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Chandrasekhar limit

The Chandrasekhar limit is the maximum mass of a stable white dwarf star. The accepted value of the Chandrasekhar limit is about 1.4 M☉. White dwarfs resist gravitational collapse through electron degeneracy pressure; the Chandrasekhar limit is the mass above which electron degeneracy pressure in the star's core is insufficient to balance the star's own gravitational self-attraction. A white dwarf with a mass greater than the limit is subject to further gravitational collapse, evolving into a different type of stellar remnant, such as a neutron star or black hole; those with masses up to the limit remain stable as white dwarfs. The limit was named after Subrahmanyan Chandrasekhar, an Indian astrophysicist who improved upon the accuracy of the calculation in 1930, at the age of 20, in India by calculating the limit for a polytrope model of a star in hydrostatic equilibrium, comparing his limit to the earlier limit found by E. C. Stoner for a uniform density star; the existence of a limit, based on the conceptual breakthrough of combining relativity with Fermi degeneracy, was indeed first established in separate papers published by Wilhelm Anderson and E. C.

Stoner in 1929. The limit was ignored by the community of scientists because such a limit would logically require the existence of black holes, which were considered a scientific impossibility at the time; the fact that the roles of Stoner and Anderson are forgotten in the astronomy community has been noted. Electron degeneracy pressure is a quantum-mechanical effect arising from the Pauli exclusion principle. Since electrons are fermions, no two electrons can be in the same state, so not all electrons can be in the minimum-energy level. Rather, electrons must occupy a band of energy levels. Compression of the electron gas increases the number of electrons in a given volume and raises the maximum energy level in the occupied band. Therefore, the energy of the electrons increases on compression, so pressure must be exerted on the electron gas to compress it, producing electron degeneracy pressure. With sufficient compression, electrons are forced into nuclei in the process of electron capture, relieving the pressure.

In the nonrelativistic case, electron degeneracy pressure gives rise to an equation of state of the form P = K1ρ5/3, where P is the pressure, ρ is the mass density, K1 is a constant. Solving the hydrostatic equation leads to a model white dwarf, a polytrope of index 3/2 – and therefore has radius inversely proportional to the cube root of its mass, volume inversely proportional to its mass; as the mass of a model white dwarf increases, the typical energies to which degeneracy pressure forces the electrons are no longer negligible relative to their rest masses. The velocities of the electrons approach the speed of light, special relativity must be taken into account. In the relativistic limit, the equation of state takes the form P = K2ρ4/3; this yields a polytrope of index 3, which has a total mass, Mlimit say, depending only on K2. For a relativistic treatment, the equation of state used interpolates between the equations P = K1ρ5/3 for small ρ and P = K2ρ4/3 for large ρ; when this is done, the model radius becomes zero at Mlimit.

This is the Chandrasekhar limit. The curves of radius against mass for the non-relativistic and relativistic models are shown in the graph, they are colored green, respectively. Μe has been set equal to 2. Radius is measured in standard solar radii or kilometers, mass in standard solar masses. Calculated values for the limit vary depending on the nuclear composition of the mass. Chandrasekhar, eq. eq. eq. gives the following expression, based on the equation of state for an ideal Fermi gas: M l i m i t = ω 3 0 3 π 2 3 2 1 2 where: ħ is the reduced Planck constant c is the speed of light G is the gravitational constant μe is the average molecular weight per electron, which depends upon the chemical composition of the star. MH is the mass of the hydrogen atom. Ω03 ≈ 2.018236 is a constant connected with the solution to the Lane–Emden equation. As √ħc/G is the Planck mass, the limit is of the order of M Pl 3 m H 2 A more accurate value of the limit than that given by this simple model requires adjusting for various factors, including electrostatic interactions between the electrons and nuclei and effects caused by nonzero temperature.

Lieb and Yau have given a rigorous derivation of the limit from a relativistic many-particle Schrödinger equation. In 1926, the British physicist Ralph H. Fowler observed that the relationship between the density and temperature of white dwarfs could be explained by viewing them as a gas of nonrelativistic, non-interacting electrons and nuclei that obey Fermi–Dirac statistics; this Fermi gas model was used by the British physicist Edmund Clifton Stoner in 1929 to calculate the relationship among the mass and density of

Valerio de la Cruz

Juan Bautista Valerio de la Cruz was an indigenous Mexican conquistador. He led soldiers in the Spanish conquest of territory from Chichameca tribes and was made governor of the province of Jilotepec in early New Spain. Juan Bautista Valerio de la Cruz was born Xicalchalchílmitl in Texcoco, he was the descendant of the famous Texcocan poet-king Nezahualcóyotl. After the Spanish occupation of Mexico, Xicalchalchílmitl was baptized by the city attorney of Mexico City, Don Bernardino de Santa Clara. According to the Jilotepec Codex, he received the name "Juan Bautista" because he was born on the feast day of John the Baptist, the name "Valerio" from his uncle, the apellation "de la Cruz" because he arrived in Jilotepec on the day of the Day of the Cross. In 1527, when de la Cruz was 10 years old, he joined the royal militia and by 1529 he had been promoted to lieutenant of the royal guard of lance and shield. After two more years of service, de la Cruz retired to cultivate his land in Texcoco. De la Cruz returned to royal service in 1534 and was sent to occupy the then-frontier city of Jilotepec with 80 Spanish arquebusiers and 400 indigenous archers.

In particular he was to protect the road to one of the primary sources of Mexican silver. His other responsibilities were to contain the Chichameca incursions in the region, maintain peace with the local indigenous population. Don Antonio de Mendoza, first viceroy of New Spain, ordered de la Cruz to raise an army and conquer territory where Chichameca tribes lived. Along with other local caciques — notably Fernando de Tapia and Nicolás de San Luis — he would go on to conquer the territory around "Jilotepec, San Miguel el Grande, Querétaro, Valle de San Felipe, Xichú, Río Verde, Nueva Galicia, Michoacán." According to the Jilotepec Codex, de la Cruz reduced the number of smaller settlements, evangelized to and converted the local Chichameca population. This was part of the Spanish strategy of conquest. By reducing the number of nomadic natives and relocating them into pueblos, the Spanish were reducing the number of potential soldiers for the Chichamecas, hastening the work of conversion, facilitating extraction of wealth.

It was said of him "nunca mostrar cariño a los indios y tenerlos muy sujetos." The Jilotepec Codex suggests that de la Cruz was working with the Franciscans in their work of conversion. Valerio de la Cruz's work was so successful in the region that around 1540 he was elected to governor of the province, by 1545 Mendoza had conferred upon him the title of Captain of the Great Chichameca. In 1550 he was named lord of Jilotepec, and in 1559, Luís de Velasco named him Captain-General of the Chichamecas, replacing Nicolás de San Luis Montañés to lead the local Otomi people against the Chichamecas. Further, de la Cruz was granted a coat of arms by Holy Roman Emperor Carlos V and permission to don the cross and habit of the Order of Santiago by Felipe II of Spain. During his time in the Jilotepec region, de la Cruz undertook many charitable acts. In 1565, thanks to the work of de la Cruz, the construction of the open chapel in Jilotepec began, its use was intended for the local indigenous population.

It was one of the largest open chapels of its time. He is credited with the construction of the first churches in Jilotepec and Huichapan, he constructed the Cruz del Doendó and reconstructed Jilotepec's Atrial Cross in front of the Church of Saint Peter and Saint Paul, two of Jilotepec's iconic stone crosses. In 1569 he began construction on multiple bridges in the region, notably in Jilotepec and Tula, to facilitate traffic on the Camino Real. Don Juan Bautista Valerio de la Cruz died in Jilotepec in 1589 and was buried with "ostentation," "pomp, solemnity" by order of the Viceroy in the Convent of Santiago in Tlatelolco, Mexico

Serendipity (software)

Serendipity is a blog and web-based content management system written in PHP and available under a BSD license. It supports PostgreSQL, MySQL, SQLite database backends, the Smarty template engine, a plugin architecture for user contributed modifications. Serendipity is available through a number of "one-click install" services such as Installatron. Serendipity's plugin architecture allows users to modify both the appearance of the blog and its features. Serendipity's SPARTACUS plugin automatically checks the central repository for plugins/templates upgrades and new functionality whenever a user checks the list. Users can install more than 120 plugins enhancing their blogs' functionality. WYSIWYG and HTML editing Built-in, powerful media database, can add media from URL or local file Multiple authors, configurable permission/usergroup system Threaded comments, nested categories, post to multiple categories Multiple languages Online plugin and template repository for easy plug-and-play installation Easy drag-and-drop sidebar plugins organization Category-based sub-blogs Static Pages Podcasting RSS planet/aggregator Robust spam blocking Tag support One-click upgrading from any version Can be embedded into your existing web pages Standards-compliant templating through Smarty Remote blogging via XML-RPC BSD-style licensing Multiple Database support Shared installations can power multiple blogs from just one codebase Native import from earlier blog applications Search engine-friendly permalink structure TrackBack and Pingback default template for frontend and backend have responsive web design The Serendipity project was started by Jannis Hermanns in the winter of 2002 still called jBlog.

Due to a naming conflict with an existing blog publishing system, Sterling Hughes suggested the name serendipity. This suggestion is based on an Essay by Sam Ruby; the short form s9y stems from abbreviations such as i18n for internationalization where the number represents the amount of omitted letters. Today the project is maintained by Garvin Hicking; the first book about Serendipity was published in German by OpenSourcePress: Serendipity - Individuelle Weblogs für Einsteiger und Profis. The publisher donated the book's copyright to the Serendipity project, who has released it under a CC-BY-NC-SA license and made a GitHub repository available online. Serendipity Official Website The Serendipity Handbook Serendipity PHP Weblog System at SourceForge Comparison of content management systems

Wootton, Staffordshire

Wootton is a village and civil parish in Staffordshire, England. The village is situated 20 miles east from Stoke-on-Trent and 20 miles northwest from Derby; the name Wootton is thought to come from the Old English wudu meaning wood and tūn meaning an enclosure. This translates to Wood Farm/Settlement. In 1870-72 John Marius Wilson's Imperial Gazetteer described Wootton as WOOTTON, a township in Ellastone parish, Stafford. Real property, £2,061. Pop. 185. Houses, 40. W. Hall was built by Inigo Jones. In early reports Wootton was predominately a farming village, with over 60% of males engaged in agriculture. To this day there remains a large farming culture, with still around 25% of the working population engaged in agriculture; the rest of the population are spread out between working in service industries or in managerial/professional occupations. Wootton Hall, the house where Rousseau stayed, was demolished in the 1930s. Wootton Lodge - The owned 17th century house is a grade I listed building in the parish.

During the English Civil War the house was held for the Crown and was badly damaged during a Parliamentary siege. It was restored in about 1700. Alton Towers - Popular holiday theme park Alton Towers is located 4 miles away from Wootton; the park attracts 2.7 million visitors from all over the globe annually. The resort encloses an area known as "Slain Hollow", reputed to be the site of a battle between King Ceolred of Mercia and King Ina of Wessex in 716 AD. A rich poetic description of the area around Wootton is The vales of Wever, a loco-descriptive poem by John Gisborne, written as a present to his host after staying at Wootton Hall, it shows the influence of Erasmus Darwin, who wrote similar topographic poetry on the district, it was admired by many poets including Wordsworth. Wootton is located about 1.5 miles off the B5032 Uttoxeter to Ashbourne road, is served by the 409 bus service between those two towns, which stops at Ellastone village. The nearest railway station is in Uttoxeter around 8 miles away which has regular trains to Crewe and Derby


Piutu known as piyutu or putu, is a traditional Filipino dish, the staple food of the Sama-Bajau people of the Philippines and the east coast of Sabah. It is made from steamed cassava, mashed and shaped into cylinders, they were traditionally wrapped in banana or palm leaves, but are sold wrapped in clear plastic today. It is torn or cut into small disks for eating, it is not flavored and thus need to be eaten with another accompanying dish seafood. The most popular accompaniments include latô salads and siagol, it serves as a replacement for rice, after the introduction of cassava to the Philippines from South America by the Spanish during the colonial period. Similar and related staple dishes are sianglag. Biamban is made from steamed tapioca flour cylinders wrapped in palm leaves. Sianglag is made from grated cassava, fried until yellowish. Both replace rice as an accompaniment to savory dishes. Pusô Puto Lontong Kakanin

War of Kings

"War of Kings" is a comic book crossover storyline written by Dan Abnett and Andy Lanning, published by Marvel Comics, set in Marvel's main shared universe. The six issue limited series was published between March and August 2009; the story is about a war between the Vulcan led Shi'ar empire and the Inhuman led Kree empire. The Guardians of the Galaxy, Nova Corps and the Starjammers become involved in various ways; the tag line was "When kings collide, the galaxy will tremble". On July 18, 2008, posted a news article featuring a modified cover of Emperor Vulcan with the phrase "Who Will Rule?", accompanied by the text "Stay tuned to and get ready for the blockbuster answer at San Diego Comic-Con!" At the SDCC it was announced that this was part of the build-up to the War of Kings, an outer-space storyline but focusing on the X-Men family of characters, rather than the cosmic entities. The core series was edited by Bill Rosemann; the event started in December 2008 with the mini-series X-Men: Kingbreaker, continued in the Secret Invasion: War of Kings one-shot and War of Kings #1-6.

Abnett and Lanning tied the main series into Guardians of the Galaxy and Nova. C. B. Cebulski wrote War of Kings: Darkhawk and War of Kings: Ascension. A series on Marvel Digital Comics, War of the Kings: Warriors by Christos Gage and Jay Faerber, tied into the storyline, featured different stories focusing on Gladiator, Blastaar and Crystal; these four stories were collected and published as War of Kings: Warriors 1-2. In the aftermath of the Secret Invasion storyline, Black Bolt and the Inhumans return to the Kree for their right to lineage as rulers, they come into his campaign of expansion for the Shi'ar. The first issue sets up this conflict and shows an attack at the wedding of Ronan the Accuser and Crystal - a betrothal arranged by the Inhuman king, Black Bolt, to unite the two races, resolve ancient hostilities and for common defense against mutual enemies; the Inhumans and Kree reply in kind. Vulcan embarks on an ambitious plan to conquer the rest of the universe. Gladiator of the Shi'ar Imperial Guard leads the assault against the Inhumans.

As Crystal of the Inhuman Royal Family and Ronan the Accuser are about to be married to unite the Inhumans with the Kree, they are attacked by Gladiator and the Guard. Gladiator is able to defeat him with some help from White Noise; the Guard captures Princess Lilandra, with the Kree and Inhumans. Ronan falls as he tries to help Crystal. Gladiator says that they have made their statement, the Imperial Guard leave. Medusa shouts. Gladiator and the Guard face off against the new batch of Nova Centurions whom they defeat. Gladiator's cousin, shows up informing him that the Emperor has ordered Gladiator to present Lilandra to him. Gladiator leaves, though he shows his dislike for his cousin and her presence. Gladiator walks a fine line in doing his duty for an emperor he dislikes while still protecting Lilandra from his wrath; the Starjammers, accompanied by a faction of the Guardians of the Galaxy, attack Gladiator's ship to extract Lilandra. He is taken out of the fight by Rocket Raccoon, aided by Marvel Girl, until he sees through their trick.

He defeats the rest of their team and recaptures Lilandra before she can escape. She pleads with him again but another Guard interrupts her and demands that Gladiator do as the Emperor ordered and kill Lilandra and the others. After battling the Starjammers and the Guardians of the Galaxy, Gladiator is swayed by Lilandra's argument against Vulcan and kills a member of the Imperial Guard loyal to the Emperor, saying that he is loyal to Lilandra. In the next issue, Lilandra is killed by Darkhawk - Razor. Gladiator begins to attack all of his enemies. Vulcan and Black Bolt battle on a ship/bomb. Black Bolt has the final strike and kills Vulcan; as Crystal and Lockjaw are about to take Black Bolt away, Vulcan gets up and pushes Black Bolt to the ground. Just as Lockjaw and Crystal escape, their ship blows up and both kings are killed. Back on the Shi'ar home planet, Gladiator becomes the new emperor; the explosion from the ship has made a hole in the fabric of space and time. This rift is the event that Starhawk was trying to prevent.

It's dubbed "The Fault." The Shi'ar fleet, suffering from the explosion, surrenders to the Inhumans, but the price is too high. A second wearer of Darkhawk armor calling himself Talon arrives on Earth and tells Chris Powell he is part of an ancient organization known as "The Fraternity of Raptors," who were created to protect the universe. After millennia of dormancy, only Darkhawk and Talon are left, their job now is to return the balance to the universe. For Chris, Talon has lied—when Chris accesses the memories in his armor, he concludes that the Fraternity of Raptors are the bad guys... just as Talon purges Chris's consciousness from the armor. A new identity for the armor, "Razor," takes control. Talon and Razor recover the Cosmic Control Rod from Catastrophus, stopping for Talon to implant a suggestion in the gestating Annihilus. Chris's personality was not wholly destroyed yet, a vision of his father tells him that much of what he believed about the armor was false: the prior history Evilhawk himself, was a lie made up by Chris's mind, the other armor is a seco