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AbstractWe prove a relative trace formula that establishes the cubic base change for GL(2). One also gets a classification of the image of base change. The case when the field extension is nonnormal gives an example where a trace formula is used to prove lifting which is not endoscopic.

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Budney, R., and J. A. Hillman. "A small infinitely-ended 2-knot group." Journal of Knot Theory and Its Ramifications 26, no. 01 (2017): 1750008. http://dx.doi.org/10.1142/s0218216517500080.

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We show that a 2-knot group discovered in the course of a census of 4-manifolds with small triangulations is an HNN extension with finite base and proper associated subgroups, and has the smallest base among such knot groups.

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Hidalgo, Ana Laura, and Belén del Carmen Galende. "Comunicación y extensión. Perspectivas, concepciones y preguntas para un abordaje situado de los procesos socioterritoriales." +E: Revista de Extensión Universitaria, no. 17.Jul-Dic (October 30, 2022): e0016. http://dx.doi.org/10.14409/extension.2022.17.jul-dic.e0016.

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El presente artículo se aboca a presentar diversas perspectivas, concepciones y preguntas para un abordaje situado de la comunicación en las prácticas sociales constitutivas de la extensión universitaria. El mismo se desarrolla sobre la base de reflexiones y sistematizaciones de diferentes experiencias que se produjeron en instancias múltiples devenidas del encuentro con la comunidad, lo cual se dio en el marco de proyectos particulares de las carreras del Departamento de Comunicación de la Facultad de Ciencias Humanas de la Universidad Nacional de San Luis.

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Böckle, Gebhard, Tony Feng, Michael Harris, Chandrashekhar B. Khare, and Jack A. Thorne. "Cyclic base change of cuspidal automorphic representations over function fields." Compositio Mathematica 160, no. 9 (2024): 1959–2004. http://dx.doi.org/10.1112/s0010437x24007243.

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Let $G$ be a split semisimple group over a global function field $K$ . Given a cuspidal automorphic representation $\Pi$ of $G$ satisfying a technical hypothesis, we prove that for almost all primes $\ell$ , there is a cyclic base change lifting of $\Pi$ along any $\mathbb {Z}/\ell \mathbb {Z}$ -extension of $K$ . Our proof does not rely on any trace formulas; instead it is based on using modularity lifting theorems, together with a Smith theory argument, to obtain base change for residual representations. As an application, we also prove that for any split semisimple group $G$ over a local fu

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Xu, Jia Chuan, Ping Ping Fan, Zeng Xiang Song, and Wei Cheng Zheng. "Surface Extension in Smoothing of Class a Surfaces for Auto-Body." Advanced Materials Research 690-693 (May 2013): 2767–71. http://dx.doi.org/10.4028/www.scientific.net/amr.690-693.2767.

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In smoothing of Class A surfaces for auto-body, the whole surface is firstly divided into many base surfaces, and then blended them into a whole surface. The base surface is often not big enough to meet the blending requirements, so it should be extended. The paper discussed the extension of Bézier curves and surfaces, and analyzed the relationships between extended curves/surfaces and vertexes. The result shows that the arrangement of control vertexes is closely related to the quality of extended curves/surfaces.

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