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Topic: Short five lemma

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Five lemma

Exact sequence

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	The Short Five Lemma and the Five Lemma
		The five lemma (proved below) is a generalization of the short five lemma, and this step of the proof will have to be modified.
		Short exact sequences can be clumped together into equivalence classes.
		The short five lemma can be generalized to five modules, top and bottom, with 5 homomorphisms connecting corresponding modules and forming a commutative diagram.
	www.mathreference.com /mod-hom,5lemma.html (744 words)

	Glossary I-P
		lemma: in a grass floret, the lower of two bracts enclosing a flower, perhaps a bract s.
		lodicule: in a grass floret, one of a pair (or three?) of tiny scales or flaps of tissue between the lemma and palea and the stamens, possibly representing reduced perianth segments, see also glume (of a spikelet).
		short shoot; the comparison is often made between axillary shoots.
	www.mobot.org /MOBOT/research/APweb/top/glossaryi_p.html (6625 words)

	PlanetMath: 5-lemma
		A special case of this is the short 5-lemma, in which
		are the trivial objects of the category (hence the rows form short exact sequences).
		Cross-references: short exact sequences, category, isomorphisms, injective, surjective, rows, commutative diagram, ring, modules, abelian category, objects
	planetmath.org /encyclopedia/5Lemma.html (101 words)

	AG RVS - A Note on a Note on a Lemma of Ladkin: Confessions of a Miscreant, namely
		Galton claims Lemma 2 from (4) is false.
		Lemma 2 of (4) is true; I shall prove a considerably stronger version;
		Lemma 4 allows a finer understanding of what the axiom M1 contributes to the structure of its models than has so far appeared in the literature.
	www.rvs.uni-bielefeld.de /publications/Reports/NNLemmaLadkin.html (2473 words)

	PlanetMath: horseshoe lemma (Site not responding. Last check: 2007-10-12)
		is commutative and has exact rows, so we may apply the short five lemma to conclude that
		By the snake lemma, there is a commutative diagram
		This is version 2 of horseshoe lemma, born on 2006-04-02, modified 2006-04-02.
	planetmath.org /encyclopedia/HorseshoeLemma.html (251 words)

	E-Flora BC Glossary of Botanical Terms Page
		Keel -- In a papilionaceous flower, the 2 lowermost connate petals; resembles the keel of a boat; in grasses, the sharp crease or ridge of the leaf blades, the lemma or the glume.
		Papilionaceous flower -- A strongly irregular flower with five petals, the lowermost 2 petals are connate (fused) and form the keel, as in Fabaceae.
		Stipitate -- Borne on a stipe or short stalk, "short-stalked".
	www.geog.ubc.ca /~brian/florae/ifbc_glossary.html (5766 words)

	Short five lemma - Wikipedia, the free encyclopedia
		In mathematics, especially homological algebra and other applications of Abelian category theory, the short five lemma is a special case of the five lemma.
		It states that for the following commutative diagram (in any Abelian category, or in the category of groups), if the rows are short exact sequences, and if g and h are isomorphisms, then f is an isomorphism as well.
		Note however that the existence of f has to be assumed from the start; two objects B and B′ that simply have isomorphic sub- and factor objects need not themselves be isomorphic (for example, in the category of Abelian groups, B could be the cyclic group of order four and B′ the viergruppe).
	en.wikipedia.org /wiki/Short_five_lemma (156 words)

	Grass Genera of the World - Clausospicula M. Lazarides
		The proximal lemmas awnless; 2 nerved, or 4 nerved; more or less equalling the female-fertile lemmas to decidedly exceeding the female-fertile lemmas; similar in texture to the female-fertile lemmas (hyaline); not becoming indurated.
		Lemmas less firm than the glumes; not becoming indurated; entire (the hyaline margins of the stipe antero-laterally decurrent on the base of the awn, with no indication of lobes); awned.
		Lemmas hairless; glabrous; non-carinate; without a germination flap; 3 nerved; with the nerves non-confluent.
	www.biologie.uni-hamburg.de /b-online/delta/grass/www/clausosp.htm (576 words)

	Grass Genera of the World - Pentameris P. Beauv.
		Lemmas similar in texture to the glumes to decidedly firmer than the glumes; not becoming indurated (membranous); incised; 2 lobed; deeply cleft; awned.
		Awns 3; median and lateral (the lateral lemma lobes each with a 1–7 mm bristle from the inner side, more or less adnate below); the median different in form from the laterals; from a sinus; geniculate (near the middle); hairless (scabrid); much longer than the body of the lemma; entered by several veins (3).
		Lemmas non-carinate; having the margins lying flat on the palea; without a germination flap; 7 nerved, or 9 nerved (-11 nerved); with the nerves non-confluent.
	delta-intkey.com /grass/www/pentamer.htm (778 words)

	Grass Genera of the World - Pentaschistis (Nees) Spach
		Lemmas similar in texture to the glumes (membranous); not becoming indurated; incised (bifid, rarely 3–4-fid); 2 lobed, or 4–5 lobed (rarely); not deeply cleft; awnless, or mucronate, or awned (generally awned from the central sinus, and with a point or straight awn on each lobe).
		Lemmas hairy, or hairless; non-carinate (dorsally rounded); without a germination flap; 5–7 nerved; with the nerves non-confluent.
		Palea present; relatively long; tightly clasped by the lemma; apically notched; awnless, without apical setae; textured like the lemma; not indurated (thinly membranous); 2-nerved (but with the nerves not reaching the apex of the palea); 2-keeled (with the keels very poorly developed).
	www.biologie.uni-hamburg.de /b-online/delta/grass/www/pentasch.htm (856 words)

	Site-specific grasses and herbs
		Three to five flowered spikelets, 4.5-7 mm long, laterally contracted, green, mostly coated purple, rachilla between florets 1 mm long, in upper half with 0.5 mm long stiff hairs.
		Lemma five-veined, 3.6-4 mm long, slightly keeled, apically acuminate, at least lower ones expiring in 0.3-1 mm long awns.
		Palea two-veined, almost as long as lemma, oblong-lanceolate, apically slightly notched; in-between keels short hair, keels with very short, acute, bristly hair.
	www.fao.org /docrep/007/y5576e/y5576e09.htm (904 words)

	Experiments and results
		In each of the five runs, the training examples were chosen randomly (a different choice for each of the five runs).
		The average accuracies on unseen examples for the five runs with smaller training sets are 99.3 (0.1)%, 94.4 (3.3)%, and 85.0 (2.4)%, respectively (the numbers in brackets are the standard deviations).
		These accuracies are as would be expected from the number of 'rules' as discussed in Section 2, i.e., 10 for the feminine, 11 for neuter, and 24 for masculine.
	nl.ijs.si /et/Bib/ECML97/node4.html (1065 words)

	Bailey Seed Company, Inc.
		Ligule: Truncate, membranous, short, 0.3 to 1.2 mm.
		Seed: The seed with lemmas has the general shape of a barley grain, but narrower and flatter.
		Transparent lemma and palea which usually, but not always, adhere to caryopsis.
	www.baileyseed.com /infoidentification.asp (2818 words)

	Wheat- Triticum species
		The flower consists of two outer membranous tissues, one termed lemma and one palea, which enclose the stamens and the single ovary which develops into the seed or kernel.
		In most wheats the lemmas and paleas are separated from the kernels in threshing - forming the chaff.
		This is an early maturing spring wheat with short, stiff stems.
	www.hort.purdue.edu /newcrop/crops/wheat.html (2108 words)

	Grass Genera of the World - Echinaria Desf.
		Glumes two; relatively large (membranous); very unequal to more or less equal; shorter than the spikelets; long relative to the adjacent lemmas; mucronate to awned (the lower with 2–5 veins excurrent as awns, the upper with an excurrent midrib); carinate.
		Lemmas decidedly firmer than the glumes (leathery); not becoming indurated; awned.
		Fruit free from both lemma and palea; small (2 mm long); not noticeably compressed; with hairs confined to a terminal tuft.
	delta-intkey.com /grass/www/echinari.htm (508 words)

	Persian Darnel: Identification, Biology and Ecology
		The seed is enclosed in the lemma and palea that remain on the seed when threshed.
		The narrow lemma has a slender and more or less straight awn attached at the tip, and the awn is equal to the lemma in length.
		Lemma – The lower bract of the floret that subtends the grass flower and palea.
	www.montana.edu /wwwpb/pubs/mt200411.html (1750 words)

	Wild Rice
		Plants are five to six ft tall and can have up to 50 tillers per plant.
		The grains with the palea and lemma (hulls) removed, range from 0.3 to 0.6 in.
		If the seed will be stored, even if for a short time, it must be placed in water to assure germination.
	www.hort.purdue.edu /newcrop/afcm/wildrice.html (9267 words)

	On a Generalization of Perfect Numbers
		The first picture-perfect number (ppn, for short) is 6, the first perfect number; but since 6 and its proper divisors are single digit, it is trivially picture-perfect.
		The proof is due to Andersen, except for the proof of Andersen’s lemma, which I have provided.
		Assuming for the meantime the validity of the lemma, suppose that p is prime.
	jlpe.tripod.com /ppn/ppn.htm (3342 words)

	Setaria genus (Site not responding. Last check: 2007-10-12)
		Spikelets ellipsoid to ovoid, glabrous, lack awns, consist of 2 short glumes, a sterile lemma (sterile floret), and a fertile floret.
		Knotroot foxtail is a native perennial with short, knotty rhizomes.
		African bristlegrass is an uncommon wetland perennial with short rhizomes.
	www.cdfa.ca.gov /phpps/ipc/weedinfo/setaria.htm (1207 words)

	POET LAUREATE TSEGAYE GABRE
		All told, five of his Amharic plays were banned in the 1960’s.
		Of the five Amharic plays produced by Poet Laureate Tsegaye between 1974 and 1979, three of them —Ha Hu Besedst Wer (ABC in Six Months), Inat Alem Tenu (adapted from Bertold Brecht’s Mother Courage) and Melekte Wez Ader (Message of the Worker) were banned.
		I was imprisoned by the past governments, in connection with my creative works; and now I am “discreetely” pensioned away by the present government and abused publicly by its official and semi-official media again in connection with my literary works.
	www.ethiopians.com /tsegaye (5012 words)

	BioMed Central \| Full text \| DOTS improves treatment outcomes and service coverage for tuberculosis in South Ethiopia: ...
		Population coverage by DOTS reached 75% in 2001, and the proportion of patients treated with short course chemotherapy increased from 7% in 1994 to 97% in 2001.
		Treatment failure was five times higher among cases that received re-treatment for previous failure compared to new cases of PTB+ (6.4% vs. 1.2%; p < 0.001); however, both groups had comparable treatment success, mainly due to a lower defaulter rate among failure cases (24% vs. 29%).
		This calls for some case detection improvement initiatives to be in place as the proportion of TB cases detected and cured under DOTS is one of the health-related indicators of the millennium development goals [24].
	www.biomedcentral.com /1471-2458/5/62 (4273 words)

	Setaria porphyrantha
		A tufted perennial on a short rhizome, 60-150 cm high.
		Culms geniculate, ascending; somewhat stout below; round, smooth and glabrous with a ring of short, silvery hairs at the insertion of the sheaths and the top of the peduncle.
		Glumes membranous, one-third to one-half the length of the spikelet, five- to seven-nerved.
	www.fao.org /ag/AGP/AGPC/doc/Gbase/data/pf000315.htm (253 words)

	Theorem
		Lemma 2.5 is then easily proven by computing
		in a straightforward manner for each of the five cases in the lemma listed on the right.
		Lemma 2.5 further implies that all but possibly the first number in this segment must be congruent to 2 mod 3.
	www.sju.edu /~dhecker/FinalDraft1.htm (1134 words)

	Writing a Math Phase Two Paper
		Finally, in the appendix, we deal with the use of such terms as lemma, proposition, and definition, which are common in treatments of advanced mathematics.
		If the definition is short, then include it in the same sentence, preceding it by ``or'' or setting it off by commas or parentheses.
		Thus a lemma never has a corollary, although a lemma may be used, on occasion, in deriving a corollary.
	www.mit.edu /course/other/mathp2/www/piil.html (5471 words)

	Conclusion
		The corpus of the five screenplays is made up of the entire dialogues among the characters in the five screenplays.
		The researcher starts her study with the horizontal comparison of the five subcorpora (as they are the focus of the study).
		An additional column of the corpus of the five screenplays, normed to the same text length as the five subcorpora, is added for reference.
	www.chss.montclair.edu /~sotillos/Julie'sResearch1.html (4549 words)

	Short Definitions
		The problem with these chemicals is that, although they can bring out the writing in the short term, they destroy the manuscript in the slightly longer term.
		Notice that a lacuna always refers to a portion of a manuscript which has been lost (due to the disappearance of leaves or the effects of water or trimming or whatever); it should not be used to refer to a section of the text which never was found in a manuscript.
		In textual criticism, "lemma" usually is used to describe the text of a running commentary or commentary manuscript.
	www.skypoint.com /~waltzmn/ShortDefs.html (7578 words)

	A Brief Introduction to Ancient Planetary Models
		The animations illustrate the models of planetary motion found in the Almagest, by Claudius Ptolemy, and some of the models formulated by Arabic astronomers that correct some of the (as felt at the time) theoretical shortcomings of the Almagest models.
		Thus while the ordinary stars maintained fixed positions in the sky relative to each other, the seven planets were observed to move relative to each other and to the fixed stars.
		The model is still geocentric, the large circle is now centered on the tip of the short vector, and the short vector still points in a direction parallel to the mean Sun.
	www.csit.fsu.edu /~dduke/annotations.htm (1757 words)

	Picture-Perfect Numbers and Other Digit-Reversal Diversions
		Andersen’s lemma: if p (not necessarily prime) is of the abovementioned form 140z10n89, then reverse(57p) = 170 + reverse(p) + reverse(3p) + reverse(19p).
		Assuming the validity of the lemma, suppose that p is prime.
		With the lemma proved, suppose now that n is in the OEIS sequence.
	jlpe.tripod.com /ppn/ppnpaper.htm (3490 words)

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