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Journal articles on the topic 'Lemmas'

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Published: 4 June 2021
Last updated: 6 September 2023

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1

Schecter, Stephen. "Exchange lemmas 1: Deng's lemma." Journal of Differential Equations 245, no. 2 (July 2008): 392–410. http://dx.doi.org/10.1016/j.jde.2007.08.011.

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2

Schecter, Stephen. "Exchange lemmas 2: General Exchange Lemma." Journal of Differential Equations 245, no. 2 (July 2008): 411–41. http://dx.doi.org/10.1016/j.jde.2007.10.021.

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3

Sivaraman, Aishwarya, Alex Sanchez-Stern, Bretton Chen, Sorin Lerner, and Todd Millstein. "Data-driven lemma synthesis for interactive proofs." Proceedings of the ACM on Programming Languages 6, OOPSLA2 (October 31, 2022): 505–31. http://dx.doi.org/10.1145/3563306.

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Interactive proofs of theorems often require auxiliary helper lemmas to prove the desired theorem. Existing approaches for automatically synthesizing helper lemmas fall into two broad categories. Some approaches are goal-directed, producing lemmas specifically to help a user make progress from a given proof state, but they have limited expressiveness in terms of the lemmas that can be produced. Other approaches are highly expressive, able to generate arbitrary lemmas from a given grammar, but they are completely undirected and hence not amenable to interactive usage. In this paper, we develop an approach to lemma synthesis that is both goal-directed and expressive. The key novelty is a technique for reducing lemma synthesis to a data-driven program synthesis problem, whereby examples for synthesis are generated from the current proof state. We also describe a technique to systematically introduce new variables for lemma synthesis, as well as techniques for filtering and ranking candidate lemmas for presentation to the user. We implement these ideas in a tool called lfind, which can be run as a Coq tactic. In an evaluation on four benchmark suites, lfind produces useful lemmas in 68% of the cases where a human prover used a lemma to make progress. In these cases lfind synthesizes a lemma that either enables a fully automated proof of the original goal or that matches the human-provided lemma.
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4

Wei, Longxing. "The Bilingual Mental Lexicon and Lemmatic Transfer in Second Language Learning." English Language Teaching and Linguistics Studies 2, no. 3 (August 31, 2020): p43. http://dx.doi.org/10.22158/eltls.v2n3p43.

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There have been numerous studies of first Language (L1) transfer in second Language (L2) learning. Various models have been proposed to explore the sources of language transfer and have also caused many controversies over the nature of language transfer and its effects on interlanguage. Different from most previous studies remaining at a surface level of observation, this study proposes an abstract approach, which is abstract because it goes beyond any superficial observation and description by exploring the nature and activity of the bilingual mental lexicon in L2 learning. This approach adopts the Bilingual Lemma Activation Model (BLAM) (Wei, 2006a, 2006b) and tests its crucial assumptions and claims: The bilingual mental lexicon does not simply contain lexemes but abstract entries, called “lemmas”, about them; lemmas in the bilingual mental lexicon are language-specific; language-specific lemmas in the bilingual mental lexicon are in contact in L2 learning, lemmas underlying L1 abstract lexical structure may replace those underlying L2 abstract lexical structure. Lemmas in the bilingual mental lexicon are about three levels of abstract lexical structure: lexical-conceptual structure, predicate-argument structure, and morphological realization patterns. The typical instances of L1 lemma transfer in L2 learning are discussed and explained in support of the BLAM.
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5

Anosov, D. V., and E. V. Zhuzhoma. "Closing lemmas." Differential Equations 48, no. 13 (December 2012): 1653–99. http://dx.doi.org/10.1134/s0012266112130010.

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6

Szemerédi, Endre. "Arithmetic Progressions, Different Regularity Lemmas and Removal Lemmas." Communications in Mathematics and Statistics 3, no. 3 (September 2015): 315–28. http://dx.doi.org/10.1007/s40304-015-0062-1.

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7

Lungu, Nicolaie, and Sorina Anamaria Ciplea. "Optimal Gronwall lemmas." Fixed Point Theory 18, no. 1 (March 1, 2017): 293–304. http://dx.doi.org/10.24193/fpt-ro.2017.1.23.

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8

Carbery, Anthony. "Covering lemmas revisited." Proceedings of the Edinburgh Mathematical Society 31, no. 1 (February 1988): 145–50. http://dx.doi.org/10.1017/s0013091500006647.

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In this note we intend to discuss the method of A. Córdoba and R. Fefferman of using covering lemmas to control maximal functions, and make some simplifications which allow us to obtain alternative proofs of some of their results.
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9

Gasser, I., P. A. Markowich, and B. Perthame. "Dispersion Lemmas Revisited." VLSI Design 9, no. 4 (January 1, 1999): 365–75. http://dx.doi.org/10.1155/1999/81341.

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We investigate regularizing dispersive effects for various classical equations, e.g., the Schrödinger and Dirac equations. After Wigner transform, these dispersive estimates are reduced to moment lemmas for kinetic equations. They yield new regularization results for the Schrödinger equation (valid up to the semiclassical limit) and the Dirac equation.
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10

Sun, Shu-Hao. "On separation lemmas." Journal of Pure and Applied Algebra 78, no. 3 (April 1992): 301–10. http://dx.doi.org/10.1016/0022-4049(92)90112-s.

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11

Nguyen, Dinh, and Mo Hong Tran. "Sequential Farkas lemmas for convex systems." Science and Technology Development Journal 17, no. 4 (December 31, 2014): 20–26. http://dx.doi.org/10.32508/stdj.v17i4.1552.

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In this paper we introduce two new versions of Farkas lemma for two kinds of convex systems in locally convex Hausdorff topological vector spaces which hold without any constraint qualification conditions. These versions hold in the limits and will be called sequential Farkas lemmas. Concretely, we establish sequential Farkas lemmas for cone-convex systems and for systems which are convex with respect to a sublinear function. The first result extends some known ones in the literature while the second is a new one.
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12

Knowles, Gerry, and Zuraidah Mohd Don. "The notion of a “lemma”." International Journal of Corpus Linguistics 9, no. 1 (April 29, 2004): 69–81. http://dx.doi.org/10.1075/ijcl.9.1.04kno.

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The notion of alemmais so familiar in corpus linguistics that it scarcely needs a formal definition. When a wordlist or a text is lemmatised, the process is apparently transparent, so that any observer can understand how the lemma relates to the original set or string of words. We shall argue in this paper that, on the contrary, the concept of lemma is not well defined, and is in need of a clear formal definition. The lemma is a fundamental concept in the processing of texts in at least some languages, a point we shall illustrate with respect to Arabic and Malay. It so happens that English lemmas are not typical of the general category, so that linguists who base their understanding of the lemma on English obtain a distorted view. It is essential to reverse the direction of argument, and to start with a general understanding of the lemma, and to consider English lemmas in the wider context.
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13

Rahim Kargar, Ali Ebadian, and Janusz Sokół. "Certain coefficient inequalities for p-valent functions." Malaya Journal of Matematik 4, no. 01 (January 1, 2016): 37–41. http://dx.doi.org/10.26637/mjm401/005.

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14

Jantzen, Bernd. "New proofs for the two Barnes lemmas and an additional lemma." Journal of Mathematical Physics 54, no. 1 (January 2013): 012304. http://dx.doi.org/10.1063/1.4775770.

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15

Wei, Longxing. "Codeswitching as Projection of Bilingual Lemmas in Contact." Studies in Linguistics and Literature 4, no. 1 (February 24, 2020): p40. http://dx.doi.org/10.22158/sll.v4n1p40.

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Unlike most previous studies of Codeswitching (CS) focused on describing surface configurations of switched items (i.e., where CS is structurally possible) or the switched items (i.e., what items from another language can be switched), this paper explores formulation processes of bilingual speech and the nature of the bilingual mental lexicon and its activity in CS. More specifically, it applies the Bilingual Lemma Activation Model (Wei, 2002, 2006b) to the data drawn from various naturally occurring CS instances. It claims that the mental lexicon does not simply contain lexemes and their meanings, but also lemmas, which are abstract entries in the mental lexicon that support the surface realization of actual lexemes. Lemmas are abstract in that they contain phonological, morphological, semantic, syntactic and pragmatic information about lexemes. It further claims that lemmas in the bilingual mental lexicon are language-specific and are in contact during a discourse involving CS at three levels of abstract lexical structure: lexical-conceptual structure, predicate-argument structure, and morphological realization patterns. The CS instances described and analyzed in this paper provide evidence that the bilingual speaker’s two linguistic systems are unequally activated in CS, and CS is an outcome of bilingual lemmas in contact.
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16

Wei, Longxing, and Xuexin Liu. "The Bilingual Lemma Activation Model as a Comparative Approach to Codeswitching." Studies in Linguistics and Literature 2, no. 2 (May 10, 2018): 77. http://dx.doi.org/10.22158/sll.v2n2p77.

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<em>This paper explores intrasentential Codeswitching (CS) as a commonly observed bilingual speech behavior. Different from surface-based models, it investigates CS at an abstract level by relating the nature and activity of the bilingual mental lexicon in bilingual speech production to the structural principles governing CS. The Matrix Language Frame (MLF) Model is adopted for describing some fundamental structural principles governing CS, and the Bilingual Lemma Activation Model (BLA) is proposed for explaining the linguistic motivations for CS. Based on the analysis of some naturally occurring CS instances involving various language pairs, this study supports the claim that one of the bilingual’s languages is activated as the Matrix Language (ML) and the other as the Embedded Language (EL), and content and system morphemes are unequally activated. It is the ML which provides the sentential frame for CS and the EL only provides content morphemes switched into this frame. It further argues that bilingual mental lexicon contains not only lexemes but also more abstract elements called “lemmas”, and lemmas in the bilingual mental lexicon are language-specific and such lemmas are in contact in CS. This study provides evidence that only conceptually activated EL lemmas can be switched into the ML sentential frame.</em>
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17

Idzik, Adam, and Konstanty Junosza-Szaniawski. "Combinatorial Lemmas for Polyhedrons." Discussiones Mathematicae Graph Theory 25, no. 1-2 (2005): 95. http://dx.doi.org/10.7151/dmgt.1264.

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18

Thomson. "SOME SYMMETRIC COVERING LEMMAS." Real Analysis Exchange 15, no. 1 (1989): 346. http://dx.doi.org/10.2307/44152015.

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19

Wen, Lan, and Zhihong Xia. "$C^1$ Connecting Lemmas." Transactions of the American Mathematical Society 352, no. 11 (July 18, 2000): 5213–30. http://dx.doi.org/10.1090/s0002-9947-00-02553-8.

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20

Johnsonbaugh, Richard, and David P. Miller. "Converses of pumping lemmas." ACM SIGCSE Bulletin 22, no. 1 (February 1990): 27–30. http://dx.doi.org/10.1145/319059.319073.

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21

Bernal-González, L., and M. C. Calderón-Moreno. "Two hyperbolic Schwarz lemmas." Bulletin of the Australian Mathematical Society 66, no. 1 (August 2002): 17–24. http://dx.doi.org/10.1017/s0004972700020633.

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In this paper, a sharp version of the Schwarz–Pick Lemma for hyperbolic derivatives is provided for holomorphic selfmappings on the unit disk with fixed multiplicity for the zero at the origin. This extends a recent result due to Beardon. A property of preserving hyperbolic distances also studied by Beardon is here completely characterised.
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22

Zhang, Wei. "On arithmetic fundamental lemmas." Inventiones mathematicae 188, no. 1 (August 25, 2011): 197–252. http://dx.doi.org/10.1007/s00222-011-0348-1.

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23

Duzaar, Frank, and Giuseppe Mingione. "Harmonic type approximation lemmas." Journal of Mathematical Analysis and Applications 352, no. 1 (April 2009): 301–35. http://dx.doi.org/10.1016/j.jmaa.2008.09.076.

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24

Nowicki, Andrzej, and Yoshikazu Nakai. "On Appelgate-Onishi's Lemmas." Journal of Pure and Applied Algebra 51, no. 3 (April 1988): 305–10. http://dx.doi.org/10.1016/0022-4049(88)90069-2.

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25

Lin, Jixiang, Shuai Shao, Na Zhang, Yang Wang, and Chunsheng Mu. "Lemmas induce dormancy but help the seed ofLeymus chinensisto resist drought and salinity conditions in Northeast China." PeerJ 4 (January 4, 2016): e1485. http://dx.doi.org/10.7717/peerj.1485.

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Leymus chinensisis a dominant grass in the Songnen grassland of Northern China. The lower germination caused by the presence of lemmas has proved to be an obstacle for the use of the seeds of this plant by humans. However, it is still unknown if the lemmas have other ecological roles such as resisting drought and saline conditions. Three experiments were designed to investigate the ecological roles of the lemmas inLeymus chinensisseeds. The results showed that lemmas significantly improved the amount of water uptake and slowed down the dehydration rate of the seeds under dry conditions. Likewise, the lemmas induced seed dormancy, and removal of the lemmas improved the germination at all temperatures. Although germination percentage of the seeds without lemmas were higher than that of seeds with lemmas under salinity stress, the recovery and total percentage were significantly lower than the seeds with lemmas, especially at 400 mM stress. These results suggest that the lemmas play a vital function in water uptake, dehydration and salt tolerance during the germination stage of the seeds as a response to adverse environmental conditions. Although lemmas showed a dormancy effect, if we want to plant this species in salinity soil in Northeast China, the approach of removing the lemmas by artificial means and improving the seed germination percentage is not feasible.
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26

RÖDL, VOJTĚCH, and MATHIAS SCHACHT. "Regular Partitions of Hypergraphs: Counting Lemmas." Combinatorics, Probability and Computing 16, no. 6 (November 2007): 887–901. http://dx.doi.org/10.1017/s0963548307008565.

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We continue the study of regular partitions of hypergraphs. In particular, we obtain corresponding counting lemmas for the regularity lemmas for hypergraphs from our paper ‘Regular Partitions of Hypergraphs: Regularity Lemmas’ (in this issue).
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27

Normann, Dag, and Sam Sanders. "On the mathematical and foundational significance of the uncountable." Journal of Mathematical Logic 19, no. 01 (June 2019): 1950001. http://dx.doi.org/10.1142/s0219061319500016.

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We study the logical and computational properties of basic theorems of uncountable mathematics, including the Cousin and Lindelöf lemma published in 1895 and 1903. Historically, these lemmas were among the first formulations of open-cover compactness and the Lindelöf property, respectively. These notions are of great conceptual importance: the former is commonly viewed as a way of treating uncountable sets like e.g. [Formula: see text] as “almost finite”, while the latter allows one to treat uncountable sets like e.g. [Formula: see text] as “almost countable”. This reduction of the uncountable to the finite/countable turns out to have a considerable logical and computational cost: we show that the aforementioned lemmas, and many related theorems, are extremely hard to prove, while the associated sub-covers are extremely hard to compute. Indeed, in terms of the standard scale (based on comprehension axioms), a proof of these lemmas requires at least the full extent of second-order arithmetic, a system originating from Hilbert–Bernays’ Grundlagen der Mathematik. This observation has far-reaching implications for the Grundlagen’s spiritual successor, the program of Reverse Mathematics, and the associated Gödel hierarchy. We also show that the Cousin lemma is essential for the development of the gauge integral, a generalization of the Lebesgue and improper Riemann integrals that also uniquely provides a direct formalization of Feynman’s path integral.
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28

Liu, Jinhai, Hehua Wang, Fucheng Luo, Yan Wang, Cui Xu, and Jinjuan Jiang. "The influence of seed structures on dormancy in seeds of <i>Urochloa</i> hybrid cultivar ‘Mulato Ⅱ’." Tropical Grasslands-Forrajes Tropicales 10, no. 3 (September 30, 2022): 156–63. http://dx.doi.org/10.17138/tgft(10)156-163.

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This study determined the effects of seed structures on seed dormancy and tested methods to break dormancy in seeds of Urochloa hybrid cultivar ‘Mulato II’. Seeds stored for 10 months in indoor ambient conditions were studied to determine effects of seed structures on seed germination and their water permeability. Results showed that seed structures presented a barrier to water permeability. Removal of lemmas, puncturing the seed coat, seed structure removal and sulfuric acid immersion all reduced seed dormancy. Water and alcohol extracts from different parts of seeds inhibited seed germination of Brassica pekinensis seeds. There were 3 mechanisms responsible for seed dormancy; first, the mechanical barrier of seed structures, which excluded water and reduced gas exchange as well as restricting growth of the embryo; second, an endogenous germination inhibitor mainly found in lemmas; and third, water permeability of the seed coat (including pericarp and testa). The mechanical removal of lemmas and immersion in concentrated sulfuric acid reduced seed dormancy, although mechanical removal of the lemma alone was effective, convenient and safer.
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29

Filip, Alexandru-Darius. "Some applications of Maia's fixed point theorem for Fredholm integral equation systems." Studia Universitatis Babes-Bolyai Matematica 67, no. 1 (March 10, 2022): 189–202. http://dx.doi.org/10.24193/subbmath.2022.1.14.

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"The aim of this paper is to study the existence and uniqueness of solutions for some Fredholm integral equation systems by applying the vectorial form of Maia's fixed point theorem. Some abstract Gronwall lemmas and an abstract comparison lemma are also obtained."
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30

Parthipan, CG, and Priyanka Kokil. "Stability of state-delayed digital filters with overflow nonlinearities." Transactions of the Institute of Measurement and Control 44, no. 8 (December 14, 2021): 1599–610. http://dx.doi.org/10.1177/01423312211059519.

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In this work, stability of digital filters in the presence of overflow nonlinearities and time-varying delay is investigated with/without external disturbance. Two new lemmas related to characterization of overflow nonlinearities are developed. The first lemma is established with better utilization of system information which includes overflow nonlinearities, previous and current states of the digital filter. The second lemma associated with overflow nonlinearities is developed with lesser constraints. Furthermore, by utilizing the established lemmas and a new Lyapunov functional, an asymptotic stability condition is presented for the digital filter with time-varying delay and overflow nonlinearities. The developed condition is shown to be more relaxed and computationally less demanding than the existing criteria. In addition to that, a sufficient condition is derived under which the digital filter with external disturbance, overflow nonlinearities, and time-varying delay has a prescribed noise attenuation level. To show the efficacy of the proposed approach, numerical examples are presented.
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31

ZHANG, ZHONG-SHUAI, SHAN-WEN JIANG, and WEN-LI CHEN. "Achnatherum pilosum (Stipeae, Poaceae), a new species from Qinghai-Tibet Plateau." Phytotaxa 350, no. 1 (May 17, 2018): 86. http://dx.doi.org/10.11646/phytotaxa.350.1.10.

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A new species of Achnatherum from Qinghai-Tibet Plateau is described and illustrated. It is distinguished from other species of the genus by attributes of ligules, panicles, glumes, lemmas, awns and anthers. Evidence from lemma epidermal pattern, cytology and morphology confirm its systematic position in Achnatherum s.s.
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32

Ashok, Pradeesha, Sathish Govindarajan, and Ninad Rajgopal. "Selection Lemmas for Various Geometric Objects." International Journal of Computational Geometry & Applications 26, no. 02 (June 2016): 67–87. http://dx.doi.org/10.1142/s0218195916500047.

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Selection lemmas are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection lemma type results typically show that there exists a point that is contained in many objects that are induced (spanned) by an underlying point set. In the first selection lemma, we consider the set of all the objects induced by a point set [Formula: see text]. This question has been widely explored for simplices in [Formula: see text], with tight bounds in [Formula: see text]. In our paper, we prove first selection lemma for other classes of geometric objects like boxes and balls in [Formula: see text]. We also consider the strong variant of this problem where we add the constraint that the piercing point comes from [Formula: see text]. We prove an exact result on the strong and the weak variant of the first selection lemma for axis-parallel rectangles and disks (for centrally symmetric point sets). We also show non-trivial bounds on the first selection lemma for axis-parallel boxes and balls in [Formula: see text]. In the second selection lemma, we consider an arbitrary [Formula: see text] sized subset of the set of all objects induced by [Formula: see text]. We study this problem for axis-parallel rectangles and show that there exists a point in the plane that is contained in [Formula: see text] rectangles. This is an improvement over the previous bound by Smorodinsky and Sharir22 when [Formula: see text] is almost quadratic.
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33

Ramnäs, Mårten. "Étendue du vocabulaire et compréhension écrite – le français à l'université en Suède." Bergen Language and Linguistics Studies 10, no. 1 (November 7, 2019): 12. http://dx.doi.org/10.15845/bells.v10i1.1430.

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This paper investigates the amount of French vocabulary needed to read (with reasonable comprehension) three authentic novels used in a first semester course of French at a Swedish university. The analysis applies the concept of lexical coverage and uses the frequency lists of Lonsdale & Le Bras (2009). The counting unit is the lemma. This study also examines the common French word list used in all Swedish universities offering French degrees. The results show that 7 000 to 9 000 lemmas will provide the 98 % coverage needed for reasonable comprehension. This is at least twice the 4 000 lemmas contained in the university list. The results therefore point to the necessity of including a vocabulary component also in higher-level French courses.
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34

CHORGHE, ALOK, L. RASINGAM, P. V. PRASANNA, and M. SANKARA RAO. "Tripogon tirumalae (Poaceae), a new species from the Seshachalam hills of Andhra Pradesh, India." Phytotaxa 131, no. 1 (September 13, 2013): 17. http://dx.doi.org/10.11646/phytotaxa.131.1.3.

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Tripogon tirumalae, a new species of grass from the Seshachalam hill ranges, Andhra Pradesh, India, is described and illustrated. The new species differs from Tripogon sivarajanii in having ciliate membranous ligules, a shorter inflorescence, more florets, bearded lemma base, and a median awn longer than the lemma; and from Tripogon trifidus in having culms 60−75 cm high, glabrous leaf sheaths, and lemmas with a single median awn which is 1.5 times longer than the lemma.
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35

Wei, Longxing. "Linguistic Codeswitching as a Cross-linguistic Lexical Bridge in Bilingual Communication." Studies in Linguistics and Literature 7, no. 1 (February 24, 2023): p69. http://dx.doi.org/10.22158/sll.v7n1p69.

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Most studies of linguistic codeswitching (CS) focus on what language items can be switched and how such switched items are intrasententially configurated at the surface sentence level. This study investigates linguistic CS at a rather abstract level by adopting the Bilingual Lemma Activation (BLA) Model (Wei, 2020). This model claims that lemmas (i.e., abstract entries in the mental lexicon about lexemes) are language-specific, language-specific lemmas are in contact in bilingual speech involving CS, and thus CS is cross-linguistically and lexical-conceptually driven in bilingual communication. In support of such a claim, this study provides evidence that bilinguals perform CS as a communicative strategy to make their intended meanings realized in terms of language-specific lemmas activated for the current exchange. Some typical instances of naturally occurring CS as observed in various language pairs involved in CS are described and explained at two levels of abstract lexical structure: lexical-conceptual structure and predicate-argument structure. This study offers some explanations of linguistic CS from a particular perspective and aims to explore the nature and activity of the bilingual mental lexicon during CS.
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36

Marian, Daniela, Sorina Anamaria Ciplea, and Nicolaie Lungu. "Optimal and Nonoptimal Gronwall Lemmas." Symmetry 12, no. 10 (October 19, 2020): 1728. http://dx.doi.org/10.3390/sym12101728.

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In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many inequalities, the upper bound is not an optimal one.
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37

Idzik, Adam, and Konstanty Junosza-Szaniawski. "Combinatorial lemmas for polyhedrons I." Discussiones Mathematicae Graph Theory 26, no. 3 (2006): 439. http://dx.doi.org/10.7151/dmgt.1336.

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38

Kaptanoğlu, H. Turgay. "Some refined Schwarz-Pick lemmas." Michigan Mathematical Journal 50, no. 3 (2002): 649–64. http://dx.doi.org/10.1307/mmj/1039029986.

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39

Lacey, Michael T., Stefanie Petermichl, Jill C. Pipher, and Brett D. Wick. "Multi-parameter Div-Curl lemmas." Bulletin of the London Mathematical Society 44, no. 6 (April 17, 2012): 1123–31. http://dx.doi.org/10.1112/blms/bds037.

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40

Idzik, Adam, and Konstanty Junosza-Szaniawski. "Combinatorial lemmas for nonoriented pseudomanifolds." Topological Methods in Nonlinear Analysis 22, no. 2 (December 1, 2003): 387. http://dx.doi.org/10.12775/tmna.2003.047.

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41

Malliaris, M., and S. Shelah. "Regularity lemmas for stable graphs." Transactions of the American Mathematical Society 366, no. 3 (August 29, 2013): 1551–85. http://dx.doi.org/10.1090/s0002-9947-2013-05820-5.

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42

Segala, Roberto. "The Essence of Coin Lemmas." Electronic Notes in Theoretical Computer Science 22 (1999): 188–207. http://dx.doi.org/10.1016/s1571-0661(05)80603-6.

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43

Xu, Yi-Hui, and Jin-Lin Liu. "New Applications of Nunokawa’s Lemmas." Journal of Function Spaces 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/241264.

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44

Navara, Mirko. "Piron's and Bell's Geometrical Lemmas." International Journal of Theoretical Physics 43, no. 7/8 (August 2004): 1587–94. http://dx.doi.org/10.1023/b:ijtp.0000048804.78491.34.

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45

Bernal-González, L., and M. C. Calderón-Moreno. "Erratum: Two hyperbolic Shwarz lemmas." Bulletin of the Australian Mathematical Society 67, no. 3 (June 2003): 521–22. http://dx.doi.org/10.1017/s000497270003731x.

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Abstract:
In [1] there is an error, as pointed out to us by J.M. Isidro. In that paper we consider the set Rm of all m-rotations, that is, Rm = {czm: |c| = 1}; the set Aut() of the automorphisms of the unit disc  and the set of the m-automorphisms of , Autm () = {ψ ∘ R ∘ ϕ : ψ, ϕ ∈ Aut(), R ∈ Rm}. We asserted thatwhere ϕa(Z) = (a − z)/(1 − āz). Equality (1) is not true. For instance, it suffices to consider f (z) = ϕ¼ ∘ ∘ z2 ∘ ϕ½. We have that f ∈ Aut2 (), f (0) = (0) and, after calculations, f (z) = (7z2 − 6z)/(6z − 7). Then it is evident that will never hold f (z) = ϕ0 ∘ R ∘ ϕ0 with R ∈ R2, because ϕ0 is equal to identity.
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46

Walther, Hans Otto. "Inclination lemmas with dominated convergence." ZAMP Zeitschrift f�r angewandte Mathematik und Physik 38, no. 2 (March 1987): 327–37. http://dx.doi.org/10.1007/bf00945417.

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47

Levin, Michael. "Gettier Cases without False Lemmas?" Erkenntnis 64, no. 3 (July 5, 2006): 381–92. http://dx.doi.org/10.1007/s10670-005-5470-2.

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48

Alon, Noga, and Omri Ben-Eliezer. "Efficient Removal Lemmas for Matrices." Order 37, no. 1 (May 23, 2019): 83–101. http://dx.doi.org/10.1007/s11083-019-09494-3.

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49

Adams, Colin. "The Silence of the Lemmas." Mathematical Intelligencer 34, no. 2 (December 13, 2011): 27–28. http://dx.doi.org/10.1007/s00283-011-9258-8.

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50

Airey, D., and B. Mance. "Hotspot Lemmas for Noncompact Spaces." Mathematical Notes 108, no. 3-4 (October 2020): 434–39. http://dx.doi.org/10.1134/s0001434620090126.

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