OpenLLM-France/wikimedia huggingface dataset:
# Lehmer mean

In mathematics, the Lehmer mean of a tuple $x$ of positive real numbers, named after Derrick Henry Lehmer, is defined as:
    $L_{p}(\mathbf {x} )={\frac {\sum _{k=1}^{n}x_{k}^{p}}{\sum _{k=1}^{n}x_{k}^{p-1}}}.$
The weighted Lehmer mean with respect to a tuple $w$ of positive weights is defined as:
    $L_{p,w}(\mathbf {x} )={\frac {\sum _{k=1}^{n}w_{k}\cdot x_{k}^{p}}{\sum _{k=1}^{n}w_{k}\cdot x_{k}^{p-1}}}.$
The Lehmer mean is an alternative to power means for interpolating between minimum and maximum via arithmetic mean and harmonic mean.

## Properties

The derivative of $p\mapsto L_{p}(\mathbf {x} )$ is non-negative
    ${\frac {\partial }{\partial p}}L_{p}(\mathbf {x} )={\frac {\left(\sum _{j=1}^{n}\sum _{k=j+1}^{n}\left[x_{j}-x_{k}\right]\cdot \left[\ln(x_{j})-\ln(x_{k})\right]\cdot \left[x_{j}\cdot x_{k}\right]^{p-1}\right)}{\left(\sum _{k=1}^{n}x_{k}^{p-1}\right)^{2}}},$
thus this function is monotonic and the inequality
    $p\leq q\Longrightarrow L_{p}(\mathbf {x} )\leq L_{q}(\mathbf {x} )$
holds.
The derivative of the weighted Lehmer mean is:
    ${\frac {\partial L_{p,w}(\mathbf {x} )}{\partial p}}={\frac {(\sum wx^{p-1})(\sum wx^{p}\ln {x})-(\sum wx^{p})(\sum wx^{p-1}\ln {x})}{(\sum wx^{p-1})^{2}}}$

## Special cases

* $\lim _{p\to -\infty }L_{p}(\mathbf {x} )$ is the minimum of the elements of $\mathbf {x}$.
* $L_{0}(\mathbf {x} )$ is the harmonic mean.
* $L_{\frac {1}{2}}\left((x_{1},x_{2})\right)$ is the geometric mean of the two values $x_{1}$ and $x_{2}$.
* $L_{1}(\mathbf {x} )$ is the arithmetic mean.
* $L_{2}(\mathbf {x} )$ is the contraharmonic mean.
* $\lim _{p\to \infty }L_{p}(\mathbf {x} )$ is the maximum of the elements of $\mathbf {x}$. Sketch of a proof: Without loss of generality let $x_{1},\dots ,x_{k}$ be the values which equal the maximum. Then $L_{p}(\mathbf {x} )=x_{1}\cdot {\frac {k+\left({\frac {x_{k+1}}{x_{1}}}\right)^{p}+\cdots +\left({\frac {x_{n}}{x_{1}}}\right)^{p}}{k+\left({\frac {x_{k+1}}{x_{1}}}\right)^{p-1}+\cdots +\left({\frac {x_{n}}{x_{1}}}\right)^{p-1}}}$

## Applications
### Signal processing

Like a power mean, a Lehmer mean serves a non-linear moving average which is shifted towards small signal values for small $p$ and emphasizes big signal values for big $p$. Given an efficient implementation of a moving arithmetic mean called smooth you can implement a moving Lehmer mean according to the following Haskell code.
* For big $p$ it can serve an envelope detector on a rectified signal.
* For small $p$ it can serve an baseline detector on a mass spectrum.
Gonzalez and Woods call this a "contraharmonic mean filter" described for varying values of p (however, as above, the contraharmonic mean can refer to the specific case $p=2$). Their convention is to substitute p with the order of the filter Q:
    $f(x)={\frac {\sum _{k=1}^{n}x_{k}^{Q+1}}{\sum _{k=1}^{n}x_{k}^{Q}}}.$
Q=0 is the arithmetic mean. Positive Q can reduce pepper noise and negative Q can reduce salt noise.
# Cocosates

The Cocosates or Cocosates Sexsignani were an Aquitani tribe dwelling in present-day Landes during the Iron Age.

## Name

They are mentioned as Cocosates by Caesar (mid-1st c. BC), and as Cocosates Sexsignani by Pliny (1st c. AD).
The etymology of the name remains obscure. It can be derived from the Gaulish stem cocos- ('scarlet red') attached to the suffix -ates ('belonging to'). Red is a colour commonly used in personal names (Cocus, Cocca, Cocidius, etc.) and associated with warfare.

## Geography

The Cocosates lived in present-day Landes. Their territory was located east of the Atlantic Ocean, west of the Oscidates and Sotiates, north of the Tarbelli and Tarusates, and south of the Boii.
Their chief town was known as Caequosa (modern Sescouze, near Castets).

## Political organization

The Cocosates were a confederation of six tribes. They were probably clients of the neighbouring Tarbelli.
# Flying Lessons

Flying Lessons may refer to:
* Flying Lessons (2007 film), a 2007 Italian film starring Giovanna Mezzogiorno
* Flying Lessons (2010 film), a 2010 American film starring Maggie Grace
* Flying Lessons (2024 film), a 2024 American documentary film
* Flying Lessons (album), a 2015 album by Fool's Gold
# Etlingera peekelii

Etlingera peekelii is a monocotyledonous plant species first described by Theodoric Valeton, and given its current name by Rosemary Margaret Smith. Etlingera peekelii is part of the genus Etlingera and the family Zingiberaceae. No subspecies are listed in the Catalog of Life.
# Emilio Méndez Pérez

Emilio Méndez Pérez (born 22 May 1949) is a Spanish physicist. His research has focused on the study of the optical and electronic properties of semiconductor nanomaterials. Particularly notable are his discoveries on the effects of an electric field on the electronic properties of quantum wells and superlattices, especially the experimental demonstration of the so-called "Stark effect" and the so-called "Wannier–Stark ladder".
In 1998, he was awarded the Prince of Asturias Awards for Technical and Scientific Research along Pedro Miguel Echenique Landiríbar.
# Geeta Mahalik

Geeta Mahalik (born 1948) is an Indian Odissi dancer. The Government of India honoured her with the Padma Shri in 2014 for her services to the field of art and culture.

## Biography

Gita Mahalik began her training at a very early age from renowned guru, Deba Prasad Dash. This was followed by coaching under Mayadhar Raut which helped Geeta to develop a style which many connoisseurs described as sheer poetry in motion.
Geeta has travelled extensively, performing in many countries across the globe like France, Switzerland, China, Italy, Spain, USA, Canada, Germany, Portugal, Greece and many other countries in the African continent. She has also performed at almost all of the major dance festivals in India, Khajuraho Dance Festival, Ellora Dance Festival, Elephanta Dance Festival, Konarak Dance Festival, Mahabalipuram Festival, Mukteshwar Dance Festival, Badri Kedar Utsav, Taj Festival, Kalidas Samaroh at Ujjain, Ganga Mahotsav and Mandu Festival featuring among them.
Geeta Mahalik presently lives in Delhi.

## Legacy

Geeta Mahalik is generally credited with giving a national flavor to the traditional style of Odissi. She is also widely known to be a master of 'Rasa' (expression).
Geeta has choreographed many dance dramas such as Lavanyavati, Krishnabhilasha and Draupadi - Antim Prashna which have won critical acclaim. It is reported that she has brought in many innovative interpretations and religious and secular overtones through her choreography.
Geeta Mahalik has founded a non-governmental organization, Geeta's Upasana, based in Delhi, for promoting arts and culture, especially odissi dance. The organization regularly stages performances in Delhi and outside.

## Positions

* Founder Director - Geeta's Upasana
* Member - Expert Committee on Odissi dance - Ministry of Culture
* Member - General Council - Sangeet Natak Akademi
* Member - General Council - Odisha Sangeet Natak Akademi

## Awards and recognitions

* Padma Shri - Government of India - 2014
* Kendra Sangeet Natak Akademi Award - 2010
* Odisha Sangeet Natak Akademi Award - 2012
* Gramini Award - India International Rural Cultural Centre
* Senior National Fellowship - Ministry of Culture, Government of India
Geeta Mahalik is on the artists panel of the Indian Council for Cultural Relations.
# Hermann Streber

Hermann Streber (b. at Munich, 27 September 1839; d. at Tölz, 9 August 1896) was a German Roman Catholic priest and writer, particularly associated with the second edition of the Kirchenlexikon.

## Life

His father was Franz Seraph Streber. He entered the Ludwigsgymnasium in 1850, but a nervous fever prevented him from qualifying for the university through the usual final school examination. From this ailment he never completely recovered.
Entering the university by a private examination in 1858, he devoted over two years to the study of philosophy and theology, attending besides historical lectures. During this period he compiled a description and catalogue of the ancient coins in the Royal Cabinet of Medals. In 1861 he entered the archiepiscopal seminary at Freising, and in 1864 was ordained priest.
After the death of his father he was unable to pursue his original intention of studying numismatics. In 1867 he was appointed religious teacher at the Wilhelmsgymnasium. Having received six months' leave of absence in 1868, he won the doctorate in theology in Rome (January, 1869). While being in Rome he lived in the priest college Santa Maria dell' Anima. He then resumed his duties as religious teacher until June, 1870, when he was dismissed for alleged "intriguing in favour of the dogma of infallibility".
He was then named pastor of Wolfersdorf, near Freising. Invited by Joseph Hergenröther to assist him in editing the new edition of the Kirchenlexikon, Streber resigned his parish, and settled in Würzburg. When Hergenröther was summoned as cardinal to Rome, Streber moved to Bonn to be near Kaulen, the new editor, and worked on the "Nomenclator". He wrote many articles for the Kirchenlexikon, the direction of which was for a time entirely in his hands.
In 1892 illness forced him to withdraw to his brother's house at Tölz, where he lived in retirement until death.
# Mamed Iskenderov

Mamed Iskenderov (17 December [O.S. 4 December] 1915 – 28 May 1985) was the chairman of the Council of Ministers of the Azerbaijan Soviet Socialist Republic from 10 July 1959 to 29 December 1961. He was a member of the Communist Party.
An ethnic Kurd, he was one of the few representatives of the indigenous minorities of the Azerbaijan SSR appointed to important government posts because he was officially registered as “Azerbaijani” (since the leadership of the Azerbaijan SSR pursued a policy of forced assimilation of its indigenous peoples, including the Kurds, among other things registering members of these communities in documents as “Azerbaijanis”).
# Eugene Kole

Fr. Eugene Kole, OFM Conv, served as Quincy University's 20th president from 1997–2002. During his tenure the school embarked on an $8.6 million fitness center renovation, remodeling of St. Francis Hall and the addition of new academic programs.

## Resignation

Kole resigned from Quincy University on October 22, 2002, after the school's Board of Trustees discovered several inconsistencies in Kole's resume. Specifically, Kole lied about receiving a master of science degree in counseling from Canisius College and a master of arts degree in psychology and counseling from La Salle University. He did have a degree from the similarly named unaccredited LaSalle University which was later closed down due to its being a diploma mill. According to Canisius College, Kole took classes in the summers of 1972 and 1973 under the name Eugene Kolodiezj.
Kole was succeeded by Fr. Mario DiCicco, O.F.M., who served as intern president for one year.
Kole later served as a chaplain at Pope Air Force Base and Langley Air Force Base.

## Death

Kole died suddenly on March 3, 2016. He was posthumously awarded a medal for meritorious civilian service by the Air Force.
# Ethmia postica

Ethmia postica is a moth in the family Depressariidae. It occurs in the interior areas of Australia, from north-western and south central Western Australia to western Queensland, New South Wales and Victoria.

## Description

E. postica's wingspan is 21–22 mm (0.83–0.87 in). The forewings of the species are white, with blackish-fuscous markings. The costal edge is of the wing is blackish, interrupted about one-fourth and near the apex. There are a number of spots on the dorsal side of the forewings. For example there is an irregular costal spot near the base and a dorsal dot at one-fourth, an irregular costal spot near the base and a dorsal dot at one-fourth. There is an irregular bar from one-fifth of the costa, reaching three-fourths across the wing and there is a small subdorsal spot before the middle. There is also a small triangular spot on the costa at two-fifths, and a dot below it and a small triangular spot on the costa beyond the middle. A transverse S-shaped mark is found beyond the middle towards the dorsum, but not reaching it, and a discal dot is found at three-fourths and there is an irregular transverse line from about three-fourths of the costa to the tornus, curved outwards from near the costa to three-fourths, whence a sharp projection proceeds to touch the lower side of the preceding discal dot. Finally, there is a slender streak along the termen, all on E. postica's forewings. Th hindwings of this species are white and thinly scaled with the costa and apical fourth fuscous, and darker towards the apex.
# Scardinius plotizza

Scardinius plotizza is a species of ray-finned fish in the family Cyprinidae. It is found in Bosnia and Herzegovina and Croatia. Its natural habitats are rivers and freshwater lakes.
# MOSiR Stadium (Stalowa Wola)

The Stadion Miejskiego Ośrodka Sportu i Rekreacji w Stalowej Woli, commonly referred to as MOSiR Stadium, is a sports stadium and former football venue located in Stalowa Wola, Poland. It served as the home ground for Stal Stalowa Wola until the club relocated to the Subcarpathian Football Center in 2020. Presently, the Municipal Sports and Recreation Center in Stalowa Wola oversees various facilities, including the athletics stadium situated near the San River and sports halls adjacent to the Hutnicza Street.

## History

The stadium, constructed in the late 1930s, was one of the earliest edifices in Stalowa Wola, boasting a maximum capacity of 12,000. It underwent renovations in 1968 and 2006. Notably, in 1994, it hosted Legia Warsaw during Stal Stalowa Wola's triumphant 1–0 Ekstraklasa victory, drawing a record attendance of 12,000.
Following the installation of seats, the stadium's capacity was reduced to 10,000. By the time the last stands were demolished, the capacity had dwindled to 2,937. The demolition process lasted until 2016, after which the construction of the Subcarpathian Football Center commenced. A small portion of the arch, including the visitor's section, was preserved until the inauguration of the new arena in 2020.
In July 2020, the MOSiR Stadium hosted the Subcarpathian Polish Athletic Association qualifying meeting.
# Ariel Schlesinger

Ariel Schlesinger (born 1980, Jerusalem) is an artist who lives and works in Berlin and Mexico City. His diverse body of work navigates sculpture, conceptual art, and installation art. Schlesinger’s installations often dislocate everyday objects, rearranging them in ways that leave viewers simultaneously amused and apprehensive. In 2017, Schlesinger won an international competition to design a public work for the entrance of the newly renovated Jewish Museum in Frankfurt.

## Life and work

Between 1999 and 2003, Schlesinger studied at the Bezalel Academy of Art and Design in Jerusalem and the School of Visual Arts in New York City. Since moving to Berlin shortly after his graduation, he’s been awarded residencies in Germany, France, Italy and Japan. In 2012, Schlesinger was named “VHV-Artist of the Year,” earning a €25,000 prize from the German insurance and reinsurance company VHV Group. The work for which he won the prize, A Car Full of Gas, has been exhibited in Berlin and across Europe.
His installations, sometimes deemed “space-interventions”, consist of ordinary objects, including cars, gas tanks, bikes, lighters, pencils, paper and socks, which are arranged in ways that both de-familiarize their everyday meaning and generate unexpected, humorous, and sinister associations. In his work A Car Full of Gas, for example, it is not human passengers that sit in the front seats of a vintage mini car, but rather two, 60-litre gas canisters, inevitably anthropomorphized given their context. From one of the car windows, a small flame burns. The clean, everyday elegance of the work has been read as an omen of catastrophe. Perhaps nobody has been as precise as Gal Katz in capturing a key motive of Schlesinger’s work: the tension between the order of perfectly immaculate objects and arrangements, on the one hand, and a poignant sense of looming calamity, on the other.
In 2017, Schlesinger won an international competition to design a large-scale public work for the newly renovated Jewish Museum of Frankfurt. The proposal consists of an 11-meter tall sculpture composed of two trees whose branches are connected such that the roots of one tree point to the sky, while the other is firmly rooted in the ground. The estimated cost of producing and installing the work, largely financed by the Rothschild family, is €350,000.

## Selected exhibitions

Alongside many group exhibitions, Schlesinger has had a large number of solo shows since his graduation in 2003—in Israel, Italy, Germany, Belgium, Switzerland, Slovenia and France.
* 2003: Herzliya Museum of Contemporary Art
* 2005, 2009, 2013, 2014 and 2016: Dvir Gallery, Tel Aviv
* 2007: Galleria Klerkx, Milan
* 2008: 2010 and 2014: Galerija Gregor Podnar, Berlin and Ljublijana
* 2011: Musée du Chateau de Montbeliard, Montbeliard; Kunstverein, Braunschweig
* 2012: Yvon Lambert, Paris; Sint-Lukasgalerie, Brussels; Künstlerhaus, Bremen
* 2014: Kunsthaus Baselland, Muttenz
* 2015: Galleria Massimo Minini, Brescia
# Micropterix stuebneri

Micropterix stuebneri is a species of moth belonging to the family Micropterigidae. It was described by Zeller, Werno and Kurz in 2013. It is only known from the Sierra Nevada in Spain.
The forewing length is 2.6–3 mm for males and 3.2-3.5 mm for females.
# Simhadri Satyanarayana Rao

Simhadri Satyanarayana Rao was a politician who held the portfolios of Endowments and Commercial Taxes in the governments of N. T. Rama Rao and N. Chandrababu Naidu.

## Political life

He joined the Telugu Desam Party under the leadership of NTR after giving up his 30 years of lucrative law practice. In the 1985 mid-term elections to the Assembly, Satyanarayana Rao trounced Mandali Venkata Krishna Rao, who had a long and unconquered stint as MLA from Avanigadda constituency. He was known for his commitment to the development of temples during his two terms and was referred to as ‘devudi mantri' (minister of gods).

## Honours

Lok Satta Party honored Simhadri on 9 December 2007, on World Anti Corruption Day, since he stood against corruption and for clean politics.

## Personal life

His son, S Chandrasekhar, is an oncologist in Hyderabad.

## Death

Satyanarayana Rao underwent treatment for kidney failure in Nagarjuna Hospital at Kanuru near Vijayawada and died after battling for life for three months. He died on 24 September 2010.
# Teen Spirit: The Stories Behind Every Nirvana Song

Teen Spirit: The Stories Behind Every Nirvana Song, also known as Nirvana: The Stories Behind The Songs is a book written by Chuck Crisafulli about the American rock band Nirvana and which was published by Omnibus Press in 1996.

## Content

The book tells the stories and meaning behind every song on the Nirvana albums Bleach (1989), Nevermind (1991), Incesticide (1992), In Utero (1993), and MTV Unplugged in New York (1994). This includes a chapter on the Nevermind hidden track, "Endless, Nameless" even though it is not listed in the contents of the book. The book also includes an interview Crisafulli did in February 1994 with Nirvana band leader Kurt Cobain who died in April 1994. It also includes a chronology of the band's history as well as the band's discography of albums and singles released in the US and UK, with the most recent release included being the 1996 live album From the Muddy Banks of the Wishkah, as well as a list of the band's compilation appearances and related recordings.

## Reception

Goodreads rated it 3.55 stars out of 5 from 114 ratings and twelve reviews. The StoryGraph gave it an average rating of 3.83.
# Tekarihogen

Tekarihogen or Dekarihokenh (Tekarihó:ken) is the title and office of an Iroquois League sachem of the Mohawk nation. The title has been rendered in English in numerous spelling variations.
The title of Dekarihokenh is hereditary through the maternal line; each office holder is a male of the Mohawk Turtle clan. He is appointed by the senior women of the clan, as the Iroquois have a matrilineal system of descent and property. Like the other sachems of the Grand Council of the Six Nations, the Dekarihokenh is part of the ceremonial leadership of the Iroquois, but not necessarily of the political leadership.
   In the council of the Six Nations Confederacy the chief who bore it served as the titular head of the Mohawks, the first in rank of that tribe’s nine sachems. Since the Mohawks headed the roll listing the council’s 49 or 50 chiefs, his name took precedence over all others.
Holders of this title included:
* Hendrick Theyanoguin
* John Brant
# Heudicourt, Eure

Heudicourt (French pronunciation:) is a commune in the Eure department in northern France.
# Heudreville

Heudreville may refer to two communes in the Eure department in northern France:
* Heudreville-en-Lieuvin
* Heudreville-sur-Eure
# Heudicourt-sous-les-Côtes

Heudicourt-sous-les-Côtes (French pronunciation:) is a commune in the Meuse department in Grand Est in north-eastern France.
# Hedgehog cactus

Hedgehog cactus may refer to:
* Pediocactus, a genus of cacti containing 6-11 species
* Echinocereus, a genus of ribbed, usually small to medium-sized cylindrical cacti, comprising about 70 species from the southern United States and Mexico in very sunny rocky places
* Echinopsis, a large genus of cacti native to South America containing 128 species
# Tempurung Cave

Tempurung Cave is a limestone cave located in Gopeng, Perak, Malaysia, spanning more than 4 kilometers, making it one of the longest caves in Peninsular Malaysia. Its name is taken in conjunction with its shape like a coconut shell. The length of this cave reaches 1.9 km and is believed to have existed since 8000 BC.
The Tempurung Cave consists of five large domes whose ceilings resemble coconut shells, with each dome having a different stalagmite and stalactite shape. Additionally, each dome is different in terms of temperature, water level, and limestone and marble content.
Tempurung Cave is a cave that is the focus of tourists that spans one kilometer from Sungai Siput to Kuala Dipang, and consists of five shell-shaped dome ceilings. It is 4.5 kilometers long, but only 1.9 kilometers of it is accessible to the local public.
Tempurung Cave is located in Gopeng, about 24 kilometers south of Ipoh City. It is also only a 15-minute drive from Sungai Kampar which is also the focus of tourists for kayaking or rafting across the rapids.
In the middle of this cave, there is a stalagmite shaped like a giant.
Since this cave is the focus of tourists, the Perak state government has preserved and conserved this cave area to make it more attractive and tourist-friendly. The cave is now equipped with lights, stairs and bridges, and other public facilities are also provided. For those who like extreme activities, a river cruise in the cave is also held.
In addition to storing natural treasures, this cave is also written in the history of Malaysia. This cave became a communist hideout in the past from 1950 to 1960. While since 1970, Tempurung Cave has been used as a tin mine.

## Direction guide

Tempurung Cave can be visited using the North-South Expressway or Federal Road. If you are using PLUS, enter the Gopeng Toll Plaza exit, turn left and continue driving for 2 km until you find the path to Tempurung Cave on the left. This special route was built to allow larger vehicles such as buses to reach the cave. Tempurung Cave's coordinate is 4.4160° N, 101.1877° E.