Journal articles: 'L1 Norms'

1

Arens, Richard, and Moshe Goldberg. "Multilinear operators and weighted l1 norms." Linear Algebra and its Applications 267 (December 1997): 1–10. http://dx.doi.org/10.1016/s0024-3795(97)80039-0.

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Fu, Haoying, Michael K. Ng, Mila Nikolova, and Jesse L. Barlow. "Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration." SIAM Journal on Scientific Computing 27, no. 6 (January 2006): 1881–902. http://dx.doi.org/10.1137/040615079.

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Qi, Jinshan, Xun Liang, and Rui Xu. "A Multiple Kernel Learning Model Based on p-Norm." Computational Intelligence and Neuroscience 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/1018789.

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By utilizing kernel functions, support vector machines (SVMs) successfully solve the linearly inseparable problems. Subsequently, its applicable areas have been greatly extended. Using multiple kernels (MKs) to improve the SVM classification accuracy has been a hot topic in the SVM research society for several years. However, most MK learning (MKL) methods employ L1-norm constraint on the kernel combination weights, which forms a sparse yet nonsmooth solution for the kernel weights. Alternatively, the Lp-norm constraint on the kernel weights keeps all information in the base kernels. Nonetheless, the solution of Lp-norm constraint MKL is nonsparse and sensitive to the noise. Recently, some scholars presented an efficient sparse generalized MKL (L1- and L2-norms based GMKL) method, in which L1 L2 established an elastic constraint on the kernel weights. In this paper, we further extend the GMKL to a more generalized MKL method based on the p-norm, by joining L1- and Lp-norms. Consequently, the L1- and L2-norms based GMKL is a special case in our method when p=2. Experiments demonstrated that our L1- and Lp-norms based MKL offers a higher accuracy than the L1- and L2-norms based GMKL in the classification, while keeping the properties of the L1- and L2-norms based on GMKL.

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Yun, Jong-Gug. "Comparison Geometry With L1-Norms of Ricci Curvature." Canadian Mathematical Bulletin 49, no. 1 (March 1, 2006): 152–60. http://dx.doi.org/10.4153/cmb-2006-016-2.

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AbstractWe investigate the geometry of manifolds with bounded Ricci curvature in L1-sense. In particular, we generalize the classical volume comparison theorem to our situation and obtain a generalized sphere theorem.

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Mustafa Chalabee, Botan A., and Bayan A. Hassan. "Cephalometric Norms of Erbil Kurdish Adults." Polytechnic Journal 10, no. 1 (June 30, 2020): 130–34. http://dx.doi.org/10.25156/ptj.v10n1y2020.pp130-134.

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Ethical group might have differential skeletal forms, thus cephalometric analysis and orthodontic material have been developed for specific ethnic groups which might be different for Kurdish Ethics.Objectives: This study is to determine the cephalometric norms of an Erbil Kurdish population according to Steiner analysis, who attend to Tishk Hospital/Diagnosis Department Materials and Methods: In this cross-sectional study, 48 lateral cephalograms of adult orthodontic subjects between 20 and 29 years with normal occlusion, and with no previous orthodontic treatment were evaluated. Lateral cephalograms were traced and analyzed based on Steiner’s cephalometric parameters. Data were analyzed using SPSS. Differences between Erbil Kurdish and Steiner’s norms were analyzed using one-sample t-test (P < 0.05). Results: The SNA, ML-NSL (Mandibular Line to NS line), U1-NA (both angular and linear measurements), interincisal angle, L1-NB (angular only), Pog-NB, L1-Pog//NB, Ls-SL, and Li-SL values were significantly different between the Erbil Kurdish population and Steiner’s norms (P < 0.05). No significant differences existed in Occl-SN (occlusal plane to SN) and L1-Nb (linear only), SNB, and ANB between the Erbil Kurdish population and the Steiner’s norms (P > 0.05). Conclusions: Cephalometric norms for Erbil Kurdish adults are different from those of Steiner’s norms. The norms obtained in our study can be used for orthodontic treatments and orthognathic surgeries in Erbil Kurdish population.

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Siangloy, Thitirat, and Chairat Charoemratrote. "Incisor and Soft Tissue Characteristics of Adult Bimaxillary Protrusion Patients among Different Skeletal Anteroposterior Classifications." Diagnostics 14, no. 10 (May 16, 2024): 1031. http://dx.doi.org/10.3390/diagnostics14101031.

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The objective of this study was to investigate the upper incisors (U1), lower incisors (L1), and soft tissue profiles of bimaxillary protrusion (BM) adult patients among skeletal Class I (BM1), II (BM2) and III (BM3). Understanding these characteristics would be useful for incisor and lip diagnostics in different skeletal classifications. Fourteen linear and twelve angular variables of the incisors and lips were evaluated in 214 lateral cephalograms (BM1 = 91, BM2 = 84, BM3 = 39). ANOVA and Bonferroni tests compared the measurements. BM1 and BM3 exhibited a greater U1 position and U1 inclination than the norms, while BM2 presented only a greater U1 position than the norms but normal U1 inclination. BM1 and BM3 had a significantly greater U1 position than BM2. BM1 and BM2 demonstrated a greater L1 position and L1 inclination than the norms, whereas BM3 displayed only a greater L1 position than the norms but normal L1 inclination. BM2 had the most anterior L1 position, whereas BM3 had the least anterior position. Only BM2 had a longer anterior dental height (ADH) than the norms, while BM1 and BM3 had a normal ADH and the significantly shortest ADH, respectively. Only BM1 had a normal upper incisor display at rest (U1R), while BM2 and BM3 displayed an increased and decreased U1R, respectively, with significant differences among the three groups. The most significantly protruded upper and lower lips were presented in BM2, but these were exhibited the least in BM3. The most significant acute nasolabial angle (NLA) was found in BM3, whereas BM2 presented the least acute NLA. A normal lip–chin–throat angle (LCTA) was observed in BM1 and BM3, while only BM2 had a greater LCTA than the norms. The most significant obtuse LCTA was found in BM2, while BM3 had the least obtuse LCTA. Therefore, both U1 and L1 in all groups presented protrusion and proclination, except for U1 in BM2, while L1 in BM3 exhibited normal inclination. The ADH and U1R were increased in BM2 but decreased in BM3. The most acute NLA was found in BM3, whereas the least acute was found in BM2. The most obtuse LCTA was in BM2, while the least was in BM3.

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Yun, Jong-Gug. "Mean Curvature Comparison with L1-norms of Ricci Curvature." Canadian Mathematical Bulletin 47, no. 2 (June 1, 2004): 314–20. http://dx.doi.org/10.4153/cmb-2004-030-0.

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Sanchez Lopez, Hector, Yajie Xu, Pulung Nurtantio Andono, Yan Chang, and Xiaodong Yang. "Planar Gradient Coil Design Using L1 and L2 Norms." Applied Magnetic Resonance 49, no. 9 (June 21, 2018): 959–73. http://dx.doi.org/10.1007/s00723-018-1020-3.

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9

Mehta, Harsh. "The L1 norms of de la Vallée Poussin kernels." Journal of Mathematical Analysis and Applications 422, no. 2 (February 2015): 825–37. http://dx.doi.org/10.1016/j.jmaa.2014.09.018.

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Kalaj, David, and Djordjije Vujadinovic. "The Gradient of a Solution of the Poisson Equation in the Unit Ball and Related Operators." Canadian Mathematical Bulletin 60, no. 3 (September 1, 2017): 536–45. http://dx.doi.org/10.4153/cmb-2017-020-7.

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AbstractIn this paper we determine the L1 ⟶ L1 and L∞ ⟶ L∞ norms of an integral operator N related to the gradient of the solution of Poisson equation in the unit ball with vanishing boundary data in sense of distributions.

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Schinzel, A., and W. M. Schmidt. "Comparison of L1- and L∞-norms of squares of polynomials." Acta Arithmetica 104, no. 3 (2002): 283–96. http://dx.doi.org/10.4064/aa104-3-4.

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12

Karuhanga, Martin. "Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip." Journal of Mathematics 2018 (December 12, 2018): 1–8. http://dx.doi.org/10.1155/2018/7172356.

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This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schrödinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L1 norms and Lln⁡L norms of the potential. Estimates involving the norms of the potential supported by a curve embedded in a strip are also presented.

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Novikov, A. "C*-algebra Positive Element Invertibility Criteria in Terms of L1-norms Equivalence and L∞-norms Equivalence." Lobachevskii Journal of Mathematics 40, no. 5 (May 2019): 677–80. http://dx.doi.org/10.1134/s1995080219050159.

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Casarino, Valentina. "Norms of Complex Harmonic Projection Operators." Canadian Journal of Mathematics 55, no. 6 (December 1, 2003): 1134–54. http://dx.doi.org/10.4153/cjm-2003-045-6.

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AbstractIn this paper we estimate the (Lp – L2)-norm of the complex harmonic projectors πℓ,ℓ′, 1 ≤ p ≤ 2, uniformly with respect to the indexes ℓ, ℓ′. We provide sharp estimates both for the projectors πℓ,ℓ′, when ℓ, ℓ′ belong to a proper angular sector in ℕ × ℕ, and for the projectors πℓ0 and π0ℓ. The proof is based on an extension of a complex interpolation argument by C. Sogge. In the appendix, we prove in a direct way the uniform boundedness of a particular zonal kernel in the L1 norm on the unit sphere of ℝ2n.

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Itakura, Hiroko. "Femininity in mixed-sex talk and intercultural communication." Pragmatics and Society 5, no. 3 (November 14, 2014): 455–83. http://dx.doi.org/10.1075/ps.5.3.09ita.

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Previous studies of language and gender discuss how men and women use gender-specific conversational styles mainly in relation to English, whereas similar studies for Asian languages remain comparatively few. Moreover, little is known about gender and conversational styles during intercultural communication. This paper explores whether speakers follow similar norms of politeness in mixed-sex talk in their L1 and in intercultural conversations in L2 English, and if femininities are modified, what factors may be involved. It reports findings from a case study of a Japanese female’s conversations with a Japanese male in Japanese and with three male L2 English speakers. It suggests that femininities might be modified to become more ‘immodest’ in English due to factors such as speakers’ varying level of adherence to native cultural norms in L1 and in L2 contexts and the male interlocutors’ ethnicity. For example, female speakers who adhere to native cultural norms in L1 conversations may see L2 intercultural contexts as opportunities to create non-traditional femininities, especially when there is no male interlocutor with shared ethnicity. The construction of L2 femininities may also be shaped by linguistic factors such as L2 proficiency or systemic differences between the two languages.

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Binks, Hanna L., and Enlli Môn Thomas. "Long-term outcomes for bilinguals in minority language contexts: Welsh–English teenagers’ performance on measures of grammatical gender and plural morphology in Welsh." Applied Psycholinguistics 40, no. 4 (April 12, 2019): 1019–49. http://dx.doi.org/10.1017/s0142716419000110.

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AbstractThis study explored the long-term effects of limited input on bilingual teenagers’ acquisition of complex morphology in Welsh. Study 1 assessed 168 12–13 and 16–17-year-old teenagers, across three bilingual groups: those whose first language was Welsh (L1 Welsh), those who learned Welsh and English simultaneously (L1 Welsh–English), and those who learned Welsh as a second language (L2 Welsh), on their receptive knowledge of grammatical gender. Study 2 assessed the same participants on their production of plural morphology. While the results of Study 1 revealed continuous progression toward adult norms among L1 Welsh-speaking bilinguals, with the simultaneous bilinguals progressing at a slower rate, the results of Study 2 revealed performances on plural morphology that were comparable to adult norms among the 16–17-year-old L1 Welsh-speaking bilinguals, and some progression among the simultaneous bilinguals. In contrast, delayed progression was seen among the L2 Welsh-speaking bilinguals across the board, with 16–17-year-old L2 participants lagging behind their L1 peers on both grammatical gender and plural morphology. The implications of these findings for our understanding of the long-term outcomes for bilinguals learning complex structures under minority language conditions are discussed.

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17

Grolmusz, Vince. "On the power of circuits with gates of low L1 norms." Theoretical Computer Science 188, no. 1-2 (November 1997): 117–28. http://dx.doi.org/10.1016/s0304-3975(96)00290-3.

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Maniatty, W. A., and B. K. Szymanski. "Fine-grain discrete Voronoi diagram algorithms in L1 and L∞ norms." Mathematical and Computer Modelling 26, no. 4 (August 1997): 71–78. http://dx.doi.org/10.1016/s0895-7177(97)00145-3.

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Omidikia, Nematollah, Mahdiyeh Ghaffari, and Róbert Rajkó. "Sparse non-negative multivariate curve resolution: L0, L1, or L2 norms?" Chemometrics and Intelligent Laboratory Systems 199 (April 2020): 103969. http://dx.doi.org/10.1016/j.chemolab.2020.103969.

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Benítez, Carlos, and Manuel Fernández. "Norms in product spaces which preserve approximation properties." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 105, no. 1 (1987): 199–203. http://dx.doi.org/10.1017/s0308210500022034.

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SynopsisLet E1 and E2 be real normed linear spaces such that the dimension of any of them is at least 2. We prove that the norms in E1 × E2 which verify a simple property of monotonicity with regard to the initial norms in E1 and E2 are the only norms in E1 × E2 which preserve best linear approximations, in the sense that ifyk ∊ Lk is best approximation to xk from the linear subspace Lk, (k = 1,2), then (y1, y2) is best approximation to (x1, x2) from L1 × L2.

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21

White, Jonathan R. "Local Norms in CALL Language Practice." International Journal of Computer-Assisted Language Learning and Teaching 6, no. 1 (January 2016): 40–54. http://dx.doi.org/10.4018/ijcallt.2016010103.

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This article presents an investigation into what norms are negotiated in a CALL classrooms by non-native speakers of English who are Internet novices. There is an on-going debate regarding the status of non-native speaker norms. Although there is more and more recognition that they are valid learner targets, native speaker norms are still reported to have the highest status for learners. Internet language use, though, has led to a change in the perception of norms, as communities of non-native speakers can set their own norms over those of native speakers. Data are analysed from academic textchat seminars which show that a community of inexperienced Internet users set their own norms, which go directly against their L1 community cultural norms of respect towards teachers. This paper proposes that it is an affordance of CALL environments that they can do this. This work is further evidence that it is smaller discourse communities that set norms separate from those of larger geo-political national communities.

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LANCONELLI, ALBERTO, and AUREL I. STAN. "A HÖLDER INEQUALITY FOR NORMS OF POISSONIAN WICK PRODUCTS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 03 (September 2013): 1350022. http://dx.doi.org/10.1142/s0219025713500227.

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An understanding of the second quantization operator of a constant times the identity operator and the Poissonian Wick product, without using the orthogonal Charlier polynomials, is presented first. We use both understanding, with and without the Charlier polynomials, to prove some inequalities about the norms of Poissonian Wick products. These inequalities are the best ones in the case of L1, L2, and L∞ norms. We close the paper with some probabilistic interpretations of the Poissonian Wick product.

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Boyarshinov, Victor, and Malik Magdon-Ismail. "Linear time isotonic and unimodal regression in the L1 and L∞ norms." Journal of Discrete Algorithms 4, no. 4 (December 2006): 676–91. http://dx.doi.org/10.1016/j.jda.2005.07.001.

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Ikeda, Kazushi, and Noboru Murata. "Geometrical Properties of Nu Support Vector Machines with Different Norms." Neural Computation 17, no. 11 (November 1, 2005): 2508–29. http://dx.doi.org/10.1162/0899766054796897.

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By employing the L1 or L∞ norms in maximizing margins, support vector machines (SVMs) result in a linear programming problem that requires a lower computational load compared to SVMs with the L2 norm. However, how the change of norm affects the generalization ability of SVMs has not been clarified so far except for numerical experiments. In this letter, the geometrical meaning of SVMs with the Lp norm is investigated, and the SVM solutions are shown to have rather little dependency on p.

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Amarorwot, Sarah, and Bebwa Isingoma. "Order of adjectives and adverbs in L2 English: Evidence from L1 Acholi speakers of Ugandan English." Studies in Linguistics, Culture, and FLT 9, no. 3 (November 24, 2021): 44–62. http://dx.doi.org/10.46687/yxuv9786.

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L2 Englishes are quintessentially characterized by cross-linguistic influence at all levels of linguistic analysis as a result of contact phenomena. This study examines the contribution of the syntax of a Ugandan indigenous language (Acholi) to how its L1 speakers speak English and the extent of variability observed among them, taking into account two grammatical aspects, i.e. how multiple attributive adjectives are sequenced in a noun phrase and the placement of adverbs in a sentence. The findings of the study show notable differences from L1 English (e.g. Standard British English), as L1 Acholi speakers of English do not necessarily pay attention to the prescribed L1 English order of adjectives. At the same time, the position of adverbs in a sentence also seems to be modeled, to some extent, on what takes place in Acholi syntax insofar as some legitimate L1 English structures are rejected by L1 Acholi speakers of English (as L2). Crucially, the study also reveals interspeaker variability among L1 Acholi speakers of English in Uganda based on occupation, with students being the closest to L1 English norms (as opposed to teachers and the business community), most likely due to exonormative orientation imposed on students in Ugandan schools.

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Fahad, S., M. A. Mustafa, Z. Ullah, T. Hussain, and A. Qayyum. "Weighted Ostrowski's Type Integral Inequalities for Mapping Whose First Derivative Is Bounded." International Journal of Analysis and Applications 20 (March 8, 2022): 16. http://dx.doi.org/10.28924/2291-8639-20-2022-16.

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The aim of paper is to develop the inequalities for L∞, Lp and L1 norms. Applications for some special weight functions and Perturbed expressions are also determined via Chebychev functional. We recaptured the previous results for different weights.

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Costa, Felipe Timóteo da, Marco Antonio Cetale Santos, and Djalma Manoel Soares Filho. "Wavenumbers illuminated by time-domain acoustic FWI using the L1 and L2 norms." Journal of Applied Geophysics 174 (March 2020): 103935. http://dx.doi.org/10.1016/j.jappgeo.2019.103935.

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Dai, Shaosheng, Dezhou Zhang, Junjie Cui, Xiaoxiao Zhang, and Jinsong Liu. "Edge preserving super-resolution infrared image reconstruction based on L1- and L2-norms." Frontiers of Optoelectronics 10, no. 2 (November 19, 2016): 189–94. http://dx.doi.org/10.1007/s12200-016-0659-3.

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Shaidurov, Vladimir V., Alexander V. Vyatkin, and Elena V. Kuchunova. "Semi-Lagrangian difference approximations with different stability requirements." Russian Journal of Numerical Analysis and Mathematical Modelling 33, no. 2 (April 25, 2018): 123–35. http://dx.doi.org/10.1515/rnam-2018-0011.

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Abstract The paper demonstrates different ways of using the semi-Lagrangian approximation depending on the fulfillment of conservation laws. A one-dimensional continuity equation and a parabolic one are taken as simple methodological examples. For these equations, the principles of constructing discrete analogues are demonstrated for three different conservation laws (or the requirements of stability in the related discrete norms similar to the L1, L2, L∞-norms). It is significant that different conservation laws yield difference problems of different types as well as different ways to justify their stability.

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Lampayan, Valentine Blez, and Marrick Neri. "Nonconvex TVq model with l1 fidelity term in image restoration." SciEnggJ 17, no. 1 (January 22, 2024): 18–26. http://dx.doi.org/10.54645/2024171mxs-35.

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Restoration of images based on a nonconvex �! variational model which contains the �" “norm,” q ∈ (0,1), is considered. The existence of a minimizer of the model is established in the discrete setting. To solve the minimization problem, Huber-type regularizations of the �" and the �!norms are performed on the model. A primal-dual semismooth Newton method with a trust region technique is adapted to solve the model and the convergence of the algorithm is presented. Applications are made on restoration of images corrupted with blur and impulse noise.

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Higginbotham, G., I. Munby, and J. Racine. "A Japanese Word Association Database of English." Vocabulary Learning and Instruction 4, no. 2 (2015): 1–20. http://dx.doi.org/10.7820/vli.v04.2.higginbotham.et.al.

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In this paper, two word association (WA) studies are presented in support of recent arguments against the use of native-speaker (NS) norms in WA research. In Study 1, first-language (L1) and second-language (L2) WA norms lists were developed and compared to learner responses as a means of measuring L2 proficiency. The results showed that L2 norms provided a more sensitive measure of L2 lexical development than did traditional NS norms. Study 2 was designed to test the utility of native norms databases in predicting the primary WA responses of Japanese learners to high-frequency English cues. With the exception of only extremely frequent cues, it was shown that native norms were not successful in predicting learner responses. The results of both studies are discussed in terms of cultural and linguistic differences, geographic distance, and dissimilarities in word knowledge between respondent populations. Finally, a proposal is made for the construction of a Japanese WA database of English responses (J-WADE). The methods by which it will be developed, key features, and employment in future research are outlined.

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Chantharasombat, Jidapa, and Nattama Pongpairoj. "Interlanguage Pragmatics: Deviant Patterns of Negative Responses to English Negative Yes/No Questions by L1 Thai Speakers." International Journal of Applied Linguistics and English Literature 7, no. 3 (May 1, 2018): 193. http://dx.doi.org/10.7575/aiac.ijalel.v.7n.3p.193.

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This study investigated the potential cause of L1 Thai speakers’ persistent deviations from target-like negative responses to negative yes/no questions in L2 English context based on the theory of interlanguage pragmatics, particularly pragmatic transfer. L1 Thai undergraduates were categorized into two groups according to their level of L2 English linguistic proficiency. A discourse completion task (DCT), which required the participants to complete their turns in a conversation under different situations, were used to elicit their negative responses. The results revealed that negative pragmatic transfer, influenced by differences in linguistic action patterns of negative responses to negative yes/no questions between Thai and English, occurred in the performance of L1 Thai speakers in both lower and higher L2 English proficiency groups. However, the overall results suggested that the lower proficiency group tended to rely more on their L1 Thai pragmatic competence and showed higher tendency of negative pragmatic transfer than the higher proficiency group. The research indicated that negative transfer from the speakers’ different L1 Thai pragmatic influence from L2 English could make an impact on their non-target-like performance. Moreover, their level of L2 English linguistic proficiency and degree of reliance on their L1 Thai pragmatic knowledge could affect their production to diverge from L2 English pragmatic norms.

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Dmitrieva, Olga, Allard Jongman, and Joan A. Sereno. "The Effect of Instructed Second Language Learning on the Acoustic Properties of First Language Speech." Languages 5, no. 4 (October 26, 2020): 44. http://dx.doi.org/10.3390/languages5040044.

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This paper reports on a comprehensive phonetic study of American classroom learners of Russian, investigating the influence of the second language (L2) on the first language (L1). Russian and English productions of 20 learners were compared to 18 English monolingual controls focusing on the acoustics of word-initial and word-final voicing. The results demonstrate that learners’ Russian was acoustically different from their English, with shorter voice onset times (VOTs) in [−voice] stops, longer prevoicing in [+voice] stops, more [−voice] stops with short lag VOTs and more [+voice] stops with prevoicing, indicating a degree of successful L2 pronunciation learning. Crucially, learners also demonstrated an L1 phonetic change compared to monolingual English speakers. Specifically, the VOT of learners’ initial English voiceless stops was shortened, indicating assimilation with Russian, while the frequency of prevoicing in learners’ English was decreased, indicating dissimilation with Russian. Word-final, the duration of preceding vowels, stop closures, frication, and voicing during consonantal constriction all demonstrated drift towards Russian norms of word-final voicing neutralization. The study confirms that L2-driven phonetic changes in L1 are possible even in L1-immersed classroom language learners, challenging the role of reduced L1 use and highlighting the plasticity of the L1 phonetic system.

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Leśniewska, Justyna, and Ewa Witalisz. "Cross-linguistic influence and acceptability judgments of L2 and L1 collocations." EUROSLA Yearbook 7 (August 10, 2007): 27–48. http://dx.doi.org/10.1075/eurosla.7.04les.

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The paper presents an investigation of the extent and nature of cross-linguistic influence on both L2 and L1 phraseological competence of advanced Polish learners of English. We review relevant research studies, which describe various types of collocational deviation from native speaker norms in the language production of advanced learners, and indicate that the collocational choices of learners may be affected by their L1, which results either in incorrect collocations, or in patterns of underuse or overuse. We administered two acceptability judgment tests to 91 Polish advanced learners of English, aged 20–22. The collocations used in the test could be classified with respect to two criteria: firstly, they were either typical or unusual collocations; secondly, they were either congruent with their L1 or L2 equivalents or not. Despite the fact that there is both empirical and theoretical support for the idea that learners may show a preference for those L2 collocations which are congruent with L1, our findings do not support this hypothesis. There is no obvious pattern of cross-linguistic influence emerging from the data. The results of this study seem to give the picture of advanced learners who function in their L2 independently of the L1.

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Levine, Glenn S. "Principles for code choice in the foreign language classroom: A focus on grammaring." Language Teaching 47, no. 3 (January 12, 2012): 332–48. http://dx.doi.org/10.1017/s0261444811000498.

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The social and cultural ‘turn’ in language education of recent years has helped move language teaching and curriculum design away from many of the more rigid dogmas of earlier generations, but the issue of the roles of the learners’ first language (L1) in language pedagogy and classroom interaction is far from settled. Some follow a strict ‘exclusive target language’ pedagogy, while others ‘resort to’ the use of the L1 for a variety of purposes (see ACTFL 2008). Underlying these competing views is the perspective of the L1 as an impediment to second language learning. Following sociocultural theory and ecological perspectives of language and learning and based on the findings of research on classroom code-switching and code choice, this paper lays out an approach to the language classroom as a multilingual social space in which learners and teacher study, negotiate, and co-construct code choice norms toward the dynamic, creative, and pedagogically effective use of both the target language and the learners’ L1(s). Learner use of the L1 for the purpose of grammatical or lexical learning is also considered, and some examples for instruction are offered.

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Ma, Changzheng, Boon Poh Ng, and Junjie Feng. "ISAR IMAGING BASED ON L1 L0 NORMS HOMOTOPY 2D BLOCK SPARSE SIGNAL RECOVERY ALGORITHM." Progress In Electromagnetics Research C 67 (2016): 135–41. http://dx.doi.org/10.2528/pierc16060701.

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Saperas-Riera, Jordi, Glòria Mateu-Figueras, and Josep Antoni Martín-Fernández. "Lp-Norm for Compositional Data: Exploring the CoDa L1-Norm in Penalised Regression." Mathematics 12, no. 9 (May 1, 2024): 1388. http://dx.doi.org/10.3390/math12091388.

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The Least Absolute Shrinkage and Selection Operator (LASSO) regression technique has proven to be a valuable tool for fitting and reducing linear models. The trend of applying LASSO to compositional data is growing, thereby expanding its applicability to diverse scientific domains. This paper aims to contribute to this evolving landscape by undertaking a comprehensive exploration of the L1-norm for the penalty term of a LASSO regression in a compositional context. This implies first introducing a rigorous definition of the compositional Lp-norm, as the particular geometric structure of the compositional sample space needs to be taken into account. The focus is subsequently extended to a meticulous data-driven analysis of the dimension reduction effects on linear models, providing valuable insights into the interplay between penalty term norms and model performance. An analysis of a microbial dataset illustrates the proposed approach.

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Osuka, Naoko. "The Effect of Study-Abroad on Pragmatic Transfer." Chinese Journal of Applied Linguistics 44, no. 1 (March 1, 2021): 3–20. http://dx.doi.org/10.1515/cjal-2021-0001.

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AbstractThis study aims to investigate the effect that studying abroad may have on pragmatic transfer in requests, refusals, and expressions of gratitude, produced by Japanese learners of English. Twenty-two Japanese college students completed a multimedia elicitation task (MET) before and after studying in the US for one semester, together with twenty-two L1 English speakers and twenty L1 Japanese speakers as baseline data. The MET is a computer-based instrument for eliciting oral data. Unlike previous studies on pragmatic transfer, which often lack statistical evidence, this study includes statistical analysis. The analysis revealed that negative pragmatic transfer occurs within a limited range. The identified transfer includes pragmalinguistic transfer, whereby, assuming that their politeness levels are equal, learners directly translate L1 expressions into L2; and sociopragmatic transfer, whereby learners transfer L1 discourse patterns and functions. Resistance to L2 norms and increased fluency can be influencing factors. The results indicated that the effect of study-abroad is limited because most of the negative transfer which was identified before studying abroad remained after studying abroad. Thus, the necessity of explicit pragmatic instruction was proposed.

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Tang, Jinping, Bo Han, Weimin Han, Bo Bi, and Li Li. "Mixed Total Variation and L1 Regularization Method for Optical Tomography Based on Radiative Transfer Equation." Computational and Mathematical Methods in Medicine 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/2953560.

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Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE). It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV) regularization and the L1 regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L1 norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for the L1 regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV and L1 regularizations, the simulation results show the validity and efficiency of the proposed method.

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Warsono, Warsono. "LANGUAGE TRANSFER IN LEARNER LANGUAGE." EduLite: Journal of English Education, Literature and Culture 1, no. 1 (February 1, 2016): 103. http://dx.doi.org/10.30659/e.1.1.103-114.

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In using the foreign language they are learning, learners tend to use forms that deviate from the target language (TL) norms. The question that arises is whether these forms are the result of transfer or the result of some other causes; and if transfer does exist in learner language, whether it diminishes with the development of the learner TL achievement. This paper tries to find answers to these questions by (1) reviewing some related literature, and (2) looking at some data of learners’ written production of Indonesian learners of English. The data were collected from the writings of the fifth semester students of the English Department (group A, representing low level of L2 achievement), and the final projects written by the English Department students (group B, representing high level of L2 achievement). In this paper, all forms that deviate from the TL norms were called errors, irrespective of whether they were, in fact, mistakes or real errors. The learners’ errors were broadly classified into two classes: intralingual errors and interlingual errors, and it was the latter that became the focus of this study on the assumption that interlingual errorswere caused by L1 transfer. The results of data analysis showed that intralingual errors were slightly higher in group A than interlingual ones; but in group B interlingual errors formed the majority of errors made by the learners (75%). It can be concluded that L1 transfer does exist in the L2 of the Indonesian learners of English. The results also showed that L1 transfer does not diminish with the development of the L2 achievement. It is strongly suggested, therefore, that Indonesian English teachers anticipate the errors caused by L1 transfer and find ways to solve the problems.

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DUAN, RENJUN, SEIJI UKAI, TONG YANG, and HUIJIANG ZHAO. "OPTIMAL CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH POTENTIAL FORCES." Mathematical Models and Methods in Applied Sciences 17, no. 05 (May 2007): 737–58. http://dx.doi.org/10.1142/s021820250700208x.

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For the viscous and heat-conductive fluids governed by the compressible Navier–Stokes equations with an external potential force, there exist non-trivial stationary solutions with zero velocity. By combining the Lp - Lq estimates for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the stationary profile in the whole space when the initial perturbation of the stationary solution and the potential force are small in some Sobolev norms. More precisely, the optimal convergence rates of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded.

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Kislitsyn, Alexey Alexeevich, and Maria Yurievna Kislitsyna. "Recognition of sample distribution functions among a system of patterns: the nearest neighbor method." Keldysh Institute Preprints, no. 29 (2023): 1–21. http://dx.doi.org/10.20948/prepr-2023-29.

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The value of the sample distribution identification error of a multidimensional discrete random variable among a library of reference patterns is studied, depending on the dimension of the random vector, the sample length and the distance between two reference distributions in the norms C and L1. It is shown that the recognition error in the L1 norm is significantly lower than in C. Reference distributions of n-grams for texts are considered as a practical application. It turned out that the accuracy of identification is mainly determined by the individual characteristics of the standards, and not by the distances between them. An algorithm has been developed to test the system of standards for recognition accuracy.

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THOMAS, ENLLI MÔN, NIA WILLIAMS, LLINOS ANGHARAD JONES, SUSI DAVIES, and HANNA BINKS. "Acquiring complex structures under minority language conditions: Bilingual acquisition of plural morphology in Welsh." Bilingualism: Language and Cognition 17, no. 3 (November 21, 2013): 478–94. http://dx.doi.org/10.1017/s1366728913000497.

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This study explored the effects of quantity and quality of input on bilingual children's acquisition of complex plural morphology in Welsh. Study 1 explored the quality of adult input and revealed target-like marking of plural forms in naturalistic adult speech. Study 2 presented eighty-eight 7–11-year-old children, across three bilingual language groups (L1 Welsh, 2L1, and L2 Welsh), with a plural production task. Results revealed performances approaching L1 adult norms among L1 Welsh-speaking bilinguals, but delayed progression among 2L1 and L2 Welsh bilinguals, although analyses of errors revealed various levels of structural knowledge. Forms requiring the addition of a plural suffix were less difficult to acquire than those involving alterations to the root, with each type acquired with greater levels of accuracy with increasing levels of exposure to the language. The implications of these findings for our understanding of bilingual acquisition of complex structures under minority language conditions are discussed.

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Livadiotis, George. "General Fitting Methods Based on Lq Norms and their Optimization." Stats 3, no. 1 (January 6, 2020): 16–31. http://dx.doi.org/10.3390/stats3010002.

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The widely used fitting method of least squares is neither unique nor does it provide the most accurate results. Other fitting methods exist which differ on the metric norm can be used for expressing the total deviations between the given data and the fitted statistical model. The least square method is based on the Euclidean norm L2, while the alternative least absolute deviations method is based on the Taxicab norm, L1. In general, there is an infinite number of fitting methods based on metric spaces induced by Lq norms. The most accurate, and thus optimal method, is the one with the (i) highest sensitivity, given by the curvature at the minimum of total deviations, (ii) the smallest errors of the fitting parameters, (iii) best goodness of fitting. The first two cases concern fitting methods where the given curve functions or datasets do not have any errors, while the third case deals with fitting methods where the given data are assigned with errors.

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Salapaka, Murti V., Petros Voulgaris, and Mohammed Dahleh. "SISO controller design to minimize a positive combination of the l1 and the H2 norms." Automatica 33, no. 3 (March 1997): 387–91. http://dx.doi.org/10.1016/s0005-1098(96)00169-0.

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Pełczyński, Aleksander, and Michał Wojciechowski. "Sobolev spaces in several variables in L1-type norms are not isomorphic to Banach lattices." Arkiv för Matematik 40, no. 2 (October 2002): 363–82. http://dx.doi.org/10.1007/bf02384541.

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Vujić, Jelena, Mirjana Daničić, and Tamara Aralica. "Caught in the cross-fire: Tackling hate speech from the perspective of language and translation pedagogy." Lodz Papers in Pragmatics 14, no. 1 (June 26, 2018): 203–23. http://dx.doi.org/10.1515/lpp-2018-0010.

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Abstract Hate speech is a phenomenon which has been in the focus of scholarly interest of linguists, philosophers, sociologists, human-rights advocates, legal and media experts. Much of this interest has been devoted to establishing criteria for identifying what constitutes hate speech across disciplines. In this paper, we argue that hate speech has profiled as a distinct subgenre of the language of politics with typical patterns and ways of addressing which can be recognized in political campaigns across the world. Therefore, we present the findings of the case study of translation exercises of English and Serbian texts containing samples of hateful language during presidential campaigns in the USA and Serbia in 2016 and 2017. Our aim is to identify the linguistico-pragmatic commonalities of hate speech in Serbian and English and examine students’ attitudes towards ethically and morally challenging language contents in their mother tongue (L1) and English as their foreign language (L2). The results indicate that in both English and Serbian the same groups (e.g. members of ethnic minorities or LGBT population, women etc.) are targeted with the hateful language which in both languages uses vulgarisms, taboo words, sexist and chauvinistic declarative expressions to achieve political goals. In addition, L1>L2 and L2>L1 translation data indicate that personal moral and ethical norms in translators are stronger in L1 thus restrictively affecting translational L2>L1 output.

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Al Fajri, Muchamad Sholakhuddin, and Ikmi Nur Oktavianti. "Stance expressions in applied linguistics research articles: A corpus-based contrastive study." Training, Language and Culture 8, no. 1 (March 25, 2024): 54–65. http://dx.doi.org/10.22363/2521-442x-2024-8-1-54-65.

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Stance, a crucial aspect of academic writing, is complex and vital for both beginner and advanced writers. However, L2 English learners and experienced writers frequently struggle with using stance markers effectively. Currently, there remains a scarcity of research comparing the utilisation of stance markers in applied linguistics research articles between native English professional writers and L1 Indonesian speakers. This study aims to fill this gap by investigating similarities and differences in the deployment of stance markers in applied linguistics research articles by authors with L1 Indonesian and L1 English backgrounds and discussing the educational implications derived from the analysis results. The analysis involves two corpora: the Indonesian academic corpus (IAC), comprising articles authored by L1 Indonesians, and the English academic corpus (EAC), consisting of articles by native English speakers. The study investigates various types of stance markers and their distribution across the corpora, revealing significant differences in their usage. L2 English authors employ more boosters and attitude markers, while L1 English writers use more hedges and self-mentions, with the most notable disparities observed in the usage of self-references. These findings underscore the necessity for educators, particularly within the Indonesian context, to sensitise learners to the discursive norms surrounding the use of stance markers in applied linguistics research articles and provide targeted instruction to enhance English learners’ proficiency in employing stance markers effectively.

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KLEMENT, ERICH PETER, ANNA KOLESÁROVÁ, RADKO MESIAR, and ANDREA STUPŇANOVÁ. "LIPSCHITZ CONTINUITY OF DISCRETE UNIVERSAL INTEGRALS BASED ON COPULAS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18, no. 01 (February 2010): 39–52. http://dx.doi.org/10.1142/s0218488510006374.

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The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L1 (Lipschitz stability) and L∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization of stochastically increasing Archimedean copulas is also given.

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R Alawfi, Dr Nadyh Naser. "Linguistic transformation and preservation of the mother tongue of Saudi Postgraduate scholarship students and their children." International Journal of English Literature and Social Sciences 7, no. 5 (2022): 199–204. http://dx.doi.org/10.22161/ijels.75.31.

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Experiences of linguistic shift (LS) and language maintenance (LM) among Saudi postgraduates who had returned home from studying internationally were investigated. Assessment of perspectives of their first language (L1) among the learners and their children was undertaken, in addition to efforts at advocating language maintenance adopted by educational facilities, cultural and religious associations, as well as the learners themselves. Furthermore, the strengthening of language maintenance in particular fields was examined. Semi-structured interviews were carried out to discuss with and observe Saudi postgraduate students, who possessed over five years of study experience in nations where the first language is English. Evidently, no robust ties to their L1 are felt by young learners, even though their language is appreciated by postgraduate learners and they exert themselves to maintain it. Thus, a decline in L1 writing capabilities occurs, while code reversals pervade their L1. The lack of impact on L1 from language shift has been established in recent studies, while the limited duration of the issue was identified in the existing literature. Maintaining one’s L1 is affected by numerous variables, challenging common perceptions. With postgraduate learners studying and working internationally, their instruction in Arabic and English has led to a multilingual society emerging when they return home. However, isolation from and eradication of cultural norms is just one of the various detrimental outcomes of linguicide which stems from language shifts. Accordingly, this study aimed to establish the extent to which a marked change in language ability occurs among Saudi postgraduate learners when they come home.

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Journal articles on the topic 'L1 Norms'

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