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Topic: The Sheaf

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	Professional Website Sheaf Solutions
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		Call 1-866-242-7944 for a free consultation on how Sheaf can design your website to generate more sales and/or donations.
	www.sheafsolutions.com (555 words)

	Sheaf (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, a sheaf F on a topological space X is something that assigns a structure F(U) (such as a set, group, or ring) to each open set U of X.
		This fails to be a sheaf because while there are many local holomorphic functions, the only functions which are bounded and holomorphic on the whole complex plane are the constant functions (see Liouville's theorem).
		In early developments of sheaf theory, it was shown that giving a sheaf F on X is as good as giving a certain topological space E together with a continuous map from E to X.
	en.wikipedia.org /wiki/Sheaf_space (2973 words)

	Coherent sheaf - Wikipedia, the free encyclopedia
		In mathematics, especially in algebraic geometry and the theory of complex manifolds, a coherent sheaf F on a locally ringed space X is a sheaf isomorphic with the cokernel of a morphism of O
		For a sheaf of rings R, a sheaf F of R-modules is said to be quasi-coherent if it has a local presentation, i.e.
		In the basic work of Serre, it was shown first that compact complex manifolds have the property that their sheaf cohomology for any coherent sheaf consists of vector spaces of finite dimension.
	en.wikipedia.org /wiki/Coherent_sheaf (700 words)

	PlanetMath: sheaf
		, we define a sheaf to be a presheaf
		is actually a sheaf of rings, because continuous functions are uniquely specified by their values on an open cover.
		This is version 9 of sheaf, born on 2002-04-28, modified 2003-12-08.
	planetmath.org /encyclopedia/Sheaf.html (708 words)

	29. The Wave-Sheaf
		With respect to quality, it was a sheaf of barley; as to its quantity, it was a single sheaf; or, however, such a quantity as only one omer of barley was taken from it, and waved before the Lord by the priest.
		This sheaf being brought to court, was threshed, winnowed, dried, and parched by the fire, and ground in a mill; all which set forth, in a lively manner, the dolorous sufferings of our Lord.
		The sheaf being threshed, was expressive of his being smitten by men; of his being buffeted and scourged, by the order of the Roman Governor, by the soldiers; all in perfect agreement with the prophecy, that they should smite the Judge of Israel with a rod upon the cheek.
	www.pbministries.org /books/gill/Sermons&Tracts/sermon_29.htm (5001 words)

	sheaf - Wiktionary
		A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.
		The sheaf of arrows shook and rattled in the case.
		To gather and bind into a sheaf; to make into sheaves; as, to sheaf wheat.
	en.wiktionary.org /wiki/sheaf (222 words)

	Sheaf at opensource encyclopedia (Site not responding. Last check: )
		The first origins of sheaf theory are hard to pin down - they may be co-extensive with the idea of analytic continuation.
		The condition that F be a sheaf is exactly that F(U) is the limit of the rest of the diagram.
		More precisely: to every sheaf F of sets on X there exists a local homeomorphism π: E → X such that F is isomorphic (in the sense of natural isomorphism, the isomorphism concept for functors) to the sheaf of sections of π that was described in the example section above.
	www.wiki.tatet.com /Sheaf.html (2627 words)

	PlanetMath: sheaf cohomology
		In this case, it does not matter if we take the derived functors in the category of sheaves of abelian groups or coherent sheaves.
		Sheaf cohomology can be explicitly calculated using Čech cohomology.
		This is version 10 of sheaf cohomology, born on 2003-08-14, modified 2005-05-15.
	planetmath.org /encyclopedia/SheafCohomology.html (220 words)

	Feasts4b
		The Sheaf of Firstfruits is typical and prophetic of the resurrection of the Lord Jesus Christ, and his Ascension to the Father, as the "firstfruits" of the coming resurrection of all the saints.
		This one sheaf represents the Lord Jesus Christ (note: Joseph, the type of the rejected beloved Son, dreams of the eleven sheaves bowing to his one sheaf - Genesis 37:5-11).
		Just as the one ripe sheaf testified to Israel that a great harvest was soon to be reaped, so did the resurrection of Christ testify to the fact that soon after there would be a great spiritual harvest of souls.
	www.churchlink.com.au /churchlink/bible_studies/feasts/feasts4.html (749 words)

	Wave Sheaf -- What We Found
		As the wave sheaf was raised and then lowered Sunday morning, so Messiah ascended to heaven that Sunday morning as the Wave Sheaf Offering for us, yet He returned to earth that same day (John 20:16-19; Matthew 28:9-10).
		When it came time to harvest the spring crop, the first sheaf of the firstfruits had to be offered to God first, before the rest of the harvest could be gathered in.
		He is to wave [elevate] the sheaf [omer] before the LORD so it will be accepted on your behalf; the priest is to wave [elevate] it on the day after the Sabbath'" (verses 10-11).
	livingtheway.org /wave2.html (5422 words)

	US Artllery - Fire Patterns (Sheafs)
		A sheaf is the planes of fire of a group of weapons.
		Open sheaf is a regular sheaf where the spacing is chosen so the sheaf has maximum width (given the burst area of each shell) without any gaps in between.
		Specially-shaped sheafs can be arranged under certain circumstances, such as strangely-shaped targets, point targets, barrages, etc, but this would be the exception.
	www.gruntonline.com /US_Forces/US_Artillery/arty2.htm (535 words)

	NASGA Message Board - No Sheaf in MWC (Site not responding. Last check: )
		JWC III I have heard it said that teh sheaf is a big crowd favorite and I think you are right, but I don't see the need to take away one of the stones or hammers to toss the sheaf.
		Posted - 06/16/2004 : 5:27:03 PM Glad to see the mere mention of the word "Sheaf" still elicits the same response as dropping a cat in a dog pound.....and don't be jealous of the Mighty, Mighty Sheaf Gawds, it' unmanly to be jealous..
		About 90% of the throwers don't mind throwing the sheaf, but it's the noisy 10% who are getting their way this year.
	www.nasgaweb.com /messageboard/topic.asp?TOPIC_ID=3117 (1993 words)

	Understanding God's Command for the Wave Sheaf
		The wave sheaf was originally offered by the children of Israel in the year that they crossed the Jordan River and entered the land God had promised to give them.
		Since the day of the wave sheaf was both "the morrow after the Sabbath" and "the morrow after the Passover," there is no question that the Passover fell on a weekly Sabbath in that particular year.
		Thus the sheaf of Joshua 5 was waved on the 15th of Abib, the earliest possible date.
	www.cbcg.org /wavesheaf.htm (9326 words)

	The Wave Sheaf Offering (No. 106b)
		The Wave Sheaf Offering needs to be kept in order to understand the full implications of Christ’s sacrifice, and the power that he was given in terms of his resurrection from the dead.
		The Wave Sheaf after the dispersion was understood to be waved on the first Holy Day of Unleavened Bread, and Pentecost was then determined to fall on a fixed date, namely, Sivan 6.
		The sacrifice of Messiah was to be extended to the Egyptians and, hence, salvation was to be of the Gentiles.
	www.ccg.org /english/s/p106b.html (7884 words)

	FM 23-91 Chptr 4 Major Concerns of the Fire Direction Center
		With the parallel sheaf, the distance between impacts of rounds from two or more mortars is the same as the distance between the mortars.
		The converged sheaf (Figure 4-2) is normally used on a point target such as a bunker or machine gun position.
		With the open sheaf, the distance between impacts of rounds from two or more mortars is half again the distance between the bursts of the rounds in a standard sheaf.
	www.globalsecurity.org /military/library/policy/army/fm/23-91/ch4.htm (7358 words)

	The Wave-Sheaf Offering
		No one was to eat any of the grain of the harvest until the first sheaf of the harvest was brought to the priest, who in turn waved it before God.
		This first sheaf of grain was called the "firstfruits" (verse 10).
		The wave sheaf is symbolic of Jesus Christ.
	www.ucgstp.org /lit/gn/gn004/gn004f02.htm (2272 words)

	Tailie.com - Sheaf (Site not responding. Last check: )
		Sheaf is both a quality -- to "have sheaf" is to be a Good Thing(tm) -- and an intimate bodily item.
		If that is still not enough, they may get sheaf in more clandestine ways, such as stealing it from you, while you are sleeping.
		Since billies are not ordinary huskies (see the physics section), their sheaves are infinitely expandable and extendable, and they can fit anything inside them, including, but not limited to, other billies.
	www.tailie.com /billie/sheaf.html (125 words)

	Sheaf Stout - Wikipedia, the free encyclopedia
		Look for Sheaf Stout in Wiktionary, our sister dictionary project.
		Look for Sheaf Stout in the Commons, our repository for free images, music, sound, and video.
		Check for Sheaf Stout in the deletion log, or visit its deletion vote page if it exists.
	en.wikipedia.org /wiki/Sheaf_Stout (145 words)

	Waving a Sheaf of Barley
		The reason for counting is that the waving of the sheaf (omer) varies on the day of the month as the Sabbath during the days of unleavened bread varies on the day of the month.
		The wave sheaf and the Feast of Weeks are always on the first day of the week but we must count to determine which day of the month the Feast of Weeks occurs.
		The waving of a sheaf of green barley during the days of unleavened bread is to seek a blessing for the crop.
	www.uhcg.org /Festivals/Wave-Sheaf.html (3829 words)

	The Mystery of the WAVE SHEAF OFFERING Revealed at Last!
		Now, this Passover sheaf was reaped in public the evening before it was offered, and it was to witness this ceremony that the crowd gathered around 'the elders,' who took care that all was done according to traditionary ordinance" (p.256-57).
		Already, on the 14th of Nisan, the spot whence the first sheaf was to be reaped had been marked out by delegates from the Sanhedrin, by tying together in bundles, while still standing, the barley that was to be cut down.
		When the time for cutting the sheaf had arrived, that is, on the EVENING OF THE 15TH OF NISAN (even though it were a Sabbath), just as the sun went down, three men, each with a sickle and basket, formally set to work.
	www.triumphpro.com /the_mystery_of_the_wave_sheaf_offering_revealed_at_last!.htm (7149 words)

	Amazon.com: Sheaf Theory (Graduate Texts in Mathematics): Books: Glen E. Bredon (Site not responding. Last check: )
		The fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces.
		It would be very helpful to the newcomer to sheaf theory if the author could explain why the functor from open sets to abelian groups is a contravariant functor, instead of a covariant one.
		Sheaf cohomology is compared with other cohomology theories in the next chapter.
	www.amazon.com /exec/obidos/tg/detail/-/0387949054?v=glance (1182 words)

	Sheaf of the Firstfruits
		The word "sheaf" gives us the idea of a bundle of wheat, but such was not the case.
		The grain that was associated with the sheaf (omer) of firstfruits was barley.
		The sheaf (omer) of firstfruits consisting of the barley, the food for the poor and animals, is a type of
	members.cox.net /thomasahobbs/yea_20.htm (4583 words)

	sheaf
		Now, when Assunta found her one morning, pacing the long, frescoed hall, by the side of the running water, and put a whole sheaf of letters into her hand, Daphne looked at them cautiously, and started to open one, then lost her courage and held them for a while to get used to them.
		Finally she went upstairs and changed her dress, putting on her short skirt and red felt hat, and walked out into the highway with Hermes skipping after her.
		"Uncle Quincey brought home a whole sheaf of those women whom he said he'd met; and one of my cousins, who was educated at Heidelberg, used to walk in his sleep, as it were, all over Europe." "Did you notice anything queer in his eyes, Miss Keene?" asked Miss Chubb vivaciously.
	www.cooldictionary.com /words/sheaf.word (470 words)

	The SECRET of the "Wave Sheaf"
		Various end-time offshoots of the Worldwide Church of God claim that Yeshua the Messiah was the spiritual antitype of the "wave sheaf" which was offered by the high priest on the "day after the Sabbath" during the feast of Unleavened Bread (Lev.23:10-11, 15-16).
		Just as the new grain could not be eaten until the wave sheaf was offered, neither could those called by YEHOVAH God begin the process of salvation until the risen Messiah had "waved" the sheaf or omer before his Father to be accepted for them.
		The true fulfillment of the wave sheaf or "omer" is the 144,000, which are the FIRSTFRUITS of the harvest, then all of those called by YEHOVAH down through the centuries to the present time.
	www.hope-of-israel.org /wave16.htm (4161 words)

	Emdros Programmer's Reference Guide (Stable): Sheaf (Site not responding. Last check: )
		The sheaf is the datastructure returned by the "SELECT (ALLFOCUS) OBJECTS" query.
		A matched_object may have an inner sheaf, which makes the datastructure recursive.
		A matched_object corresponds to an object_block(_first) or (opt_)gap_block in a topographic MQL query.
	emdros.org /progref/page.php?pid=1138 (183 words)

	Pentecost 2001-Ritenbaugh's Errors: Part 2
		John offers no evidence that the symbolism of the wave sheaf is contradicted when the wave sheaf day immediately follows the Passover, yet he concludes that the symbolism is violated.
		Whether the wave sheaf day immediately follows the Passover day or falls 72 hours after Passover, as in the year of Christ’s death, is irrelevant to the question of whether or not the weekly Sabbath from which we count to Pentecost must fall within the Days of Unleavened Bread.
		John argues that the wave sheaf symbolizes the beginning of the harvest, which entails labor, and therefore should be offered on a common workday—never on a Sabbath, which symbolizes rest from labor.
	www.cbcg.org /ritenbaugh_2.htm (5140 words)

	Sheaf Dining Chair Gallery, Sheaf Dining Chair, Oak Chair, Oak Dining Chair, Sheaf Dining Chair
		Sheaf Dining Chair Gallery, Sheaf Dining Chair, Oak Chair, Oak Dining Chair, Sheaf Dining Chair
		Sheaf Chairs, Oak Sheaf Chairs, Sheaf Dining chairs.
		These elegant, stylish sheaf chairs are sure to be the pride and joy of your home plus the envy of all your neighbors and friends.
	www.handcraftedtable.com /All_Chairs/Sheaf_Chairs/All_Sheaf_Chairs.htm (144 words)

	What is this Wave Sheaf Sunday thing
		Our understanding of the importance of the wave sheaf in relation to both Christ’s acceptance and the count to Pentecost should lead us to see that the gospel writers were establishing the exact day of Christ’s acceptance.
		Lev 23:11 'He shall wave the sheaf before the LORD, to be accepted on your behalf; on the day after the Sabbath the priest shall wave it.
		Leviticus 23:14 and Deuteronomy 16:9: The sheaf was to be waved before both harvesting and eating the crop.
	www.ironsharpeningiron.com /pentecost16.htm (2535 words)

	BBC - South Yorkshire Greedy Cow - The Sheaf View (Site not responding. Last check: )
		It's a lovely lovely pub, which could probably sell more beer than it actually does, 'cause its popularity means there's always quite a deep queue at the bar.
		You didn't mention how cheap the real ale is! (In fact I have a sneaking suspicion that they charge more for the lager to subsidise it!) Prices recently went up slightly, but you can still get a top quality pint for under 2 quid, which is pretty good these days.
		I visited Sheaf View yesterday and was ABSOLUTELY delighted by the cherry beer (I still am!).
	www.bbc.co.uk /southyorkshire/greedycow/pubs/heeley/sheaf_view.shtml (615 words)

	Passover: Sheaf of First Fruits
		The Priest was then to take this one sheaf and wave it before the Lord in His house.
		This one Barley Sheaf was to be taken to the house of the Lord and waved in presentation before Jehovah.
		He shall wave the sheaf before the LORD, to be accepted on your behalf; on the day after the Sabbath the priest shall wave it.
	www.rhm-net.org /resources/passover_sheaf_of_first_fruits.htm (2108 words)

	The Sheaf Fraser Road Millhouses Sheffield
		Access is via the entances on Fraser Road or from the car park at the rear which offers Disabled access, The car park also has CCTV for security.
		A great time was had by all, Photos of the day can be seen on the Gallery page.
		The Sheaf is now changing over the coming weeks, New entertainment and new projects, We hope you will come and join us on this interesting and fun journey in making The Sheaf once again a focal point in the community of Woodseats.
	www.thesheaf.me.uk (304 words)

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