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1055411 | Short Stories (Harry Chapin album) | https://en.wikipedia.org/w/index.php?title=Short%20Stories%20(Harry%20Chapin%20album) | Short Stories (Harry Chapin album)
Short Stories (Harry Chapin album)
Short Stories is the third studio album by the American singer-songwriter Harry Chapin, released in 1973. (see 1973 in music). "W·O·L·D", "Mr Tanner" and "Mail Order Annie" remained amongst his most popular work for the rest of his life. "W·O·L·D" went to number 36 on the Billboard Hot 100 chart and had great commercial success in the top 10 in other countries such as Canada and the Netherlands.
# Personnel.
- Harry Chapin – guitar, vocals
- Dave Armstrong – harmonica
- Tomi Lee Bradley – vocals
- Bobby Carlin – drums
- Jeanne French – vocals
- Paul Leka – keyboards
- Michael Masters – cello
- Ronald Palmer – guitar, vocals
- Buddy Salzman – drums
- | 25,900 |
1055411 | Short Stories (Harry Chapin album) | https://en.wikipedia.org/w/index.php?title=Short%20Stories%20(Harry%20Chapin%20album) | Short Stories (Harry Chapin album)
rd studio album by the American singer-songwriter Harry Chapin, released in 1973. (see 1973 in music). "W·O·L·D", "Mr Tanner" and "Mail Order Annie" remained amongst his most popular work for the rest of his life. "W·O·L·D" went to number 36 on the Billboard Hot 100 chart and had great commercial success in the top 10 in other countries such as Canada and the Netherlands.
# Personnel.
- Harry Chapin – guitar, vocals
- Dave Armstrong – harmonica
- Tomi Lee Bradley – vocals
- Bobby Carlin – drums
- Jeanne French – vocals
- Paul Leka – keyboards
- Michael Masters – cello
- Ronald Palmer – guitar, vocals
- Buddy Salzman – drums
- John Wallace – bass guitar, vocals
- Tim Scott – cello | 25,901 |
1055418 | Xinyi | https://en.wikipedia.org/w/index.php?title=Xinyi | Xinyi
Xinyi
Xinyi is an atonal pinyin romanization of various Chinese words. It may refer to:
# Clothing.
- Xinyi (clothing) (), a form of undershirt worn during the Han era
# Places.
- Xinyi, Jiangsu (), a county-level city in Xuzhou, Jiangsu
- Xinyi, Guangdong (), a county-level city in Maoming, Guangdong
- Xinyi District, Taipei (), Taiwan
- Xinyi District, Keelung (), Taiwan
- Xinyi Subdistrict, Harbin (), subdivision of Daowai District, Harbin, Heilongjiang
- Xinyi Subdistrict, Hegang (), subdivision of Dongshan District, Hegang, Heilongjiang
- Xinyi Subdistrict, Xiaoyi (), subdivision of Xiaoyi, Shanxi
- Xinyi, Shandong (), town in and subdivision of Yanzhou District, Jining, Shandong
- | 25,902 |
1055418 | Xinyi | https://en.wikipedia.org/w/index.php?title=Xinyi | Xinyi
, a county-level city in Xuzhou, Jiangsu
- Xinyi, Guangdong (), a county-level city in Maoming, Guangdong
- Xinyi District, Taipei (), Taiwan
- Xinyi District, Keelung (), Taiwan
- Xinyi Subdistrict, Harbin (), subdivision of Daowai District, Harbin, Heilongjiang
- Xinyi Subdistrict, Hegang (), subdivision of Dongshan District, Hegang, Heilongjiang
- Xinyi Subdistrict, Xiaoyi (), subdivision of Xiaoyi, Shanxi
- Xinyi, Shandong (), town in and subdivision of Yanzhou District, Jining, Shandong
- Xinyi, Lishi District (), town in and subdivision of Lishi District, Lüliang, Shanxi
- Xinyi, Nantou (), township of Nantou County, Taiwan
# Companies.
- Xinyi Glass (), a glass manufacturer | 25,903 |
1055431 | Casa Calvet | https://en.wikipedia.org/w/index.php?title=Casa%20Calvet | Casa Calvet
Casa Calvet
Casa Calvet () is a building, designed by Antoni Gaudí for a textile manufacturer which served as both a commercial property (in the basement and on the ground floor) and a residence. It is located at Carrer de Casp 48, Eixample district of Barcelona. It was built between 1898 and 1900.
Gaudí scholars agree that this building is the most conventional of his works, partly because it had to be squeezed in between older structures and partly because it was sited in one of the most elegant sections of Barcelona. Its symmetry, balance and orderly rhythm are unusual for Gaudí's works. However, the curves and double gable at the top, the projecting oriel at the entrance— almost baroque | 25,904 |
1055431 | Casa Calvet | https://en.wikipedia.org/w/index.php?title=Casa%20Calvet | Casa Calvet
in its drama, and isolated witty details are "modernista" elements.
Bulging balconies alternate with smaller, shallower balconies. Mushrooms above the oriel at the center allude to the owner's favorite hobby.
Columns flanking the entrance are in the form of stacked bobbins— an allusion to the family business of textile manufacture. Lluís Permanyer claims that "the gallery at ground level is the façade's most outstanding feature, a daring combination of wrought iron and stone in which decorative historical elements such as a cypress, an olive tree, horns of plenty, and the Catalan coat of arms can be discerned".
Three sculpted heads at the top also allude to the owner: One is Sant Pere Màrtir | 25,905 |
1055431 | Casa Calvet | https://en.wikipedia.org/w/index.php?title=Casa%20Calvet | Casa Calvet
ims that "the gallery at ground level is the façade's most outstanding feature, a daring combination of wrought iron and stone in which decorative historical elements such as a cypress, an olive tree, horns of plenty, and the Catalan coat of arms can be discerned".
Three sculpted heads at the top also allude to the owner: One is Sant Pere Màrtir Calvet i Carbonell (the owner's father) and two are patron saints of Vilassar, Andreu Calvet's home town.
Between 1899 and 1906, the Arts Building Annual Award (Concurso annual de edificios artísticos) awarded modernist pieces, like the Casa Calvet, the Casa Lleó Morera and the Casa Trinxet.
# See also.
- List of Modernisme buildings in Barcelona | 25,906 |
1055399 | Barium chloride | https://en.wikipedia.org/w/index.php?title=Barium%20chloride | Barium chloride
Barium chloride
Barium chloride is the inorganic compound with the formula BaCl. It is one of the most common water-soluble salts of barium. Like most other barium salts, it is white, toxic, and imparts a yellow-green coloration to a flame. It is also hygroscopic, converting first to the dihydrate BaCl(HO). It has limited use in the laboratory and industry.
# Structure and properties.
BaCl crystallizes in two forms (polymorphs). One form has the cubic fluorite (CaF) structure and the other the orthorhombic cotunnite (PbCl) structure. Both polymorphs accommodate the preference of the large Ba ion for coordination numbers greater than six. The coordination of Ba is 8 in the fluorite structure | 25,907 |
1055399 | Barium chloride | https://en.wikipedia.org/w/index.php?title=Barium%20chloride | Barium chloride
and 9 in the cotunnite structure. When cotunnite-structure BaCl is subjected to pressures of 7–10 GPa, it transforms to a third structure, a monoclinic post-cotunnite phase. The coordination number of Ba increases from 9 to 10.
In aqueous solution BaCl behaves as a simple salt; in water it is a 1:2 electrolyte and the solution exhibits a neutral pH. Its solutions react with sulfate ion to produce a thick white precipitate of barium sulfate.
Oxalate effects a similar reaction:
When it is mixed with sodium hydroxide, it gives the dihydroxide, which is moderately soluble in water.
# Preparation.
On an industrial scale, it is prepared via a two step process from barite (barium sulfate):
This | 25,908 |
1055399 | Barium chloride | https://en.wikipedia.org/w/index.php?title=Barium%20chloride | Barium chloride
first step requires high temperatures.
In place of HCl, chlorine can be used.
Barium chloride can in principle be prepared from barium hydroxide or barium carbonate. These basic salts react with hydrochloric acid to give hydrated barium chloride.
# Uses.
Although inexpensive, barium chloride finds limited applications in the laboratory and industry. In industry, barium chloride is mainly used in the purification of brine solution in caustic chlorine plants and also in the manufacture of heat treatment salts, case hardening of steel. Its toxicity limits its applicability.
# Safety.
Barium chloride, along with other water-soluble barium salts, is highly toxic. Sodium sulfate and magnesium | 25,909 |
1055399 | Barium chloride | https://en.wikipedia.org/w/index.php?title=Barium%20chloride | Barium chloride
y and industry. In industry, barium chloride is mainly used in the purification of brine solution in caustic chlorine plants and also in the manufacture of heat treatment salts, case hardening of steel. Its toxicity limits its applicability.
# Safety.
Barium chloride, along with other water-soluble barium salts, is highly toxic. Sodium sulfate and magnesium sulfate are potential antidotes because they form barium sulfate BaSO, which is relatively non-toxic because of its insolubility.
# External links.
- International Chemical Safety Card 0614. ("anhydrous")
- International Chemical Safety Card 0615. ("dihydrate")
- Barium chloride's use in industry.
- ChemSub Online: Barium chloride. | 25,910 |
1055439 | Verities & Balderdash | https://en.wikipedia.org/w/index.php?title=Verities%20&%20Balderdash | Verities & Balderdash
Verities & Balderdash
Verities & Balderdash is the fourth studio album by the American singer/songwriter Harry Chapin, released in 1974. (see 1974 in music). "Cat's in the Cradle" was Chapin's highest charting single, finishing at #38 for the year on the 1974 Billboard year-end Hot 100 chart. The follow-up single, "I Wanna Learn a Love Song," charted on the Billboard Hot 100 Singles Chart at #44, and Billboard Adult Contemporary at #7. A promotional single, "What Made America Famous?", was released to radio stations as a 45. The album was certified gold on December 17, 1974.
The album was advertised with the slogan: "As only Harry can tell it."
The album was the only work by Chapin to | 25,911 |
1055439 | Verities & Balderdash | https://en.wikipedia.org/w/index.php?title=Verities%20&%20Balderdash | Verities & Balderdash
exclusively use professional studio musicians, rather than his touring band, as had been the case in previous projects.
# Personnel.
Band
- Harry Chapin - guitar, lead vocals
- John Tropea - acoustic guitar, sitar
- Don Payne - bass
- Allan Schwartzberg - drums
- Don Grolnick - piano, electric piano, harpsichord
- Ron Bacchiocchi - synthesizer
- Irving Spice - concertmaster
- George Simms - background vocals
- Frank Simms - background vocals
- Dave Kondziela - background vocals
- Zizi Roberts - female vocals
Production
- Ron Bacchiocchi - recording engineer
- Paul Leka - mixing
- Fred Kewley - mixing
- Glen Christensen - art direction
- Bill Hofman - illustration
- Ruth Bernal | 25,912 |
1055439 | Verities & Balderdash | https://en.wikipedia.org/w/index.php?title=Verities%20&%20Balderdash | Verities & Balderdash
s, rather than his touring band, as had been the case in previous projects.
# Personnel.
Band
- Harry Chapin - guitar, lead vocals
- John Tropea - acoustic guitar, sitar
- Don Payne - bass
- Allan Schwartzberg - drums
- Don Grolnick - piano, electric piano, harpsichord
- Ron Bacchiocchi - synthesizer
- Irving Spice - concertmaster
- George Simms - background vocals
- Frank Simms - background vocals
- Dave Kondziela - background vocals
- Zizi Roberts - female vocals
Production
- Ron Bacchiocchi - recording engineer
- Paul Leka - mixing
- Fred Kewley - mixing
- Glen Christensen - art direction
- Bill Hofman - illustration
- Ruth Bernal - photography
- Shiah Grumet - design | 25,913 |
1055436 | Crown Street railway station | https://en.wikipedia.org/w/index.php?title=Crown%20Street%20railway%20station | Crown Street railway station
Crown Street railway station
Crown Street Station was a passenger railway terminal station on Crown Street, Liverpool, England. The station was the world's first intercity passenger station, opening in 1830, also being the railway terminal station for Liverpool. Used for passengers for only six years the station was demolished as the site was converted into a goods yard. The goods yard remained in use until 1972. The location of the station is now a park with little trace of the station or goods yard.
# History.
The station opened on 15 September 1830 as the Liverpool passenger terminus of the Liverpool and Manchester Railway, the world's first public passenger line. This gave the station | 25,914 |
1055436 | Crown Street railway station | https://en.wikipedia.org/w/index.php?title=Crown%20Street%20railway%20station | Crown Street railway station
the distinction of being the world's first dedicated intercity passenger railway station as the first train ran from Liverpool. Manchester's corresponding Liverpool Road terminus station opened on the same day, being the destination of the first train from Liverpool.
The architecture is attributed to George Stephenson. The station was accessed by a long single track tunnel from the deep Edge Hill Cutting to the east, sometimes known as the Cavendish Cutting. Together with the adjacent Wapping Tunnel, these were the first tunnels to be bored under a metropolis. Stationary steam engines, located in the cutting, operated a continuous rope system to haul wagons up inclines from Edge Hill station | 25,915 |
1055436 | Crown Street railway station | https://en.wikipedia.org/w/index.php?title=Crown%20Street%20railway%20station | Crown Street railway station
and up the Wapping Tunnel from Park Lane Goods Depot, earlier known as Wapping railway goods station, at Liverpool's south end docks. The Wapping Tunnel runs under the Crown Street station site.
Crown Street station was too far from Liverpool city centre. Its use as a passenger station ended after only six years of use in 1836 when Lime Street Station was opened. The site of the Crown Street station was converted to a goods yard. An additional twin track tunnel was built from the Edge Hill cutting in 1846 to improve throughput to the goods yard. The goods yard closed permanently when services through the two tunnels ended in 1972. The Wapping Tunnel along with the original Crown Street tunnel | 25,916 |
1055436 | Crown Street railway station | https://en.wikipedia.org/w/index.php?title=Crown%20Street%20railway%20station | Crown Street railway station
also ceased operation in 1972.
# Millfield.
Immediately to the south of Crown Street station was an area known as Millfield or Gray's yard. This included a large marshalling and storage area as well as a substantial works involved in the construction and maintenance of wagons and carriages.
# Current use of the site.
The area has been landscaped as a park with the original 1830 single track tunnel's western portal covered over. The 1846 Crown Street tunnel is now used as a headshunt for trains. Student accommodation for the nearby University of Liverpool has been built on a part of the old goods yard site. The site of the station itself is landscaped. The Wapping Tunnel's ventilation tower | 25,917 |
1055436 | Crown Street railway station | https://en.wikipedia.org/w/index.php?title=Crown%20Street%20railway%20station | Crown Street railway station
n history. There are also a small number of stone sleeper blocks close to the fence on Falkner Street.
# Potential new station.
The proposal for Paddington Village mentions that a station in the 2014 Liverpool City Region, (LCR) Long Term Rail Strategy would be of use, the station would be on the Wapping Tunnel. However, the Paddington Village Spatial Regeneration Framework document of October 2016, page 36, specifically gives a map with a station on the old Crown Street station site, stating the locations as Crown Street/Myrtle Street.
# Sources.
- http://www.spartacus-educational.com/RAliverpoolST.htm
- http://www.subbrit.org.uk/sb-sites/sites/l/liverpool_edge_hill_cutting/index.shtml | 25,918 |
1055450 | Geoffroy Saint-Hilaire | https://en.wikipedia.org/w/index.php?title=Geoffroy%20Saint-Hilaire | Geoffroy Saint-Hilaire
Geoffroy Saint-Hilaire
Geoffroy Saint-Hilaire may refer to:
- Étienne Geoffroy Saint-Hilaire (1772–1844), French naturalist
- Isidore Geoffroy Saint-Hilaire (1805–1861), French zoologist who coined the term "ethology", son of Étienne Saint-Hilaire
- Albert Geoffroy Saint-Hilaire (1835–1919), French zoologist, coined the binomial nomenclature name for the Chinese monal pheasant, son of Isidore Saint-Hilaire | 25,919 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
Casa Vicens
Casa Vicens () is a house in Barcelona, designed by Antoni Gaudí, now a museum. It is located in the neighbourhood of Gràcia on Carrer de les Carolines, 20-26. It is considered one of the first buildings of Art Nouveau and was the first house designed by Gaudí.
The style of Casa Vicens is a reflection of Neo-Mudéjar architecture, one of the popular styles that can be seen throughout Gaudí's architecture, including oriental and neoclassical as well. However, what was unique about Gaudí was that he mixed different styles together and incorporated a variety of different materials, such as iron, glass, ceramic tiles and concrete, many of which can be seen in this building. Gaudí broke | 25,920 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
away from tradition and created his new language of architecture, and Casa Vicens represents a new chapter in the history of Catalan architecture as well as the beginning of a successful career for Gaudí.
In 1883, Gaudí received the commission from Manuel Vicens i Montaner for the completion of a summer residence. In February 1883, Manuel Vicens requested permission from the City Council of Vila de Gràcia to build a summer house on Calle Sant Gervasi 26 (currently Carolines 20-26). A month earlier he had requested permission to demolish the house he had inherited from his mother, Rosa Montaner given the poor state of conservation of the same.
Although Mr. Manuel Vicens remains a quite unknown | 25,921 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
character, his will mentions his profession: brokerage and exchange, which would mean that he alleged his connection with ceramics and that he would be reinforced by the inventory of 1885 of the ceramic factory Pujol i Bausis that is conserved in the Municipal Archive of Esplugues de Llobregat, there is documented Mr. Manuel Vicens i Montaner, of Gracia, as a debtor of 1,440 pesetas.
This early work exhibits several influences, most notably the Moorish (or Mudéjar) influence. Casa Vicens marks the first time Gaudí utilized an orientalist style, mixing together Hispano-Arabic inspiration. This was a style of architecture that completely breaks with the norm of the period. Not only does this | 25,922 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
house mark Gaudí's coming of age, being his first major work of architecture, but it also represents the flowering of Catalan modern architecture.
# History.
## Initial construction.
The plans for construction (site, main floor, facade and section) date back to January 15, 1883. Gaudí was granted a construction permit on March 8 of the same year (Number 239-71; certificate 613). This is recorded in the files of Las Corts de Sarriá. The house is constructed of undressed stone, rough red bricks, and colored ceramic tiles in both checkerboard and floral patterns.
At the time of this construction, Gaudí was just beginning his career. Gaudí graduated from the Provincial School of Architecture | 25,923 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
in Barcelona in 1878. Throughout his time in school and in the period shortly after, his work portrayed a rather Victorian style, similar to that of his predecessors; however, shortly after finishing school he began to develop his own style that was characterized by Neo-Mudéjar influence. Some characteristics of this style include the juxtaposition of geometric masses, the use of ceramic tiles, metalwork, and abstract brick ornamentation.
## Renovations.
In 1899, Casa Vicens was acquired by Dr. Antonio Jover, a surgeon from Havana, Cuba who was the grandfather of the owners of the building prior to its sale to MoraBanc in 2014. In 1924, Jover moved into the house. Before that, it had only | 25,924 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
been used as a holiday home. During the time of his ownership the house was a private building and was not open to the public. However, the one day that visitors could enter was on 22 May for Saint Rita's day.
In 1925, architect Juan Sierra de Martínez added on a new bay to the rear of the building, following the same style as Gaudí, and also significantly extended the size of the garden. He also modified the main floor entrances. With the widening of Carrer de las Carolinas, the access to the house had to be changed. The former entrance was converted into windows that open directly on to the street and can still be seen today. These renovations were done with maximum respect for the original | 25,925 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
work, and Gaudí himself even approved these plans. During this time, he was busy constructing the Sagrada Família and was too busy to assist with the renovations for Casa Vicens. Martínez also built a cupola-topped chapel dedicated to Saint Rita at the angle furthest from the house. He continued this project until its completion date in 1926. Due to this work, Martínez won the prize for the best and most emblematic building of the city of Barcelona (Concurs annual d'edificis arístics) in 1927, awarded by the city council.
A final restoration took place between the years 2001 and 2004. The aim of this restoration was to consolidate the facades and furnishings. This work was done under architect | 25,926 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
Ignacio Herrero Jover.
# Construction.
## Exterior.
The roof of Casa Vicens is sloped on two sides and has four gables. A small path was built around the edge of the roof that allows for easy and accessible maintenance if necessary. A characteristic seen throughout Gaudí's work is that the ventilation conducts and chimneys are intricately decorated in similar styles as the facade, adding to and extending the artistic drama of the architecture.
## Layout.
The house is divided into four levels: a basement, two floors for living and a loft. The original building was small and measured only 12 x 16 meters with two individual bays. A brick waterfall fountain was built as well. The basement is | 25,927 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
302 meters, the ground floor is 332 meters plus 22 meters of terrace, the first floor is 225 meters plus 79 meters of terrace, and the second floor is 272 meters. The total area of the house is roughly 1266 meters.
On the ground floor, there is an extensive sitting-dining room, a small Turkish-style smoking room, and two additional rooms. This floor was slightly elevated to allow for better ventilation and improved lighting of the basement. The second floor was where the family's bedrooms were. A horseshoe-shaped stairway served as access to this floor. The third floor, or the attic, was where the servants lived. The horseshoe-shaped stairway also continued up to this floor. However, after | 25,928 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
the renovations in 1925 the location of the stairway that gave access to the bedrooms was changed. The basement, or bottom floor contained just enough space for a storage room, junk room and a kitchen. The basement received its light from an English-style courtyard.
# Artistic style.
Casa Vicens was built using a variety of different materials and vibrant colors. This style was a key characteristic of modern architecture. Some key elements include bricks, tiles and iron. The architecture of the house itself was unique, however the combination of paintings, sculptures and the applied arts adds essential complements that are characteristic of the modern style of Gaudí.
Neo-Mudéjar architecture | 25,929 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
is a type of Moorish revival architecture that Gaudí incorporated into Casa Vicens. This revival movement began in Madrid in the late 19th century, later spreading to other parts of the country. It is considered Spain's special mixture of Muslim-Christian design. Some features of this ancient style such as horse-shoe arches, and abstract and vibrant facade ornamentation can be seen in Casa Vicens; the horse-shoe shaped staircase and the brick ornamentation on the front facade. El Capricho (1833-1835) and the Güell Estate of the later 1880s are two other examples of Neo-Mudéjar style in Gaudí's architecture.
## Interior.
The dining room is the most decorated room in the house and incorporated | 25,930 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
many figures from nature, such as birds and vines. Gaudí used pressed cardboard to create three dimensional model figures of ivy, fruit and flowers for the interior of the building. The dome painting in the sitting room gives one the impression of looking through a glass dome, to the sky. The interior ceiling ornamentation is decorated with colorful plants and flowers.
## Exterior.
The first two levels of the house, as seen from the front facade facing Carrer de les Carolines, are lined with horizontal roles of ceramic tiles decorated with French marigolds that can also be seen on the floors in the interior of the house. These marigolds grew on the grounds of the estate, are an example of | 25,931 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
how Gaudí derived much of inspiration from his love of nature. The cast iron railings with their plant motifs and iron palm leaves that form the gates to the house are other ways that Gaudí incorporated nature into his work. Plants that had to be destroyed for the construction of the building, such as the marigolds or the palm trees, were incorporated into the details of the building. Casa Milá, popularly known as La Pedrera, is another example of Gaudí modern architecture whose design based on the ocean with its curved edges and seaweed motifs is another example of nature serving as his inspiration.
From the second floor up, these tiles switch to vertical and the floral pattern on them is | 25,932 |
1055410 | Casa Vicens | https://en.wikipedia.org/w/index.php?title=Casa%20Vicens | Casa Vicens
rtical and the floral pattern on them is replaced with green and white tiles. Elegant cherub like figures sit on the edge of the small balcony that faces the street. He paid particular attention to each and every detail, such as creating ridged edges to the corners of the building to avoid the austere appearance of classical architecture.
# Museum.
Casa Vicens was a private residence until 2014. After being purchased by MoraBanc, a major restoration was conducted and it was opened to the public as a museum in November 2017.
# See also.
- List of Modernisme buildings in Barcelona
# External links.
- Casa Vicens official web
- Casa Vicens information website
- Blueprints of Casa Vicens | 25,933 |
1055440 | Spy Games | https://en.wikipedia.org/w/index.php?title=Spy%20Games | Spy Games
Spy Games
Spy Games ("History Is Made at Night") is a 1999 film directed by Ilkka Järvi-Laturi, and starring Bill Pullman, Irène Jacob, and Bruno Kirby. Written by Patrick Amos, the film is about a jaded CIA agent and a young and beautiful SVR agent fighting to save the world, their lives, and their secret love in post Cold War Helsinki. Filmed in Helsinki, Finland and New York City, the movie incorporates elements of romance, action, and thriller genres. The film premiered at the Toronto International Film Festival on 10 September 1999.
# Plot.
Harry (Bill Pullman) is a seasoned CIA agent who is looking to forget his past and become his cover identity—a jazz club owner in Helsinki, Finland. | 25,934 |
1055440 | Spy Games | https://en.wikipedia.org/w/index.php?title=Spy%20Games | Spy Games
Natasha (Irène Jacob) is a young, ambitious SVR (KGB) agent who is looking to secure a future for herself amidst the chaos of the new Russian Federation and her floundering intelligence agency. Originally assigned to spy on Harry, Natasha has fallen in love with the object of her spying, and her assignment has led to a torrid love affair between the two. Like all couples, they are keeping secrets from each other—but in their case, the secrets have international implications.
Harry's life with Natasha is disrupted when a young, over-zealous CIA agent, Dave (Glenn Plummer), comes to Helsinki to intercept a videotape encoded with state secrets en route from New York City. The videotape's hidden | 25,935 |
1055440 | Spy Games | https://en.wikipedia.org/w/index.php?title=Spy%20Games | Spy Games
code is so sensitive that those who come in contact with the tape are soon killed. Dave is pursuing the unsuspecting courier, a manic ex-bond trader named Max (Bruno Kirby), who is unaware of what he is carrying. Max took the job by chance, following his recent prison term for stock market fraud. Natasha sees the videotape as a possible ticket out of the SVR and into the United States and the American Dream. In fact, everyone involved except Harry is planning to exploit the encoded videotape. Harry's only plan is to prevent Natasha from getting herself killed—or worse, from leaving him for U.S.
# Cast.
- Bill Pullman as Harry Howe / Ernie Halliday
- Irène Jacob as Natasha Scriabina / Anna | 25,936 |
1055440 | Spy Games | https://en.wikipedia.org/w/index.php?title=Spy%20Games | Spy Games
Belinka
- Bruno Kirby as Max Fisher
- Glenn Plummer as Dave Preston
- Udo Kier as Ivan Bliniak
- André Oumansky as Yuri
- Féodor Atkine as Romanov
- Janne Kinnunen as Pekka
- Linda Zilliacus as Maija (as Linda Gyllenberg)
- Jevgeni Haukka as Slava
- Marcia Diamond as Lauren
- Henry Saari as Porn Man
- Louise Hodges as Porn Woman (as Louise Hodges)
- Bob Sherman as CIA Elder
- Kimmo Eloranta as Bodyguard
# Production.
- Casting
Director Ilkka Järvi-Laturi wanted Bill Pullman for the lead character of Harry. "When we started casting, I knew right away that Bill was our man to play Harry ... He's an absolute natural for the part—intelligent, wry, and charmingly good looking." Producer | 25,937 |
1055440 | Spy Games | https://en.wikipedia.org/w/index.php?title=Spy%20Games | Spy Games
Kerry Rock saw Bill in more practical terms: "Bill was the cornerstone of the casting process. We needed someone the right age, who was enough of a name, who could do the humor as well as being scary and believably violent at the tough spots of the story." Co-star Bruno Kirby also found Bill to be the perfect match: "The great thing about Bill is that he looks very straight, but if you look him in the eye, there's a real crazy sense of humor there."
- Filming locations
On working in Helsinki, Bill Pullman observed, "There's nothing like working on a movie to see great places, it's better than going to any travel agent. We've had some of the best locations—a former czar's fishing hut that was | 25,938 |
1055440 | Spy Games | https://en.wikipedia.org/w/index.php?title=Spy%20Games | Spy Games
our Lapland hotel in December. And in Helsinki there some of the best art nouveau architecture anybody's seen." Bruno Kirby pleasantly surprised by his filming experience in Helsinki: "I was expecting this dark place, with nowhere decent to eat, with unfriendly people. In reality, it's been the opposite. It's a wonderful city, with wonderful, highly educated people, great restaurants and great shops. The people want to talk, and they are very proud of their city, and they love the fact we're using Helsinki for Helsinki."
- Helsinki, Finland
- Helsinki-Vantaa International Airport, Vantaa, Finland
- New York City, New York, USA
- Soundtrack
Courtney Pine did the original soundtrack and plays | 25,939 |
1055440 | Spy Games | https://en.wikipedia.org/w/index.php?title=Spy%20Games | Spy Games
at restaurants and great shops. The people want to talk, and they are very proud of their city, and they love the fact we're using Helsinki for Helsinki."
- Helsinki, Finland
- Helsinki-Vantaa International Airport, Vantaa, Finland
- New York City, New York, USA
- Soundtrack
Courtney Pine did the original soundtrack and plays in the band in the film. To reflect the main character's job running a jazz nightclub, the music soundtrack is a combination of sixties soul and cool jazz.
- Release
The film premiered at the Toronto International Film Festival on 10 September 1999, and opened in Finland on 22 October 1999. "Spy Games" was released in the United States in DVD format 11 July 2000. | 25,940 |
1055424 | Devil's Footprints | https://en.wikipedia.org/w/index.php?title=Devil's%20Footprints | Devil's Footprints
Devil's Footprints
The Devil's Footprints was a phenomenon that occurred during February 1855 around the Exe Estuary in East and South Devon, England. After a heavy snowfall, trails of hoof-like marks appeared overnight in the snow covering a total distance of some . The footprints were so called because some people believed that they were the tracks of Satan, as they were allegedly made by a cloven hoof. Many theories have been made to explain the incident, and some aspects of its veracity have also been questioned.
# Incident.
On the night of 8–9 February 1855 and one or two later nights, after a heavy snowfall, a series of hoof-like marks appeared in the snow. These footprints, most of | 25,941 |
1055424 | Devil's Footprints | https://en.wikipedia.org/w/index.php?title=Devil's%20Footprints | Devil's Footprints
which measured about four inches long, three inches across, between eight and sixteen inches apart and mostly in a single file, were reported from more than thirty locations across Devon and a couple in Dorset. It was estimated that the total distance of the tracks amounted to between . Houses, rivers, haystacks and other obstacles were travelled straight over, and footprints appeared on the tops of snow-covered roofs and high walls which lay in the footprints' path, as well as leading up to and exiting various drain pipes as small as four inches in diameter. From a news report:
"It appears on Thursday night last, there was a very heavy snowfall in the neighbourhood of Exeter and the South | 25,942 |
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of Devon. On the following morning the inhabitants of the above towns were surprised at discovering the footmarks of some strange and mysterious animal endowed with the power of ubiquity, as the footprints were to be seen in all kinds of unaccountable places – on the tops of houses and narrow walls, in gardens and court-yards, enclosed by high walls and pailings, as well in open fields."
The area in which the prints appeared extended from Exmouth, up to Topsham, and across the Exe Estuary to Dawlish and Teignmouth. R.H. Busk, in an article published in "Notes and Queries" during 1890, stated that footprints also appeared further afield, as far south as Totnes and Torquay, and that there were | 25,943 |
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other reports of the prints as far away as Weymouth (Dorset) and even Lincolnshire.
# Evidence.
There is little direct evidence of the phenomenon. The only known documents were found after the publication during 1950 of an article in the Transactions of the Devonshire Association asking for further information about the event. This resulted in the discovery of a collection of papers belonging to Reverend H. T. Ellacombe, the vicar of Clyst St George during the 1850s. These papers included letters addressed to the vicar from his friends, among them the Reverend G. M. Musgrove, the vicar of Withycombe Raleigh, the draft of a letter to "The Illustrated London News" marked 'not for publication' | 25,944 |
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and several apparent tracings of the footprints.
During many years the noted researcher Mike Dash collated all the available primary and secondary source material into a paper entitled "The Devil's Hoofmarks: Source Material on the Great Devon Mystery of 1855" which was published in "Fortean Studies" during 1994.
# Theories.
Many explanations have been made for the incident. Some investigators are sceptical that the tracks really extended for more than a hundred miles, arguing that no-one would have been able to follow their entire course in a single day. Another reason for scepticism, as Joe Nickell indicates, is that the eye-witness descriptions of the footprints varied from person to person.
In | 25,945 |
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his "Fortean Studies" article, Mike Dash concluded that there was no one source for the "hoofmarks": some of the tracks were probably hoaxes, some were made by "common quadrupeds" such as donkeys and ponies, and some by wood mice (see below). He admitted, though, that these cannot explain all the reported marks and "the mystery remains".
## Balloon.
Author Geoffrey Household suggested that "an experimental balloon" released by mistake from Devonport Dockyard had left the mysterious tracks by trailing two shackles on the end of its mooring ropes. His source was a local man, Major Carter, whose grandfather had worked at Devonport at the time. Carter claimed that the incident had been quieted | 25,946 |
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because the balloon also wrecked a number of conservatories, greenhouses, and windows before finally descending to earth in Honiton.
While this could explain the shape of the prints, sceptics have disagreed about whether the balloon could have travelled such a random zigzag course without its trailing ropes and shackles becoming caught in a tree or similar obstruction.
## Hopping mice.
Mike Dash suggested that at least some of the prints, including some of those found on rooftops, could have been made by hopping rodents such as wood mice. The print left behind after a mouse leaps resembles that of a cloven animal, due to the motions of its limbs when it jumps. Dash stated that the theory | 25,947 |
1055424 | Devil's Footprints | https://en.wikipedia.org/w/index.php?title=Devil's%20Footprints | Devil's Footprints
that the Devon prints were made by rodents was originally proposed as long ago as March 1855, in "The Illustrated London News".
## Kangaroo.
In a letter to the "Illustrated London News" during 1855, Rev. G. M. Musgrave wrote: "In the course of a few days a report was circulated that a couple of kangaroos escaped from a private menagerie (Mr Fische's, I believe) at Sidmouth." It seems, though, that nobody ascertained whether the kangaroos had escaped, nor how they could have crossed the Exe estuary, and Musgrave himself said that he invented with the story to distract his parishioners' concerns about a visit from the devil:
## Badgers.
During July 1855, Richard Owen stated the theory that | 25,948 |
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the footprints were from a badger, arguing the animal was 'the only plantigrade quadruped we have in this island' and it 'leaves a footprint larger than would be supposed from its size'. The number of footprints, he suggested, was indicative of the activity of several animals because 'it is improbable that one badger only should have been awake and hungry' and added that the animal was 'a stealthy prowler and most active and enduring in search of food'.
# Similar incidents.
Reports of similar anomalous, obstacle-unheeded footprints exist from other parts of the world, although none is of such a scale as that of the case of the Devil's Footprints. This example was reported 15 years earlier | 25,949 |
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in "The Times":
In the "Illustrated London News" of 17 March 1855, a correspondent from Heidelberg wrote, "upon the authority of a Polish Doctor in Medicine", that on the Piaskowa-góra (Sand Hill), a small elevation on the border of Galicia, but in Congress Poland, such marks are to be seen in the snow every year, and sometimes in the sand of this hill, and "are attributed by the inhabitants to supernatural influences".
On the night of 12 March 2009, marks claimed to be similar to those left during 1855 were found in Devon. During 2013 trails were reported in Girvan, Scotland possibly as part of an April Fool's hoax.
# See also.
- Jersey Devil – the appearance during January 1909 of similar | 25,950 |
1055424 | Devil's Footprints | https://en.wikipedia.org/w/index.php?title=Devil's%20Footprints | Devil's Footprints
sometimes in the sand of this hill, and "are attributed by the inhabitants to supernatural influences".
On the night of 12 March 2009, marks claimed to be similar to those left during 1855 were found in Devon. During 2013 trails were reported in Girvan, Scotland possibly as part of an April Fool's hoax.
# See also.
- Jersey Devil – the appearance during January 1909 of similar mysterious footprints in New Jersey, USA
- Phantom kangaroo
- The Great Thunderstorm, Widecombe – another legend of the Devil in Devon
- Urban legend
- "Dark Was the Night" (2014)
# External links.
- Charles Fort, "The Book of the Damned", Chapter 28.
- "The Devil's Footprints" "Mysterious Britain & Ireland" | 25,951 |
1055456 | E-Dreams | https://en.wikipedia.org/w/index.php?title=E-Dreams | E-Dreams
E-Dreams
e-Dreams is a 2002 American documentary film directed by Wonsuk Chin portraying the rise and fall of Kozmo.com, an online convenience store that used bike messengers to deliver goods ordered online within an hour.
The movie follows Joseph Park and Yong Kang, 28-year-old Korean Americans, whose company started as Park's idea in 1998 and by January 1999 became a reality in a warehouse with a small group of employees and grew to 3,000 employees and an 11-city network within a year. Kozmo.com raised $280 million in capital and attracted attention from Amazon.com and Starbucks. However, the lack of a sustainable business plan and the inability to raise additional capital due to the dot-com | 25,952 |
1055456 | E-Dreams | https://en.wikipedia.org/w/index.php?title=E-Dreams | E-Dreams
e a reality in a warehouse with a small group of employees and grew to 3,000 employees and an 11-city network within a year. Kozmo.com raised $280 million in capital and attracted attention from Amazon.com and Starbucks. However, the lack of a sustainable business plan and the inability to raise additional capital due to the dot-com bust and stock market correction that began in April 2000 forced the company out of business by 2001.
# External links.
- e-Dreams at the Internet Movie Database
- e-Dreams Distributed by Elliptic Entertainment [DEAD LINK]
- Film Threat Review
- FilmCritic.com Review
- Louis Proyect's review
- MetaCritic review
- Reel.com review
- Rotten Tomatoes reviews | 25,953 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
Sheaf cohomology
In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology describes the obstructions to solving a geometric problem globally when it can be solved locally. The central figure of this study is Alexander Grothendieck and his 1957 Tohoku paper.
Sheaves, sheaf cohomology, and spectral sequences were invented by Jean Leray at the prisoner-of-war camp Oflag XVII-A in Austria. From 1940 to 1945, Leray and other prisoners organized a "université en captivité" in the camp.
Leray's definitions were simplified and clarified in the 1950s. It became clear that sheaf cohomology | 25,954 |
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was not only a new approach to cohomology in algebraic topology, but also a powerful method in complex analytic geometry and algebraic geometry. These subjects often involve constructing global functions with specified local properties, and sheaf cohomology is ideally suited to such problems. Many earlier results such as the Riemann–Roch theorem and the Hodge theorem have been generalized or understood better using sheaf cohomology.
# Definition.
The category of sheaves of abelian groups on a topological space "X" is an abelian category, and so it makes sense to ask when a morphism "f": "B" → "C" of sheaves is injective (a monomorphism) or surjective (an epimorphism). One answer is that "f" | 25,955 |
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is injective (resp. surjective) if and only if the associated homomorphism on stalks "B" → "C" is injective (resp. surjective) for every point "x" in "X". It follows that "f" is injective if and only if the homomorphism "B"("U") → "C"("U") of sections over "U" is injective for every open set "U" in "X". Surjectivity is more subtle, however: the morphism "f" is surjective if and only if for every open set "U" in "X", every section "s" of "C" over "U", and every point "x" in "U", there is an open neighborhood "V" of "x" in "U" such that "s" restricted to "V" is the image of some section of "B" over "V". (In words: every section of "C" lifts "locally" to sections of "B".)
As a result, the question | 25,956 |
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arises: given a surjection "B" → "C" of sheaves and a section "s" of "C" over "X", when is "s" the image of a section of "B" over "X"? This is a model for all kinds of local-vs.-global questions in geometry. Sheaf cohomology gives a satisfactory general answer. Namely, let "A" be the kernel of the surjection "B" → "C", giving a short exact sequence
of sheaves on "X". Then there is a long exact sequence of abelian groups, called sheaf cohomology groups:
where "H"("X","A") is the group "A"("X") of global sections of "A" on "X". For example, if the group "H"("X","A") is zero, then this exact sequence implies that every global section of "C" lifts to a global section of "B". More broadly, the | 25,957 |
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exact sequence makes knowledge of higher cohomology groups a fundamental tool in aiming to understand sections of sheaves.
Grothendieck's definition of sheaf cohomology, now standard, uses the language of homological algebra. The essential point is to fix a topological space "X" and think of cohomology as a functor from sheaves of abelian groups on "X" to abelian groups. In more detail, start with the functor "E" ↦ "E"("X") from sheaves of abelian groups on "X" to abelian groups. This is left exact, but in general not right exact. Then the groups "H"("X","E") for integers "i" are defined as the right derived functors of the functor "E" ↦ "E"("X"). This makes it automatic that "H"("X","E") is | 25,958 |
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zero for "i" 0, and that "H"("X","E") is the group "E"("X") of global sections. The long exact sequence above is also straightforward from this definition.
The definition of derived functors uses that the category of sheaves of abelian groups on any topological space "X" has enough injectives; that is, for every sheaf "E" there is an injective sheaf "I" with an injection "E" → "I". It follows that every sheaf "E" has an injective resolution:
Then the sheaf cohomology groups "H"("X","E") are the cohomology groups (the kernel of one homomorphism modulo the image of the previous one) of the complex of abelian groups:
Standard arguments in homological algebra imply that these cohomology groups | 25,959 |
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are independent of the choice of injective resolution of "E".
The definition is rarely used directly to compute sheaf cohomology. It is nonetheless powerful, because it works in great generality (any sheaf on any topological space), and it easily implies the formal properties of sheaf cohomology, such as the long exact sequence above. For specific classes of spaces or sheaves, there are many tools for computing sheaf cohomology, some discussed below.
# Functoriality.
For any continuous map "f": "X" → "Y" of topological spaces, and any sheaf "E" of abelian groups on "Y", there is a pullback homomorphism
for every integer "j", where "f"*("E") denotes the inverse image sheaf or pullback sheaf. | 25,960 |
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If "f" is the inclusion of a subspace "X" of "Y", "f"*("E") is the restriction of "E" to "X", often just called "E" again, and the pullback of a section "s" from "Y" to "X" is called the restriction "s"|.
Pullback homomorphisms are used in the Mayer–Vietoris sequence, an important computational result. Namely, let "X" be a topological space which is a union of two open subsets "U" and "V", and let "E" be a sheaf on "X". Then there is a long exact sequence of abelian groups:
# Sheaf cohomology with constant coefficients.
For a topological space "X" and an abelian group "A", the constant sheaf "A" means the sheaf of locally constant functions with values in "A". The sheaf cohomology groups | 25,961 |
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"H"("X","A") with constant coefficients are often written simply as "H"("X","A"), unless this could cause confusion with another version of cohomology such as singular cohomology.
For a continuous map "f": "X" → "Y" and an abelian group "A", the pullback sheaf "f"*("A") is isomorphic to "A". As a result, the pullback homomorphism makes sheaf cohomology with constant coefficients into a contravariant functor from topological spaces to abelian groups.
For any spaces "X" and "Y" and any abelian group "A", two homotopic maps "f" and "g" from "X" to "Y" induce the "same" homomorphism on sheaf cohomology:
It follows that two homotopy equivalent spaces have isomorphic sheaf cohomology with constant | 25,962 |
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coefficients.
Let "X" be a paracompact Hausdorff space which is locally contractible, even in the weak sense that every open neighborhood "U" of a point "x" contains an open neighborhood "V" of "x" such that the inclusion "V" → "U" is homotopic to a constant map. Then the singular cohomology groups of "X" with coefficients in an abelian group "A" are isomorphic to sheaf cohomology with constant coefficients, "H"*("X","A"). For example, this holds for "X" a topological manifold or a CW complex.
As a result, many of the basic calculations of sheaf cohomology with constant coefficients are the same as calculations of singular cohomology. See the article on cohomology for the cohomology of spheres, | 25,963 |
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projective spaces, tori, and surfaces.
For arbitrary topological spaces, singular cohomology and sheaf cohomology (with constant coefficients) can be different. This happens even for "H". The singular cohomology "H"("X",Z) is the group of all functions from the set of path components of "X" to the integers Z, whereas sheaf cohomology "H"("X",Z) is the group of locally constant functions from "X" to Z. These are different, for example, when "X" is the Cantor set. Indeed, the sheaf cohomology "H"("X",Z) is a countable abelian group in that case, whereas the singular cohomology "H"("X",Z) is the group of "all" functions from "X" to Z, which has cardinality
For a paracompact Hausdorff space "X" | 25,964 |
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and any sheaf "E" of abelian groups on "X", the cohomology groups "H"("X","E") are zero for "j" greater than the covering dimension of "X". (This does not hold in the same generality for singular cohomology: for example, there is a compact subset of Euclidean space R that has nonzero singular cohomology in infinitely many degrees.) The covering dimension agrees with the usual notion of dimension for a topological manifold or a CW complex.
# Flabby and soft sheaves.
A sheaf "E" of abelian groups on a topological space "X" is called acyclic if "H"("X","E") = 0 for all "j" 0. By the long exact sequence of sheaf cohomology, the cohomology of any sheaf can be computed from any acyclic resolution | 25,965 |
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of "E" (rather than an injective resolution). Injective sheaves are acyclic, but for computations it is useful to have other examples of acyclic sheaves.
A sheaf "E" on "X" is called flabby (French: "flasque") if every section of "E" on an open subset of "X" extends to a section of "E" on all of "X". Flabby sheaves are acyclic. Godement defined sheaf cohomology via a canonical flabby resolution of any sheaf; since flabby sheaves are acyclic, Godement's definition agrees with the definition of sheaf cohomology above.
A sheaf "E" on a paracompact Hausdorff space "X" is called soft if every section of the restriction of "E" to a closed subset of "X" extends to a section of "E" on all of "X". | 25,966 |
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Every soft sheaf is acyclic.
Some examples of soft sheaves are the sheaf of real-valued continuous functions on any paracompact Hausdorff space, or the sheaf of smooth ("C") functions on any smooth manifold. More generally, any sheaf of modules over a soft sheaf of commutative rings is soft; for example, the sheaf of smooth sections of a vector bundle over a smooth manifold is soft.
For example, these results form part of the proof of de Rham's theorem. For a smooth manifold "X", the Poincaré lemma says that the de Rham complex is a resolution of the constant sheaf R:
where Ω is the sheaf of smooth "j"-forms and the map Ω → Ω is the exterior derivative "d". By the results above, the sheaves | 25,967 |
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Ω are soft and therefore acyclic. It follows that the sheaf cohomology of "X" with real coefficients is isomorphic to the de Rham cohomology of "X", defined as the cohomology of the complex of real vector spaces:
The other part of de Rham's theorem is to identify sheaf cohomology and singular cohomology of "X" with real coefficients; that holds in greater generality, as discussed above.
# Čech cohomology.
Čech cohomology is an approximation to sheaf cohomology that is often useful for computations. Namely, let formula_11 be an open cover of a topological space "X", and let "E" be a sheaf of abelian groups on "X". Write the open sets in the cover as "U" for elements "i" of a set "I", and fix | 25,968 |
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an ordering of "I". Then Čech cohomology formula_12 is defined as the cohomology of an explicit complex of abelian groups with "j"th group
There is a natural homomorphism formula_14. Thus Čech cohomology is an approximation to sheaf cohomology using only the sections of "E" on finite intersections of the open sets "U".
If every finite intersection "V" of the open sets in formula_11 has no higher cohomology with coefficients in "E", meaning that "H"("V","E") = 0 for all "j" 0, then the homomorphism from Čech cohomology formula_12 to sheaf cohomology is an isomorphism.
Another approach to relating Čech cohomology to sheaf cohomology is as follows. The Čech cohomology groups formula_17 are | 25,969 |
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defined as the direct limit of formula_12 over all open covers formula_11 of "X" (where open covers are ordered by refinement). There is a homomorphism formula_20 from Čech cohomology to sheaf cohomology, which is an isomorphism for "j" ≤ 1. For arbitrary topological spaces, Čech cohomology can differ from sheaf cohomology in higher degrees. Conveniently, however, Čech cohomology is isomorphic to sheaf cohomology for any sheaf on a paracompact Hausdorff space.
The isomorphism formula_21 implies a description of "H"("X","E") for any sheaf "E" of abelian groups on a topological space "X": this group classifies the "E"-torsors (also called principal "E"-bundles) over "X", up to isomorphism. (This | 25,970 |
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statement generalizes to any sheaf of groups "G", not necessarily abelian, using the non-abelian cohomology set "H"("X","G").) By definition, an "E"-torsor over "X" is a sheaf "S" of sets together with an action of "E" on "X" such that every point in "X" has an open neighborhood on which "S" is isomorphic to "E", with "E" acting on itself by translation. For example, on a ringed space ("X","O"), it follows that the Picard group of invertible sheaves on "X" is isomorphic to the sheaf cohomology group "H"("X","O"*), where "O"* is the sheaf of units in "O".
# Relative cohomology.
For a subset "Y" of a topological space "X" and a sheaf "E" of abelian groups on "X", one can define relative cohomology | 25,971 |
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groups:
for integers "j". Other names are the cohomology of "X" with support in "Y", or (when "Y" is closed in "X") local cohomology. A long exact sequence relates relative cohomology to sheaf cohomology in the usual sense:
When "Y" is closed in "X", cohomology with support in "Y" can be defined as the derived functors of the functor
the group of sections of "E" that are supported on "Y".
There are several isomorphisms known as excision. For example, if "X" is a topological space with subspaces "Y" and "U" such that the closure of "Y" is contained in the interior of "U", and "E" is a sheaf on "X", then the restriction
is an isomorphism. (So cohomology with support in a closed subset "Y" | 25,972 |
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only depends on the behavior of the space "X" and the sheaf "E" near "Y".) Also, if "X" is a paracompact Hausdorff space that is the union of closed subsets "A" and "B", and "E" is a sheaf on "X", then the restriction
is an isomorphism.
# Cohomology with compact support.
Let "X" be a locally compact topological space. (In this article, a locally compact space is understood to be Hausdorff.) For a sheaf "E" of abelian groups on "X", one can define cohomology with compact support "H"("X","E"). These groups are defined as the derived functors of the functor of compactly supported sections:
There is a natural homomorphism "H"("X","E") →
"H"("X","E"), which is an isomorphism for "X" compact.
For | 25,973 |
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a sheaf "E" on a locally compact space "X", the compactly supported cohomology of "X" × R with coefficients in the pullback of "E" is a shift of the compactly supported cohomology of "X":
It follows, for example, that "H"(R,Z) is isomorphic to Z if "j" = "n" and is zero otherwise.
Compactly supported cohomology is not functorial with respect to arbitrary continuous maps. For a proper map "f": "Y" → "X" of locally compact spaces and a sheaf "E" on "X", however, there is a pullback homomorphism
on compactly supported cohomology. Also, for an open subset "U" of a locally compact space "X" and a sheaf "E" on "X", there is a pushforward homomorphism known as extension by zero:
Both homomorphisms | 25,974 |
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occur in the long exact localization sequence for compactly supported cohomology, for a locally compact space "X" and a closed subset "Y":
# Cup product.
For any sheaves "A" and "B" of abelian groups on a topological space "X", there is a bilinear map, the cup product
for all "i" and "j". Here "A"⊗"B" denotes the tensor product over Z, but if "A" and "B" are sheaves of modules over some sheaf "O" of commutative rings, then one can map further from "H"(X,"A"⊗"B") to "H"(X,"A"⊗"B"). In particular, for a sheaf "O" of commutative rings, the cup product makes the direct sum
into a graded-commutative ring, meaning that
for all "u" in "H" and "v" in "H".
# Complexes of sheaves.
The definition | 25,975 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
of sheaf cohomology as a derived functor extends to define cohomology of a topological space "X" with coefficients in any complex "E" of sheaves:
In particular, if the complex "E" is bounded below (the sheaf "E" is zero for "j" sufficiently negative), then "E" has an injective resolution "I" just as a single sheaf does. (By definition, "I" is a bounded below complex of injective sheaves with a chain map "E" → "I" that is a quasi-isomorphism.) Then the cohomology groups "H"("X","E") are defined as the cohomology of the complex of abelian groups
The cohomology of a space with coefficients in a complex of sheaves was earlier called hypercohomology, but usually now just "cohomology".
More generally, | 25,976 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
for any complex of sheaves "E" (not necessarily bounded below) on a space "X", the cohomology group "H"("X","E") is defined as a group of morphisms in the derived category of sheaves on "X":
where Z is the constant sheaf associated to the integers, and "E"["j"] means the complex "E" shifted "j" steps to the left.
# Poincaré duality and generalizations.
A central result in topology is the Poincaré duality theorem: for a closed oriented connected topological manifold "X" of dimension "n" and a field "k", the group "H"("X","k") is isomorphic to "k", and the cup product
is a perfect pairing for all integers "j". That is, the resulting map from "H"("X","k") to the dual space "H"("X","k")* is | 25,977 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
an isomorphism. In particular, the vector spaces "H"("X","k") and "H"("X","k")* have the same (finite) dimension.
Many generalizations are possible using the language of sheaf cohomology. If "X" is an oriented "n"-manifold, not necessarily compact or connected, and "k" is a field, then cohomology is the dual of cohomology with compact support:
For any manifold "X" and field "k", there is a sheaf "o" on "X", the orientation sheaf, which is locally (but perhaps not globally) isomorphic to the constant sheaf "k". One version of Poincaré duality for an arbitrary "n"-manifold "X" is the isomorphism:
More generally, if "E" is a locally constant sheaf of "k"-vector spaces on an "n"-manifold "X" | 25,978 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
and the stalks of "E" have finite dimension, then there is an isomorphism
With coefficients in an arbitrary commutative ring rather than a field, Poincaré duality is naturally formulated as an isomorphism from cohomology to Borel–Moore homology.
Verdier duality is a vast generalization. For any locally compact space "X" of finite dimension and any field "k", there is an object "D" in the derived category "D"("X") of sheaves on "X" called the dualizing complex (with coefficients in "k"). One case of Verdier duality is the isomorphism:
For an "n"-manifold "X", the dualizing complex "D" is isomorphic to the shift "o"["n"] of the orientation sheaf. As a result, Verdier duality includes Poincaré | 25,979 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
duality as a special case.
Alexander duality is another useful generalization of Poincaré duality. For any closed subset "X" of an oriented "n"-manifold "M" and any field "k", there is an isomorphism:
This is interesting already for "X" a compact subset of "M" = R, where it says (roughly speaking) that the cohomology of R−"X" is the dual of the sheaf cohomology of "X". In this statement, it is essential to consider sheaf cohomology rather than singular cohomology, unless one makes extra assumptions on "X" such as local contractibility.
# Higher direct images and the Leray spectral sequence.
Let "f": "X" → "Y" be a continuous map of topological spaces, and let "E" be a sheaf of abelian groups | 25,980 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
on "X". The direct image sheaf "f""E" is the sheaf on "Y" defined by
for any open subset "U" of "Y". For example, if "f" is the map from "X" to a point, then "f""E" is the sheaf on a point corresponding to the group "E"("X") of global sections of "E".
The functor "f" from sheaves on "X" to sheaves on "Y" is left exact, but in general not right exact. The higher direct image sheaves R"f""E" on "Y" are defined as the right derived functors of the functor "f". Another description is that R"f""E" is the sheaf associated to the presheaf
on "Y". Thus, the higher direct image sheaves describe the cohomology of inverse images of small open sets in "Y", roughly speaking.
The Leray spectral sequence | 25,981 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
relates cohomology on "X" to cohomology on "Y". Namely, for any continuous map "f": "X" → "Y" and any sheaf "E" on "X", there is a spectral sequence
This is a very general result. The special case where "f" is a fibration and "E" is a constant sheaf plays an important role in homotopy theory under the name of the Serre spectral sequence. In that case, the higher direct image sheaves are locally constant, with stalks the cohomology groups of the fibers "F" of "f", and so the Serre spectral sequence can be written as
for an abelian group "A".
A simple but useful case of the Leray spectral sequence is that for any closed subset "X" of a topological space "Y" and any sheaf "E" on "X", writing | 25,982 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
"f": "X" → "Y" for the inclusion, there is an isomorphism
As a result, any question about sheaf cohomology on a closed subspace can be translated to a question about the direct image sheaf on the ambient space.
# Finiteness of cohomology.
There is a strong finiteness result on sheaf cohomology. Let "X" be a compact Hausdorff space, and let "R" be a principal ideal domain, for example a field or the ring Z of integers. Let "E" be a sheaf of "R"-modules on "X", and assume that "E" has "locally finitely generated cohomology", meaning that for each point "x" in "X", each integer "j", and each open neighborhood "U" of "x", there is an open neighborhood "V" ⊂ "U" of "x" such that the image of "H"("U","E") | 25,983 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
→ "H"("V","E") is a finitely generated "R"-module. Then the cohomology groups "H"("X","E") are finitely generated "R"-modules.
For example, for a compact Hausdorff space "X" that is locally contractible (in the weak sense discussed above), the sheaf cohomology group "H"("X",Z) is finitely generated for every integer "j".
One case where the finiteness result applies is that of a constructible sheaf. Let "X" be a topologically stratified space. In particular, "X" comes with a sequence of closed subsets
such that each difference "X"−"X" is a topological manifold of dimension "i". A sheaf "E" of "R"-modules on "X" is constructible with respect to the given stratification if the restriction of | 25,984 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
"E" to each stratum "X"−"X" is locally constant, with stalk a finitely generated "R"-module. A sheaf "E" on "X" that is constructible with respect to the given stratification has locally finitely generated cohomology. If "X" is compact, it follows that the cohomology groups "H"("X","E") of "X" with coefficients in a constructible sheaf are finitely generated.
More generally, suppose that "X" is compactifiable, meaning that there is a compact stratified space "W" containing "X" as an open subset, with "W"–"X" a union of connected components of strata. Then, for any constructible sheaf "E" of "R"-modules on "X", the "R"-modules "H"("X","E") and "H"("X","E") are finitely generated. For example, | 25,985 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
any complex algebraic variety "X", with its classical (Euclidean) topology, is compactifiable in this sense.
# Cohomology of coherent sheaves.
In algebraic geometry and complex analytic geometry, coherent sheaves are a class of sheaves of particular geometric importance. For example, an algebraic vector bundle (on a locally Noetherian scheme) or a holomorphic vector bundle (on a complex analytic space) can be viewed as a coherent sheaf, but coherent sheaves have the advantage over vector bundles that they form an abelian category. On a scheme, it is also useful to consider the quasi-coherent sheaves, which include the locally free sheaves of infinite rank.
A great deal is known about the | 25,986 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
cohomology groups of a scheme or complex analytic space with coefficients in a coherent sheaf. This theory is a key technical tool in algebraic geometry. Among the main theorems are results on the vanishing of cohomology in various situations, results on finite-dimensionality of cohomology, comparisons between coherent sheaf cohomology and singular cohomology such as Hodge theory, and formulas on Euler characteristics in coherent sheaf cohomology such as the Riemann–Roch theorem.
# Sheaves on a site.
In the 1960s, Grothendieck defined the notion of a site, meaning a category equipped with a Grothendieck topology. A site "C" axiomatizes the notion of a set of morphisms "V" → "U" in "C" being | 25,987 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
a "covering" of "U". A topological space "X" determines a site in a natural way: the category "C" has objects the open subsets of "X", with morphisms being inclusions, and with a set of morphisms "V" → "U" being called a covering of "U" if and only if "U" is the union of the open subsets "V". The motivating example of a Grothendieck topology beyond that case was the étale topology on schemes. Since then, many other Grothendieck topologies have been used in algebraic geometry: the fpqc topology, the Nisnevich topology, and so on.
The definition of a sheaf works on any site. So one can talk about a sheaf of sets on a site, a sheaf of abelian groups on a site, and so on. The definition of sheaf | 25,988 |
1055357 | Sheaf cohomology | https://en.wikipedia.org/w/index.php?title=Sheaf%20cohomology | Sheaf cohomology
f sets on a site, a sheaf of abelian groups on a site, and so on. The definition of sheaf cohomology as a derived functor also works on a site. So one has sheaf cohomology groups "H"("X", "E") for any object "X" of a site and any sheaf "E" of abelian groups. For the étale topology, this gives the notion of étale cohomology, which led to the proof of the Weil conjectures. Crystalline cohomology and many other cohomology theories in algebraic geometry are also defined as sheaf cohomology on an appropriate site.
# References.
- . English translation.
# External links.
- The thread "Sheaf cohomology and injective resolutions" on MathOverflow
- The thread "Sheaf cohomology" on Stack Exchange | 25,989 |
1055458 | Healthy eating pyramid | https://en.wikipedia.org/w/index.php?title=Healthy%20eating%20pyramid | Healthy eating pyramid
Healthy eating pyramid
The Healthy Eating Pyramid (alternately, Healthy Eating Plate) is a nutrition guide developed by the Harvard School of Public Health, suggesting quantities of each food category that a human should eat each day. The healthy eating pyramid is intended to provide a sound eating guide than the widespread food guide pyramid created by the USDA.
The new pyramid aims to include more recent research in dietary health not present in the USDA's 1992 guide. The original USDA pyramid has been criticized for not differentiating between refined grains and whole grains, between saturated fats and unsaturated fats, and for not placing enough emphasis on exercise and weight control.
# | 25,990 |
1055458 | Healthy eating pyramid | https://en.wikipedia.org/w/index.php?title=Healthy%20eating%20pyramid | Healthy eating pyramid
Food groups.
In general terms, the healthy eating pyramid recommends the following intake of different food groups each day, although exact amounts of calorie intake depends on sex, age, and lifestyle:
- At most meals, whole grain foods including oatmeal, whole-wheat bread, and brown rice; 1 piece or .
- Plant oils, including olive oil, canola oil, soybean oil, corn oil, and sunflower seed oil; per day
- Vegetables, in abundance 3 or more each day; each serving = .
- 2–3 servings of fruits; each serving = 1 piece of fruit or .
- 1–3 servings of nuts, or legumes; each serving = .
- 1–2 servings of dairy or calcium supplement; each serving = non fat or of whole.
- 1–2 servings of poultry, | 25,991 |
1055458 | Healthy eating pyramid | https://en.wikipedia.org/w/index.php?title=Healthy%20eating%20pyramid | Healthy eating pyramid
3 servings of fruits; each serving = 1 piece of fruit or .
- 1–3 servings of nuts, or legumes; each serving = .
- 1–2 servings of dairy or calcium supplement; each serving = non fat or of whole.
- 1–2 servings of poultry, fish, or eggs; each serving = or 1 egg.
- Sparing use of white rice, white bread, potatoes, pasta and sweets;
- Sparing use of red meat and butter.
# See also.
- 5 A Day
- Dietary supplement
- Dieting
- List of diets
- Essential nutrient
- Food and Nutrition Service
- Food pyramid (nutrition)
- Functional food
- Health food restaurants
- Healthy diet
- Human nutrition
- MyPlate
- Nutrition education
- Orthorexia nervosa (an obsession with healthy eating) | 25,992 |
1055460 | Greatest Stories Live | https://en.wikipedia.org/w/index.php?title=Greatest%20Stories%20Live | Greatest Stories Live
Greatest Stories Live
Greatest Stories Live is the first live album by the American singer/songwriter Harry Chapin, recorded over three nights at three California venues, and released in 1976. Certain elements had to be re-recorded in the studio due to technical problems with the live recordings. The original LP release featured three new studio tracks, two of which ("She Is Always Seventeen" and "Love Is Just Another Word") were excluded from the CD release. "A Better Place to Be" was released as a single, and did manage to crack the Billboard Hot 100 chart.
The album is popular for its extended cut of "30,000 Pounds of Bananas", infamous for Chapin's recounting of his brothers' remarks after | 25,993 |
1055460 | Greatest Stories Live | https://en.wikipedia.org/w/index.php?title=Greatest%20Stories%20Live | Greatest Stories Live
hearing the original ending: "Harry...it sucks." The quote became so popular with Harry Chapin fans that concert shirts were sold with the quotation on it.
# Track listing (CD release).
- "She Is Always Seventeen" and "Love Is Just Another Word" appear between "30,000 Pounds of Bananas" and "The Shortest Story" on side 4 of the original 1976 vinyl release.
# Personnel.
- Harry Chapin - guitar, vocals
- Ron Bacchiocchi - synthesizer, percussion, clavinet
- Ed Bednarski - clarinet
- Stephen Chapin - synthesizer, piano, vocals
- Tom Chapin - guitar, banjo, vocals
- Christine Faith - vocals
- Cheryl Ferrio - vocals
- Howie Fields - drums
- David Kondziela - vocals
- Paul Leka - piano, | 25,994 |
1055460 | Greatest Stories Live | https://en.wikipedia.org/w/index.php?title=Greatest%20Stories%20Live | Greatest Stories Live
clavinet
- Ed Bednarski - clarinet
- Stephen Chapin - synthesizer, piano, vocals
- Tom Chapin - guitar, banjo, vocals
- Christine Faith - vocals
- Cheryl Ferrio - vocals
- Howie Fields - drums
- David Kondziela - vocals
- Paul Leka - piano, clavinet
- Michael Masters - cello
- Tim Moore - piano
- Mark Mundy - vocals
- Ronald Palmer - guitar, vocals
- Don Payne - bass
- Kathy Ramos - vocals
- Tim Scott - cello
- Allan Schwartzberg - drums
- Frank Simms - vocals
- George Simms - vocals
- Ken Smith - percussion
- Bob Springer - percussion
- John Tropea - guitar
- Betsy Wager - vocals
- Doug Walker - bass, guitar, vocals
- John Wallace - bass, vocals
- Sue White - vocals | 25,995 |
1055437 | Deniable encryption | https://en.wikipedia.org/w/index.php?title=Deniable%20encryption | Deniable encryption
Deniable encryption
In cryptography and steganography, plausibly deniable encryption describes encryption techniques where the existence of an encrypted file or message is deniable in the sense that an adversary cannot prove that the plaintext data exists.
The users may convincingly deny that a given piece of data is encrypted, or that they are able to decrypt a given piece of encrypted data, or that some specific encrypted data exists. Such denials may or may not be genuine. For example, it may be impossible to prove that the data is encrypted without the cooperation of the users. If the data is encrypted, the users genuinely may not be able to decrypt it. Deniable encryption serves to undermine | 25,996 |
1055437 | Deniable encryption | https://en.wikipedia.org/w/index.php?title=Deniable%20encryption | Deniable encryption
an attacker's confidence either that data is encrypted, or that the person in possession of it can decrypt it and provide the associated plaintext.
# Function.
Deniable encryption makes it impossible to prove the existence of the plaintext message without the proper decryption key. This may be done by allowing an encrypted message to be decrypted to different sensible plaintexts, depending on the key used. This allows the sender to have plausible deniability if compelled to give up his or her encryption key.
The notion of "deniable encryption" was used by Julian Assange and Ralf Weinmann in the Rubberhose filesystem and explored in detail in a paper by Ran Canetti, Cynthia Dwork, Moni Naor, | 25,997 |
1055437 | Deniable encryption | https://en.wikipedia.org/w/index.php?title=Deniable%20encryption | Deniable encryption
and Rafail Ostrovsky in 1996.
## Scenario.
Deniable encryption allows the sender of an encrypted message to deny sending that message. This requires a trusted third party. A possible scenario works like this:
- 1. Bob suspects his wife Alice is engaged in adultery. That being the case, Alice wants to communicate with her secret lover Carl. She creates two keys, one intended to be kept secret, the other intended to be sacrificed. She passes the secret key (or both) to Carl.
- 2. Alice constructs an innocuous message M1 for Carl (intended to be revealed to Bob in case of discovery) and an incriminating love letter M2 to Carl. She constructs a cipher-text C out of both messages, M1 and M2, | 25,998 |
1055437 | Deniable encryption | https://en.wikipedia.org/w/index.php?title=Deniable%20encryption | Deniable encryption
and emails it to Carl.
- 3. Carl uses his key to decrypt M2 (and possibly M1, in order to read the fake message, too).
- 4. Bob finds out about the email to Carl, becomes suspicious and forces Alice to decrypt the message.
- 5. Alice uses the sacrificial key and reveals the innocuous message M1 to Bob. Since it is impossible for Bob to know for sure that there might be other messages contained in C, he might assume that there "are" no other messages (alternatively, Bob may not be familiar with the concept of plausible encryption in the first place, and thus may not be aware it is even possible for C to contain more than one message).
Another possible scenario involves Alice sending the same | 25,999 |
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