Samantha912/NLP_A2_WTH huggingface dataset:
In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator  acting on an inner product space is called positive-semidefinite (or non-negative) if, for every ,  and , where  is the domain of . Positive-semidefinite operators are denoted as .  The operator is said to be positive-definite, and written , if  for all .

In physics (specifically quantum mechanics), such operators represent quantum states, via the density matrix formalism.

Cauchy–Schwarz inequality 

If  then

Indeed, let  Applying Cauchy–Schwarz inequality to the inner product

as  proves the claim.

It follows that  If  is defined everywhere, and  then

On a complex Hilbert space, if A ≥ 0 then A is symmetric 
Without loss of generality, let the inner product  be anti-linear on the first argument and linear on the second. (If the reverse is true, then we work with  instead). For  the polarization identity

and the fact that  for positive operators, show that  so  is symmetric.

In contrast with the complex case, a positive-semidefinite operator on a real Hilbert space  may not be symmetric. As a counterexample, define  to be an operator of rotation by an acute angle  Then  but  so  is not symmetric.

If A ≥ 0 and Dom A = , then A is self-adjoint and bounded 
The symmetry of  implies that  and  For  to be self-adjoint, it is necessary that  In our case, the equality of domains holds because  so  is indeed self-adjoint. The fact that  is bounded now follows from the Hellinger–Toeplitz theorem.

This property does not hold on

Order in self-adjoint operators on  
A natural ordering of self-adjoint operators arises from the definition of positive operators. Define  if the following hold:

  and  are self-adjoint
 

It can be seen that a similar result as the Monotone convergence theorem holds for monotone increasing, bounded, self-adjoint operators on Hilbert spaces.

Application to physics: quantum states 

The definition of a quantum system includes a complex separable Hilbert space  and a set  of positive trace-class operators  on  for which  The set  is the set of states. Every  is called a state or a density operator. For  where  the operator  of projection onto the span of  is called a pure state. (Since each pure state is identifiable with a unit vector  some sources define pure states to be unit elements from  States that are not pure are called mixed.

References 

 

Operator theory
Península de Hualpén Nature Sanctuary is a protected area near Concepción in Biobío Region of central Chile. The sanctuary covers the Hualpén Peninsula, which extends into the Pacific Ocean west of the city of Hualpén and north of the mouth of the Biobío River.

References

1976 establishments in Chile
Protected areas established in 1976
Protected areas of Biobío Region
Valdivian temperate forests
Nature sanctuaries of Chile
Qila-e-Ark is a palace fort in Aurangabad, Maharashtra, India, built by the sixth mughal emperor Aurangzeb Alamgir in 1650. The palace fort was denotified from the state archeological department in 1971.
The palace was used as a government college during the Nizam's period, later the college was shifted. And since the denotification, the palace is in ruins. The palace has many notable buildings namely Zenana mahal or Zebunnisa Mahal, Mardana mahal, Durbar, Aurangzeb's Mosque.

since years several organizations and experts have been suggesting that the palace can be restored and be opened to the public which will revive the palace and the tourism industry. Many organizations in Aurangabad are organizing heritage walks in the qila e ark to spread awareness about the monument.

List of gates

Palace complex

References

Palaces in Maharashtra
Aurangabad, Maharashtra
History of Maharashtra
History of India
Mughal architecture
Manihot carthaginensis subsp. glaziovii, also known as Manihot glaziovii, the tree cassava or Ceara rubber tree, is a species of deciduous flowering plant in the spurge family, Euphorbiaceae, that is native to eastern Brazil.

Description

Leaves - palmipartite, peltate; lobes broadly ovate to obovate; green above, glaucous beneath.
Flowers - show branched inflorescence. Unisexual flowers are greenish-white or pale yellow with reddish markings.
Fruit - globose.

Common names
French - manioc de ceara, maniçoba, ceara, caouchouc de ceara
Portuguese - maniçoba
Swahili - mpira 
Yoruba - gbaguda

Uses
The tree cassava was used a source of rubber, instead of Hevea brasiliensis throughout the world. The plant is introduced largely in the world, but now it is classified as one of the highly invasive plant of the world.

This species is useful in casssava breeding because it is a wild relative. Several quantitative trait loci (QTLs) are known to be usable or in use for introgression into cultivated cassava. This includes those for cassava brown streak disease resistance found by Abaca et al., 2013 and four found by Nzuki et al., 2017.

Invasiveness 
The species is invasive in New Caledonia.

References

Further reading
History of Manihot glaziovii
An acid phosphatase from Manihot glaziovii as an alternative to alkaline Phosphatase for molecular cloning experiments.
Characterisation and evaluation of a novel feedstock, Manihot glaziovii, Muell. Arg, for production of bioenergy carriers: Bioethanol and biogas.

Manihoteae
Flora of Brazil
Plant subspecies
A concentric reducer is used to join pipe sections or tube sections on the same axis. The concentric reducer is cone-shaped, and is used when there is a shift in diameter between pipes. For example, when a 1" pipe transitions into a 3/4" pipe and the top or bottom of the pipe doesn't need to remain level. This pipe reducer may be used when there is a single diameter change or multiple diameter changes.
Unlike eccentric reducers, concentric reducers have a common center line. Concentric reducers are useful when cavitation is present.
 Eccentricity occurs when the centerline is offset.

See also 
 Piping and plumbing fitting
 Reducer

References

Piping
Pumps
Plumbing
Echinorhinus is the only extant genus in the family Echinorhinidae.

Taxonomy
Echinorhinidae are traditionally classified in the order Squaliformes, together with kitefin and gulper sharks. However, a phylogenetic estimate based on gene capture data and  mitochondrial data suggests that they are not squaliform sharks, but may be more likely to be appropriately classed in their own group, as a sister group to angel sharks and sawsharks. Phylogenetic placement of Echinorhinidae has been ambiguous in morphological and molecular studies, either being included within Squaliformes, considered sister to Squaliformes, or placed in a separate group with Sawsharks (Pristiophoriformes) or angel sharks (Squatiniformes). For this reason they are sometimes given their own order, Echinorhiniformes.

Etymology
The name is from Greek echinos meaning "spiny" and rhinos meaning "nose".

Species
 Echinorhinus brucus Bonnaterre, 1788 (bramble shark)
 Echinorhinus cookei Pietschmann, 1928 (prickly shark)

Description
This genus includes two extant species of uncommon, little-known sharks. Both species are relatively large sharks, at  in body length. They are characterized by a short nose and by rough, thorn-like dermal denticles scattered over its body, some of which may be fused together. They have no anal fin. Two small spineless dorsal fins are positioned far back.

Biology
They are ovoviviparous, with the mother retaining the egg-cases inside her body until they hatch, producing litters up to 24 pups. They feed on smaller sharks, smaller bony fish, and on crabs and cephalopods.

Distribution
These sharks are found worldwide in cold temperate to tropical seas from the surface down to .

See also

 List of prehistoric cartilaginous fish genera
 List of fish families

References

 
 
 
 FAO Species Catalogue Volume 4 Parts 1 and 2 Sharks of the World

Echinorhinidae
Extant Campanian first appearances
Shark genera
Taxa named by Henri Marie Ducrotay de Blainville
Seliște is a commune in Nisporeni District, Moldova. It is composed of two villages, Păruceni and Seliște.

Notable people
 Tudor Cataraga

References

Communes of Nisporeni District
My Little Pony: Pony Life is an animated children's television series based on Hasbro's My Little Pony franchise. The series is produced by Entertainment One, in collaboration with Boulder Media. The series is the successor and spin-off to 2010's My Little Pony: Friendship Is Magic and the fourth animated series based on the franchise overall. The series features a new animation style, setting and comedic tone. The series premiered on Treehouse TV in Canada on June 21, 2020 and on Discovery Family in the United States on November 7, 2020. A second season was announced before the series made its debut in the United States. The second season premiered on Tiny Pop in the UK on April 2, 2021, and in the United States on Discovery Family, following it on April 10, 2021.

Series overview

Episodes

Season 1 (2020–21)

Season 2 (2021)

Shorts

See also 
 List of My Little Pony: Friendship Is Magic episodes

Notes

References

External links 
 
 Two Episodes of Pony Life Possibly Revaled "The Best of the Worst" and "Princess Probz" - June 13th Airdate
 Two New Episodes of Pony Life Possibly Revealed: How Applejack Got Her Hat Back and Cute-Pocalypse Meow
 Yet Two More Pony Life Episode Titles and Synopses Appear: Bad Thing No 3 and Pinkie Pie: Hyper Helper
 More Pony Life Episodes Revealed - #7 -The Trial Less Trotten; Death of a Sales-Pony / #8 - Bighoof Walking; The Fluttershy Effect

Lists of American children's animated television series episodes
Produce 48 is a 2018 South Korean competition television show on Mnet in which a girl group is formed from a large pool of South Korean and Japanese idols, most of whom are represented by major idol talent agencies such as AKB48 Group. The show starts with 96 contestants, with occasional rounds of competition and voting, some of which result in elimination from the contest. Of the 96 contestants, 57 of them are from South Korean management companies, and 39 of them are from Japanese idol groups, composed of current members of AKB48 and their sister groups. The final 12 contestants, with no nationality caps, as voted only by Korean viewers, will promote as a group for two and a half years.

Contestants
The spelling of names in English is according to the official website. The Korean contestants are presented in Eastern order (family name, given name), while the names of the Japanese contestants are presented in Western order (given name, family name) and also with their Japanese names. The age listed is according to the East Asian age reckoning. Episode rankings presented below are not accurate & episode 4 rankings are missing. 

Color key:

Contestants by ranking as shown below:

Group Battle Performances (Episode 3–4) 

Color key

Bold denotes the person who picked the team members. Sakura Miyawaki chose her team first, and 14 other captains were randomly selected to choose their members afterwards.

Position Evaluation Performances (Episode 6–7)

Each contestant chose to perform in either the Vocal/Rap or Dance position on a particular song, starting with Noe Yamada, who ranked #14 in the previous episode. The top 12 from the previous episode were then allowed to choose a filled group and replace the lowest-ranking contestant, forcing them to choose a mystery song for either Vocal/Rap (BoA's "Merry Chri") or Dance (Jax Jones's "Instruction"). The top contestant for each song received a 5,000 vote bonus, while the top contestant among all Vocal/Rap songs and the top contestant among all Dance songs received a 100,000 vote bonus.  For the Vocal/Rap position, final rankings of only several girls were shown. Also, the number of votes received by "Merry Chri" team members was not posted.

Color key

Concept Evaluation (Episode 9–10) 
The Concept Evaluation votes came from the studio audience. The winning team was the group that performed "Rollin' Rollin'"; they received a bonus of 20,000 votes each, with the top vote getter within the team, Miru Shiroma, receiving 50,000 votes.

Color key

Debut Evaluation Performances (Episode 12)

Color key

Notes

References

 
Produce 101
Produce 101
Produce 101
The Sasaki metric is a natural choice of Riemannian metric on the tangent bundle of a Riemannian manifold.
Introduced by Shigeo Sasaki in 1958.

Construction

Let  be a Riemannian manifold, denote by  the tangent bundle over .
The Sasaki metric  on  is uniquely defined by the following properties:
The map  is a Riemannian submersion.
The metric on each tangent space  is the Euclidean metric induced by .
Assume  is a curve in  and  is a parallel vector field along . Note that  forms a curve in . For the Sasaki metric, we have for any ; that is, the curve  normally crosses the tangent spaces .

References
S. Sasaki, On the differential geometry of tangent bundle of Riemannian manifolds, Tôhoku Math. J.,10 (1958), 338–354.

Riemannian manifolds
Feyenoord is a Dutch professional football club from Rotterdam, that plays in the Eredivisie. Founded as Wilhelmina in 1908, the club changed its name in 1912 to SC Feijenoord (since 1973 Feyenoord for international reasons) and moved to De Kuip in 1937. Feyenoord is one of the most successful clubs in the Netherlands, winning 15 Eredivisie titles, 11 KNVB Cups and two Johan Cruijff Shields. The club also has won one European Cup, two UEFA Cups and one Intercontinental Cup. The club is historically one of the three clubs that have dominated the Eredivisie (first tier) of Dutch football, the others being Ajax and PSV. These three clubs have always played in the Eredivisie, since its inception in 1952, and have never been relegated to lower divisions.

List of players 

Appearances and goals are for first-team league matches only, including both the Netherlands Football League Championship and Eredivisie.
Players are listed according to the date of their first team debut for the club.

Statistics correct as of 04 January 2023.

Table headers
 Nationality – If a player played international football, the country/countries he played for are shown. Otherwise, the player's nationality is given as their country of birth.
 Feyenoord career – The year of the player's first appearance for Feyenoord to the year of his last appearance.
 Appearances – The number of league games played.
 Goals – The number of league goals scored.

References

 
Association football player non-biographical articles
Feyenoord
The 30th Reconnaissance Squadron is an active United States Air Force Unit, originally constituted as the 30th Photographic Reconnaissance Squadron in February 1943.  It has held this designation since September 2005.

30th Reconnaissance Squadron may also refer to:
 The 920th Air Refueling Squadron, constituted as the 30th Reconnaissance Squadron (Heavy) but redesignated 420th Bombardment Squadron (Heavy) before being activated in June 1942. 
 The 30th Tactical Reconnaissance Squadron active as the 30th Reconnaissance Squadron (Fighter) from April 1943 to August 1943. 

See also
 The 30th Photographic Reconnaissance Squadron
 The 30th Strategic Reconnaissance Squadron
 The 30th Tactical Reconnaissance Squadron, active from August 1943 to May 1944
 The 30th Tactical Reconnaissance Squadron, active from November 1952 to April 1976
 The 30th Weather Reconnaissance Squadron
Rita Thijs (born 7 February 1958) is a Belgian sprinter. She competed in the women's 4 × 400 metres relay at the 1976 Summer Olympics.

References

1958 births
Living people
Athletes (track and field) at the 1976 Summer Olympics
Belgian female sprinters
Belgian female middle-distance runners
Olympic athletes for Belgium
Place of birth missing (living people)
Olympic female sprinters
20th-century Belgian women
This is the list of notable stars in the constellation Perseus, sorted by decreasing brightness.

See also 
 List of stars by constellation

Ambiguity 
Some sources, including Starry Night (planetarium software), an atlas,  and a web site attribute the name 'Atik' to Zeta Persei instead of nearby Omicron Persei.

References 

 
 
 

List
Perseus
Eleutherodactylus patriciae is a species of frog in the family Eleutherodactylidae endemic to the Cordillera Central, Dominican Republic, at elevations of  asl. Its natural habitats are closed upland forest and forest remnants.
It is threatened by habitat loss caused by agriculture and by disturbance from ecotourism. Also chytridiomycosis is a threat.

References

patriciae
Endemic fauna of the Dominican Republic
Amphibians of the Dominican Republic
Amphibians described in 1965
Taxonomy articles created by Polbot
The following is a navigational list of notable literary works which are set at Christmas time, or contain Christmas amongst the central themes.

Novels and novellas
Agatha Christie, Hercule Poirot's Christmas
Charles Dickens, A Christmas Carol
Charles Dickens, The Chimes
Charles Dickens, The Cricket on the Hearth
Charles Dickens, The Battle of Life
Charles Dickens, The Haunted Man and The Ghost's Bargain
Janet Evanovich, Visions of Sugar Plums
Frederick Forsyth, The Shepherd
Jostein Gaarder, The Christmas Mystery
John Grisham, Skipping Christmas
Maureen Johnson, John Green and Lauren Myracle, Let It Snow
C. S. Lewis, The Lion, the Witch and the Wardrobe
Christopher Moore, The Stupidest Angel: A Heartwarming Tale of Christmas Terror

Short stories
Hans Christian Andersen, "The Fir-Tree"
Truman Capote, "A Christmas Memory" (published in Mademoiselle)
John Cheever, "Christmas is a Sad Season for the Poor"
Agatha Christie, The Adventure of the Christmas Pudding
Agatha Christie, A Christmas Tragedy
Fyodor Dostoevsky, "A Christmas Tree and a Wedding"
Fyodor Dostoevsky, "The Beggar Boy at Christ's Christmas Tree" () (from A Writer's Diary)
Arthur Conan Doyle, "The Adventure of the Blue Carbuncle"
Nikolai Gogol, "Christmas Eve" (from Evenings on a Farm Near Dikanka)
O. Henry, The Gift of the Magi
E. T. A. Hoffmann, "Nussknacker und Mausekönig" (The Nutcracker and the Mouse King)
Leo Tolstoy, "Papa Panov's Special Christmas" (translation of Saillens)
Dylan Thomas, A Child's Christmas in Wales
Philip Van Doren Stern, The Greatest Gift 
Kurt Vonnegut, While Mortals Sleep (book of short stories)

Children's 
 Janet and Allan Ahlberg, The Jolly Christmas Postman
 Maya Angelou, Amazing Peace
L. Frank Baum, The Life and Adventures of Santa Claus
 Julia Donaldson, and Axel Scheffler, Stick Man
 Richard Paul Evans, The Christmas Box, The Light of Christmas
Cornelia Funke, When Santa Fell to Earth
Dr. Seuss, How the Grinch Stole Christmas!
Astrid Lindgren, Brenda Brave Helps Grandmother (Kajsa Kavat hjälper mormor)
Astrid Lindgren, A Calf for Christmas (När Bäckhultarn for till stan)
Astrid Lindgren, Christmas in the Stable (Jul i stallet)
Astrid Lindgren, The Runaway Sleigh Ride (Titta Madicken, det snöar!)
Astrid Lindgren, The Tomten (Tomte är vaken)
Astrid Lindgren, The Tomten and the Fox (Räven och Tomten)
 Martin Waddell, Room for a Little One: A Christmas Tale

Poetry
"Old Santeclaus with Much Delight"
Clement Clarke Moore, "A Visit from St. Nicholas" (also known as "'Twas the Night before Christmas")
George Robert Sims, Christmas Day in the Workhouse
T. S. Eliot, "Journey of the Magi"
Viktor Rydberg, Tomten

Collections
 Bettye Collier-Thomas, A Treasury of African American Christmas Stories
 David Sedaris, Holidays on Ice
J. R. R. Tolkien, Letters from Father Christmas
 Jeanette Winterson, Christmas Days

Nonfiction

Francis Pharcellus Church, "Yes, Virginia, there is a Santa Claus" (1897 newspaper editorial)

References 

Christmas
 
Christmas
literature
Line 10 of Chongqing Rail Transit is a rapid transit line that opened on 28 December 2017. Rapid trains started operating on Line 10 in June 2020.

The trains on Line 10, which links Jiangbei Airport and Chongqing North railway station, are equipped with a luggage rack on each car.

Opening timeline

Stations (north to south)

Notes

References

 
Railway lines opened in 2017
Airport rail links in China
2017 establishments in China
Arthur Forbes Gordon Kilby  (3 February 1885 – 25 September 1915) was an English officer in the British Army during the First World War, and recipient of the Victoria Cross.

Early life
Forbes was born on 3 February 1885 in East Hayes, Cheltenham, the only son of Sandford and Alice F. Kilby, He was educated at Bilton Grange near Rugby and Winchester College. He graduated from the Royal Military College, Sandhurst in 1905, and was commissioned into the South Staffordshire Regiment.

Military career
Kilby was promoted to Captain on 1 April 1910 when he was only 25. An accomplished linguist, he was fluent in Hungarian and German, and when war broke out in August 1914 he was learning Spanish. He was posted to the British Expeditionary Force in France and Flanders with the 2nd Battalion, The South Staffordshire Regiment during the First World War.

Kilby was 30 years old, and a captain when he performed an act for which he was awarded the VC and during which he died. He was killed in action on 25 September 1915 whilst leading his company attacking enemy positions near Cuinchy, on the Le Bassee Canal, on the first day of the Battle of Loos. Kilby's extreme heroism and gallantry during this attack was noted and he was awarded a posthumous Victoria Cross on 30 March 1916.

Citation

Legacy
Kilby's heroism was acknowledged by the German defenders who erected a memorial cross at the location of his death.  His body was eventually found on 19 February 1929 and interred at Arras Road Cemetery, Roclincourt, Plot III, Row N, Grave 27.

In 1919 a memorial was placed in St Nicholas's Chapel, York Minster; which was inscribed with details of Arthur Kilby's deeds and awards, and contained a bust of him surmounted by the family coat-of-arms.  His name is also listed on a war memorial in St Cuthbert's Church, Peasholme Green, York.

In 2012, Kilby's Victoria Cross, along with another awarded to Private Sidney Godley, the very first VC recipient of World War I, was sold at a London auction for £276,000 each to Lord Ashcroft. Captain Kilby's medal are now part of the Lord Ashcroft Medal Collection in the Imperial War Museum in London.

References

Monuments to Courage (David Harvey, 1999)
The Register of the Victoria Cross (This England, 1997)
VCs of the First World War - The Western Front 1915 (Peter F. Batchelor & Christopher Matson, 1999)

1885 births
1915 deaths
South Staffordshire Regiment officers
British Army personnel of World War I
British World War I recipients of the Victoria Cross
British military personnel killed in World War I
Military personnel from Cheltenham
Recipients of the Military Cross
British Army recipients of the Victoria Cross
People educated at Winchester College
Graduates of the Royal Military College, Sandhurst
People educated at Bilton Grange
Missing in action of World War I