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Bouyei language

The Bouyei language (autonym: Haausqyaix, also spelled Buyi, Buyei or Puyi; ; tiếng Bố Y or tiếng Giáy) is a language spoken by the Bouyei ethnic group of Southern Guizhou Province, China. Classified as a member of the Northern Tai group in the Tai language branch of the Tai–Kadai language family, the language has over 2.5 million native speakers and is also used by the Giay people (Giáy) in some parts of Vietnam. There are native speakers living in France or the United States as well, which emigrated from China or Vietnam. About 98% of the native speakers are in China.

Bouyei's characteristics are similar to the other members of its language branch. It is generally monosyllabic and word order and particles are the main forms of grammar. Bouyei's syllable initials match up closely to the other Northern Tai languages, with relatively fast simplification and merging. Bouyei sentences can be shown to contain many different levels of phrasing.

The contemporary Bouyei script was developed after the abandonment of the Bouyei-Zhuang Script Alliance Policy in 1981 and was designed from 1981 to 1985. It is focused and phonologically representative and takes the Wangmo County dialect as its foundation.

China
According to a 1950s survey performed by the Chinese government, the Bouyei language as spoken in Guizhou can be divided into three general dialect groups (Snyder 2008).

 * 1) The Southern Guizhou (Qian) group – the largest of the three – from the Qianxinan Bouyei and Miao Autonomous Prefecture, which is mostly intelligible with the Guibian and Guibei Zhuang dialects. This vernacular is spoken in the counties of Wangmo, Ceheng, Luodian, Dushan, Libo, Duyun, Pingtang, Zhenfeng, Anlong, Xingren, and Xinyi.
 * 2) The Central Guizhou (Qian) group – next most spoken of the three – which is spread throughout Qiannan Buyei and Miao Autonomous Prefecture and the suburbs of Guiyang, and is partially intelligible with the Southern Guizhou dialects (it is very similar to the Zhuang dialects of northern Guangxi). This vernacular is spoken in the counties of Longli, Guiding, Qingzhen, Pingba, Kaiyang, Guiyang, and Anshun.
 * 3) The Western Guizhou (Qian) dialects – the least spoken of the three – which is spoken in the counties of Zhenning, Guanling, Ziyun, Qinglong, Pu'an, Liuzhi, Panxian, Shuicheng, Bijie, and Weining. The western dialects show more unique features than the other two groups. Some western dialects have aspirated stops, which is an uncommon feature in northern Tai languages (Snyder 2008).

Wu, Snyder, & Liang (2007) is the most comprehensive Bouyei survey to date, and covers the following data points.

 * Qiannan Bouyei and Miao Autonomous Prefecture
 * Guyang, Changshun County (鼓扬镇)
 * Nanzhai, Dushan County (难寨村)
 * Jichang, Dushan County (基长镇)
 * Fuxi, Duyun County (富溪村)
 * Gonggu Township, Guiding County (巩固乡), now merged
 * Danggu, Huishui County (党古村)
 * Fucun, Libo County (福村)
 * Yangchang, Longli County (羊场镇)
 * Luokun, Luodian County (罗甸县罗悃)
 * Poqiu, Luodian County (罗甸县坡球)
 * Xiliang Township, Pingtang County (西凉乡), now merged
 * Zhangbu Township, Pingtang County (掌布乡)

 * Qianxinan Bouyei and Miao Autonomous Prefecture
 * Pingle Township, Anlong County (平乐乡), now merged
 * Huarong, Ceheng County (册亨县花冗)
 * Zitang, Qinglong County (紫塘村)
 * Fuxing, Wangmo County (复兴镇)
 * Bajie, Xingyi County (巴结镇)
 * Mingu, Zhenfeng County (珉谷镇)

 * Anshun City
 * Huangla Buyei and Miao Ethnic Township, Anshun (黄腊布依族苗族乡)
 * Banle, Zhenning County (镇宁县板乐)
 * Shitouzhai, Zhenning County (镇宁县石头寨)
 * Huohua Township, Ziyun County (火花乡)
 * Nonghe, Ziyun County (弄河村)

 * Liuzhi Special District
 * Fa'er Buyei, Miao, and Yi Ethnic Township, Shuicheng County (发耳布依族苗族彝族乡)

The Yei Zhuang varieties of Wenshan Prefecture, Yunnan are closely related to the Bouyei varieties of Guizhou. Many other languages outside China with the names "Yei", "Yay", "Yoy", are also closely related.

Vietnam
Bouyei is also spoken in northern Vietnam by several groups, the Bouyei people of Muong Khuong District of Lào Cai Province and in Quan Ba District of Ha Giang Province and the Giáy. Edmondson and Gregerson (2001) has determined their language to be most similar to the Bouyei dialects of southwest Guizhou. The Giáy are an officially recognized group in Vietnam who now number nearly 50,000. Some household registries of the Giáy of Vietnam indicate that their ancestors had left Guizhou 160 years ago during the Qing dynasty, and traveled overland to southern Yunnan and then Vietnam (Edmondson & Gregerson 2001). This coincides with the Miao Rebellion (1854–73) of Guizhou. The Giáy are found in the following locations of Vietnam.

Some Giày are in Yên Bái Province.
 * Lào Cai province
 * Tả Van village near Sa Pa
 * Bát Xát District
 * Mường Khương District
 * Bảo Yên District
 * Hà Giang Province
 * Yên Minh District
 * Đồng Văn District
 * Lai Châu Province
 * Mường Tè District
 * Phong Thổ District
 * Cao Bằng Province
 * Bảo Lạc District

The Giáy of Mường Khương District of Lào Cai who call themselves Tu Dí [thu zi] can only speak a form of Chinese, and no Giáy. Their autonym comes from their ancestral place of origin, which is Duyun of Guizhou province, China. According to their household records, they had arrived in Maguan County and in Honghe Prefecture about 200 years ago. Similarly, some Giáy of Vietnam report that they have relatives still living in Hekou, Yunnan province, China (Edmondson & Gregerson 2001).

The Pu Nả people of Tam Đường District, Lai Châu Province, Vietnam call themselves the Vần Nả (with vần meaning 'people'), and number about 5,000 individuals (Lò 2012:11–20). They are also called Quý Châu (Guizhou 贵州), Sa Quý Châu, Củi Chu, Pu Y, or Pâu Thìn. The Pu Nả live in the following villages of Tam Đường District (Lò 2012:18).

 * Bản Giang commune
 * bản Coc Pa
 * bản Giang
 * bản Nà Bỏ
 * bản Nà Sài
 * bản Nà Cơ
 * bản Tẩn Phủ Nhiêu
 * Thèn Xin commune
 * bản Lở Thàng
 * Thèn Xin
 * San Thàng commune
 * bản Tả Xin Chải
 * Xéo Xin Chải
 * Phan Lỉn

The Yay language described by William J. Gedney is in fact the Giáy dialect of Mường Hum, Bát Xát District, Lào Cai (Edmondson & Gregerson 2001). There are also other related Northern Tai languages spoken in Vietnam as well, such Bố Y, Nhang, and Quy Châu (possibly closely related to Tai Mène of Laos). The Bố Y had originally came from around Wangmo County in southwestern Guizhou. Some subgroups of Bố Y call themselves the Pu Na or Pu Thin, meaning 'people of the paddy field'.

Laos
There are also some speakers in Laos. In Laos, the Giáy people are called Yang, which is also used four various Rau peoples living there.

The Yang people, also spelled Nhang, are located in Louang Namtha Province, Oudomxay Province and Phongsaly Province. This three provinces are bordered by Yunnan, and one border Vietnam.

Consonants
The Bouyei script recognizes 32 consonants, with names formed by the consonant in an initial position followed by a long "a" vowel.

Pink: p, t, k, q, z, and c are used only to write Chinese loanwords.

Beige: sl and hr are used for sounds that occur only in certain dialects.

V is pronounced as a before a "u".

An absent consonant may produce a glottal sound. is also heard as a final sound.

Vowels and diphthongs
Bouyei has 77 vowels and diphthongs.

The endings $⟨-er⟩$, $⟨-ao⟩$ , $⟨-ou⟩$ , $⟨-ia⟩$ , $⟨-io⟩$ , $⟨-iao⟩$ , $⟨-ua⟩$ , $⟨-uai⟩$ , and $⟨-ui⟩$ are used in writing Chinese loanwords.

Vowels may also have allophones of.

Another vowel sound may occur phonemically in the dialects of Anshun, Qinglong, Shuicheng, Zhenning, and Ziyun.

Tones
Bouyei has six tones, corresponding to the eight sheng of Middle Chinese: all six in open syllables or with a final or, reduced to two "entering" tones with a final stop.

Marking letters are placed at the end of syllables to indicate tone. Loanword marking letters y, f, j, and q match with Mandarin tones 1, 2, 3, and 4 respectively.

Phonological shifts
Bouyei shows de-voicing of Proto-Tai–Kadai's voiced consonants ( →, → ,  → ), and loss of aspiration.

Proto-Tai–Kadai's tones experienced a splitting into modern Bouyei, shown in the following table.

Ancient Bouyei script
Ancient Bouyei writing was created by borrowing elements from Chinese characters or by mimicking their forms, and is similar to Sawndip. Items collected were mostly Shaman's books of the Buyi ancestors, which were used to select auspicious days, lucky numbers and directions, and divination. The scriptures also produced Nuo books and literary works. The Nuo scripts have been widely circulated among the Buyi people in Libo region for more than a thousand years to praise goodness, condemn evil, advocate filiality, and to promote truth, kindness and beauty; and these have become the code of conduct among the local Buyei people. The epic poem Wang Yulian was a literary work that is believed to be the retelling of a Chinese story in Buyei language. Its manual copies are popular in Zhexiang Township, Wangmo County in Buyei and Miao Autonomous Prefecture in Southwest Guizhou.

Old Modern Bouyei
In November 1956, a scientific conference was held in Guiyang to discuss the creation and implementation of a Latin-based alphabet for Bouyei. The result was a script similar some Zhuang romanizations that used the Longli County dialect as its base. The script was approved by the Chinese government and was put into use in 1957, though its use ceased in 1960.

Current Bouyei script
In 1981 a conference on Bouyei history revised the script developed in 1956 in an attempt to make it more practical and phonologically representative of Wangmo County speech. It also was approved by the Chinese government, and was adopted on an experimental basis in 1982. Feedback was largely positive, and the script was officially brought into use in March 1985 and continues to be used to the present.

Old and current Bouyei Romanization comparisons

Tone Marking Letters

title: Bouyei language


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Leroy Matthiesen

Leroy Matthiesen (June 11, 1921 – March 22, 2010) was an American prelate of the Roman Catholic Church. He served as the sixth bishop of the Diocese of Amarillo in Texas from 1980 to 1997.

Early life
Leroy Matthiesen was born June 11, 1921, in Olfen, an unincorporated community in Runnels County, Texas. He grew up on a cotton farm.

Priesthood
Matthiesen was ordained a priest by Cardinal Amleto Cicognani for the Diocese of Amarillo on March 10, 1946. After receiving a Master of Journalism degree in 1948, Matthiesen was appointed editor of the diocesan newspaper The West Texas Catholic. The paper featured his column “Wise and Otherwise” until 1998.

In 1954, Matthiesen was appointed the founding pastor of St. Laurence Parish in Amarillo. In 1961. he received a Master of School Administration degree and in 1962 was appointed rector of St. Lucian's Preparatory Seminary in Amarillo.

Matthiesen was awarded a Doctor of Journalism degree in 1961, and in 1968 was named principal of Alamo Catholic High School. During this period, he also served for nine years as pastor of St. Francis Parish in Amarillo.

Bishop of Amarillo
On May 30, 1980, Pope John Paul II appointed Matthiesen as bishop of the Diocese of Amarillo. He was consecrated on May 30, 1980. by Archbishop Patrick Flores. Matthiesen received the Isaac Hecker Award for Social Justice in 1984. In September 1981, in protest of the assembly of the neutron bomb at a facility in Pantex, Texas, Matthiesen called for workers there to resign their jobs in protest. None were reported to have obeyed his call. He remarked: "I'm no rabble rouser. On the whole I accomplished what I wanted to by bringing an issue to the consciousness of people. It's amazing how people have begun to live with the unlivable."In 1992, Matthiessen called for a stay of execution for Johnny Frank Garrett, a Texas man convicted of raping and murdering 76 year-old Sister Tadea Benz at an Amarillo convent. Garrett was executed on February 12, 1992.

Matthiesen admitted eight priests into the Diocese of Amarillo after they had undergone treatment following accusations of sexual impropriety. His most controversial priest assignments are Orville Blum, Mattheisen appointed as Principal of Alamo Catholic High and pastor of Sacred Heart Church in Amarillo. Im addition. Salazar and Ed Graff. Both of these priests were known to be serious sexual abusers and Matthiesen was warned not to assign them to parishes by other Church officials.

Retirement and legacy
On January 21, 1997, John Paul II accepted Matthiesen's resignation as bishop of the Diocese of Amarillo. Matthiesen received the Ketteler Award for Social Justice from the Sisters of Divine Providence in 2002. In 2002, he celebrated mass at a conference center in Louisville, Kentucky, to commemorate the 25th anniversary of New Ways Ministry. This mass violated a Vatican directive not to celebrate mass for this group.

In 2003, the diocese settled a lawsuit brought by a Texas woman. She claimed that Rosendo Herrera, a priest in the diocese, had impregnated her when she was 17 years ago. The plaintiff claimed that the diocese and Matthiessen tried to cover up the scandal. The diocese settled for approximately $27,000 for the child. In November 2004, the diocese settled a lawsuit for $50,000 in which Matthiessen was listed as a codefendant. A different female plaintiff claimed that Herrera had engaged in wrongful contact with her. Also in 2004, Matthiessen stirred controversy when he started a fundraising effort to assist three priests whom his successor bishop had removed from public ministry.

In 2009, Matthiessen was presented with the Teacher of Peace Award from Pax Christi USA. In his retirement, Matthiesen published three books:

 * Wise and Otherwise: The Life and Times of a Cottonpicking Texas Bishop (2004)
 * The Golden Years: The History of St. Laurence Cathedral in Amarillo (2005)
 * Lieber Bernard und Elise: The Lives and Times of a German Texas Family (2009)

Leroy Matthiesen died on March 22, 2010, in Amarillo at age 88.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Leroy Matthiesen


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Catawba River

The Catawba River is a major river located in the Southeastern United States. It originates in Western North Carolina and flows into South Carolina, where it later becomes known as the Wateree River. The river is approximately 220 miles (350 km) long. It rises in the Appalachian Mountains and drains into the Piedmont, where it has been impounded through a series of reservoirs for flood control and generation of hydroelectricity. The river is named after the Catawba tribe of Native Americans, which lives on its banks. In their language, they call themselves "yeh is-WAH h’reh", meaning "people of the river."

The river rises in the Blue Ridge Mountains in western McDowell County, North Carolina, approximately 20 miles (30 km) east of Asheville. It flows ENE, falling over two waterfalls, Upper Catawba Falls and Catawba Falls, before being dammed by Lake James, and joining the Linville River. It passes north of Morganton, then southeast through Lake Rhodhiss and Lake Hickory just north of Hickory, and into the Lake Norman reservoir. From Lake Norman it flows south, passing west of Charlotte, then flowing through the Mountain Island Lake and Lake Wylie reservoirs, where it exits the reservoirs approximately 10 miles (15 km) south of the border between North Carolina and South Carolina. The confluence of the South Fork Catawba River and Catawba River is submerged by Lake Wylie near the NC/SC state line.

The river flows into northern South Carolina, passing Rock Hill, through Fishing Creek Reservoir near Great Falls, and into the Lake Wateree reservoir, approximately 30 miles (50 km) northeast of Columbia. At the now-submerged confluence with Wateree Creek, it becomes known as the Wateree River.

Dams
The Catawba has been controlled by several dams, including the following:

North Carolina
 * Lake James Dam
 * Rhodhiss Dam
 * Oxford Dam
 * Lookout Shoals Dam
 * Cowans Ford Dam, creating Lake Norman
 * Mountain Island Lake Dam

South Carolina
 * Lake Wylie Dam in India Hook
 * Fishing Creek Reservoir in Great Falls
 * Dearborn-Great Falls Dam
 * Cedar Creek Reservoir Dam
 * Lake Wateree Dam

Headwaters and basin
The Catawba basin begins on the eastern slopes of the Blue Ridge Mountains, North Carolina, near Evans Knob and Cross Mountain, at the edge of Pisgah National Forest. The Broad River begins collecting water on mountain slopes just to the south, with the two rivers waters meeting up again at the confluence of the Wateree and Congaree Rivers near Wateree, South Carolina.

Controversy
In 2006 the river became the center of a water use controversy between the residents of the Catawba watershed and Cabarrus County, North Carolina. The cities of Concord and Kannapolis are expecting a daily shortfall of 22 e6USgal of water a day by 2035 in their Rocky River watershed and want to pump up to 36 e6USgal of water daily from the Catawba River. The Concord/Kannapolis Interbasin Transfer (IBT) proposal calls for water to be permanently transferred from one river basin to another river basin. Such a transfer is unlike the more common water usage, in which municipalities within the Catawba basin pump water from the river and treat it for residential use. Much of that treated water eventually returns to the Catawba River.

Though neither Concord nor Kannapolis is located in the Catawba River basin (both are located in the Rocky River branch of the larger Pee Dee River basin), the cities said the Catawba River is a regional resource. Opponents of the IBT argued that towns and cities along the Catawba River basin are growing as well, and that the cities' request is too large.

On January 10, 2007, the North Carolina state environmental panel authorized Concord and Kannapolis to pump up to 10 e6USgal a day from the Catawba River. This decision represented a compromise recommended by hearing officers for the Environmental Management Commission. The mayors of Morganton and Valdese said that they were adamantly against the transfer and that the panel's ruling was skewed and biased. Concord's city manager said the approval of the water transfer was "bittersweet", since the panel authorized an amount much lower than was originally requested and the action is likely to be delayed by lawsuits. "“Well, (officials from) Hickory are going to file an appeal,” said Concord Mayor Scott Padgett, who spoke briefly with Hickory Mayor Rudy Wright after the EMC meeting. “His major concern is changing the (interbasin transfer) process. My appeal to him is that there should be a truce. To file an appeal is just going to prolong something we deserve, is less than what we asked for and is going to further hard feelings this has already created.”"

The controversy ended in early 2010 when all the parties reached a settlement. It further limits the amount of water available to Concord and Kannapolis under drought conditions.

A river at risk
Starting in the early autumn months of 2007, residents and businesses of the Catawba basin, along with large swaths of the Southern United States, began to feel the effects of an extreme drought. On October 15, 2007, the Morganton News Herald reported that North Carolina Governor Mike Easley described the drought as "the worst in recorded history".

On January 29, 2008, Duke Energy, the utility responsible for managing the Catawba River, extended its estimated time frame for Stage 4 water restrictions to August. The extension was possible because of conservation measures and the 6 inches of rain the basin received in December. However, area leaders converged on Valdese to hear presentations from representatives of the N.C. Rural Center, N.C. Department of Commerce, N.C. Department of Environment and Natural Resources, and the Appalachian Regional Commission about grants and loans available to help pay for solutions to the drought.

In April 2008 the environmental group American Rivers named the Catawba-Wateree River "the most endangered river in America." Reasons cited for the river's condition are the drought, the presence of 11 hydroelectric dams, global warming, and unchecked development along its banks, with the latter reported as the most serious threat.

On June 11, 2008, South Carolina Governor Mark Sanford signed legislation denoting the Catawba as a state scenic river. The designation carries no land-use restrictions, but it allows the state to convene an advisory group to address river-related concerns.

On June 29, 2009, the EPA announced that four of the top 44 "High Hazard Ash Ponds" in the United States are on the Catawba River. Two ash ponds are adjacent to and discharge into Mountain Island Lake. The EPA High Hazard list also includes ash ponds on Lake Wylie and Lake Norman.

On December 11, 2014, Duke Energy received approval from North Carolina to dump coal ash (containing arsenic, lead, thallium and mercury, among other heavy metals) from the Marshall Steam Station into Lake Norman in order to repair a rusted, leaking pipe at their facility. Groundwater at the Marshall Steam Station flows toward Lake Norman, and the contaminated field abuts the lake for about 30 feet of shoreline near its largest coal ash basin, threatening water quality in the lake.

On October 3, 2015, Duke Energy reported that a sinkhole had formed at the base of the Marshall Steam Station dam north of Charlotte on Lake Norman. The Department of Environmental Quality (DEQ) says Duke Energy placed a liner in the hole and filled it with crushed stone.

The Catawba River basin is one of only four areas left in the southeast with significant populations of Hymenocallis coronaria, the Shoals spider lily. It has one large population left at Landsford Canal State Park.

Crossings
The Catawba River is crossed by many highways over its course. (Note: this list may be incomplete) North Carolina South Carolina
 * Lake James to Rhodhiss Lake
 * Power House Road bridge, near Glen Alpine
 * Watermill Glen Alpine Road bridge, near Glen Alpine
 * Independence Boulevard bridge, in Morganton
 * NC 181 bridge, in Morganton
 * US 64 bridge, in Morganton
 * Huffman Bridge, near Amherst
 * Castle Bridge, near Rutherford College
 * Rhodhiss Lake to Lake Norman
 * Burke Street/Caldwell Drive bridge, in Rhodhiss
 * US 321 bridge, near Hickory
 * NC 127 bridge, near Hickory
 * NC 16 bridge, near Conover
 * Cecil H. Hoffman Bridge (I-40), near Catawba
 * US 70 bridge, near Catawba
 * Buffalo Shoals Road/Hudson Chapel Road bridge, near Long Island
 * NC 150 bridge, near Terrell
 * Lake Norman to Lake Wylie
 * NC 73 bridge, near Lowesville
 * Rozzelle's Ferry Bridge (NC 16), near Mountain Island
 * Randy M. Pendleton Memorial Bridge (NC 27), near Mount Holly
 * Cameron Morrison Bridge (I-85), near Belmont
 * Sloans Ferry Bridge (US 29/US 74), near Belmont
 * Buster Boyd Bridge (NC 49/SC 49), near Lake Wylie
 * Lake Wylie to Lake Wateree
 * John McKee Spratt Memorial Bridge (I-77), near Rock Hill
 * Thomas B. Spratt Memorial Bridge (US 21), near Rock Hill
 * SC 5 bridge, near Catawba
 * Roach S. Stewart Memorial Bridge (SC 9), near Fort Lawn
 * Tom G. Mangum Bridge (SC 97/SC 200), near Great Falls

title: Catawba River


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O'Brien Trophy (ice hockey)

The O'Brien Trophy, or O'Brien Cup,  as labelled on the trophy itself, is a retired trophy that was awarded in the  National Hockey Association (NHA) and the National Hockey League (NHL) ice hockey leagues of North America from 1910 to 1950. It was originally donated to the NHA by Canadian Senator M. J. O'Brien in honour of his son, Ambrose O'Brien. The Cup was fabricated using silver from an O'Brien mine.

The Cup has been awarded under four definitions. From 1910 through 1917, it was awarded to the NHA champion. In 1921, the Cup was transferred to the NHL and awarded to the NHL playoff champion until 1926–27. From 1927–28 until 1937–38, it was awarded to the Canadian Division regular season champion. Starting with the 1938–39 season, it was awarded to the NHL playoff runner-up. After 1949–50, the Cup was retired and has not been awarded since. In total, the Cup has been awarded in 41 seasons to twelve different teams. The Cup is now in the collection of the Hockey Hall of Fame.

History
The Cup was donated to the National Hockey Association by Canadian Senator Michael J. O'Brien in honour of his son, Ambrose O'Brien, who was credited with the formation of the National Hockey Association, the forerunner to the NHL. The Cup was originally to be given to the NHA's championship team. Made entirely from silver from the O'Brien mine, the trophy's value was estimated at CA$600 (over CA$0 in  dollars). Like the Stanley Cup, trustees were named for the trophy. These were NHA executives Harry Trihey, Emmett Quinn and T. Yates Foster. Later, Stanley Cup trustee William Foran would become the sole trustee of the O'Brien Cup. On December 2, 1911, the NHA officially designated the trophy as the league's championship trophy.

When the NHA was suspended in 1917, the Cup was held by the Montreal Canadiens. It remained in their care until 1921. In November 1921, it was announced that the Cup would be given over to the National Hockey League to be awarded annually to the NHL playoff champions. NHL president Frank Calder arranged with Ambrose O'Brien a new deed of gift. The Cup, which Calder had secured following the death of Montreal President George Kennedy, was then presented to the NHL champion Ottawa Senators. In 1925, the NHL inaugurated the Prince of Wales Trophy, which also was presented to the NHL playoff champions.

From 1927–28 onwards, one year after the NHL expanded to two divisions in 1926, the Cup was awarded to the winner of the Canadian Division, while the Prince of Wales Trophy was awarded to the winner of the American Division. It would be awarded under this definition until the end of the 1937–38 season.

The 1938–39 NHL season saw the NHL move back to a single division, and from that point on the Cup was awarded to the playoff runner-up. The Cup was not formally awarded from 1939 to 1943 and it would not be until 1944 that the winning teams from that period were inscribed on the trophy. At the end of the 1949–50 NHL season, the trophy was retired and has not been awarded since. It is now in the collection of the Hockey Hall of Fame in Toronto, Ontario, Canada and is on display with other historic trophies in the entrance to the Panasonic Hometown Hockey exhibit.

The Montreal Canadiens have won it the most, having won the Cup eleven times. The Toronto Maple Leafs have won it the second most, a total of eight times, six as the Maple Leafs, once as the St. Patricks and once as the Torontos. The Detroit Red Wings have won the Cup the most times of any American team, having won it five times.

Winners

 * Key
 * * = Defunct Teams

NHL playoff runner-up
Source: Fischler(1983), p. 34.

title: O'Brien Trophy (ice hockey)


text:
Laguna Seca

Laguna Seca Raceway (branded as WeatherTech Raceway Laguna Seca, and previously Mazda Raceway Laguna Seca for sponsorship reasons) is a paved road racing track in central California used for both auto racing and motorcycle racing, built in 1957 near both Salinas and Monterey, California, United States.

The racetrack is 2.238 mi long, with a 180 ft elevation change. Its eleven turns are highlighted by the circuit's signature turn, the downhill-plunging "Corkscrew" at Turns 8 and 8A. A variety of racing, exhibition, and entertainment events are held at the raceway, ranging from superkarts to sports car racing to music festivals. Laguna Seca is classified as an FIA Grade Two circuit.

The name Laguna Seca is Spanish for dry lake: the area where the track now lies was once a lake, and the course was built around the dry lake bed. After the course was reconfigured, two artificial ponds were added.

History
The earliest development of the local area occurred in 1867 with the founding of the nearby Laguna Seca Ranch, which has operated continuously for 140 years with grazing and equestrian uses.

The track was built in 1957 at a cost of $1.5 million raised from local businesses and individuals on part of the US Army's Fort Ord (a maneuver area and field artillery target range) after the nearby Pebble Beach Road Races were abandoned for being too dangerous. In 1974 the property was deeded over to the Monterey County Parks Department and continues to be part of the park system.

The first race, held on November 9, 1957, was won by Pete Lovely driving a Ferrari. In the intervening years, the track has hosted USRRC, Can-Am, Trans-Am, Formula 5000, IMSA GT, CART, Indy Car, American Le Mans Series, Grand American, Monterey Historic Automobile Races, Speed World Challenge, AMA (American Motorcyclist Association), WSBK Superbike World Championship and MotoGP motorcycle races (but 125/Moto3 and 250/Moto2 are not admitted).

The day-to-day operations of the track, along with the management and promotion of major racing events, are now handled by A&D Narigi Consulting, LLC. John V. Narigi is the General Manager and President. Until January 1, 2020, it was managed by the Sports Car Racing Association of the Monterey Peninsula (SCRAMP), which is a non-profit organization. With oversight by a board of local residents, SCRAMP operates with a professional staff on-site with the goal of generating income through the operations of the racetrack which is then redistributed to local charities.

The track itself has undergone significant changes over the past two decades to meet evolving safety homologation requirements of the Fédération Internationale de Motocyclisme (FIM), Fédération Internationale de l'Automobile (FIA) and other sanctioning bodies. Changes include the addition of the entire infield area in 1988 (present-day turns 3, 4, and 5, eliminating the straight that started at present-day turn 2 and ended at present-day turn 5) extending the track from its original 1.9 mi length to meet the minimum-track-length criteria of the FIM for MotoGP events, plus the more recent relocation of pedestrian bridges and embankments, and the expansion of gravel pits outside turns 1, 2, 5, 6, 8, 9, 10 for additional runoff. The original media center was demolished in 2006 to make way for additional run-off room in Turn 1. Also in 2006, the 'hump' at the top of the Rahal Straight was flattened to accommodate the MotoGP riders, though some claim that this increases the wind effects that can perturb a race motorcycle. Remnants of the old configuration can still be seen from the parking lot between turns two and five. They are found underneath a road leading to the parking area for entrant trailers and RVs.

The famous Turn 8 and 8A combination, popularly referred to as 'the Corkscrew', is considered one of the motorsport world's most challenging turns, due to the 18 metre drop in elevation as well as its blind crest and apex on the uphill approach.

Turn 2, with its difficult and technical double-apex, has been renamed the 'Andretti Hairpin', in honor of former Formula 1 World Champion Mario Andretti, while Turn 9 has been renamed 'Rainey Curve' in honor of 500cc Grand Prix motorcycle racing World Champion Wayne Rainey, a resident of nearby Salinas, California. Also, the straight that runs between Turn 6 and Turn 7 has been renamed the 'Rahal Straight' after four-time consecutive Champ Car race winner Bobby Rahal.

A Champ Car World Series weekend had been a prominent event from 1983 through 2004, when its spot on the calendar was shifted to the San Jose Grand Prix. On the last lap of the 1996 CART race, Alex Zanardi passed Bryan Herta on the inside of the Corkscrew to take the victory. Uruguayan driver Gonzalo Rodríguez died during the practice session of the 1999 CART race after crashing at the same corner. Because of the incident, runoff was installed at the end of the Rahal Straight.

Champ Car announced on September 11, 2007, that they would be returning the Northern California race to Laguna Seca from San Jose over the May 16–18 weekend in 2008. But the subsequent merger of Champ Car and IndyCar resulted in the race being canceled. On July 17, 2018, IndyCar announced a return of IndyCars to Laguna Seca, with the event to be held the weekend of Sept. 20–22, 2019.

The track is also the site of the annual Rolex Monterey Motorsports Reunion, formerly known as the Monterey Historic Automobile Races. The event features an extraordinarily eclectic mixture of race cars on the course. Each year features a different marque. Considered one of the two greatest historic racing events (along with the Goodwood Festival in England), attendance often rivals, or surpasses the professional racing events listed above.

There are many permanent dry and hook-up camping facilities located at the raceway, which are available year-round as part of the Laguna Seca Recreation Area, the county park in which the racetrack is set.

The track's primary corporate sponsor is WeatherTech which began in April 2018. As part of the sponsorship, the track is now officially referred to as WeatherTech Raceway Laguna Seca. Previously, the sponsorship belonged to Mazda for 17 years with the track being known as Mazda Raceway Laguna Seca.

A 2015 study by California State University, Monterey Bay and commissioned by SCRAMP states that the raceway generated $62.1 million (2015 USD) to the Monterey County economy and $5.2 million in state and local taxes.

Lap records
On August 20, 2006, Toyota F1 test driver Ricardo Zonta set an unofficial lap record of 1:06.309. The previous record time was 1:07.722, set by Hélio Castroneves in a Penske Champ Car during qualifying for the 2000 CART Honda Grand Prix of Monterey. The unofficial record was re-taken by a Champ Car on March 10, 2007, by Sébastien Bourdais, who lapped in 1:05.880 during Champ Car Spring Training. The unofficial record was again re-taken by a Formula One car on May 19, 2012, by Marc Gené, who lapped in 1:05.786 in a Ferrari F2003-GA during the 2012 Ferrari Racing Days.

Christian Lundgaard is the unofficial qualifying record-holder with a lap time of 1:06.4610.

At the 2008 Monterey Sports Car Championships, David Brabham set a pole position time of 1:10.103 in a Le Mans Prototype.

At the 2012 United States motorcycle Grand Prix, Jorge Lorenzo set a pole time of 1:20.554 on the Yamaha YZR-M1. During the 2014 Superbike World Championship season, Tom Sykes set the superbike qualifying record time of 1:21.811 on the Kawasaki Ninja ZX-10R.

The 2019 McLaren Senna holds the current production car lap record. Driver Randy Pobst piloted the unmodified McLaren to a 1:27.62 lap time during MotorTrend's 2019 best driver car award testing.

The 2016 Porsche 911 GT2 RS previously held the current unofficial production car lap record with 1:28.30.

The Porsche 918 Spyder held the previous unofficial production car lap record with 1:29.89.

A Mission Motors Mission R, ridden by Steve Rapp, previously held the outright EV lap record with a time of 1:31.376. This was set during qualifying for the 2011 FIM e-Power International Championship/TTXGP World Series race.

In 2018, Earl Bamber clocked an unofficial best lap time of 1:07 around Laguna Seca in the Porsche 919 EVO, despite not intentionally trying to set a lap record.

A McLaren MP4/13, driven by Pato O'Ward set an unofficial lap time of 1:10.24 at the 2021 Velocity Invitational festival.

Official race lap records
As of May 2024, the fastest official race lap records at Laguna Seca for different classes are listed as:

Automotive
When not being used by the major events the track can be rented. Approximately twice a year the Sports Car Club of America holds regional club races for the San Francisco Region. Various clubs rent the track throughout the year for informal high-performance driving schools that allow the public to drive their own cars at speed. The raceway has also played host to prototype testing of the Nissan GT-R in 2007.

The track is featured in video games such as the Gran Turismo series (since the second installment, including the bike version Tourist Trophy), the Forza Motorsport series, and the MotoGP series. In a bid to compare real life versus video games, Jeremy Clarkson of the British automotive show Top Gear attempted to beat his Gran Turismo 4 time of 1:41.148 in a Honda NSX by racing the real track in the same car in 2005. During the trials, Clarkson determined that the game omitted a few details of the track, and the game's physics allowed him to brake later when coming into turns than he could in real life. As a consequence, he managed a best time of only 1:57 on the real course. However, both he and the track instructor agreed that it is possible to complete the course in 1:41 in a Honda NSX if the driver were sufficiently experienced, talented, and most importantly fearless.

It was also used in 1976 for the film Herbie Goes to Monte Carlo as a qualifying track.

Other non-automotive events
Laguna Seca and the part of the old Fort Ord that is now Bureau of Land Management land annually host the Sea Otter Classic "Celebration of Cycling". The event has now become the largest cycling festival in the United States, bringing in over 10,000 racers and over 100,000 spectators – and is now the first major event of the year, typically held in April – for both the road bike and mountain bike professional seasons.

Several times each year, bicycles are permitted on the track for 2 hours. The admission fee is $10 per bicycle rider.

Laguna Seca served as the finish line for Stage 4 of the 2016 Amgen Tour of California and Stage 3 of the 2018 Amgen Tour of California bicycle races.

The raceway has been occasionally as a venue for concerts and other non-sporting events. The Grateful Dead performed on the racetrack in May 1987; later that night, the band filmed their music video for "Touch of Grey" there.

On September 17, 1987, Pope John Paul II celebrated mass at Laguna Seca Raceway, where 72,000 people had gathered to see him.

In the 1990s, the raceway was the venue for the Laguna Seca Daze music festival, which featured performances from music acts in the folk, alternative rock and jam band genres. Artists who performed at the festival include Bob Dylan, Phish, Blues Traveler, 10,000 Maniacs, Big Head Todd and the Monsters, Meat Puppets, 4 Non Blondes, Jeff Healey, The Allman Brothers Band, Gin Blossoms and Shawn Colvin.

On June 24, 2011, John Mueller of Muellerized Suspension Systems married Sheila Stone on the top of the Corkscrew at Laguna Seca. This is the location where the ashes of Lee Mueller (4-time SCCA National Champion, IMSA GTU Champion, 3-time winner of the 24 Hours of Daytona, and 12 Hours of Sebring winner), John Mueller's father, were spread.

In spring 2020, due to the COVID-19 pandemic, graduation ceremonies took place at the raceway. Local schools participating included Carmel High School (June 3, 2020) and Pacific Grove High School (May 29, 2020). After collecting diplomas, graduates and their families were able to drive around the track in celebration.

Current events

 * May: IMSA SportsCar Championship Motul Course de Monterey, Michelin Pilot Challenge WeatherTech Raceway Laguna Seca 120, Lamborghini Super Trofeo North America, Global MX-5 Cup, Trans-Am West Coast Championship, Ferrari Challenge North America
 * June: IndyCar Series IndyCar Monterey Grand Prix, Indy NXT, Porsche Sprint Challenge USA West, Formula Car Challenge, Radical Cup North America
 * July: MotoAmerica MotoAmerica Superbike Speedfest at Monterey, Formula Car Challenge

Former events

 * A1 Grand Prix (2006)
 * AMA Grand National Championship (1972–1976, 1980–1986)
 * AMA Superbike Championship (1976–1988, 1992–2013)
 * American Le Mans Series
 * American Le Mans Monterey (1999–2013)
 * Can-Am (1966–1973, 1978–1982)
 * Championship Auto Racing Teams/Champ Car World Series
 * Marlboro Challenge (1989, 1991)
 * Monterey Grand Prix (1983–2004)
 * FIA GT Championship (1997–1998)
 * Formula 750 (1978–1979)
 * Formula BMW Americas (2004–2005, 2008)
 * Grand Prix motorcycle racing
 * United States motorcycle Grand Prix (1988–1991, 1993–1994, 2005–2013)
 * GT World Challenge America (1990, 1999–2007, 2009, 2011–2012, 2015–2019)
 * IMSA GT Championship
 * Monterey Grand Prix (1976–1977)
 * Monterey Sports Car Grand Prix (1974–1987, 1989, 1991–1994, 1997–1998)
 * Intercontinental GT Challenge
 * California 8 Hours (2017–2019)
 * NASCAR Winston West Series (1973, 1975–1977, 1980–1981, 2000–2001)
 * North American Touring Car Championship (1996–1997)
 * Pacific Grand Prix (1960–1963)
 * Porsche Carrera Cup North America (2022–2023)
 * Porsche Rennsport Reunion (2011, 2015, 2018, 2023)
 * Rolex Sports Car Series (2005–2009, 2011–2013)
 * SCCA National Championship Runoffs (2014)
 * SCCA National Sports Car Championship (1957)
 * Sidecar World Championship (1989–1991)
 * Superbike World Championship (1995–2004, 2013–2019)
 * Trans-Am Series (1969–1972, 1978–1982, 2000–2001, 2004, 2019, 2021–2022)
 * USAC Road Racing Championship (1960–1962)

Formula One
In 1989, the year following the last Formula One race in Detroit, choices for a new location for the United States Grand Prix came down to Laguna Seca and Phoenix. The aforementioned 1988 improvements to the track were made in part to lure the F1 race. In the final decision, Laguna Seca was thought to be too remote and too small for an F1 crowd, and so Phoenix was granted the Grand Prix.

Fatalities

 * Gonzalo Rodríguez – 1999 Honda Grand Prix of Monterey
 * Dani Rivas – 2015 MotoAmerica (SBK meet)
 * Bernat Martínez – 2015 MotoAmerica (SBK meet)

title: Laguna Seca


text:
Graph homomorphism

In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a function between the vertex sets of two graphs that maps adjacent vertices to adjacent vertices.

Homomorphisms generalize various notions of graph colorings and allow the expression of an important class of constraint satisfaction problems, such as certain scheduling or frequency assignment problems. The fact that homomorphisms can be composed leads to rich algebraic structures: a preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs). The computational complexity of finding a homomorphism between given graphs is prohibitive in general, but a lot is known about special cases that are solvable in polynomial time. Boundaries between tractable and intractable cases have been an active area of research.

Definitions
In this article, unless stated otherwise, graphs are finite, undirected graphs with loops allowed, but multiple edges (parallel edges) disallowed. A graph homomorphism $f$  from a graph $$G = (V(G), E(G))$$ to a graph $$ H = (V(H), E(H))$$, written

is a function from $$V(G)$$ to $$V(H)$$ that preserves edges. Formally, $$(u,v) \in E(G)$$ implies $$(f(u),f(v)) \in E(H)$$, for all pairs of vertices $$u, v$$ in $$V(G)$$. If there exists any homomorphism from G to H, then G is said to be homomorphic to H or  H-colorable. This is often denoted as just

The above definition is extended to directed graphs. Then, for a homomorphism f : G → H, (f(u),f(v)) is an arc (directed edge) of H whenever (u,v) is an arc of G.

There is an injective homomorphism from G to H (i.e., one that maps distinct vertices in G to distinct vertices in H) if and only if G is isomorphic to a subgraph of H. If a homomorphism f : G → H is a bijection, and its inverse function $f : G → H$ is also a graph homomorphism, then f is a graph isomorphism.

Covering maps are a special kind of homomorphisms that mirror the definition and many properties of covering maps in topology. They are defined as surjective homomorphisms (i.e., something maps to each vertex) that are also locally bijective, that is, a bijection on the neighbourhood of each vertex. An example is the bipartite double cover, formed from a graph by splitting each vertex v into v0 and v1 and replacing each edge u,v with edges u0,v1 and v0,u1. The function mapping v0 and v1 in the cover to v in the original graph is a homomorphism and a covering map.

Graph homeomorphism is a different notion, not related directly to homomorphisms. Roughly speaking, it requires injectivity, but allows mapping edges to paths (not just to edges). Graph minors are a still more relaxed notion.

Cores and retracts

Two graphs G and H are homomorphically equivalent if G → H and H → G. The maps are not necessarily surjective nor injective. For instance, the complete bipartite graphs K2,2 and K3,3 are homomorphically equivalent: each map can be defined as taking the left (resp. right) half of the domain graph and mapping to just one vertex in the left (resp. right) half of the image graph.

A retraction is a homomorphism r from a graph G to a subgraph H of G such that r(v) = v for each vertex v of H. In this case the subgraph H is called a retract of G.

A core is a graph with no homomorphism to any proper subgraph. Equivalently, a core can be defined as a graph that does not retract to any proper subgraph. Every graph G is homomorphically equivalent to a unique core (up to isomorphism), called the core of G. Notably, this is not true in general for infinite graphs. However, the same definitions apply to directed graphs and a directed graph is also equivalent to a unique core. Every graph and every directed graph contains its core as a retract and as an induced subgraph.

For example, all complete graphs Kn and all odd cycles (cycle graphs of odd length) are cores. Every 3-colorable graph G that contains a triangle (that is, has the complete graph K3 as a subgraph) is homomorphically equivalent to K3. This is because, on one hand, a 3-coloring of G is the same as a homomorphism G → K3, as explained below. On the other hand, every subgraph of G trivially admits a homomorphism into G, implying K3 → G. This also means that K3 is the core of any such graph G. Similarly, every bipartite graph that has at least one edge is equivalent to K2.

Connection to colorings
A k-coloring, for some integer k, is an assignment of one of k colors to each vertex of a graph G such that the endpoints of each edge get different colors. The k-colorings of G correspond exactly to homomorphisms from G to the complete graph Kk. Indeed, the vertices of Kk correspond to the k colors, and two colors are adjacent as vertices of Kk if and only if they are different. Hence a function defines a homomorphism to Kk if and only if it maps adjacent vertices of G to different colors (i.e., it is a k-coloring). In particular, G is k-colorable if and only if it is Kk-colorable.

If there are two homomorphisms G → H and H → Kk, then their composition G → Kk is also a homomorphism. In other words, if a graph H can be colored with k colors, and there is a homomorphism from G to H, then G can also be k-colored. Therefore, G → H implies χ(G) ≤ χ(H), where χ denotes the chromatic number of a graph (the least k for which it is k-colorable).

Variants
General homomorphisms can also be thought of as a kind of coloring: if the vertices of a fixed graph H are the available colors and edges of H describe which colors are compatible, then an H-coloring of G is an assignment of colors to vertices of G such that adjacent vertices get compatible colors. Many notions of graph coloring fit into this pattern and can be expressed as graph homomorphisms into different families of graphs. Circular colorings can be defined using homomorphisms into circular complete graphs, refining the usual notion of colorings. Fractional and b-fold coloring can be defined using homomorphisms into Kneser graphs. T-colorings correspond to homomorphisms into certain infinite graphs. An oriented coloring of a directed graph is a homomorphism into any oriented graph. An L(2,1)-coloring is a homomorphism into the complement of the path graph that is locally injective, meaning it is required to be injective on the neighbourhood of every vertex.

Orientations without long paths
Another interesting connection concerns orientations of graphs. An orientation of an undirected graph G is any directed graph obtained by choosing one of the two possible orientations for each edge. An example of an orientation of the complete graph Kk is the transitive tournament $T$k with vertices 1,2,…,k and arcs from i to j whenever i < j. A homomorphism between orientations of graphs G and H yields a homomorphism between the undirected graphs G and H, simply by disregarding the orientations. On the other hand, given a homomorphism G → H between undirected graphs, any orientation $H$ of H can be pulled back to an orientation $G$ of G so that $G$ has a homomorphism to $H$. Therefore, a graph G is k-colorable (has a homomorphism to Kk) if and only if some orientation of G has a homomorphism to $T$k.

A folklore theorem states that for all k, a directed graph G has a homomorphism to $T$k if and only if it admits no homomorphism from the directed path $P$k+1. Here $P$n is the directed graph with vertices 1, 2, …, n and edges from i to i + 1, for i = 1, 2, …, n − 1. Therefore, a graph is k-colorable if and only if it has an orientation that admits no homomorphism from $P$k+1. This statement can be strengthened slightly to say that a graph is k-colorable if and only if some orientation contains no directed path of length k (no $P$k+1 as a subgraph). This is the Gallai–Hasse–Roy–Vitaver theorem.

Examples
Some scheduling problems can be modeled as a question about finding graph homomorphisms. As an example, one might want to assign workshop courses to time slots in a calendar so that two courses attended by the same student are not too close to each other in time. The courses form a graph G, with an edge between any two courses that are attended by some common student. The time slots form a graph H, with an edge between any two slots that are distant enough in time. For instance, if one wants a cyclical, weekly schedule, such that each student gets their workshop courses on non-consecutive days, then H would be the complement graph of C7. A graph homomorphism from G to H is then a schedule assigning courses to time slots, as specified. To add a requirement saying that, e.g., no single student has courses on both Friday and Monday, it suffices to remove the corresponding edge from H.

A simple frequency allocation problem can be specified as follows: a number of transmitters in a wireless network must choose a frequency channel on which they will transmit data. To avoid interference, transmitters that are geographically close should use channels with frequencies that are far apart. If this condition is approximated with a single threshold to define 'geographically close' and 'far apart', then a valid channel choice again corresponds to a graph homomorphism. It should go from the graph of transmitters G, with edges between pairs that are geographically close, to the graph of channels H, with edges between channels that are far apart. While this model is rather simplified, it does admit some flexibility: transmitter pairs that are not close but could interfere because of geographical features can be added to the edges of G. Those that do not communicate at the same time can be removed from it. Similarly, channel pairs that are far apart but exhibit harmonic interference can be removed from the edge set of H.

In each case, these simplified models display many of the issues that have to be handled in practice. Constraint satisfaction problems, which generalize graph homomorphism problems, can express various additional types of conditions (such as individual preferences, or bounds on the number of coinciding assignments). This allows the models to be made more realistic and practical.

Formal view
Graphs and directed graphs can be viewed as a special case of the far more general notion called relational structures (defined as a set with a tuple of relations on it). Directed graphs are structures with a single binary relation (adjacency) on the domain (the vertex set). Under this view, homomorphisms of such structures are exactly graph homomorphisms. In general, the question of finding a homomorphism from one relational structure to another is a constraint satisfaction problem (CSP). The case of graphs gives a concrete first step that helps to understand more complicated CSPs. Many algorithmic methods for finding graph homomorphisms, like backtracking, constraint propagation and local search, apply to all CSPs.

For graphs G and H, the question of whether G has a homomorphism to H corresponds to a CSP instance with only one kind of constraint, as follows. The variables are the vertices of G and the domain for each variable is the vertex set of H. An evaluation is a function that assigns to each variable an element of the domain, so a function f from V(G) to V(H). Each edge or arc (u,v) of G then corresponds to the constraint ((u,v), E(H)). This is a constraint expressing that the evaluation should map the arc (u,v) to a pair (f(u),f(v)) that is in the relation E(H), that is, to an arc of H. A solution to the CSP is an evaluation that respects all constraints, so it is exactly a homomorphism from G to H.

Structure of homomorphisms
Compositions of homomorphisms are homomorphisms. In particular, the relation → on graphs is transitive (and reflexive, trivially), so it is a preorder on graphs. Let the equivalence class of a graph G under homomorphic equivalence be [G]. The equivalence class can also be represented by the unique core in [G]. The relation → is a partial order on those equivalence classes; it defines a poset.

Let G < H denote that there is a homomorphism from G to H, but no homomorphism from H to G. The relation → is a dense order, meaning that for all (undirected) graphs G, H such that G < H, there is a graph K such that G < K < H (this holds except for the trivial cases G = K0 or K1). For example, between any two complete graphs (except K0, K1, K2) there are infinitely many circular complete graphs, corresponding to rational numbers between natural numbers.

The poset of equivalence classes of graphs under homomorphisms is a distributive lattice, with the join of [G] and  [H] defined as (the equivalence class of) the disjoint union [G ∪ H], and the meet of [G] and  [H] defined as the tensor product [G × H] (the choice of graphs G and H representing the equivalence classes [G] and [H] does not matter). The join-irreducible elements of this lattice are exactly connected graphs. This can be shown using the fact that a homomorphism maps a connected graph into one connected component of the target graph. The meet-irreducible elements of this lattice are exactly the multiplicative graphs. These are the graphs K such that a product G × H has a homomorphism to K only when one of G or H also does. Identifying multiplicative graphs lies at the heart of Hedetniemi's conjecture.

Graph homomorphisms also form a category, with graphs as objects and homomorphisms as arrows. The initial object is the empty graph, while the terminal object is the graph with one vertex and one loop at that vertex. The tensor product of graphs is the category-theoretic product and the exponential graph is the exponential object for this category. Since these two operations are always defined, the category of graphs is a cartesian closed category. For the same reason, the lattice of equivalence classes of graphs under homomorphisms is in fact a Heyting algebra.

For directed graphs the same definitions apply. In particular → is a partial order on equivalence classes of directed graphs. It is distinct from the order → on equivalence classes of undirected graphs, but contains it as a suborder. This is because every undirected graph can be thought of as a directed graph where every arc (u,v) appears together with its inverse arc (v,u), and this does not change the definition of homomorphism. The order → for directed graphs is again a distributive lattice and a Heyting algebra, with join and meet operations defined as before. However, it is not dense. There is also a category with directed graphs as objects and homomorphisms as arrows, which is again a cartesian closed category.

Incomparable graphs
There are many incomparable graphs with respect to the homomorphism preorder, that is, pairs of graphs such that neither admits a homomorphism into the other. One way to construct them is to consider the odd girth of a graph G, the length of its shortest odd-length cycle. The odd girth is, equivalently, the smallest odd number g for which there exists a homomorphism from the cycle graph on g vertices to G. For this reason, if G → H, then the odd girth of G is greater than or equal to the odd girth of H.

On the other hand, if G → H, then the chromatic number of G is less than or equal to the chromatic number of H. Therefore, if G has strictly larger odd girth than H and strictly larger chromatic number than H, then G and H are incomparable. For example, the Grötzsch graph is 4-chromatic and triangle-free (it has girth 4 and odd girth 5), so it is incomparable to the triangle graph K3.

Examples of graphs with arbitrarily large values of odd girth and chromatic number are Kneser graphs and generalized Mycielskians. A sequence of such graphs, with simultaneously increasing values of both parameters, gives infinitely many incomparable graphs (an antichain in the homomorphism preorder). Other properties, such as density of the homomorphism preorder, can be proved using such families. Constructions of graphs with large values of chromatic number and girth, not just odd girth, are also possible, but more complicated (see Girth and graph coloring).

Among directed graphs, it is much easier to find incomparable pairs. For example, consider the directed cycle graphs $C$n, with vertices 1, 2, …, n and edges from i to i + 1 (for i = 1, 2, …, n − 1) and from n to 1. There is a homomorphism from $C$n to $C$k (n, k ≥ 3) if and only if n is a multiple of k. In particular, directed cycle graphs $C$n with n prime are all incomparable.

Computational complexity
In the graph homomorphism problem, an instance is a pair of graphs (G,H) and a solution is a homomorphism from G to H. The general decision problem, asking whether there is any solution, is NP-complete. However, limiting allowed instances gives rise to a variety of different problems, some of which are much easier to solve. Methods that apply when restraining the left side G are very different than for the right side H, but in each case a dichotomy (a sharp boundary between easy and hard cases) is known or conjectured.

Homomorphisms to a fixed graph
The homomorphism problem with a fixed graph H on the right side of each instance is also called the H-coloring problem. When H is the complete graph Kk, this is the graph k-coloring problem, which is solvable in polynomial time for k = 0, 1, 2, and NP-complete otherwise. In particular, K2-colorability of a graph G is equivalent to G being bipartite, which can be tested in linear time. More generally, whenever H is a bipartite graph, H-colorability is equivalent to K2-colorability (or K0 / K1-colorability when H is empty/edgeless), hence equally easy to decide. Pavol Hell and Jaroslav Nešetřil proved that, for undirected graphs, no other case is tractable:

 * Hell–Nešetřil theorem (1990): The H-coloring problem is in P when H is bipartite and NP-complete otherwise.

This is also known as the dichotomy theorem for (undirected) graph homomorphisms, since it divides H-coloring problems into NP-complete or P problems, with no intermediate cases. For directed graphs, the situation is more complicated and in fact equivalent to the much more general question of characterizing the complexity of constraint satisfaction problems. It turns out that H-coloring problems for directed graphs are just as general and as diverse as CSPs with any other kinds of constraints. Formally, a (finite) constraint language (or template) Γ is a finite domain and a finite set of relations over this domain. CSP(Γ) is the constraint satisfaction problem where instances are only allowed to use constraints in Γ.
 * Theorem (Feder, Vardi 1998): For every constraint language Γ, the problem CSP(Γ) is equivalent under polynomial-time reductions to some H-coloring problem, for some directed graph H.

Intuitively, this means that every algorithmic technique or complexity result that applies to H-coloring problems for directed graphs H applies just as well to general CSPs. In particular, one can ask whether the Hell–Nešetřil theorem can be extended to directed graphs. By the above theorem, this is equivalent to the Feder–Vardi conjecture (aka CSP conjecture, dichotomy conjecture) on CSP dichotomy, which states that for every constraint language Γ, CSP(Γ) is NP-complete or in P. This conjecture was proved in 2017 independently by Dmitry Zhuk and Andrei Bulatov, leading to the following corollary:
 * Corollary (Bulatov 2017; Zhuk 2017): The H-coloring problem on directed graphs, for a fixed H, is either in P or NP-complete.

Homomorphisms from a fixed family of graphs
The homomorphism problem with a single fixed graph G on left side of input instances can be solved by brute-force in time |V(H)|O(, so polynomial in the size of the input graph H. In other words, the problem is trivially in P for graphs G of bounded size. The interesting question is then what other properties of G, beside size, make polynomial algorithms possible.

The crucial property turns out to be treewidth, a measure of how tree-like the graph is. For a graph G of treewidth at most k and a graph H, the homomorphism problem can be solved in time |V(H)|O(k) with a standard dynamic programming approach. In fact, it is enough to assume that the core of G has treewidth at most k. This holds even if the core is not known.

The exponent in the |V(H)|O(k)-time algorithm cannot be lowered significantly: no algorithm with running time |V(H)|o(tw(G) /log tw(G)) exists, assuming the exponential time hypothesis (ETH), even if the inputs are restricted to any class of graphs of unbounded treewidth. The ETH is an unproven assumption similar to P ≠ NP, but stronger. Under the same assumption, there are also essentially no other properties that can be used to get polynomial time algorithms. This is formalized as follows:
 * Theorem (Grohe): For a computable class of graphs $$\mathcal{G}$$, the homomorphism problem for instances $$(G,H)$$ with $$G \in \mathcal{G}$$ is in P if and only if graphs in $$\mathcal{G}$$ have cores of bounded treewidth (assuming ETH).

One can ask whether the problem is at least solvable in a time arbitrarily highly dependent on G, but with a fixed polynomial dependency on the size of H. The answer is again positive if we limit G to a class of graphs with cores of bounded treewidth, and negative for every other class. In the language of parameterized complexity, this formally states that the homomorphism problem in $$\mathcal{G}$$ parameterized by the size (number of edges) of G exhibits a dichotomy. It is fixed-parameter tractable if graphs in $$\mathcal{G}$$ have cores of bounded treewidth, and W[1]-complete otherwise.

The same statements hold more generally for constraint satisfaction problems (or for relational structures, in other words). The only assumption needed is that constraints can involve only a bounded number of variables (all relations are of some bounded arity, 2 in the case of graphs). The relevant parameter is then the treewidth of the primal constraint graph.

In lattice theory and category theory

 * (AMSI Vacation Research Scholarships, student research report supervised by Brian Davey and Jane Pitkethly, La Trobe University).
 * (AMSI Vacation Research Scholarships, student research report supervised by Brian Davey and Jane Pitkethly, La Trobe University).

title: Graph homomorphism


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List of rivers of South Carolina

This is a list of rivers in the U.S. state of South Carolina:

By drainage basin
This list is arranged by drainage basin, from north to south, with respective tributaries indented under each larger stream's name. All rivers in South Carolina drain to the Atlantic Ocean.

 * Little River
 * Pee Dee River
 * Old Dead River
 * Sampit River
 * Black River
 * Black Mingo Creek
 * Pocotaligo River
 * Little Pee Dee River
 * Lumber River
 * Lynches River
 * Little River
 * Jeffries Creek
 * Black Creek
 * Santee River (North Santee River and South Santee River are distributaries)
 * Little River
 * Wateree River
 * Catawba River
 * Fishing Creek
 * Congaree River
 * Dead River
 * Old Dead River
 * Broad River
 * Little River
 * Enoree River
 * Tyger River
 * Fairforest Creek
 * North Tyger River
 * Middle Tyger River
 * South Tyger River
 * Sandy River
 * Little Sandy River
 * Pacolet River
 * Lawsons Fork Creek
 * North Pacolet River
 * South Pacolet River
 * Saluda River
 * Little Saluda River
 * Bush River
 * Little River
 * Reedy River
 * North Saluda River
 * Middle Saluda River
 * South Saluda River
 * Oolenoy River
 * Gills Creek
 * Wando River
 * Cooper River
 * Back River
 * Ashley River
 * Stono River
 * Kiawah River
 * Edisto River (North Edisto River and South Edisto River are distributaries)
 * Four Holes Swamp
 * North Fork Edisto River
 * Bull Swamp Creek
 * South Fork Edisto River
 * Little River
 * Ashepoo River
 * Combahee River
 * Little Salkehatchie River
 * Salkehatchie River
 * Coosaw River
 * Morgan River (SC)
 * Story River
 * Beaufort River
 * Broad River
 * Colleton River
 * Pocotaligo River
 * Coosawhatchie River
 * Tulifiny River
 * May River
 * New River
 * Wright River
 * Savannah River
 * Stevens Creek
 * Little River
 * Rocky River
 * Seneca River
 * Keowee River
 * Little River
 * Flat Shoals River
 * Toxaway River
 * Horsepasture River
 * Whitewater River
 * Thompson River
 * Tugaloo River
 * Chauga River
 * Chattooga River
 * East Fork Chattooga River

Alphabetically

 * Ashepoo River
 * Ashley River
 * Back River
 * Bates Old River
 * Beaufort River
 * Black River
 * Black Mingo Creek
 * Broad River (northern)
 * Broad River (southern)
 * Bull Swamp Creek
 * Bush River
 * Catawba River
 * Chattooga River
 * Chauga River
 * Chechessee River
 * Combahee River
 * Colleton River
 * Congaree River
 * Cooper River (incl. East & West Branches, and Back River)
 * Coosaw River
 * Coosawhatchie River
 * Dead River
 * East Fork Chatooga River
 * Edisto River (incl. North & South Forks)
 * Enoree River
 * Flat Shoals River
 * Four Holes Swamp
 * Gills Creek
 * Great Pee Dee River
 * Grove Creek
 * Harbor River
 * Horsepasture River
 * Keowee River
 * Little Lynches River
 * Little Pee Dee River
 * Little River (Broad River tributary)
 * Little River (Edisto River tributary)
 * Little River (Horry County, South Carolina)
 * Little River (Lynches River tributary)
 * Little River (McCormick County, South Carolina)
 * Little River (Oconee County, South Carolina)
 * Little River (Saluda River tributary)
 * Little River (Santee River tributary)
 * Little Salkehatchie River
 * Little Saluda River
 * Little Sandy River
 * Lumber River
 * Lynches River
 * May River
 * Morgan River (SC)
 * New River
 * Oolenoy River
 * Okatee River
 * Old Dead River (Marlboro County)
 * Old Dead River (Richland County, Congaree National Park)
 * Pacolet River (incl. North, South, and Lawson's Fork Creek)
 * Pocotaligo River (Black River tributary)
 * Pocotaligo River (Broad River tributary)
 * Reedy River
 * Rocky River
 * Salkehatchie River
 * Saluda River (incl. North, Middle, and South Forks)
 * Sampit River
 * Sandy River
 * Santee River (incl. North & South)
 * Savannah River
 * Seneca River
 * Stevens Creek
 * Stono River
 * Story River
 * Thompson River
 * Toxaway River
 * Tugaloo River
 * Tyger River (incl. North, Middle, and South)
 * Waccamaw River
 * Wando River
 * Wateree River
 * Whitewater River
 * Wright River

title: List of rivers of South Carolina


text:
Lamb of God (band)

Lamb of God is an American heavy metal band from Richmond, Virginia. Formed in 1994 as Burn the Priest, the group consists of bassist John Campbell, vocalist Randy Blythe, guitarists Mark Morton and Willie Adler, and drummer Art Cruz. The band is considered a significant member of the new wave of American heavy metal movement.

Since their formation, Lamb of God has released eleven studio albums, including two under the name Burn the Priest; their most recent album, Omens, was released in October 2022. The band has also released one live album, one compilation album, three DVDs, two EPs, and twenty-eight singles.

The band's cumulative sales equal almost two million in the United States, including two albums certified Gold by the RIAA. In 2010 and 2011 the band received Grammy nominations for songs from their 2009 album Wrath. They also received a nomination in 2016 for their song "512". Lamb of God has toured with the Ozzfest twice. Other appearances include Download Festival and Sonisphere Festival in the UK, Soundwave Festival, Mayhem Festival 2010 and Gigantour. From 2008 to 2010 they toured as part of Metallica's World Magnetic Tour, and supported Slayer on their final world tour in 2018 and 2019.

Formation and Burn the Priest (1994–1999)
In 1994, bassist John Campbell, drummer Chris Adler, and guitarists Mark Morton and Matt Conner started a band named Burn the Priest. The band members knew each other from the college they were all attending, Virginia Commonwealth University, in Richmond, Virginia. Morton and Conner left the band soon after its inception to pursue a master's degree and work on other bands respectively. Adler and Campbell replaced Morton with Abe Spear. For the next five years, the band practiced in Richmond and around Virginia. In 1995, the band released its self-titled first demo. After the demo, Burn the Priest recorded two split EPs with Agents of Satan and ZED respectively. After the band's first three demos, Burn the Priest added vocalist Randy Blythe to its line up.

In 1997, Morton returned to the band. Two years later, the band released its first full-length self-titled album, Burn the Priest, through Legion Records. Mikey Brosnan of Legion Records saved up $2,500 for the recording and then broke them in Philadelphia, Pennsylvania, through DIY shows. The album was produced by Today Is the Day guitarist and vocalist Steve Austin. Spear left the band, leaving an open position for a guitarist. Adler's younger brother Willie became the band's second guitarist a year later, and a deal with Prosthetic Records was signed. Contrary to rumour, the band did not change their name to Lamb of God after being banned from venues; these bans occurred afterwards. They changed their name because of the altered line-up and to avoid being mistaken for a satanic metal band.

New American Gospel and As the Palaces Burn (2000–2003)
With a new name and label, the band released its second album, New American Gospel, in September 2000. Patrick Kennedy of Allmusic compared the band to Pantera stating, "The essential signatures of post-Pantera metal are in abundance on Lamb of God's inaugural album. New American Gospel provides a mighty oak upon which gritty American metal's faith is maintained, effectively bridging the '90s' insistence upon drill-sergeant technicality and the old school's determined focus on riff construction." Chris Adler commented: "This is a classic record. We had all the elements come together to make one of the heaviest, yet contagious records of our career. It was difficult to contain us—we didn't even understand at the time what we had created."

Lamb of God toured for two years before releasing their third studio album, As the Palaces Burn, on May 6, 2003. Kirk Miller of Rolling Stone gave the album three out of five stars, writing that "unlike many of their overreaching, Slipknot-influenced contemporaries, Lamb of God deliver a meticulously crafted metal assault." The album was voted the number one album of 2003 by both Revolver Magazine and Metal Hammer. The band was part of the first Headbangers Ball tour, where they recorded a DVD including live performances and a documentary, titled Terror and Hubris. The DVD was a success, debuting at number 31 on the Billboard Top Music Videos chart.

Ashes of the Wake (2004–2005)
Lamb of God released Ashes of the Wake in August 2004. The album debuted at number 27 on the Billboard 200, and sold over 35,000 copies in its first week. The album was distributed through the band's new record label, Epic Records. Johnny Loftus of Allmusic praised the album, saying "With the genre getting clogged by PVC goofs and Alice in Chains impersonators, Lamb of God balances the equation of power, rage, tradition, and craft. It kills the filler." The title track of the album featured Testament guitarist Alex Skolnick and ex–Megadeth guitarist Chris Poland. Ashes of the Wake eventually became their first Recording Industry Association of America certified studio album, being awarded gold status in February 2016.

The band supported Ashes of the Wake with extensive touring, including a second stage slot on Ozzfest in 2004, and the 2005 Sounds of the Underground tour. The band was awarded 2nd Best Album of the Year by Revolver magazine behind Mastodon's Leviathan, and was awarded Best Music Video for "Laid to Rest" (2005). While on tour, the band recorded a performance and released it with the name of Killadelphia. The release was made available as a DVD and a CD. The DVD was certified platinum by the Recording Industry Association of America in 2007.

In 2006, a cover version of the first single from the album, "Laid to Rest", was featured as a playable track in Guitar Hero II. The original version was released for Guitar Hero Smash Hits in 2009. The original version is also available as downloadable content for Rock Band.

Sacrament (2005–2007)
In August 2006, Lamb of God released its fifth studio album Sacrament. The album debuted at number eight on the Billboard 200 and sold nearly 65,000 copies in its first week of sales, nearly doubling the first week sales of Ashes of the Wake. The album received generally positive reviews, with Cosmo Lee of Stylus Magazine stating, "Sacrament has the band's most memorable songs to date. Musically, there's no fat. The band plays with laser precision and songs move smoothly through riffs and transitions." Ed Thompson of IGN referred to Sacrament "one of the best metal albums of 2006", and Jon Pareles of Blender called it a "speed rush all the way through". Sacrament would become the band's second gold record issued by the RIAA in September 2019.

The band appeared on major tours to support the album, including The Unholy Alliance with Slayer, Mastodon, Children of Bodom, and Thine Eyes Bleed, Gigantour, supporting Megadeth; main stage at Ozzfest; an appearance at the Download Festival, and an exclusive co-headlining tour with Killswitch Engage, Soilwork, and DevilDriver, where Killswitch Engage and Lamb of God shared headlining spots alternately each show. Lamb of God was nominated for Best Metal Performance at the 2007 Grammy Awards for "Redneck", but lost out to Slayer's "Eyes of the Insane".

In December 2007, the band rereleased the album as Sacrament: Deluxe Producer Edition. The release contained all of the original songs from Sacrament on the first disc, and the second disc was a CD-ROM featuring all of the vocal, bass, guitar, and drum tracks in 192 kbit/s MP3 format, enabling the buyer to produce their own interpretation of the songs. Blythe stated, "you sometimes have to do something special to get kids to even buy an album these days rather than download it." The band took a break to write new material throughout 2008 and prepare a new record for release, slated for 2009. The band negotiated for a new record label to distribute records outside the United States. Chris Adler stated Epic Records in the United States "couldn't be more perfect", but wants a different label for international releases.

In spite of the success of the tour, the band was not without at least one serious altercation which has since been widely publicized. After playing a sell-out show in Glasgow, Scotland, members of the band and crew were involved in heavy drinking. After a brief amount of time, vocalist Randy Blythe, whilst wearing a kilt and attempting to speak with a Scottish accent, became verbally violent towards both drummer Chris Adler and guitarist Mark Morton, the latter of whom then struck Blythe from behind on the bus in response. The incident developed into grabbing, pushing and separating until Blythe and Morton then encountered each other outside on the footpath. The fight between the two was especially lackluster due to intoxication, but it resulted in Morton bringing Blythe down hard on the pavement beneath him, briefly incapacitating Blythe. Two days and at least one show later, the duo reconciled over drinks.

Wrath (2008–2009)
On May 2, Lamb of God announced via MySpace their new DVD, Walk with Me in Hell, would be released on July 1, 2008. The DVD is a double-disc and has nearly five hours of footage, containing the feature documentary Walk with Me in Hell and multiple live performance extras from the Sacrament World Tour. In August 2008, it was announced, by studio producer Cole Higley, that the band had commenced work on the follow-up to Sacrament, and that its release was scheduled for February 2009. Josh Wilbur was also named as the producer for the record. They also toured with Metallica as a direct support act starting in December 2008. The recording process of the new record was made available to view online live through the band's website, with two webcams installed in the studio (specifically in the drum room and mixing room).

On February 23, 2009, the band released their sixth studio album internationally via Roadrunner Records, titled Wrath and one day later in America via Epic Records. The album is dedicated to Mikey Bronsnan, who helped them get started in Philadelphia. In November 2008, Bronsnan was killed by a drunk driver. According to drummer Chris Adler, "Without Mikey, we'd very well might not be a band today." Drummer Chris Adler was quoted saying "This album is going to surprise a lot of people. Typically bands that get to where we are in our career begin to slack off, smell the roses and regurgitate. We chose a different path. No one wants to hear another band member hyping a new record. ‘Wrath’ needs no hype. We have topped ourselves and on February 24 you will feel it." "Wrath" debuted on the Billboard 200 at number two, selling over 68,000 copies in its first week.

In support of Wrath, the band in spring of 2009 embarked on the first leg of their world tour, No Fear Energy Tour headlined by themselves with main support from Children of Bodom and As I Lay Dying, and rotating opening slots with God Forbid and Municipal Waste. The band played in Europe in the summer to perform with Metallica on the World Magnetic Tour along with Mastodon, while also playing headlining shows of their own and performing at major European festivals. For the final six dates of the tour, Unearth's Buz McGrath filled in for Mark Morton, as he left early to be with his wife and his first child.

Lamb of God was announced to also serve as Metallica's direct support for the North American leg of their 2009 world tour, as well as finishing the year off by headlining shows in Australia and New Zealand with Shadows Fall and DevilDriver.

Resolution and Blythe's arrest (2010–2013)
Lamb of God performed for the first time in the Philippines for the annual PULP Summer Slam on April 17, 2010 with thrash metal band Testament and performed there again on February 18, 2012. The band also played in India for the first time on May 15, 2010, headlining the Summer Storm festival in Bangalore. They played for their Turkish fans at Kucukciftlik Park, Istanbul, on May 17. Lamb of God was featured on the 2010 Mayhem Festival, playing on the main stage alongside Korn, Rob Zombie, and Five Finger Death Punch. Paul Waggoner, guitarist for Between the Buried and Me, filled in for Lamb of God guitarist Mark Morton during the Mayhem Festival. In June 2010, the band played on the main stage at the Download Festival. It was their third appearance at Download Festival. On April 19, 2010, IGN released a 'making of' video that features Lamb of God working on their next single, "Hit the Wall". The single is featured in the Iron Man 2 video game. On February 15, 2011, Lamb of God announced that "Hit the Wall" would be available to buy via digital download. The band was also featured on the soundtrack for Namco Bandai Games' 2010 remake of Splatterhouse. Lamb of God was announced as one of the bands (the other being Baroness) to support Metallica on their Australian tour in late 2010. In a September 2010 interview, drummer Chris Adler mentioned that Lamb of God will enter the studio in February 2011 to begin work on a seventh album. In November, Chris also mentioned that the band will work with producer Josh Wilbur again.

Lamb of God was nominated for a Grammy in 2010 for Best Metal Performance, but lost out to Judas Priest's "Dissident Aggressor". The band was once again nominated in 2011, at the 53rd Grammy Awards, but lost, this time to Iron Maiden's "El Dorado".

On October 31, 2011, it was announced that the band is set to release their seventh studio album, Resolution, on January 24, 2012. The band also revealed the album's track list and cover art. On January 19, 2012, Lamb of God released a second music video for the single 'Ghost Walking', the first video being the lyric video. The video, which is completely animated, depicts a man fleeing from assassins in order to enter the abort codes for a large unidentified weapon. All the animation was completed by Moreframes Animation, and it was premiered on the music channel Vevo and YouTube.

In February 2012 Lamb of God played the Soundwave Festival in Australia and the Download Festival on the main stage in June.

On June 27, 2012, the Czech police arrested Randy Blythe for his actions during a 2010 concert in Prague. Blythe was charged, in the Prague 8 district court, with committing intentional bodily harm after an incident in which 19-year-old fan Daniel Nosek climbed up onto the stage with him. Blythe pushed the teen who then hit his head on the floor when he fell and later died of the injury. Lamb of God canceled their upcoming tour but resumed touring 38 days later when Blythe was released on bail. Blythe was indicted on the charges in December 2012. According to a verdict delivered by the Municipal Court in Prague on March 5, 2013, Blythe had thrown Nosek off the stage and had moral responsibility for the fan's death but he was not criminally liable. The decision was appealed, and upheld by the Prague High Court in June 2013.

First hiatus, VII: Sturm und Drang, and The Duke EP (2014–2016)
Despite statements from band members that Lamb of God planned to enter the studio in 2014 to begin recording their eighth studio album, hoping to complete it by the end of the same year, Chris Adler said in an interview with The Virginian-Pilot that besides the large amount legal fees the band encountered from Randy Blythe's trial, the band's inactivity during the trial had eventually depleted the band's funds and thus were unable to fulfill those plans.

On January 26, 2014, Randy Blythe posted a picture and a statement on his Instagram saying he would be taking a long break from Lamb of God. The band, after the then-current album cycle would be on hiatus, except for some summer festival appearances. By September, however, Blythe revealed that he was planning to release a new Lamb of God record, which uses lyrics he had written while he was incarcerated along with his book, Dark Days: A Memoir in early 2015.

The band began teasing a new album, with the placeholder title Lamb of God VII via Instagram and Twitter in late April 2015. A website, lambofgodvii.com, initially comprising an empty black screen, went online in early May. The "VII" (the roman numeral for the number seven) refers to the album being the band's seventh, and does not take into account the first of their albums, released with a slightly different line-up as Burn the Priest. On May 15, 2015, it was announced that the title of the new album VII: Sturm und Drang, and would be released in July via Epic and Nuclear Blast Entertainment. The first song, "Still Echoes" was made available for streaming on LambofGodVII.com, and available for digital download on May 18. In June of the same year, the band released a video for the song "512". On November 14, 2016, Lamb of God released a new EP titled "The Duke", which featured two new songs from the VII: Sturm und Drang recordings and three live tracks. The title track is dedicated to a fan and friend of vocalist Randy Blythe, Wayne Ford, who died after a five-year battle with leukaemia. In addition to the new release, several members of the band auctioned off their instruments, signed CDs, lyric books and gold records to raise money for the Leukemia and Lymphoma Society.

Second Lamb of God hiatus and Burn the Priest cover album (2017–2018)
On April 4, 2017, Blythe said it was time for the band to "really go on hiatus" after their summer North American tour; this was in reference to the first hiatus being on the back of his release from prison and acquittal. On August 10, guitarist Mark Morton confirmed that the band would be going on hiatus but stated that they would still be making music but did not hint at whether this was either for an upcoming release or indeed for Lamb of God at all.

On January 22, 2018, Lamb of God was announced as one of the bands supporting the Slayer Farewell Tour. On March 22, Lamb of God announced that on May 18, 2018, they would release a cover album, Legion: XX under their original name Burn the Priest. It is the band's first album as Burn the Priest since their 1999 album.

On October 23, 2018, Lamb of God drummer Chris Adler was interviewed on the 486th Metal Injection Livecast and in the interview with Metal Injection he revealed that the band is aiming for a December 2019 release date for Lamb of God's tenth studio album. He also revealed in the interview that he had a conversation with fellow heavy metal drummer Lars Ulrich of the band Metallica about what it was like to work with ex-Metallica guitarist and current Megadeth lead vocalist and guitarist Dave Mustaine prior to working with him on Megadeth's 15th album, Dystopia, which was released in 2016.

Departure of Chris Adler, self-titled album, and Omens (2019–2023)
In 2017, Chris Adler was involved in a motorcycle accident that shattered his collarbone and right shoulder. While Adler had largely recovered to rejoin Lamb of God in time for its summer 2018 tour with Slayer, further complications from the injuries forced him to take a leave of absence from the band in July. Winds of Plague and former Prong drummer Art Cruz was brought in to replace Adler for the remainder of the tour. For several months, Adler's future with the band was uncertain, with Blythe stating in a June 2019 interview that "it's hard to see what's going to happen with [him]." On July 19, 2019, the band released a statement declaring that they parted ways with Adler, with Cruz becoming his permanent replacement. They additionally stated that they had begun pre-production on their forthcoming 10th album. On October 23, 2019, Adler released his own statement about his departure from Lamb of God revealing that he "did not make the decision to leave my life’s work" and he "is unwilling to paint by numbers".

On February 5, 2020, the band released "Checkmate" as the debut single from their self-titled album, Lamb of God, which marks the first song to feature Cruz. The album was initially planned to be released on May 8, but was postponed to June 19, 2020 due to the coronavirus pandemic. Lamb of God toured in support of the album, including a co-headlining US trek with Megadeth in the summer and fall of 2021.

In a September 2020 interview with Australia's Subculture Entertainment, Lamb of God guitarist Mark Morton was asked how he was spending his coronavirus downtime. He responded, "Writing and recording and creating new music is my favorite part out of all the things we get to do. There's a lot of elements, a lot of components about being in a band like Lamb of God. Performing and touring is one of them. Writing and recording is another one of them. The writing and recording part is far and away my favorite part of what we get to do. And so I have been doing some writing. I've been writing some stuff for Lamb of God, some stuff for other people, some stuff for my own solo project, so there's a lot of new music jumping out of me right now."

On February 4, 2021, the band released a song called "Ghost Shaped People" off the upcoming deluxe version of their 2020 self-titled album. The reissue of the album was released on March 26, 2021. On April 1, 2022, the band released a cover of Megadeth's "Wake Up Dead" (1986). The cover also features Megadeth. For select dates throughout 2022, Phil Demmel filled in for both Willie Adler on guitar and John Campbell on bass.

Lamb of God's ninth studio album, Omens, was released on October 7, 2022, nearly four months after the release of its lead single "Nevermore". The band supported the album by touring North America with Killswitch Engage and Europe with Kreator, Thy Art Is Murder and Gatecreeper throughout the fall and winter of 2022. They also opened for Pantera on the North American leg of their reunion tour during the summer of 2023.

Upcoming twelfth studio album (2024–present)
When asked in a February 2024 interview with the RRBG podcast about the next Lamb of God album, bassist John Campbell said: "We're gonna put out some records on the same rough schedule that we always do. We put out a record, tour the shit out of it, take a little time back, start working on another one, record it, tour the shit out of it. So, yeah, there's definitely — we are still alive and kicking, and there will be more records. In the next five years, there will definitely be a new Lamb of God record. I don't think I'm giving away any secrets with that."

As the Palaces Burn documentary
In February 2014, a documentary film featuring Lamb of God entitled As the Palaces Burn was released worldwide. The documentary, directed by Don Argott, began filming in 2012 and was set to focus on fans of the band but drastically altered its scope following the arrest of lead singer Randy Blythe on charges of committing intentional bodily harm stemming from the death of a fan following a concert in Prague two years earlier. The film has been met with positive reviews by critics.

Musical style and influences
Lamb of God is considered a significant member of the New Wave of American Heavy Metal movement,  having been referred to as one of "big four" bands of the movement, along with Killswitch Engage, Shadows Fall and Unearth. The band is mainly considered a groove metal band. Their music has also been described as metalcore,  thrash metal,  and death metal. Lamb of God's 2000 album New American Gospel has been described as "grindcore and death metal for the hardcore kids". The band's 2004 album Ashes of the Wake has been described "to showcase their thrash and melodic death metal influences and break out of the metalcore category critics tried to push the band into." The band incorporated more thrash metal elements in later albums, which was shown as a direction on Wrath (2009) and Resolution (2012). Burn the Priest has been called a fusion of thrash metal, death metal and hardcore punk. The Burn the Priest cover album, Legion: XX has been described as crossover thrash, hardcore punk, punk rock and sludge metal.

Lamb of God's influences include Pantera, The Accüsed, Septic Death, Drunk Injuns, The Faction, Black Sabbath, Obituary, Bolt Thrower, Corrosion of Conformity, Napalm Death, D.R.I., Machine Head, Shellac, At the Gates, Metallica, Testament, Slayer, Meshuggah, Megadeth, Aerosmith, and the Jesus Lizard. Although Lamb of God is a heavy metal band, the band's vocalist Randy Blythe is a more avid fan of punk rock than heavy metal, and refuses to consider himself a "metalhead".

Band members
Current members
 * John Campbell – bass (1994–present)
 * Mark Morton – lead guitar (1994, 1997–present)
 * Willie Adler – rhythm guitar (1999–present, US only 2022–present)
 * Randy Blythe – vocals (1995–present)
 * Art Cruz – drums (2019–present)

Former members
 * Chris Adler – drums (1994–2019; hiatus 2018–2019)
 * Matt Conner – rhythm guitar (1994)
 * Abe Spear – rhythm guitar (1994–1999), lead guitar (1994–1997)

Live musicians
 * Doc Coyle – lead guitar (2009)
 * Buz McGrath – lead guitar (2009)
 * Matt DeVries – bass (2013)
 * Paul Waggoner – lead guitar (2014)
 * Phil Demmel – rhythm guitar, bass (2022–present)

As Burn the Priest

 * Burn the Priest (1999)
 * Legion: XX (2018)

As Lamb of God

 * New American Gospel (2000)
 * As the Palaces Burn (2003)
 * Ashes of the Wake (2004)
 * Sacrament (2006)
 * Wrath (2009)
 * Resolution (2012)
 * VII: Sturm und Drang (2015)
 * Lamb of God (2020)
 * Omens (2022)

Grammy Awards

 * 2007
 * "Redneck"
 * rowspan="3"| Best Metal Performance
 * Nominated
 * 2010
 * "Set to Fail"
 * Nominated
 * 2011
 * "In Your Words"
 * Nominated
 * 2013
 * "Ghost Walking"
 * Best Hard Rock/Metal Performance
 * Nominated
 * 2016
 * "512"
 * Best Metal Performance
 * Nominated
 * 2016
 * "512"
 * Best Metal Performance
 * Nominated
 * Nominated

Kerrang! Awards

 * 2009 || Lamb of God || Best International Band || Nominated
 * 2009 || Lamb of God || Best International Band || Nominated

Spike Guys' Choice Awards

 * 2007 || Lamb of God || Ballsiest Band || Nominated
 * 2007 || Lamb of God || Ballsiest Band || Nominated

Revolver Golden Gods Awards

 * 2010 || Lamb of God || Best Live Band || Nominated
 * rowspan=3|2012
 * Chris Alder
 * Best Drummer
 * Nominated
 * Willie Adler and Mark Morton
 * Best Guitarists
 * Nominated
 * "Resolution"
 * Album of the Year
 * Nominated
 * 2013 || Lamb of God || Best Live Band || Nominated
 * rowspan=2|2014
 * Lamb of God
 * Best Live Band
 * Nominated
 * "As the Palaces Burn"
 * Best Film & Video presented by Eagle Rock Entertainment
 * Nominated
 * Lamb of God
 * Best Live Band
 * Nominated
 * "As the Palaces Burn"
 * Best Film & Video presented by Eagle Rock Entertainment
 * Nominated
 * Nominated

Metal Hammer Golden Gods Awards

 * 2004 || Lamb of God || Best Underground Act || Nominated
 * rowspan="3"| 2007 || Lamb of God || Best Live Band || Won
 * Lamb of God || Best International Band || Nominated
 * Sacrament || Album of the Year || Nominated
 * rowspan="2"| 2009 || Lamb of God || Best International Band || Nominated
 * Wrath || Best Album || Won
 * 2010 || Lamb of God || Best International Band || Won
 * 2012 || Lamb of God || Best International Band || Won
 * 2016 || Lamb of God || Best Live Band || Won
 * rowspan="2"| 2009 || Lamb of God || Best International Band || Nominated
 * Wrath || Best Album || Won
 * 2010 || Lamb of God || Best International Band || Won
 * 2012 || Lamb of God || Best International Band || Won
 * 2016 || Lamb of God || Best Live Band || Won
 * 2012 || Lamb of God || Best International Band || Won
 * 2016 || Lamb of God || Best Live Band || Won
 * 2016 || Lamb of God || Best Live Band || Won
 * 2016 || Lamb of God || Best Live Band || Won

title: Lamb of God (band)


text:
Wenshan District

Wenshan District is a district in Taipei, Taiwan. It is the southernmost district of the twelve districts in Taipei. Wenshan previously referred to the region south of the Taipei Basin (including Xindian and Pinglin).

History
In 1894 (late Qing era), the local gentry changed the name from "Fist Mountain" (拳山) to the more elegant "Fort Wenshan" (文山堡, from 文山秀氣). The greater Wenshan area (大文山區) is roughly the area of Bunsan District (文山郡), Taihoku Prefecture from the Japanese era. It included modern Wenshan district as well as Xindian, Shenkeng, Shiding, Pinglin, and Wulai.

Republic of China
After the handover of Taiwan from Japan to the Republic of China in 1945, the government divided the region into three areas, which are Jingmei, Muzha and Shenkeng on 1 March 1950. On 1 July 1968, Jingmei and Muzha townships were reassigned to Taipei City from Taipei County and later combined to become Wenshan District on 12 March 1990.

Culture
Notable attractions in this district include the Zhinan Temple (指南宮), Taipei Zoo, Maokong, Jingmei Night Market, Xianji Rock (仙跡岩) and Fudekeng Environmental Restoration Park. The Examination Yuan and the National Chengchi University are also Daan is better served by the Taipei Metro, The Wenshan Line, Maokong Gondola and Xindian Line in this district. ten stations of which are located in the city: Xinhai, Wanfang Hospital, Wanfang Community, Muzha, Taipei Zoo, Taipei Zoo South, Zhinan Temple Station, Maokong, Wanlong and Jingmei. Wenshan District also contains the city mayor's residence.

Government institutions

 * Coast Guard Administration
 * Examination Yuan

Education

 * National Chengchi University
 * Taiwan Police College

Infrastructures

 * Muzha Refuse Incineration Plant

Transportation
The district is served by the following stations of the Taipei Metro:
 * Taipei Zoo station
 * Muzha metro station
 * Wanfang Community metro station
 * Wanfang Hospital metro station
 * Xinhai metro station
 * Jingmei metro station
 * Wanlong metro station

Additionally, the following may also be reached from Wenshan District:
 * Maokong Gondola
 * Formosa Freeway, Nat'l Hwy no.3
 * Muzha Interchange at 20 km
 * Taipei connection line
 * 萬芳交流道 (3)
 * 木柵交流道 (5)
 * Tai 9 line (Beixin Road), County Road 106 (Muzha Road)
 * Xinyi Expressway

title: Wenshan District