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Atlas (topology)

In mathematics topology, one describes a manifold using an atlas. An atlas consists of individual charts that speaking, describe individual regions of the manifold. If the manifold is the surface of the Earth an atlas has its more common meaning. In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundles and other fibre bundles; the definition of an atlas depends on the notion of a chart. A chart for a topological space M is a homeomorphism φ from an open subset U of M to an open subset of a Euclidean space; the chart is traditionally recorded as the ordered pair. An atlas for a topological space M is an indexed family of charts on M which covers M. If the codomain of each chart is the n-dimensional Euclidean space M is said to be an n-dimensional manifold; the plural of atlas is atlases. An atlas i ∈ I on an n -dimensional manifold M is called an adequate atlas if the image of each chart is either R n or R + n, i ∈ I is a locally finite open cover of M, M = ⋃ i ∈ I φ i − 1, where B 1 is the open ball of radius 1 centered at the origin and R + n is the closed half space.

Every second-countable manifold admits an adequate atlas. Moreover, if V = j ∈ J is an open covering of the second-countable manifold M there is an adequate atlas i ∈ I on M such that i ∈ I is a refinement of V. A transition map provides a way of comparing two charts of an atlas. To make this comparison, we consider the composition of one chart with the inverse of the other; this composition is not well-defined unless we restrict both charts to the intersection of their domains of definition. To be more precise, suppose that and are two charts for a manifold M such that U α ∩ U β is non-empty; the transition map τ α, β: φ α → φ β is the map defined by τ α, β = φ β ∘ φ α − 1. Note that since φ α and φ β are both homeomorphisms, the transition map τ α, β is a homeomorphism. One desires more structure on a manifold than the topological structure. For example, if one would like an unambiguous notion of


Cryphonectria is a fungal genus in the order Diaporthales. The most well-known and well-studied species in the genus is Cryphonectria parasitica, the species which causes chestnut blight; the genus was, for a time, considered synonymous with Endothia, but the two are now recognised as distinct. Taxonomic studies in 2006 limited the genus to four species, but a fifth, Cryphonectria naterciae, was described in 2011 from Portugal. Cryphonectria abscondita Cryphonectria acaciarum Cryphonectria cubensis Cryphonectria decipiens Cryphonectria japonica Cryphonectria macrospora Cryphonectria moriformis Cryphonectria naterciae Cryphonectria nitschkei Cryphonectria parasitica Cryphonectria variicolorAccording to Chestnut blight was first discovered in North America in 1904 on Castanea dentata. By the 1940s it had killed most wild American chestnut trees, which were one of the most abundant species in the eastern U. S; the infection takes place through bark wounds. In the early stage, clear yellow-brown spots appear on the young twigs.

In the next stage the cambium layer is infected, the tree trunk becomes disformed, the split bark parts start to swell as parasitic fungus produces more peridermia and yellow colored pycnidia start to appear on the bark. The tree's leaves wilt and branches start dying off; the release of fungal spores lasts through the whole vegetative season

White Pongo

White Pongo known as Adventure Unlimited in the United Kingdom, is a 1945 American film directed by Sam Newfield. In the jungles of the Belgian Congo, a group of natives are dancing around a great fire with a human sacrifice named Gunderson, They are attacked by an albino gorilla called the White Pongo. During the attack an elderly scientist who lives with the tribe frees Gunderson and gives him his deceased colleague's diary that contains his findings on the white gorilla. Gunderson arrives in a nearby settlement in a feverish state; the diary has seemed to prove that the white gorilla of myth exists that local anthropologists believe is the evolutionary missing link. A safari is formed with a group of individuals, several of whom have their own nefarious reasons for going, but one is an undercover Rhodesian Secret Serviceman; the group battle one another. In the climax, the White Pongo, stalking the group, kidnaps one of the safari members and duels with a normal-colored gorilla; the rest of the safari rescue their comrade.

The White Pongo comes out victorious over his rival, but is wounded by the safari and taken with them to the boat back to London. Richard Fraser as Geoffrey Bishop Maris Wrixon as Pamela Bragdon Lionel Royce as Peter Van Dorn Al Eben as Hans Kroegert Gordon Richards as Sir Harry Bragdon Michael Dyne as Clive Carswell George Lloyd as Baxter Larry Steers as Doctor Kent Milton Kibbee as Gunderson Egon Brecher as Dr. Gerig Joel Fluellen as Mumbo JumboUncredited: Ray "Crash" Corrigan as the White Pongo. Ray Corrigan, a Western actor, was an experienced "gorilla man," and played a similar role earlier that year in The White Gorilla, where he starred both as a jungle explorer and as the gorilla; the White Pongo costume was years brought out of storage to be used as the monster suit in Jerry Warren's 1956 Abominable Snowman movie, Man Beast. Leo Erdody was the musical director. White Pongo on IMDb White Pongo is available for free download at the Internet Archive Review of film at Variety

Lamentatio sanctae matris ecclesiae Constantinopolitanae

Lamentatio sanctae matris ecclesiae Constantinopolitanae is a motet by the Renaissance composer Guillaume Dufay. Its topic is a lament of the fall of Constantinople to the Ottoman Turks in 1453; because of its Byzantine subject matter, it is sometimes grouped together with Vasilissa ergo gaude, Apostolus gloriosus and Balsamus et munda cera as one of Dufay's "Byzantine motets". The motet belongs to a series of four Lamentations for the fall of Constantinople composed by Dufay and mentioned for the first time in one of his letters addressed to Piero and Giovanni de' Medici; the letter must have been written on February 22, 1454, although the exact year is not specified in the text. The musical score and the texts of the French Chanson and the Latin Cantus Firmus are found in two contemporary manuscript sources: Codex 2794 of the Biblioteca Riccardiana in Florence, MS 871N in Montecassino, it is believed to have been composed in the context of the "Feast of the Pheasant", a banquet and extravagant political show organised in Lille by Philip the Good of Burgundy on 17 February 1454.

Its purpose was to propagate the idea of a crusade for the recapture of the city. It is, unclear whether the piece was performed on that occasion. There are contemporary accounts of the banquet, which name and describe in much detail various pieces of music performed at it, but they fail to mention this piece. At one point in the show, according to the chronicles, an actor dressed as a woman in white satin clothes, personifying the Church of Constantinople entered the hall of the banquet riding on an elephant, to recite a "complaint and lamentation in a piteous and feminine voice", it has been surmised. The piece is a four-voice chanson-motet, it follows the structure of a motet insofar as it has a cantus firmus line based on Gregorian plainchant in its tenor voice, but the structure of a chanson insofar as there is only one other text sung, in French, in the upper voices. The text is a poem in Middle French, presenting the voice of a mother lamenting the sufferings of her son and addressing God as her son's father – evoking both the image of the Virgin Mary in the Lamentation of Christ, the personification of the Church as the mystical mother of the faithful.

The tenor text is a modified quotation taken from the Book of Lamentations, the biblical lament about the fall of Jerusalem: Omnes amici ejus spreverunt eam, non est qui consoletur eam ex omnibus caris ejus. Online performance by Collegium Cantorum, Washington. Online sheet music by M. A. B. Soloists

Abbotts Moss Nature Reserve

Abbotts Moss is a 12-hectare nature reserve near Delamere Forest, northwest of Winsford, Cheshire. It is managed by the Cheshire Wildlife Trust under lease from the Forestry Commission and lies within a larger Site of Special Scientific Interest; the reserve is south of the A556 road near Sandiway and is divided in two by the Whitegate Way, a former railway line now used as a footpath and bridleway. The SSSI citation notes that the site is an acidic wetland of particular importance because of two mature Schwingmoors, namely South Moss and Shemmy Moss. A Schwingmoor or quaking bog occurs when plants such as Sphagnum mosses and cotton grass Eriophorum sp. colonise the surface of a waterbody and form a floating mat of vegetation. Locally uncommon plants growing here include common cottongrass Eriophorum angustifolium, cranberry Vaccinium oxycoccos, round-leaved sundew Drosera rotundifolia, crowberry Empetrum nigrum, hare’s-tail cottongrass Eriophorum vaginatum, bog rosemary Andromeda polifolia, white beak-sedge Rhynchospora alba and the carnivorous lesser bladderwort Utricularia minor.

Dragonflies include the nationally rare white-faced darter Leucorrhinia dubia and the locally uncommon downy emerald Cordulia aenea and black darter Sympetrum danae. Abbotts Moss is one of only two sites in Cheshire. Eurasian woodcock Scolopax rusticola breed, as do common redstart Phoenicurus phoenicurus and tree pipit Anthus trivialis. Over 150 species of spider have been recorded within the reserve

Bob Etheridge

Bobby Ray "Bob" Etheridge is an American politician, the U. S. Representative for North Carolina's 2nd congressional district from 1997 to 2011, he is the executive director of the North Carolina office of the U. S. Farm Service Agency, he served as a county commissioner, state representative and state superintendent of public instruction. He is a member of the Democratic Party and was an unsuccessful candidate for the Democratic nomination for Governor of North Carolina in 2012. Born in Sampson County, North Carolina, Etheridge attended the Cleveland School and was a high school basketball standout, he attended Campbell University on an athletic scholarship and became the first member of his family to earn a diploma when he received a business degree in 1965. He served in the United States Army from 1965 to 1967, he has completed graduate work in the field of economics. Etheridge is a part-time tobacco farmer and hardware store owner. Etheridge began his political career as a Harnett County commissioner from 1973 through 1976.

He was elected in 1978 to the North Carolina House of Representatives, served five terms and rose to chair the House Appropriations Committee. Having gained a reputation for his strong stances on educational issues, he was elected in 1988 and served two terms as North Carolina Superintendent of Public Instruction. 1996Ethridge ran for North Carolina's 2nd congressional district and defeated incumbent Republican U. S. Congressman David Funderburk 53%–46%. 1998He won re-election to a second term with 57% of the vote. 2000He won re-election to a third term with 58% of the vote. 2002–2008During this time period, he never won re-election with less than 65% of the vote. 2010 Etheridge was challenged by Republican nominee Renee Ellmers and Libertarian nominee Tom Rose. Ellmers defeated Etheridge 49.5%–48.7%. Etheridge requested a recount of the vote. On November 19, 2010, the State Board of Elections director Gary Bartlett confirmed Ellmers won by about 1,483 votes; that day, Etheridge conceded the election.

Etheridge served on the Agriculture and Homeland Security committees. He has focused on farm issues, educational matters, providing a balanced budget. Alternative EnergyIn 2006, Etheridge joined U. S. Congresswoman Stephanie Herseth in proposing increased research and development of biofuels to reduce the United States' dependence on foreign oil. Health Care ReformEtheridge voted to pass the Affordable Health Care for America Act in November 2009 and the Patient Protection and Affordable Care Act. "Who are you?" incidentIn June 2010, Etheridge was approached by two young men on a Washington, D. C. sidewalk. The pair, who identified themselves as students working on a project, asked Etheridge if he "fully supported the Obama agenda" while videorecording his response. In the video, Etheridge first says "Who are you?" then is seen grabbing one of the young men by the wrists and back of the shirt, while asking the young men who they were. The young men responded that they were "students working on a project".

One of them is heard asking the congressman three times to let go of him while the Congressman continued to hold on to him. Etheridge apologized for the incident in a statement saying "I and profoundly regret my reaction, I apologize to all involved". Etheridge called a press conference, he refused to speculate on the motivation of those involved and said that it had been a "long day". An article in The New York Times subsequently stated that unnamed "Republican political strategists acknowledge they were behind the episode."Political analysts commented on the potential effect of this confrontation on Etheridge's chances of re-election against Republican candidate Renee Ellmers. Subsequently, on June 18, a 32-year-old man, Brandon Leslie, said he had been a victim of a similar incident occurring in 1996 in which Etheridge grabbed him when he was a high school student; that report was disputed by the retired principal who stated that "the student was in the wrong". 111th CongressCommittee on the Budget Committee on Ways and Means Subcommittee on Trade Subcommittee on Oversight New Democrat Coalition, a moderate, pro-growth organization Democratic At-Large Whip On February 1, 2011, Governor Bev Perdue announced her appointment of Etheridge as head of the North Carolina Office of Economic Recovery and Investment, replacing Dempsey Benton, which oversees funds to the state from the American Recovery and Reinvestment Act of 2009.

In February 2012, Etheridge announced his candidacy for Governor of North Carolina. He lost the Democratic primary to Lt. Gov. Walter H. Dalton. After Dalton lost to Pat McCrory in the general election, Etheridge came within a few votes of being elected chairman of the North Carolina Democratic Party in 2013 though he did not publicly campaign for the post. Etheridge and his wife Faye have eight grandchildren. A Presbyterian, he and his wife are active in both teach Sunday School. For his decades-long work for the Boy Scouts of America, Etheridge was awarded the Silver Beaver Award, he has served as Grand Orator. North Carolina Democratic Party Bob Etheridge for Governor official campaign site Biography at the Biographical Directory of the United States Congress Profile at Vote Smart Financial information at the Federal Election Commission New Democrat Coalition