OpenLLM-France/wikimedia huggingface dataset:
# Initial value theorem

In mathematical analysis, the initial value theorem is a theorem used to relate frequency domain expressions to the time domain behavior as time approaches zero.
Let
    $F(s)=\int _{0}^{\infty }f(t)e^{-st}\,dt$
be the (one-sided) Laplace transform of ƒ(t). If $f$ is bounded on $(0,\infty )$ (or if just $f(t)=O(e^{ct})$) and $\lim _{t\to 0^{+}}f(t)$ exists then the initial value theorem says
    $\lim _{t\,\to \,0}f(t)=\lim _{s\to \infty }{sF(s)}.$

## Proofs
### Proof using dominated convergence theorem and assuming that function is bounded

Suppose first that $f$ is bounded, i.e. $\lim _{t\to 0^{+}}f(t)=\alpha$. A change of variable in the integral $\int _{0}^{\infty }f(t)e^{-st}\,dt$ shows that
    $sF(s)=\int _{0}^{\infty }f\left({\frac {t}{s}}\right)e^{-t}\,dt$.
Since $f$ is bounded, the Dominated Convergence Theorem implies that
    $\lim _{s\to \infty }sF(s)=\int _{0}^{\infty }\alpha e^{-t}\,dt=\alpha .$

### Proof using elementary calculus and assuming that function is bounded

Of course we don't really need DCT here, one can give a very simple proof using only elementary calculus:
Start by choosing $A$ so that $\int _{A}^{\infty }e^{-t}\,dt<\epsilon$, and then note that $\lim _{s\to \infty }f\left({\frac {t}{s}}\right)=\alpha$ uniformly for $t\in (0,A]$.

### Generalizing to non-bounded functions that have exponential order

The theorem assuming just that $f(t)=O(e^{ct})$ follows from the theorem for bounded $f$:
Define $g(t)=e^{-ct}f(t)$. Then $g$ is bounded, so we've shown that $g(0^{+})=\lim _{s\to \infty }sG(s)$. But $f(0^{+})=g(0^{+})$ and $G(s)=F(s+c)$, so
    $\lim _{s\to \infty }sF(s)=\lim _{s\to \infty }(s-c)F(s)=\lim _{s\to \infty }sF(s+c)=\lim _{s\to \infty }sG(s),$
since $\lim _{s\to \infty }F(s)=0$.
# Cayley's nodal cubic surface

In algebraic geometry, the Cayley surface, named after Arthur Cayley, is a cubic nodal surface in 3-dimensional projective space with four conical points. It can be given by the equation
    $wxy+xyz+yzw+zwx=0\$
when the four singular points are those with three vanishing coordinates. Changing variables gives several other simple equations defining the Cayley surface.
As a del Pezzo surface of degree 3, the Cayley surface is given by the linear system of cubics in the projective plane passing through the 6 vertices of the complete quadrilateral. This contracts the 4 sides of the complete quadrilateral to the 4 nodes of the Cayley surface, while blowing up its 6 vertices to the lines through two of them. The surface is a section through the Segre cubic.
The surface contains nine lines, 11 tritangents and no double-sixes.
A number of affine forms of the surface have been presented. Hunt uses $(1-3x-3y-3z)(xy+xz+yz)+6xyz=0$ by transforming coordinates $(u_{0},u_{1},u_{2},u_{3})$ to $(u_{0},u_{1},u_{2},v=3(u_{0}+u_{1}+u_{2}+2u_{3}))$ and dehomogenizing by setting $x=u_{0}/v,y=u_{1}/v,z=u_{2}/v$. A more symmetrical form is
    $x^{2}+y^{2}+z^{2}+x^{2}z-y^{2}z-1=0.$
# Inman Mills, South Carolina

Inman Mills is a census-designated place (CDP) in Spartanburg County, South Carolina, United States. The population was 1,050 at the 2010 census.

## Geography

Inman Mills is located at 35°2′28″N 82°5′58″W﻿ / ﻿35.04111°N 82.09944°W﻿ / 35.04111; -82.09944 (35.041210, -82.099394). It lies adjacent to the incorporated city of Inman.
According to the United States Census Bureau, the CDP has a total area of 1.3 square miles (3.4 km$^2$), all land.

## Demographics

As of the census of 2000, there were 1,151 people, 435 households, and 261 families residing in the CDP. The population density was 911.5 inhabitants per square mile (351.9/km$^2$). There were 464 housing units at an average density of 367.5 per square mile (141.9/km$^2$). The racial makeup of the CDP was 90.88% White, 7.12% African American, 0.09% Asian, 1.13% from other races, and 0.78% from two or more races. Hispanic or Latino of any race were 2.95% of the population.
There were 435 households, out of which 21.1% had children under the age of 18 living with them, 43.9% were married couples living together, 12.9% had a female householder with no husband present, and 39.8% were non-families. 37.0% of all households were made up of individuals, and 23.4% had someone living alone who was 65 years of age or older. The average household size was 2.07 and the average family size was 2.65.
In the CDP, the population was spread out, with 13.9% under the age of 18, 6.2% from 18 to 24, 20.8% from 25 to 44, 19.3% from 45 to 64, and 39.9% who were 65 years of age or older. The median age was 54 years. For every 100 females, there were 60.8 males. For every 100 females age 18 and over, there were 57.3 males.
The median income for a household in the CDP was $26,776, and the median income for a family was $37,391. Males had a median income of $26,838 versus $19,922 for females. The per capita income for the CDP was $15,958. About 4.2% of families and 28.1% of the population were below the poverty line, including 7.0% of those under age 18 and 54.3% of those age 65 or over.
# Sunnyvale School District

Sunnyvale School District may refer to:
* Sunnyvale Independent School District in Sunnyvale, Texas
* Sunnyvale School District (California) in Sunnyvale, California
# Cemais Uwch Nyfer

Cemais Uwch Nyfer was a mediaeval Welsh commote in the Dyfed cantref of Cemais, in what is now Pembrokeshire. It consisted of the territory between the Afon Nyfer and Fishguard, and its civil headquarters were at Newport.
The commote was made part of the Norman March in the 12th century, and had at least eight Norman castles (Newport, Little Newcastle, Puncheston, Castlebythe, Henry's Moat, Maenclochog, Llangolman and Llanfyrnach). It ceased to be significant at the time of the Laws in Wales Acts 1535–1542, its functions being taken over by the Hundred of Cemais. It is in the predominantly Welsh-speaking north of Pembrokeshire.

## Parishes

It was composed of the following parishes:
| Parish | Parish | Parish |
| Castlebythe | Llanfair Nant-y-gof | Meline (part) |
| Dinas | Llanfyrnach | Morfil |
| Eglwyswen | Llangolman | Mynachlog-ddu |
| Fishguard | Llanllawer | Nevern (part) |
| Henry's Moat | Llanychaer | Newport |
| Little Newcastle | Llanychlwydog | Pontfaen |
| Llandeilo Llwydarth | Maenclochog | Puncheston |
# Sun-Joo Shin

Sun-Joo Shin is a Korean-American philosopher known for her work on diagrammatic reasoning in mathematical logic, including the validity of reasoning using Venn diagrams, the existential graphs of Charles Sanders Peirce, and the philosophical distinction between diagrammatic and symbolic reasoning. She is a professor of philosophy at Yale University.

## Education and career

Shin was an undergraduate in Korea. There, she became interested in the philosophy of art and the work of Maurice Merleau-Ponty, but did not have the funding for graduate study in France. Instead, she obtained a fellowship to Ohio State University, but transferred to Stanford University a year later, in 1987, after earning a master's degree at Ohio State. At Stanford, under the influence of Jon Barwise and John Etchemendy, her interests shifted to logic, and by 1991 she had completed her dissertation, Valid reasoning and visual representation, under the supervision of Etchemendy.
Shin's first faculty position was at the University of Notre Dame. In 2002 she moved from Notre Dame to her present position at Yale University.

## Books

Shin's books include:
* The Logical Status of Diagrams (Cambridge University Press, 1995)
* The Iconic Logic of Peirce’s Graphs (MIT Press, 2002)
* Visual Reasoning with Diagrams (edited with Amirouche Moktefi, Birkhäuser, 2013)

## Personal life

Shin is married to Henry E. Smith, the Fessenden Professor of Law at Harvard University.
# Ceramic metal-halide lamp

A ceramic metal-halide lamp (CMH), also generically known as a ceramic discharge metal-halide (CDM) lamp, is a type of metal-halide lamp that is 10–20% more efficient than the traditional quartz metal halide and produces a superior color rendition (80-96 CRI).
Applications for these lamps include shop lighting, street lighting, architectural lighting and agricultural lighting including grow lights. A CMH light was first exhibited by the Thorn Lighting Group in 1981 at the Hannover World Light Fair, and the first commercial ceramic metal halide lamps were distributed by Philips in 1994.
The term "Light Emitting Ceramic" (LEC) is sometimes generically used to describe ceramic metal-halide lamps in grow lights in general, though that term is actually the registered trademark of a specific brand of ceramic metal halide light.

## Operation

The ceramic metal halide is a variation of the metal-halide lamp which is itself a variation of the old (high-pressure) mercury-vapor lamp. A CMH uses a ceramic arc tube instead of the fused quartz arc tube of a traditional metal halide lamp. Ceramic arc tubes allow higher arc tube temperatures, which some manufacturers claim results in better efficacy, color rendering, and color stability.
The discharge is contained in a ceramic tube, usually made of sintered alumina, similar to that used in the high pressure sodium lamp. During operation, the temperature of this ceramic tube can exceed 1200 kelvins. The ceramic tube is filled with mercury, argon and metal-halide salts (for example, sodium iodide). Because of the high wall temperature, the metal halide salts are partly vaporized. Inside the hot plasma, these salts are dissociated into metallic atoms and iodine.
The metallic atoms are the main source of light in these lamps, creating a white light with a CRI (color rendering index) of up to 96. The exact correlated color temperature and CRI depend on the specific mixture of metal halide salts. There are also warm-white ceramic metal halide lamps, with somewhat lower CRI (78-82) which still give a more clear and natural-looking light than the old mercury-vapour and sodium-vapour lamps when used as street lights, besides being more economical to use.
The ceramic tube is an advantage in comparison to earlier fused quartz. During operation, at high temperature and radiant flux, metal ions tend to penetrate the silica, depleting the inside of the tube. Alumina is not prone to this effect.
CMH lights have a long life of up to 24,000 hours.

## Efficacy

Ceramic metal halide lamps use one fifth of the power of comparable tungsten incandescent light bulbs for the same light output (80–117 lm/W) and retain color stability better than most other gas discharge lamps. Like other high-intensity discharge lamps, they require a correctly rated electrical ballast in order to operate.
# Ceramic mixing technology

Ceramic mixing technology is used to mix and blend ceramics to create end products such as: ceramic powder blends, injection molding feedstock, electronics, decorative finishes, refractory linings, batteries and fuel cells, thermally conductive pastes, investment casting slurries, dental ceramics and advanced composites.
A wide range of equipment is available for these requirements.
# Ceramic heat cell

A ceramic heat cell, also known as Caloric Porous Structure Cell (CPSC), is a ceramic device to burn a fuel without flame, converting the thermal energy to mechanical work. In principle any fuel that can be vapourised and pre-mixed with air can be used. "Ultra vaporized steam" replaces the exploding air/fuel mixture as the work medium. The flameless combustion keeps emissions of hydrocarbons, carbon monoxide, and nitrous oxides extremely low. Exhaust gas can be recirculated, which further reduces emissions.
A ceramic heat cell made by German firm Enginion is claimed to generate up to 30 megawatts of power per cubic meter, operating at a moderate temperature of 1200 °C, with output varying from 5% to 100% of this, responding in 5 milliseconds. Emissions are claimed to be well below 10 parts per million even without exhaust gas recirculation. A glow plug is used to start the cell.
# Paul Sadala

Paul Sadala (died April 2014), alias "Morgan", was a Congolese militant, poacher and faction leader. Throughout the 2000s, Sadala grew into an elephant poaching kingpin in northeastern Congo, particularly in and around the Okapi Wildlife Reserve. He was arrested on at least two occasions by ICCN park rangers. In 2011, styled Morgan, he initiated the militant group "Mai Mai Lumumba" while it was commonly known as "Mai Mai Morgan". Morgan and his rebels were accused of committing the most severe crimes, such as cannibalism, rape, kidnapping and murder. Their most high-profile attacks included a siege of Epulu village, the headquarters of the Okapi Wildlife Reserve early on the morning of June 24, 2012. Morgan occupied Epulu until the afternoon of June 25, 2012 before vanishing back into the forest. In the wake of this attack, 7 people were killed, while the entire captive population of okapi in Epulu's breeding center were also shot and killed by the rebels. FARDC soldiers arrived and looted the village. Morgan enjoyed support from FARDC units in Bafwasende and Kisangani In January 2013, Morgan occupied the large town of Mambasa for several hours before finally being repelled by the Congolese army.
Morgan and his poaching and rebellious associates fought a bloody war, which focused mostly on occupying territory in the Ituri forest. On April 12, 2014, Morgan turned himself in to a local chief at Badengaido claiming that his followers and wives were suffering in the forest. While FARDC forces arranged for his extradition to Bunia, a gun battle erupted on April 14, 2014, the events of which are not well understood. The Congolese army were attacked with armed weapons, and as he was escaping from the gun battle, Morgan was shot in the legs and died from blood loss. The Congolese government continues to pursue loyalists to this faction, which is led by a Mbuti pygmy named Manu, and would turn themselves in after the death of Morgan.
# From Cleveland 2 Cali

From Cleveland 2 Cali is a compilation album from Bone Thugs-N-Harmony group member Flesh-N-Bone, introducing rappers signed to his record label, Flesh Bone Incorporated. There were only 1,000 copies printed up for the original release. This album has been long out of print.

## Track listing

* "Intro"
* "Dead Ringer" (Afta Maff)
* "Roof Is Leaking" (Flesh-n-Bone)
* "Pump Pump" (Bar-Nun)
* "Redemption" (Afta Maff)
* "Mind Games" (Ms. Illegal)
* "Mr. Playa Hata" (Bar-Nun)
* "Death Before Dishonor" (Afta Maff featuring B.G. Knocc Out)
* "AK Spray" (featuring Spice 1 & Flesh-n-Bone)
* "Hardtimes" (featuring E Mortal Thugs and 2 Gun)
* "Bar-Nun Kingdom" (Bar-Nun)
* "Judged by 12, Then Carried by 6" (Layzie Bone)
* "Hard Dick and Bubble Gum" (Afta Maff featuring D-Flex, Juice, Big Man and C-Note)
* "What Chu Gone Do" (Afta Maff)
# Ishimoda Shō

Ishimoda Shō (石母田 正, 9 September 1912 – 18 January 1986), born in Sapporo, was a Japanese historian specializing in ancient Japanese history, with a particular interest in the nature of the structural transition from the ancient to the medieval period. As an orthodox materialist, he was a lifetime member of the Communist Party, and influential Marxist scholar in the analyses on Japanese history conducted by members of the post-war Rekiken group. In the 1950s, after the success of the Chinese Communist Revolution in 1949, he espoused that model as the Asian alternative to Westernization, which had failed in Japan.

## Life

Born in his mother's family house in Hokkaidō, Ishimoda was raised in what is now Ishinomaki city, Miyagi Prefecture, where his father was mayor. He enrolled in the faculty of philosophy at Tokyo Imperial University, but switched to Japanese history. On graduation he became a journalist for the Asahi Shimbun, then professor at Hosei University. In 1973 he was diagnosed as suffering from Parkinson's disease.

## Works

His first major work "The formation of the medieval world" was written before the war. but the manuscript was destroyed when his house went up in flames during a wartime incendiary bombing raid over Tokyo. A legend often mentioned by prominent academics to their students has it that, soon after war's end, he returned to what remained of his house, shut himself in for a summer and rewrote the whole work. According to the afterword by Ishii Susumu appended to a popular reprint of this work however, he secluded himself in a room of his home in October 1944, and, with the curtains drawn, wrote out the whole 700 page manuscript within just one month.
Recently Ishimoda's historical materialism has come in for criticism. However it cannot be denied that he prompted and quickened the reconstruction of the discipline in postwar world of Japanese historical studies, which at the time was caught up in the chaos and stagnation caused by the collapse of an historicism centered on Japan's Imperial institution.
# Schönecken

Schönecken is a municipality in the district of Bitburg-Prüm, in Rhineland-Palatinate, western Germany.
# Keith Gattis (album)

Keith Gattis is the self-titled debut album of American country music singer Keith Gattis. It was released in 1996 via RCA Records. The album includes the singles "Little Drops of My Heart", which peaked at number 53 on Hot Country Songs, and "Real Deal".

## Critical reception

Chuck Hamilton of Country Standard Time gave the album a positive review, saying that Gattis "covers a variety of hard country styles and has the vocal equipment to handle it all convincingly." It received 4.5 stars out of 5 from Michael McCall of Allmusic, who compared Gattis' voice favorably to Johnny Paycheck and George Jones.

## Track listing

All songs written by Keith Gattis except as noted.
* "Real Deal" (Gattis, Jim Dowell) — 3:08
* "Everywhere I See You There" — 3:25
* "The Puppet" — 3:32
* "Back in Your Arms" — 3:12
* "Whoop-De-Do" (Jeff Carson, Buddy Blackmon, Vip Vipperman) — 2:50
* "Little Drops of My Heart" — 3:51
* "Scrapin' Off the Pain" — 3:23
* "Heartache Hero" (Kim Williams, Ron Harbin, Kim Tribble) — 2:46
* "Only Lonely Fool" — 3:32
* "Look Out Below" (Gattis, James T. Heffernan) — 2:42

## Personnel

Compiled from liner notes.

### Musicians

* Harold Bradley — tic tac bass
* Mark Casstevens — acoustic guitar
* Glen Duncan and Rob Hajacos — twin fiddles
* Keith Gattis — vocals, acoustic guitar
* Paul Leim — drums
* Larry Marrs — bass guitar, background vocals
* Brent Mason — electric guitar
* Hargus "Pig" Robbins — piano
* Hal Rugg — steel guitar
* Marty Stuart — mandolin

### Technical

* Don Cobb — digital editing
* Carlos Greer — digital editing
* Joe Hayden — assistant engineer
* Amy Hughes — assistant engineer
* Ken Hutton — assistant engineer
* Sandy Jenkins — assistant engineer
* Tom King — assistant engineer
* John Kunz — assistant engineer
* Warren Peterson — overdubs
* Denny Purcell — mastering
* Chris Rowe — digital editing
* Steve Sexton — assistant engineer
* Dave Sinco — overdubs
* Brian Tankersley — mixing
* Rhett Travis — assistant engineer
* King Williams — assistant engineer
* Norro Wilson — producer

## Chart performance

| Year | Single | Peak chart positions | Peak chart positions |
| Year | Single | US Country | CAN Country |
| 1996 | "Little Drops of My Heart" | 53 | 63 |
| 1996 | "Real Deal" | — | 83 |
| "—" denotes releases that did not chart ||||
# Cheilosia comosa

Cheilosia comosa (Loew 1863), the prairie blacklet, is a species of syrphid fly observed in across North America. Hoverflies can remain nearly motionless in flight. The adults are also known as flower flies for they are commonly found on flowers from which they get both energy-giving nectar and protein-rich pollen. Larvae when known are plant feeders.
# Cheilosia chrysocoma

Cheilosia chrysocoma is a European species of hoverfly.

## Description

External images For terms see Morphology of Diptera The wing length is 8-10·25 mm. Wing cross veins darkened. Antennae with third segment brownish-red to yellowish-red and squarish above at the tip and the arista almost bare. Face with a small and rounded central knob situated lower than is usual in Cheilosia. Abdomen with conspicuously bright foxy-tawny pubescence. Mimics Osmia (Apidae).

## Distribution

Cheilosia chrysocoma is a Palearctic species. North Europe and Central Europe East to Russian Far East and Siberia.

## Biology

The habitat is wetland and Alnus and Salix woodland. Fen carr and alluvial softwood forest. Along tracks and in glades, on low-growing vegetation in the sun. Flowers visited include Caltha, Crataegus, Narcissus, Prunus, Ranunculus and Salix.
Females have been seen egg-laying on Angelica sylvestris which may be the larval host plant. Flight period is April to June.
# Modern Love (1929 film)

Modern Love is a 1929 American sound part-talkie comedy film directed by Arch Heath and written by Albert DeMond and Beatrice Van. In addition to sequences with audible dialogue or talking sequences, the film features a synchronized musical score and sound effects along with English intertitles. The soundtrack was recorded using the Western Electric sound-on-film system. The film stars Charley Chase, Kathryn Crawford, Jean Hersholt, Edward Martindel, Anita Garvin and Betty Montgomery. The film was released on July 21, 1929, by Universal Pictures.

## Plot

In order to keep her job, a young dress designer must keep her recent marriage a secret from her boss. An important client arrives from Paris and her boss decides to hold a dinner party for the man at the girl's house. When her husband finds out that the client wants to take her back to Paris so she can "study", he comes up with a plan to stop it, and it begins with his being the "server" at the dinner party.

## Cast

* Charley Chase as John Jones
* Kathryn Crawford as Patricia Brown
* Jean Hersholt as François Renault
* Edward Martindel as Andre Weston
* Anita Garvin as Mrs. Weston
* Betty Montgomery as The Blonde
* Dorothy Coburn as Half and Half
# Chasing Danger

Chasing Danger is a 1939 American adventure film directed by Ricardo Cortez and written by Robert Ellis and Helen Logan. The film stars Preston Foster, Lynn Bari, Wally Vernon, Henry Wilcoxon, Joan Woodbury and Harold Huber. The film was released on May 5, 1939, by 20th Century Fox.

## Cast

* Preston Foster as Steve Mitchell
* Lynn Bari as Renée Claire
* Wally Vernon as Waldo Winkle
* Henry Wilcoxon as Captain Andre Duvac
* Joan Woodbury as Hazila
* Harold Huber as Carlos Demitri
* Roy D'Arcy as Corbin
* Stanley Fields as Captain of the S.S. Fontaine
* Pedro de Cordoba as Gurra Din
* Jody Gilbert as The Veiled Girl
# T. H. Baughman

T. H. (Tim) Baughman (born 1947) teaches European and polar exploration history at the University of Maryland Eastern Shore. He graduated with a bachelor's degree from Stetson University in 1968. M.A. from The Ohio State University; Ph.D. from Florida State University. He is a professor emeritus at the University of Central Oklahoma where he was Dean of the College of Liberal Arts from 2000 to 2004 He is the author of several books and articles on polar exploration and lectures widely on European and polar history and a frequent leader of international expeditions for Zegrahm Expeditions.

## Selected publications

* Before the Heroes Came: Antarctica in the 1890s (University of Nebraska Press, 1994)
* Ice: The Antarctic Diary of Charles F. Passel (Texas Tech University Press, 1995)
* Pilgrims on the Ice: Robert Falcon Scott’s First Antarctic Expedition (University of Nebraska Press, 1999)
* Shackleton of the Antarctic (University of Nebraska Press, 2008)
* History of Western Civilization Kindle Edition (Amazon Digital, 2012)
* Ages and Stages: Biographical Vignettes Kindle Edition (Amazon Digital, 2017)
# Scopula manengouba

Scopula manengouba is a moth of the family Geometridae. It is found in Tanzania.