Journal articles: 'Second Variation'

1

Giménez, José, Lorena López, N. Merentes, and J. L. Sánchez. "On Bounded Second Variation." Advances in Pure Mathematics 02, no. 01 (2012): 22–26. http://dx.doi.org/10.4236/apm.2012.21005.

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2

Massa, Enrico, Danilo Bruno, Gianvittorio Luria, and Enrico Pagani. "Geometric constrained variational calculus. II: The second variation (Part I)." International Journal of Geometric Methods in Modern Physics 13, no. 01 (January 2016): 1550132. http://dx.doi.org/10.1142/s0219887815501327.

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Within the geometrical framework developed in [Geometric constrained variational calculus. I: Piecewise smooth extremals, Int. J. Geom. Methods Mod. Phys. 12 (2015) 1550061], the problem of minimality for constrained calculus of variations is analyzed among the class of differentiable curves. A fully covariant representation of the second variation of the action functional, based on a suitable gauge transformation of the Lagrangian, is explicitly worked out. Both necessary and sufficient conditions for minimality are proved, and reinterpreted in terms of Jacobi fields.

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3

Agrachev, A. A. "Spectrum of the Second Variation." Proceedings of the Steklov Institute of Mathematics 304, no. 1 (January 2019): 26–41. http://dx.doi.org/10.1134/s0081543819010036.

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4

Lê, Hông Vân, and Jiří Vanžura. "McLean’s second variation formula revisited." Journal of Geometry and Physics 113 (March 2017): 188–96. http://dx.doi.org/10.1016/j.geomphys.2016.10.002.

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5

Upton, C. J. F. "A generalization of second variation." Analysis Mathematica 11, no. 3 (September 1985): 241–56. http://dx.doi.org/10.1007/bf01907420.

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6

IOFA, MIKHAIL Z. "SECOND VARIATION OF INDUCED CURVATURE TERM IN BRANE-WORLD ACTION." Modern Physics Letters A 25, no. 06 (February 28, 2010): 431–36. http://dx.doi.org/10.1142/s0217732310032512.

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In a 5D spacetime with a 3-brane embedded we calculate the second variation of the scalar 4D curvature term on the brane under variations of the 5D metric. It is shown that the second variation of the 4D scalar curvature term in adapted coordinates is expressed only through variations of the components of the 5D metric with 4D indices.

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7

Li-Jost, Xianqing. "Bifurcation near solutions of variational problems with degenerate second variation." Manuscripta Mathematica 86, no. 1 (December 1995): 1–14. http://dx.doi.org/10.1007/bf02567974.

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8

Massa, Enrico, Gianvittorio Luria, and Enrico Pagani. "Geometric constrained variational calculus. III: The second variation (Part II)." International Journal of Geometric Methods in Modern Physics 13, no. 04 (March 31, 2016): 1650038. http://dx.doi.org/10.1142/s0219887816500389.

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The problem of minimality for constrained variational calculus is analyzed within the class of piecewise differentiable extremaloids. A fully covariant representation of the second variation of the action functional based on a family of local gauge transformations of the original Lagrangian is proposed. The necessity of pursuing a local adaptation process, rather than the global one described in [1] is seen to depend on the value of certain scalar attributes of the extremaloid, here called the corners’ strengths. On this basis, both the necessary and the sufficient conditions for minimality are worked out. In the discussion, a crucial role is played by an analysis of the prolongability of the Jacobi fields across the corners. Eventually, in the appendix, an alternative approach to the concept of strength of a corner, more closely related to Pontryagin’s maximum principle, is presented.

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9

Lee, Nala H. "Style variation in the second formant." Language Ecology 4, no. 1 (December 31, 2020): 115–30. http://dx.doi.org/10.1075/le.00012.lee.

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Abstract Baba Malay speakers perceive words ending with [al], [aɾ], and [as] as kasar ‘coarse’, and their counterparts ending with [ɛ] as halus ‘refined’. The contrast is neither phonetic, phonological or morphological. Instead, it may be mitigated by sound symbolism operationalized by F2. The frontness of [ɛ] is associated with a smaller articulatory space in the oral cavity, and hence refinedness, as compared to the more backwards coarse forms. This study employs a matched-guise perceptual task. Refined forms are elicited from speakers. The F2 in the relevant endings is adjusted twice upwards and twice downwards in steps of 100Hz. Listeners rate these guises on a scale of 1 to 5, 5 being most associated with ‘refined’ values. Results show that the higher F2 is, the more likely listeners are to associate the guise with ‘refined’ values.

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10

박인규. "Second Language Variation: Optimality Theoretic Analyses." Studies in English Language & Literature 38, no. 4 (November 2012): 307–21. http://dx.doi.org/10.21559/aellk.2012.38.4.014.

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11

Coppieters, René, Hugh Douglas Adamson, and Rene Coppieters. "Variation Theory and Second Language Acquisition." Language 66, no. 1 (March 1990): 163. http://dx.doi.org/10.2307/415289.

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12

Burt, Susan Meredith, Robert Bayley, and Dennis R. Preston. "Second Language Acquisition and Linguistic Variation." Language 74, no. 2 (June 1998): 434. http://dx.doi.org/10.2307/417931.

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13

Plastino, A., and M. C. Rocca. "MaxEnt, second variation, and generalized statistics." Physica A: Statistical Mechanics and its Applications 436 (October 2015): 572–81. http://dx.doi.org/10.1016/j.physa.2015.05.084.

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14

de Haan, Laurens, and Ulrich Stadtmüller. "Generalized regular variation of second order." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 61, no. 3 (December 1996): 381–95. http://dx.doi.org/10.1017/s144678870000046x.

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AbstractAssume that for a measurable funcion f on (0, ∞) there exist a positive auxiliary function a(t) and some γ ∈ R such that . Then f is said to be of generalized regular variation. In order to control the asymptotic behaviour of certain estimators for distributions in extreme value theory we are led to study regular variation of second order, that is, we assume that exists non-trivially with a second auxiliary function a1(t). We study the possible limit functions in this limit relation (defining generalized regular variation of second order) and their domains of attraction. Furthermore we give the corresponding relation for the inverse function of a monotone f with the stated property. Finally, we present an Abel-Tauber theorem relating these functions and their Laplace transforms.

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15

Coppieters, René. "Variation theory and second language acquisition." Language 66, no. 1 (1990): 163–67. http://dx.doi.org/10.1353/lan.1990.0038.

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16

Anil K Tomer, Nitish Mittal, Akankshita Behera, and Neha Mittal. "A Case Report on Mandibular Second Molar Regarding Single C-Shaped Canal." International Healthcare Research Journal 2, no. 6 (September 10, 2018): 138–39. http://dx.doi.org/10.26440/ihrj/02_06/197.

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C-shaped canal variation is commonly seen in mandibular second molars. Extra canals is not always a variation in root canals. Radiograph is a must for the identification of single canal. Thorough idea of the proper anatomy of root canals is utmost important to diagnose the variations.

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17

Zähner, Christopher. "Second language acquisition and the computer: variation in second language acquisition." ReCALL 7, no. 1 (May 1995): 34–48. http://dx.doi.org/10.1017/s0958344000005097.

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In this paper I will argue that learner variation in second language acquisition poses a potentially serious problem for the successful design and application of CALL and ICALL software'. Whereas a teacher is able to use direct and immediate feedback from students to adapt to different learning styles, rates of progress and acquisition paths, the possibilities of computer software are much more limited.

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18

Winget, M., and Y. Yasui. "Variation in risk of second primary cancer." Canadian Medical Association Journal 184, no. 1 (November 28, 2011): 19–20. http://dx.doi.org/10.1503/cmaj.111424.

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19

Tundup, Rinchen, Aditi Sharma, and Kailash Sharma. "On bounded second Riesz p(.)-variable~variation." New Trends in Mathematical Science 4, no. 6 (October 26, 2018): 45–53. http://dx.doi.org/10.20852/ntmsci.2018.314.

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20

Ross, Marty. "The second variation of nonorientable minimal submanifolds." Transactions of the American Mathematical Society 349, no. 8 (1997): 3093–104. http://dx.doi.org/10.1090/s0002-9947-97-01936-3.

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21

Dyson, Bronwen Patricia. "Variation, individual differences and second language processing." Linguistic Approaches to Bilingualism 6, no. 4 (March 10, 2016): 341–95. http://dx.doi.org/10.1075/lab.14007.dys.

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Abstract Research on second language acquisition has located individual variation, without clarifying whether language processing prompts learners to differ systematically in the production of syntax and morphology. To address this issue, the study examined the hypothesis on variation in Processability Theory. This theory predicts that, within second language development, individual learners vary systematically in how they respond to developmental conflicts. Specifically, learners have distinct types, which are evident in their use of options and 'trailers' (structures which emerge late). Longitudinal spoken data were collected over one academic year from six adolescent ESL learners. The results revealed different learner types in terms of syntactic options and trailers. However, the learners had less clear types for the morphological options, used unpredicted options, and lacked consistency in their use of syntactic and morphological trailers. The paper suggests that learners vary in processing due to diverse orientations towards the acquisition of either syntax or morphology.

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22

Agrachev†, A., G. Stefani‡, and P. Zezza§. "An invariant second variation in optimal control." International Journal of Control 71, no. 5 (January 1998): 689–715. http://dx.doi.org/10.1080/002071798221533.

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23

Hua, Zhu. "Review: Second Language Acquisition and Linguistic Variation." International Journal of Applied Linguistics 11, no. 2 (December 2001): 283–85. http://dx.doi.org/10.1111/1473-4192.00021.

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24

Tian, Guihua, and Zhao Zheng. "The second variation of a null geodesic." Journal of Mathematical Physics 44, no. 12 (2003): 5681. http://dx.doi.org/10.1063/1.1623931.

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25

Kanno, Kazue. "Consistency and variation in second language acquisition." Second Language Research 14, no. 4 (October 1998): 376–88. http://dx.doi.org/10.1191/026765898667204482.

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This article proposes that L2 learners differ from native speakers with respect to two benchmarks–the extent to which native-like success on one principle of UG predicts comparable success on other principles (lateral consistency), and the extent to which this level of success is stable over time (longitudinal). Results of two experimental studies on the acquisition of Japanese as a second language show that L2 learners exhibit neither lateral nor longitudinal consistency with respect to UG, at least in the early stages of the acquisition process.

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26

Lee, S. J., S. Das Gupta, and R. K. Bhaduri. "Second-order variation in Thomas-Fermi theory." Physical Review A 41, no. 5 (March 1, 1990): 2363–69. http://dx.doi.org/10.1103/physreva.41.2363.

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27

Kvålseth, Tarald O. "Coefficient of variation: the second-order alternative." Journal of Applied Statistics 44, no. 3 (May 14, 2016): 402–15. http://dx.doi.org/10.1080/02664763.2016.1174195.

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28

Wescott, Daniel J. "Sex Variation in the Second Cervical Vertebra." Journal of Forensic Sciences 45, no. 2 (March 1, 2000): 14707J. http://dx.doi.org/10.1520/jfs14707j.

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29

Barza, Sorina, and Pilar Silvestre. "Functions of bounded second $$p$$ p -variation." Revista Matemática Complutense 27, no. 1 (September 28, 2013): 69–91. http://dx.doi.org/10.1007/s13163-013-0136-0.

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30

Dambrine, M., and J. Lamboley. "Stability in shape optimization with second variation." Journal of Differential Equations 267, no. 5 (August 2019): 3009–45. http://dx.doi.org/10.1016/j.jde.2019.03.033.

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31

Das, Bikramjit, and Marie Kratz. "Risk concentration under second order regular variation." Extremes 23, no. 3 (June 28, 2020): 381–410. http://dx.doi.org/10.1007/s10687-020-00382-3.

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32

Selvakumar, Haridoss, Swaminathan Kavitha, Rajendran Bharathan, and Jacob Sam Varghese. "Five Canalled and Three-Rooted Primary Second Mandibular Molar." Case Reports in Dentistry 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/216491.

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A thorough knowledge of root canal anatomy and its variation is necessary for successful completion of root canal procedures. Morphological variations such as additional root canals in human deciduous dentition are rare. A mandibular second primary molar with more than four canals is an interesting example of anatomic variations, especially when three of these canals are located in the distal root. This case shows a rare anatomic configuration and points out the importance of looking for additional canals.

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33

Goldstein, David M. "Variation versus Change." Indo-European Linguistics 4, no. 1 (2016): 53–97. http://dx.doi.org/10.1163/22125892-00401006.

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Enclitic distribution in Greek (and archaic Indo-European generally) is governed by a set of generalizations known as Wackernagel’s Law, according to which enclitics occur in “second position.” As has long been known, surface exceptions to Wackernagel’s Law in Homer are uncommon, but in Herodotus are far more frequent. Wackernagel himself attributed this difference to syntactic change: in Homer a single mechanism is responsible for second-position clitic distribution, while in Herodotus the old second-position rule competes with new placement rules. Although the nature of these innovative mechanisms has never been explicated, philologists have adopted this view with apparent unanimity. The central claim of this paper is that the alleged syntactic change is an illusion. What Wackernagel and others have observed in Homer and Herodotus is a difference in usage, not grammar. Specifically, Herodotus uses constructions that yield non-canonical surface patterns (i.e., the clitic is not “second” in its clause) more often than Homer. As the same generalizations capture the distribution of clitics in both Homer and Herodotus, there is no validity to the claim that Wackernagel’s Law is weaker in the classical period than in the archaic, or that there are new distributional rules at work.

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34

Tian, Xiao-Hui, Wei Zhou, Kun-Qian Ren, Chi Zhang, Xiaoyue Liu, Guang-Tai Xue, Jia-Chen Duan, et al. "Effect of dimension variation for second-harmonic generation in lithium niobate on insulator waveguide [Invited]." Chinese Optics Letters 19, no. 6 (2021): 060015. http://dx.doi.org/10.3788/col202119.060015.

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35

Sadigov, Misraddin Allahverdi oglu. "VARIATION PROBLEM CONTAINING SECOND DERIVATIVES OF UNKNOWN FUNCTIONS." Chronos: natural and technical sciences 6, no. 1(34) (March 3, 2021): 30–42. http://dx.doi.org/10.52013/2712-9691-34-1-6.

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The property subdifferential of an integral and terminal functional in a space of the type of absolutely continuous functions is studied. Necessary and sufficient conditions for an extremum for a variational problem containing the second derivatives of unknown functions are obtained. With the help of the subdifferential introduced by the author, a nonconvex generalized variational problem containing the second derivatives of unknown functions is considered, and the necessary condition for an extremum is obtained.

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36

WU Yu-lian, 吴玉莲, 冯象初 FENG Xiang-chu, and 姜东焕 JIANG Dong-huan. "Second Order Total Generalized Variation for Image Zooming." ACTA PHOTONICA SINICA 42, no. 6 (2013): 732–36. http://dx.doi.org/10.3788/gzxb20134206.0732.

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37

Hanberry, B. B. "Defining heterogeneity as a second level of variation." Web Ecology 15, no. 1 (June 19, 2015): 25–28. http://dx.doi.org/10.5194/we-15-25-2015.

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Abstract. The term heterogeneity has been defined in various ways so that the meaning of heterogeneity has become ambiguous. However, heterogeneity can be defined carefully as a distinct response to multiple single types of underlying variation, that is, a secondary level of variation (or "metavariation"). Identification of heterogeneity is affected by multiple factors, including researcher decisions, and ecosystems at a specified scale can contain both heterogeneous and homogenous variables. A formalized definition may also reduce the suggestion that heterogeneity is more beneficial than homogeneity.

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38

SHEN, Yibing. "Second variation of harmonic maps between Finsler manifolds." Science in China Series A 41, no. 1 (2004): 39. http://dx.doi.org/10.1360/03ys0040.

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39

Prévost, Philippe. "Morphological variation in early adult second language French." EUROSLA Yearbook 4 (September 3, 2004): 147–75. http://dx.doi.org/10.1075/eurosla.4.08pre.

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40

Cheung, Leung-Fu, and Pui-Fai Leung. "The second variation formula for exponentially harmonic maps." Bulletin of the Australian Mathematical Society 59, no. 3 (June 1999): 509–14. http://dx.doi.org/10.1017/s0004972700033207.

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We derive the formula in the title and deduce some consequences. For example we show that the identity map from any compact manifold to itself is always stable as an exponentially harmonic map. This is in sharp contrast to the harmonic or p-harmonic cases where many such identity maps are unstable. We also prove that an isometric and totally geodesic immersion of Sm into Sn is an unstable exponentially harmonic map if m ≠ n and is a stable exponentially harmonic map if m = n.

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41

Liu, Qing, Tiantian Mao, and Taizhong Hu. "THE SECOND-ORDER REGULAR VARIATION OF ORDER STATISTICS." Probability in the Engineering and Informational Sciences 28, no. 2 (December 13, 2013): 209–22. http://dx.doi.org/10.1017/s0269964813000430.

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Let X1, …, Xn be non-negative, independent and identically distributed random variables with a common distribution function F, and denote by X1:n ≤ ··· ≤ Xn:n the corresponding order statistics. In this paper, we investigate the second-order regular variation (2RV) of the tail probabilities of Xk:n and Xj:n − Xi:n under the assumption that $\bar {F}$ is of the 2RV, where 1 ≤ k ≤ n and 1 ≤ i < j ≤ n.

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42

White, Lydia. "Universal Grammar, crosslinguistic variation and second language acquisition." Language Teaching 45, no. 3 (June 15, 2012): 309–28. http://dx.doi.org/10.1017/s0261444812000146.

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According to generative linguistic theory, certain principles underlying language structure are innately given, accounting for how children are able to acquire their mother tongues (L1s) despite a mismatch between the linguistic input and the complex unconscious mental representation of language that children achieve. This innate structure is referred to as Universal Grammar (UG); it includes universal principles, as well as parameters which allow for constrained variation across languages.

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43

Liang, S. M., C. J. Tsai, and L. N. Wu. "Efficient, robust second-order total variation diminishing scheme." AIAA Journal 34, no. 1 (January 1996): 193–95. http://dx.doi.org/10.2514/3.13042.

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44

Urbano, Francisco. "Second variation of one-sided complete minimal surfaces." Revista Matemática Iberoamericana 29, no. 2 (2013): 479–94. http://dx.doi.org/10.4171/rmi/727.

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45

Zhu, Meng. "The second variation of the Ricci expander entropy." Pacific Journal of Mathematics 251, no. 2 (June 3, 2011): 499–510. http://dx.doi.org/10.2140/pjm.2011.251.499.

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46

López Ferrero, Carmen. "Pragmatic Variation in First and Second Language Contexts." Pragmática Sociocultural / Sociocultural Pragmatics 1, no. 2 (November 1, 2013): 298–306. http://dx.doi.org/10.1515/soprag-2013-0013.

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47

Cao, Huai-Dong, and Meng Zhu. "On second variation of Perelman’s Ricci shrinker entropy." Mathematische Annalen 353, no. 3 (July 21, 2011): 747–63. http://dx.doi.org/10.1007/s00208-011-0701-0.

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48

Lazenby, Richard A. "Population variation in second metacarpal sexual size dimorphism." American Journal of Physical Anthropology 118, no. 4 (July 11, 2002): 378–84. http://dx.doi.org/10.1002/ajpa.10110.

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49

Knoll, Florian, Kristian Bredies, Thomas Pock, and Rudolf Stollberger. "Second order total generalized variation (TGV) for MRI." Magnetic Resonance in Medicine 65, no. 2 (December 8, 2010): 480–91. http://dx.doi.org/10.1002/mrm.22595.

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50

Guthrie, Kate Hardeman. "Gender and second language style." Asia-Pacific Language Variation 2, no. 2 (December 31, 2016): 157–87. http://dx.doi.org/10.1075/aplv.2.2.03har.

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Abstract Gender has been shown to be a salient factor in acquisition of second language variation (Adamson & Regan, 1991; Major, 2004; Meyerhoff & Schleef, 2012; Rehner, Mougeon, & Nadasdi, 2003; Schleef, Meyerhoff, & Clark, 2011). However, these studies have primarily focused on learner production of target language variation and style in the sense of attention paid to speech. There has been little focus on learner perceptions of the social meanings associated with L2 variants and styles. The present article addresses this gap in the research by examining L2 learner perceptions of a gendered style of speaking in Mandarin Chinese known as sajiao. Results from a perception experiment confirm the salience of gender in the acquisition of L2 variation and show that American L2 Mandarin learners have acquired some of the social meanings associated with sajiao but not others. An acoustic phonetic analysis of sajiao is also presented.

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Journal articles on the topic 'Second Variation'

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