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Talk:Maruti 800

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Untitled
why in the world mehran/paki car is discussed in while the article is about Maruti 800,Indian car?and the statement like 100% imported is farce.They have already have vendors from India. --0-- —Preceding unsigned comment added by 59.93.41.147 (talk) 19:09, 2 January 2010 (UTC)

Comments like "It's fun to drive", or "the more comfortable Maruti Zen" are not in keeping with the NPOV of Wikipedia. Needs cleanup.

Done.

"It was launched in December 1984 with almost 100% import content." Where is the reference for this? Table 2.5 entitled 'Local Content in foreign cars' in this study entitled "Indian Auto Supply Chain at the cross roads" states the Maruti 800, Alto, and Wagon R are of 90% Indian local content.L1CENSET0K1LL 04:38, 18 January 2006 (UTC)

Specifications Table
I tried adding a table of specifications to this page. But the "external links" section shows up on top of the "Specifications" section. Can someone clean this up please. (Unsigned Comment added by Vijayplus77 at 11:39, 1 March 2006)

→Fixed it - you forgot to end the table with a }. yugobrandon 04:21, 26 January 2007 (UTC)

The Gross vehicle weight(GVW) is stated as 2000kg. And the curb weight is 650 kg. GVW cannot be 3 times the curb weight. Something seems wrong here! Baji Jagannath Ram Rao 08:25, 25 July 2014 (UTC)

Citation
Like they noted, the article needs citations... I'm working on it... :)

Regards,...

Amartya ray2001 (talk) 21:10, 11 September 2010 (UTC)

External links modified (January 2018)
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title: Talk:Maruti 800


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Marion Davis

Marion Davis may refer to:

 * Marion Keene, known as Marion Davis, British big band singer
 * Marion Davis Berdecio, born Marion Davis, spy

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

title: Marion Davis


text:
Albanian Coalition "Perspective"

The Albanian Coalition "Perspective" is an Albanian political party in Montenegro.

History
The party received 0.8% of the vote in the 2009 elections, winning one seat. For the 2012 elections it joined the For Unity coalition, alongside the New Democratic Power – FORCA (which also held one seat) and the Citizens Initiative. The For Unity alliance received 1.45% of the vote, winning a single seat.

title: Albanian Coalition "Perspective"


text:
General Francisco Mujica International Airport

Morelia International Airport (Aeropuerto Internacional de Morelia); officially Aeropuerto Internacional General Francisco J. Mujica (General Francisco J. Mujica International Airport) is an international airport located in Álvaro Obregón, Michoacán, Mexico. It serves the Metropolitan Area of Morelia, Michoacán, and is the largest airport in the state of Michoacán. In addition to providing domestic flights within Mexico, it serves as a gateway for international travel, connecting Central Mexico to multiple destinations in the United States.

The airport also supports various tourism, flight training, and general aviation activities. It is named in honor of former Governor of Michoacán Francisco José Múgica and it is operated by Grupo Aeroportuario del Pacífico. In 2022, the airport reached the million-passenger milestone for the first time; traffic increased to 1,384,300 passengers in 2023., ranking as the eighth-busiest airport in Mexico for international passenger traffic.

History
The airport began its operations in 1984, initially offering only one daily flight using a DC-9 aircraft to Mexico City. Over the years, it has been served by various airlines, including Aero California, Aero Sudpacífico, Aeromar, Aviacsa, Avolar, Líneas Aéreas Azteca, Continental (now United), Mexicana, TAESA, and TAR. In 2019, the airport underwent expansion efforts to enhance its capabilities. During the same year, Volaris established a crew base at the airport to support its growing number of flight routes connecting Morelia to destinations within Mexico and the United States.

Facilities
The airport is located at an elevation of 1839 m above mean sea level. It has a single runway, designated as 05/23, which measures 3408 m in length and is surfaced with asphalt.

The commercial aviation apron covers an area of 40284 m2 and includes nine stands for receiving narrow-body aircraft. The general aviation apron has a total area of 12060 m2 and offers twelve stands for fixed-wing aircraft along with two heliports for private aviation and occasional use by third-level commercial aviation.

The passenger terminal is a single-story building that accommodates both arrivals and departures for domestic and international flights. It features a departure concourse with four gates without jetbridges, a VIP lounge, check-in areas, security zones, baggage claim areas, an arrivals hall, car rental services, taxi stands, and various retail stores. Adjacent to the terminal, other facilities include a hotel, parking areas, civil aviation hangars, and designated spaces for general aviation.

Busiest routes

 * Notes

Accidents and incidents

 * 9 September 1978 - A de Havilland Canada DHC-6 Twin Otter of Lineas Aéreas del Centro flying scheduled service to the old Morelia Airport from Mexico City, crashed shortly after takeoff from Mexico City International Airport. There were 18 fatalities among the 21 passengers. The aircraft was also damaged beyond repair.
 * 20 October 2002 - Aerolíneas Internacionales Flight 888, a Boeing 727-100 scheduled to fly from Morelia to León/Guanajuato, allegedly encountered 9 small, spherical UFOs prior to its 10AM takeoff roll. As reported by the crew and a witness on the ground, the sighting lasted around 10 minutes, with said objects maneuvering simultaneously. After the objects moved away, the flight was able to continue without further incident.
 * 19 September 2010 - Aeroméxico Flight 6531, bound to Morelia from Las Vegas, suffered a fuel leak. The Boeing 737-700 returned to Las Vegas for an emergency landing. There were no fatalities among the 102 passengers.


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Talk:Choda

Choda is also a nickname from a Spanish name Danilo(Daniel, Danielo).It is a twisted nickname from Dacha that is often used as a nickname for Danilo.

The drinking game
Deleted info on this as unverifiable and non-notable. Please see WP:V and WP:Notability. Mmoyer 03:04, 2 February 2007 (UTC)

title: Talk:Choda


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Postmaster-General's Department

The Postmaster-General's Department (PMG) was a department of the Australian federal government, established at Federation in 1901, whose responsibilities included the provision of postal and telegraphic services throughout Australia. It was abolished in December 1975 and replaced by the Postal and Telecommunications Department. Two separate legal entities had been established in July 1975 to take over the department's operations: Telecom Australia (colloquially "Telecom"; later became Telstra) and Australia Post.

History
The Postmaster-General's Department was created in 1901 to take over all postal and telegraphy services in Australia from the states and administer them on a national basis. The department was administered by the postmaster-general.

The first permanent secretary of the department was Sir Robert Townley Scott, who held office from 1 July 1901 until his retirement on 31 December 1910.

In its first 25 years, the department grew from 6,000 to 10,000 offices and from 18,000 to 47,000 staff. Earnings grew from £2.4 million to £10 million per annum.

In mid-1975 the department was disaggregated into the Australian Telecommunications Commission (trading as Telecom Australia) and the Australian Postal Commission (trading as Australia Post). In 1993 the Spectrum Management Agency was formed to take responsibility of radio and television broadcast licensing, which was then merged into the Australian Communications Authority, that later became the Australian Communications and Media Authority. Telecom Australia changed its name to Telstra in 1995 and has since been privatised.

Abolition
The department was abolished in December 1975 by the Fraser government, and replaced by the Postal and Telecommunications Department. The change was intended to take account of the increase in the functions of the department to include all electronic media matters which had previously been the responsibility of the Department of the Media.

List of departmental secretaries and directors-general

 * 1901–1910: Robert Scott
 * 1911–1923: Justinian Oxenham
 * 1923–1939: Harry Brown
 * 1940–1946: Daniel McVey
 * 1946–1949: Bede Fanning
 * 1949–1958: Giles Chippindall
 * 1958: Van Vanthoff
 * 1959–1961: Mervyn Stradwick
 * 1961–1965: Frank O'Grady
 * 1965–1968: Trevor Housley
 * 1968–1972: John Knott
 * 1972–1975: Eber Lane
 * 1975: Fred Green

title: Postmaster-General's Department


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Canaan Dog

The Canaan Dog is a dog breed developed in the early 20th century from semiwild pariah dogs that were the descendants of animals present in the region since biblical times. It is a breed of pariah dog found across the Middle East. It can be found in Jordan, Israel, Lebanon, Palestine, and the Sinai Peninsula and these, or dogs nearly identical, were also found in Syria over 9,000 years ago. It is the national dog of Israel. As of 2012, there were 2,000 to 3,000 Canaan Dogs across the world.

Naming
The Canaan dog is also known as the Kelef K'naani, Israel Canaan Dog, Bedouin Sheep dog  and Palestinian Pariah Dog,   The breed standard was created by Israeli Professor Rudolphina Menzel in 1966.

History
Since time immemorial, the Bedouins have used this dog for guarding their herds and camps. At the time of the Diaspora, the Israelites were forcefully removed from their land and according to tradition had to leave behind their dogs which reverted to the wild.

Excavations in Israel unearthed the Ashkelon dog cemetery, the largest known animal cemetery in the ancient world, containing 700 dog skeletons, all of which were anatomically similar to the Canaan dog of modern times. The cemetery dates back to the time of occupation by the Persian Empire and archaeologists hypothesize that the dogs were revered as sacred animals.

Dr. Rudolphina Menzel (1891–1973) used these intelligent scavenger-dogs mainly found in the desert as guard dogs. In the 1930s, Menzel was asked by the Haganah to build up a service dog organization. She captured a select group of semi-wild individuals, tamed, trained and bred them. Menzel found the dogs highly adaptable, trainable, and easy to domesticate. It took her about six months to capture her first dog, Dugma (Hebrew דוגמא, "Example") and within a few weeks she was able to take him into town and on buses. She began a breeding program in 1934, providing working dogs for the military and she gave pups to be pets and home guard dogs. She initiated a selective breeding program to produce the breed known today as the Canaan dog.

In 1949, Menzel founded The Institute for Orientation and Mobility of the Blind, and in 1953, she started to train Canaan dogs as guide dogs for the blind. Although she was able to train several dogs, she found that the breed was too independent and too small for general guide dog use, although some of her dogs were used successfully by children. Her breeding program was concentrated with the Institute, where a foundation of kennel-raised Canaan dogs was established, carrying the name "B'nei Habitachon". In addition, a controlled collection of dogs of the original type was continued, primarily from the Bedouin of the Negev. She later supplied breeding stock to Shaar Hagai Kennels which continued in the breeding of the Canaan dog.

After her death in 1973, Shaar Hagai Kennels, managed by Dvora Ben Shaul and Myrna Shiboleth, continued the breeding program according to her instructions.

Collection of wild Canaan dogs in Israel has become very difficult, because many of the Canaan dogs living in the open there were destroyed by the Israeli government in the fight against rabies. The spread of the human population into areas that were formerly isolated, along with their pet dogs, has resulted in the loss of the natural habitat of the Canaan. Even the majority of Bedouin dogs today, other than those of tribes still living a traditional and isolated life style, are mixed with other breeds. It is possible that there are still original Canaans among Bedouin tribes that still live the traditional nomadic life elsewhere, and perhaps in Egypt. Myrna Shiboleth visits the Negev regularly, looking for good specimens living by the Bedouin camps, that she can breed with her dogs and use to strengthen the gene pool.

Appearance

The Canaan Dog is a "wild type" dog in appearance. It is a medium-sized square built dog, with a wedge-shaped head, erect and low set ears with a broad base and rounded tips. Its outer coat is dense, harsh and straight of short to medium-length. The undercoat should be close and profuse according to season. Color ranges from black to cream and all shades of brown and red between, usually with small white markings, or all white with colour patches. Spotting of all kinds is permitted, as well as white or black masks.

In writing the first official standard for the Canaan Dog, Menzel wrote: "Special importance must be placed on the points that differentiate the Canaan Dog from the German Shepherd Dog, whose highly bred form he sometimes resembles: the Canaan-dog is square, the loin region short, the forequarters highly erect, the hindquarters less angular, the neck as noble as possible, the tail curled over the back when excited, the trot is short (see also differences in head and color)".

Temperament
Canaan dogs are alert, react quickly and distrust strangers. They are strongly defensive but not aggressive.

Skills
Canaan dogs can compete in dog agility trials, obedience, showmanship, flyball, tracking, and herding events. Herding instincts and trainability can be measured at noncompetitive herding tests. Canaans exhibiting basic herding instincts can be trained to compete in herding trials.

Breed recognition
The Canaan dog was first recognized by the Israel Kennel Club in 1953 and by the FCI (Federation Cynologique Internationale) in 1966. The first accepted standard was written by Dr. Menzel. In 1986, the first Canaan dogs were brought to Finland from Sha'ar Hagai Kennel, in Israel. The Canaan Dog is today recognized by all the world's kennel clubs and is being bred in many countries. There are breed clubs in the U.S., Canada, the U.K., Finland, Germany, Israel and France.

Canada
The first Canaan dog came to Canada May 16, 1970. The dogs came from a kennel in Delaware. The Canadian Canaan Club was formed in 1972, and the first executive of the Club was elected on March 15, 1973. The club has since been dissolved. The Canaan dog obtained entry into the Miscellaneous Class of the Canadian Kennel Club on December 1, 1975. In January 1993, the breed was accepted in the Working Group, as the Canadian Kennel Club did not have a Herding group at that time.

United Kingdom
The first Canaan Dog was brought to the UK from Lebanon in 1965, before they were a recognized breed. In December 1970, they were recognized by the Kennel Club, and the breed was placed in the Utility Group. In May 1992 the inaugural meeting of the Canaan Dog Club of the United Kingdom took place. Since 1996 the breed has begun to grow in numbers in the UK, though it is still quite numerically small.

United States
On September 7, 1965, Menzel sent four dogs to Ursula Berkowitz of Oxnard, California, the first Canaan dogs in the United States. The Canaan Dog Club of America was formed the same year, and stud book records were kept from these first reports. In June 1989, the Canaan dog entered the American Kennel Club (AKC) Miscellaneous Class, and then joined the Herding Group in 1997. Its profile was raised when John F. Kennedy Jr. purchased a Canaan dog, Friday, in 1995. Canaan dogs were registered in the AKC Stud Book as of June 1, 1997. The dogs began competing in conformation on August 12, 1997. The United Kennel Club recognized the Canaan Dog in 1992 as part of the Sighthound & Pariah Dog Group and has the Israel Canaan Dog Club of America as the parent club. About 50 puppies are born each year.

title: Canaan Dog


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Kirloskar

Kirloskar may refer to
 * Kirloskar Group an Indian conglomerate that relates to
 * Kirloskar Brothers, a pump manufacturing company
 * Kirloskar Pneumatic Company Limited
 * Toyota Kirloskar Motor, a subsidiary of Toyota, which is partly owned by Kirloskar Group
 * Laxmanrao Kirloskar (1869–1956), an Indian businessman and the founder of the Kirloskar Group
 * S. L. Kirloskar (1903–1994), an Indian businessman, son of Laxmanrao
 * Sanjay Kirloskar (born 1957), an Indian businessman, grandson of S. L. Kirloskar
 * Annasaheb Kirloskar (1843–1885), an Indian playwright

title: Kirloskar


text:
Passionada

Passionada is a 2002 American romantic comedy film. It is directed by Dan Ireland and stars Jason Isaacs, Sofia Milos and Emmy Rossum, co-starring Seymour Cassel and Theresa Russell. The story is by David Bakalar, and the screenplay is by Jim and Steve Jermanok. The film is set in New Bedford, Massachusetts, a formerly wealthy port town with a sizable population of Portuguese descent.

Plot summary
Celia Amonte (Milos) is a Portuguese American widow who lives in New Bedford, Massachusetts with her daughter Vicky (Rossum); her late husband was a fisherman lost at sea. Vicky sneaks out of the house to go to a casino, where she meets Charlie Beck (Isaacs), a British card counter, and attempts to convince him to teach her his trade. Charlie is apprehended by the casino staff, and told that he can either work to find other card counters, or be banned from the casino. After accepting a ban, Charlie meets with his friends Daniel (Cassel) and Lois Vargas (Russell) at the Shawmut Diner, where they attempt to convince him to stop card counting. Charlie goes to a Portuguese restaurant with Daniel and Lois, and becomes interested in Celia after seeing her sing fado. He repeatedly tries to date Celia, and is rebuffed. Charlie later finds Celia's address in the phone book and goes to her house, where he encounters Vicky. Vicky agrees to help Charlie pursue her mother in exchange for card counting lessons, and threatens to reveal his identity as a gambler should he refuse.

Vicky tells Charlie that her mother is interested in fisherman; Charlie lies to Celia and claims to be in town to open a fish-processing plant. Celia becomes increasingly interested in Charlie, and admits her feelings for him, and struggles since her husband's death, while on a date at Ned Point Light. After a festival, Vicky stays out all night at a casino, causing Celia to worry and go looking for her. While out, she sees Charlie with Lois in his car, and suspects an affair. Charlie reveals his lies to Celia and asks for her forgiveness; she tells him to never come to her house again. Devastated, Charlie prepares to leave New Bedford. Lois visits Celia at her home, and convinces her to take Charlie back. After singing one night, Celia follows a trail of fish on the ground to find Charlie, who has become a successful fisherman. He explains that he wants her back, and would be willing to do any job to be with her. She accepts him, and the two kiss.

Sometime later, Charlie is employed at the casino to find card counters, while Celia, now married to Charlie, is a singer at the casino.

Cast

 * Jason Isaacs as Charlie Beck, a card counter who wishes to date Celia, and takes advice from Vicky in exchange for card counting lessons
 * Sofia Milos as Celia Amonte, a Portuguese American widow whose husband was lost at sea; she has refused to date since his death.
 * Emmy Rossum as Vicky Amonte, Celia's daughter who agrees to help Charlie date her mother to learn how to count cards.
 * Seymour Cassel as Daniel Vargas, a wealthy former gambler and friend of Charlie.
 * Theresa Russell as Lois Vargas, Daniel's wife.
 * Lupe Ontiveros as Angelica Amonte, Celia's mother-in-law and next-door-neighbor.

title: Passionada


text: Talk:-ologist

title: Talk:-ologist


text:
User:Notmart

Hi there! New contributor from Philadelphia, PA

title: User:Notmart


text:
Shell theorem

In classical mechanics, the shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetrical body. This theorem has particular application to astronomy.

Isaac Newton proved the shell theorem and stated that:
 * 1) A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center.
 * 2) If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.

A corollary is that inside a solid sphere of constant density, the gravitational force within the object varies linearly with distance from the center, becoming zero by symmetry at the center of mass. This can be seen as follows: take a point within such a sphere, at a distance $$r$$ from the center of the sphere. Then you can ignore all of the shells of greater radius, according to the shell theorem (2). But the point can be considered to be external to the remaining sphere of radius r, and according to (1) all of the mass of this sphere can be considered to be concentrated at its centre. The remaining mass $$m$$ is proportional to $$r^3$$ (because it is based on volume). The gravitational force exerted on a body at radius r will be proportional to $$m/r^2$$ (the inverse square law), so the overall gravitational effect is proportional to $r^3/r^2 =r$, so is linear in $r$.

These results were important to Newton's analysis of planetary motion; they are not immediately obvious, but they can be proven with calculus. (Gauss's law for gravity offers an alternative way to state the theorem.)

In addition to gravity, the shell theorem can also be used to describe the electric field generated by a static spherically symmetric charge density, or similarly for any other phenomenon that follows an inverse square law. The derivations below focus on gravity, but the results can easily be generalized to the electrostatic force.

Derivation of gravitational field outside of a solid sphere
There are three steps to proving Newton's shell theorem (1). First, the equation for a gravitational field due to a ring of mass will be derived. Arranging an infinite number of infinitely thin rings to make a disc, this equation involving a ring will be used to find the gravitational field due to a disk. Finally, arranging an infinite number of infinitely thin discs to make a sphere, this equation involving a disc will be used to find the gravitational field due to a sphere.

The gravitational field $$E$$ at a position called $$P$$ at $$(x,y) = (-p,0)$$ on the x-axis due to a point of mass $$M$$ at the origin is $$E_\text{point} = \frac{GM}{p^2}$$ Suppose that this mass is moved upwards along the y-axis to the point $(-p,R)$. The distance between $$P$$ and the point mass is now longer than before; It becomes the hypotenuse of the right triangle with legs $$p$$ and $$R$$ which is $\sqrt{p^2 + R^2}$. Hence, the gravitational field of the elevated point is: $$E_\text{elevated point} = \frac{GM}{p^2+R^2}$$

The magnitude of the gravitational field that would pull a particle at point $$P$$ in the x-direction is the gravitational field multiplied by $$\cos(\theta)$$ where $$\theta$$ is the angle adjacent to the x-axis. In this case, $\cos(\theta) = \frac{p}{\sqrt{p^2 + R^2}}$.|undefined Hence, the magnitude of the gravitational field in the x-direction, $$E_x$$ is: $$E_x = \frac{GM\cos{\theta}}{p^2+R^2}$$ Substituting in $$\cos(\theta)$$ gives $$E_x = \frac{GMp}{\left(p^2+R^2\right)^{3/2}}$$ Suppose that this mass is evenly distributed in a ring centered at the origin and facing point $$P$$ with the same radius $R$. Because all of the mass is located at the same angle with respect to the x-axis, and the distance between the points on the ring is the same distance as before, the gravitational field in the x-direction at point $$P$$ due to the ring is the same as a point mass located at a point $$R$$ units above the y-axis: $$E_\text{ring} = \frac{GMp}{\left(p^2+R^2\right)^{3/2}}$$

To find the gravitational field at point $$P$$ due to a disc, an infinite number of infinitely thin rings facing $P$, each with a radius $y$, width of $dy$, and mass of $$dM$$ may be placed inside one another to form a disc. The mass of any one of the rings $$dM$$ is the mass of the disc multiplied by the ratio of the area of the ring $$2\pi y\,dy$$ to the total area of the disc $\pi R^2$. So, $dM=\frac{M\cdot 2y\,dy}{R^2}$. Hence, a small change in the gravitational field, $$E$$ is: $$dE = \frac{Gp\,dM}{(p^2+y^2)^{3/2}}$$

Substituting in $$dM$$ and integrating both sides gives the gravitational field of the disk: $$E = \int \frac{GMp\cdot \frac{2y\, dy}{R^2}}{(p^2+y^2)^{3/2}}$$ Adding up the contribution to the gravitational field from each of these rings will yield the expression for the gravitational field due to a disc. This is equivalent to integrating this above expression from $$y=0$$ to $y=R$, resulting in: $$E_\text{disc} = \frac{2GM}{R^2} \left( 1-\frac{p}{\sqrt{p^2+R^2}}\right)$$ To find the gravitational field at point $$P$$ due to a sphere centered at the origin, an infinite amount of infinitely thin discs facing $P$, each with a radius $R$, width of $dx$, and mass of $$dM$$ may be placed together.

These discs' radii $$R$$ follow the height of the cross section of a sphere (with constant radius $$a$$) which is an equation of a semi-circle: $R = \sqrt{a^2-x^2}$. $$x$$ varies from $$-a$$ to $a$.

The mass of any of the discs $$dM$$ is the mass of the sphere $$M$$ multiplied by the ratio of the volume of an infinitely thin disc divided by the volume of a sphere (with constant radius $a$). The volume of an infinitely thin disc is $\pi R^2\, dx$, or $\pi\left(a^2-x^2\right) dx$. So, $dM = \frac{\pi M(a^2-x^2)\,dx}{\frac{4}{3}\pi a^3}$. Simplifying gives $dM = \frac{3M(a^2-x^2)\,dx}{4a^3}$.

Each discs' position away from $$P$$ will vary with its position within the 'sphere' made of the discs, so $$p$$ must be replaced with $p+x$.

Replacing $$M$$ with $dM$, $$R$$ with $\sqrt{a^2-x^2}$, and $$p$$ with $$p+x$$ in the 'disc' equation yields: $$dE = \frac{\left( \frac{2G\left[3M\left(a^2-x^2\right)\right]}{4a^3} \right) }{\sqrt{a^2-x^2}^2}\cdot \left(1-\frac{p+x}{\sqrt{(p+x)^2+\sqrt{a^2-x^2}^2}}\right)\, dx$$ Simplifying, $$\int dE = \int_{-a}^a \frac{3GM}{2a^3} \left(1 - \frac{p + x}{\sqrt{p^2 + a^2 + 2px}}\right) dx$$ Integrating the gravitational field of each thin disc from $$x=-a$$ to $$x=+a$$ with respect to $x$, and doing some careful algebra, yields Newton's shell theorem: $$E = \frac{GM}{p^2}$$ where $$p$$ is the distance between the center of the spherical mass and an arbitrary point $P$. The gravitational field of a spherical mass may be calculated by treating all the mass as a point particle at the center of the sphere.

Outside a shell
A solid, spherically symmetric body can be modeled as an infinite number of concentric, infinitesimally thin spherical shells. If one of these shells can be treated as a point mass, then a system of shells (i.e. the sphere) can also be treated as a point mass. Consider one such shell (the diagram shows a cross-section):

(Note: the $$d\theta$$ in the diagram refers to the small angle, not the arc length. The arc length is $R\, d\theta$ .)

Applying Newton's Universal Law of Gravitation, the sum of the forces due to the mass elements in the shaded band is
 * $$dF = \frac{Gm}{s^2} dM.$$

However, since there is partial cancellation due to the vector nature of the force in conjunction with the circular band's symmetry, the leftover component (in the direction pointing towards $m$) is given by
 * $$dF_r = \frac{Gm}{s^2} \cos(\varphi) \, dM$$

The total force on $m$, then, is simply the sum of the force exerted by all the bands. By shrinking the width of each band, and increasing the number of bands, the sum becomes an integral expression:

 * $$F_r = \int dF_r$$

Since $$G$$ and $$m$$ are constants, they may be taken out of the integral:

 * $$F_r = Gm \int \frac{\cos(\varphi)}{s^2} \, dM. $$

To evaluate this integral, one must first express $$dM$$ as a function of $$d\theta$$

The total surface of a spherical shell is
 * $$4\pi R^2 $$

while the surface area of the thin slice between $$\theta$$ and $$\theta+d\theta$$ is
 * $$2\pi R\sin(\theta) R \,d\theta = 2\pi R^2\sin(\theta) \,d\theta$$

If the mass of the shell is $M$, one therefore has that

 * $$dM = \frac {2\pi R^2\sin(\theta) }{4\pi R^2} M\,d\theta = \frac{1}{2} M\sin(\theta) \,d\theta$$

and

 * $$F_r = \frac{GMm}{2} \int \frac{\sin(\theta) \cos(\varphi)} {s^2}\,d\theta $$

By the law of cosines,

 * $$\cos(\varphi) = \frac{r^2 + s^2 - R^2}{2rs}$$

and

 * $$\cos(\theta) = \frac{r^2 + R^2 - s^2}{2rR}.$$

These two relations link the three parameters $\theta$, $$\varphi$$ and $$s$$ that appear in the integral together. As $$\theta$$ increases from $$0$$ to $$\pi$$ radians, $$\varphi$$ varies from the initial value 0 to a maximal value before finally returning to zero at $\theta=\pi$. At the same time, $$s$$ increases from the initial value $$r-R$$ to the final value $$r+R$$ as $$\theta$$ increases from 0 to $$\pi$$ radians. This is illustrated in the following animation:

(Note: As viewed from $m$, the shaded blue band appears as a thin annulus whose inner and outer radii converge to $$R \sin(\theta)$$ as $$d\theta$$ vanishes.)

To find a primitive function to the integrand, one has to make $$s$$ the independent integration variable instead of $\theta$.

Performing an implicit differentiation of the second of the "cosine law" expressions above yields

 * $$-\sin(\theta) \,d\theta = \frac{-2s}{2rR} \, ds$$

and thus

 * $$\sin(\theta) \,d\theta = \frac{s}{rR} \, ds.$$

It follows that

 * $$F_r = \frac{GMm}{2} \frac{1}{rR} \int \frac{s\cos(\varphi)} {s^2}\,ds = \frac{GMm}{2rR} \int \frac{\cos(\varphi)} s \,ds $$

where the new integration variable $$s$$ increases from $$r-R$$ to $r+R$.

Inserting the expression for $$\cos(\varphi)$$ using the first of the "cosine law" expressions above, one finally gets that

 * $$F_r = \frac{GMm}{4r^2 R} \int \left( 1 + \frac{r^2 - R^2}{s^2} \right)\ ds\ .$$

A primitive function to the integrand is

 * $$s - \frac{r^2 - R^2}{s}\ ,$$

and inserting the bounds $$r-R$$ and $$r+R$$ for the integration variable $$s$$ in this primitive function, one gets that
 * $$F_r = \frac{GMm}{r^2},$$

saying that the gravitational force is the same as that of a point mass in the center of the shell with the same mass.

Spherical Shell to Solid Sphere
It is possible to use this spherical shell result to re-derive the solid sphere result from earlier. This is done by integrating an infinitesimally thin spherical shell with mass of $dM$, and we can obtain the total gravity contribution of a solid ball to the object outside the ball

 * $$F_{total} = \int dF_r = \frac{Gm}{r^2} \int dM.$$

Uniform density means between the radius of $$x$$ to $x+dx$, $$dM$$ can be expressed as a function of $x$, i.e.,

 * $$dM = \frac{4 \pi x^2 dx}{\frac{4}{3} \pi R^3} M = \frac{3Mx^2 dx}{R^3}$$

Therefore, the total gravity is

 * $$F_\text{total} = \frac{3GMm}{r^2 R^3} \int_0^R x^2 \, dx = \frac{GMm}{r^2}$$

As found earlier, this suggests that the gravity of a solid spherical ball to an exterior object can be simplified as that of a point mass in the center of the ball with the same mass.

Inside a shell
For a point inside the shell, the difference is that when θ is equal to zero, ϕ takes the value $\pi$ radians and s the value R − r. When θ increases from 0 to π radians, ϕ decreases from the initial value π radians to zero and s increases from the initial value R − r to the value R + r.

This can all be seen in the following figure

Inserting these bounds into the primitive function

 * $$s - \frac{r^2 - R^2}{s}$$

one gets that, in this case

 * $$F_r = 0, $$

saying that the net gravitational forces acting on the point mass from the mass elements of the shell, outside the measurement point, cancel out.

Generalization: If $f=\frac{k}{r^p}$, the resultant force inside the shell is:

 * $$F(r) = \frac{GMm}{4r^2 R} \int_{R-r}^{R+r} \left( \frac{1}{s^{p-2}} + \frac{r^2 - R^2}{s^p} \right) \, ds$$

The above results into $$F(r)$$ being identically zero if and only if $$p=2$$

Outside the shell (i.e. $$r>R$$ or $$r < -R$$):

 * $$F(r) = \frac{GMm}{4r^2 R} \int_{r-R}^{r+R} \left( \frac{1}{s^{p-2}} + \frac{r^2 - R^2}{s^p} \right) \, ds$$

Derivation using Gauss's law
The shell theorem is an immediate consequence of Gauss's law for gravity saying that

 * $$\int_S {\mathbf g}\cdot \,d{\mathbf {S}} = -4 \pi GM$$

where M is the mass of the part of the spherically symmetric mass distribution that is inside the sphere with radius r and

 * $$\int_S {\mathbf g}\cdot \,d{\mathbf {S}} = \int_S {\mathbf g}\cdot {\hat\mathbf{n}}\,dS$$

is the surface integral of the gravitational field $$\mathbf{g}$$ over any closed surface inside which the total mass is M, the unit vector $$\hat\mathbf{n}$$ being the outward normal to the surface.

The gravitational field of a spherically symmetric mass distribution like a mass point, a spherical shell or a homogeneous sphere must also be spherically symmetric. If $$\hat\mathbf{n}$$ is a unit vector in the direction from the point of symmetry to another point the gravitational field at this other point must therefore be

 * $$ \mathbf g = g(r) \hat\mathbf{n}$$

where g(r) only depends on the distance r to the point of symmetry

Selecting the closed surface as a sphere with radius r with center at the point of symmetry the outward normal to a point on the surface, $\hat\mathbf{n}$, is precisely the direction pointing away from the point of symmetry of the mass distribution.

One, therefore, has that

 * $$ \mathbf {g} = g(r)\hat\mathbf{n}$$

and

 * $$\int_S \mathbf g \cdot \,d{\mathbf S} = g(r) \int_S \,dS = g(r) 4\pi r^2 $$

as the area of the sphere is 4πr2.

From Gauss's law it then follows that
 * $$ g(r) 4\pi r^2 = -4 \pi GM ,$$

or,
 * $$ g(r) = -\frac {GM}{r^2}.$$

Converses and generalizations
It is natural to ask whether the converse of the shell theorem is true, namely whether the result of the theorem implies the law of universal gravitation, or if there is some more general force law for which the theorem holds. More specifically, one may ask the question:

In fact, this allows exactly one more class of force than the (Newtonian) inverse square. The most general force as derived by Vahe Gurzadyan in Gurzadyan theorem is:

 * $$ F = -\frac{G M m}{r^2} + \frac{\Lambda m c^2 r}{3} $$

where $$G$$ and $$\Lambda$$ can be constants taking any value. The first term is the familiar law of universal gravitation; the second is an additional force, analogous to the cosmological constant term in general relativity.

If we further constrain the force by requiring that the second part of the theorem also holds, namely that there is no force inside a hollow ball, we exclude the possibility of the additional term, and the inverse square law is indeed the unique force law satisfying the theorem.

On the other hand, if we relax the conditions, and require only that the field everywhere outside a spherically symmetric body is the same as the field from some point mass at the center (of any mass), we allow a new class of solutions given by the Yukawa potential, of which the inverse square law is a special case.

Another generalization can be made for a disc by observing that

 * $$dM=\frac{R^2}{2} \frac{d\theta \, \sin^2(\theta)}{\pi R^2}M=\frac{ \sin^2(\theta)}{2 \pi}M \, d\theta $$

so:

 * $$F_r = \frac{GMm}{2 \pi} \int \frac{ \sin^2 (\theta) \cos(\varphi)} {s^2} \, d\theta,$$

where $M=\pi R^2 \rho$, and $$\rho$$ is the density of the body.

Doing all the intermediate calculations we get:

 * $$F(r) = \frac{G m \rho}{8r^3} \int_{R-r}^{R+r} { \frac{\left(r^2 + s^2 - R^2\right)\sqrt{2\left(r^2 R^2 + r^2 s^2 + R^2 s^2\right) - s^4 - r^4 - R^4} }{s^2} } \, ds$$

Introduction
Propositions 70 and 71 consider the force acting on a particle from a hollow sphere with an infinitesimally thin surface, whose mass density is constant over the surface. The force on the particle from a small area of the surface of the sphere is proportional to the mass of the area and inversely as the square of its distance from the particle. The first proposition considers the case when the particle is inside the sphere, the second when it is outside. The use of infinitesimals and limiting processes in geometrical constructions are simple and elegant and avoid the need for any integrations. They well illustrate Newton's method of proving many of the propositions in the Principia.

His proof of Propositions 70 is trivial. In the following, it is considered in slightly greater detail than Newton provides.

The proof of Proposition 71 is more historically significant. It forms the first part of his proof that the gravitational force of a solid sphere acting on a particle outside it is inversely proportional to the square of its distance from the center of the sphere, provided the density at any point inside the sphere is a function only of its distance from the center of the sphere.

Although the following are completely faithful to Newton's proofs, very minor changes have been made to attempt to make them clearer.

Force on a point inside a hollow sphere

Fig. 2 is a cross-section of the hollow sphere through the center, S and an arbitrary point, P, inside the sphere. Through P draw two lines IL and HK such that the angle KPL is very small. JM is the line through P that bisects that angle. From the inscribed angle theorem, the triangles IPH and KPL are similar. The lines KH and IL are rotated about the axis JM to form two cones that intersect the sphere in two closed curves. In Fig. 1 the sphere is seen from a distance along the line PE and is assumed transparent so both curves can be seen.

The surface of the sphere that the cones intersect can be considered to be flat, and $ \angle PJI = \angle PMK $.

Since the intersection of a cone with a plane is an ellipse, in this case the intersections form two ellipses with major axes IH and KL, where $ \frac{IH}{KL} = \frac{PJ}{PM} $.

By a similar argument, the minor axes are in the same ratio. This is clear if the sphere is viewed from above. Therefore the two ellipses are similar, so their areas are as the squares of their major axes. As the mass of any section of the surface is proportional to the area of that section, for the two elliptical areas the ratios of their masses $ \propto \frac{PJ^2}{PM^2} $.

Since the force of attraction on P in the direction JM from either of the elliptic areas, is direct as the mass of the area and inversely as the square of its distance from P, it is independent of the distance of P from the sphere. Hence, the forces on P from the two infinitesimal elliptical areas are equal and opposite and there is no net force in the direction JM.

As the position of P and the direction of JM are both arbitrary, it follows that any particle inside a hollow sphere experiences no net force from the mass of the sphere.

Note: Newton simply describes the arcs IH and KL as 'minimally small' and the areas traced out by the lines IL and HK can be any shape, not necessarily elliptic, but they will always be similar.

Force on a point outside a hollow sphere

Fig. 1 is a cross-section of the hollow sphere through the center, S with an arbitrary point, P, outside the sphere. PT is the tangent to the circle at T which passes through P. HI is a small arc on the surface such that PH is less than PT. Extend PI to intersect the sphere at L and draw SF to the point F that bisects IL. Extend PH to intersect the sphere at K and draw SE to the point E that bisects HK, and extend SF to intersect HK at D. Drop a perpendicular IQ on to the line PS joining P to the center S. Let the radius of the sphere be a and the distance PS be D.

Let arc IH be extended perpendicularly out of the plane of the diagram, by a small distance ζ. The area of the figure generated is $ IH\cdot \zeta $, and its mass is proportional to this product.

The force due to this mass on the particle at P $$ \propto \frac{IH\cdot \zeta}{PI^2} $$ and is along the line PI.

The component of this force towards the center $$ \propto \frac{IH\cdot PQ\cdot \zeta}{PI^3} $$.

If now the arc HI is rotated completely about the line PS to form a ring of width HI and radius IQ, the length of the ring is 2π·IQ and its area is 2π·IQ·IH. The component of the force due to this ring on the particle at P in the direction PS becomes $ \propto \frac{IH\cdot IQ\cdot PQ}{PI^3} $.

The perpendicular components of the force directed towards PS cancel out since the mass in the ring is distributed symmetrically about PS. Therefore, the component in the direction PS is the total force on P due to the ring formed by rotating arc HI about PS.

From similar triangles: $ \frac{IQ}{PI} = \frac{FS}{D}$; $ \frac{PQ}{PI} = \frac{PF}{D}$, and $ \frac{RI}{PI} = \frac{DF}{PF}$.

If HI is sufficiently small that it can be taken as a straight line, $$ \angle SIH $$ is a right angle, and $ \angle RIH = \angle FIS $, so that $ \frac{HI}{RI} = \frac{a}{IF}$.

Hence the force on P due to the ring $ \propto \frac{IH\cdot IQ\cdot PQ}{PI^3} = \frac{a\cdot DF\cdot FS\cdot PF}{IF\cdot PF\cdot D\cdot D} = \frac{a\cdot DF\cdot FS}{IF\cdot D^2} $.

Assume now in Fig. 2 that another particle is outside the sphere at a point p, a different distance d from the center of the sphere, with corresponding points lettered in lower case. For easy comparison, the construction of P in Fig. 1 is also shown in Fig. 2. As before, ph is less than pt.

Generate a ring with width ih and radius iq by making angle $$ fiS = FIS $$ and the slightly larger angle $ dhS = DHS $, so that the distance PS is subtended by the same angle at I as is pS at i. The same holds for H and h, respectively.

The total force on p due to this ring is

 * $$ \propto \frac{ih\cdot iq\cdot pq}{pi^3} = \frac{a\cdot df\cdot fS}{if\cdot d^2} $$

Clearly $ fS = FS $, $ if = IF $, and $ eS = ES $.

Newton claims that DF and df can be taken as equal in the limit as the angles DPF and dpf 'vanish together'. Note that angles DPF and dpf are not equal. Although DS and dS become equal in the limit, this does not imply that the ratio of DF to df becomes equal to unity, when DF and df both approach zero. In the finite case DF depends on D, and df on d, so they are not equal.

Since the ratio of DF to df in the limit is crucial, more detailed analysis is required. From the similar right triangles, $ \frac {DF}{PF} = \frac{ED}{ES}$ and $ ED^2 = (DF + FS)^2 - ES^2 $, giving $ \frac {\left(PF^2 - ES^2\right)DF^2}{PF^2} + 2\cdot FS\cdot DF + FS^2 - ES^2 = 0 $. Solving the quadratic for DF, in the limit as ES approaches FS, the smaller root, $ DF = ES - FS $. More simply, as DF approaches zero, in the limit the $$ DF^2 $$ term can be ignored: $$ 2\cdot FS\cdot DF + FS^2 - ES^2 = 0 $$ leading to the same result. Clearly df has the same limit, justifying Newton’s claim.

Comparing the force from the ring HI rotated about PS to the ring hi about pS, the ratio of these 2 forces equals $ \frac{d^2}{D^2} $.

By dividing up the arcs AT and Bt into corresponding infinitesimal rings, it follows that the ratio of the force due to the arc AT rotated about PS to that of Bt rotated about pS is in the same ratio, and similarly, the ratio of the forces due to arc TB to that of tA both rotated are in the same ratio.

Therefore, the force on a particle any distance D from the center of the hollow sphere is inversely proportional to $ D^2 $, which proves the proposition.

Shell theorem in general relativity
An analogue for shell theorem exists in general relativity (GR).

Spherical symmetry implies that the metric has time-independent Schwarzschild geometry, even if a central mass is undergoing gravitational collapse (Misner et al. 1973; see Birkhoff's theorem). The metric thus has form
 * $$ds^2 = - (1-2M/r)\, dt^2 + (1-2M/r)^{-1} \, dr^2 + r^2 \, d\Omega^2$$

(using geometrized units, where $G=c=1$). For $$r>R>0$$ (where $$R$$ is the radius of some mass shell), mass acts as a delta function at the origin. For $r < R$, shells of mass may exist externally, but for the metric to be non-singular at the origin, $$M$$ must be zero in the metric. This reduces the metric to flat Minkowski space; thus external shells have no gravitational effect.

This result illuminates the gravitational collapse leading to a black hole and its effect on the motion of light-rays and particles outside and inside the event horizon (Hartle 2003, chapter 12).

title: Shell theorem


text:
It Did Make a Difference

It Did Make a Difference is an album by one of Sweden's first hardcore punk band, Step Forward. It is the complete discography of the band, released on CD. Being one of the few hardcore punk bands of Sweden back in 1989, their fast and energetic tunes were the starting point of Sweden's hardcore scene. Members of this band went to form bands like Refused and others.

Track listing
Does It Make A Difference Recordings (1990)
 * 1) Away
 * 2) For myself
 * 3) Think ahead
 * 4) Nothing to say
 * 5) My love
 * 6) Deal with it
 * 7) 3 mil till Vännäs
 * 8) Does it make a difference
 * 9) The dream
 * 10) Killing for profit
 * 11) Filler (Minor Threat cover)

I Am Me Recordings (1989)
 * 1) Change today
 * 2) Stop the madness
 * 3) A point of view
 * 4) I am me
 * 5) False people
 * 6) Face the reality
 * 7) Tomorrows world
 * 4 u
 * 1) Steppin stone (The Monkees cover)
 * 2) It isn't funny at all
 * Try
 * 1) I am me
 * 2) The dream
 * 4 u
 * 1) We're gonna fight (7 Seconds cover)

Live Recordings
 * 1) What do you say Moe?
 * 2) A point of view
 * 3) Nothing to say
 * 4) Feeding the fire
 * 5) Hide from truth
 * 6) Does it make a difference?
 * 7) Seeing is believing
 * 8) Racial hatred
 * 9) My love
 * 10) My life
 * 11) Mommy can I go out and kill tonight? (Misfits cover)

Rehearsal Recordings
 * 1) Step forward
 * 2) Something else

Personnel

 * Dennis Lyxzén - lead vocals, layout, production, master
 * Toft Stade - bass, layout, production, master
 * Jens Norden - drums, percussion
 * Henrik Janson - guitar
 * José Saxlund - layout
 * Eskil - production, mastering
 * Jonas Lyxzén - photos

title: It Did Make a Difference


text: Talk:Opsonize

title: Talk:Opsonize


text: Category:Towns in the Scottish Borders

title: Category:Towns in the Scottish Borders


text:
Chandio

The Chandio (چانڊيو) is a Baloch tribe  in the Sindh and Balochistan provinces of Pakistan. The Chandio tribe follows a tribal system with their tribal leader, Nawab Ghaibi Sardar Khan Chandio.

Notable people with this name

 * Jalal Chandio (1944 – 2001), Sindhi music folk singer
 * Maula Bakhsh Chandio, Member, Senate of Pakistan
 * Gulab Chandio - Pakistani television and film actor.

title: Chandio


text:
Talk:Push

"🫸" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=%F0%9F%AB%B8&redirect=no 🫸] has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached. The Banner talk 20:29, 27 July 2023 (UTC)

title: Talk:Push


text:
Talk:Sea lane

Untitled
The claims of the origins in the history section are unsubstantiated, I've added citation tags. These facts need to be supported or they should be removed since I have documented contrary information about the origins of sea lanes, which I will add shortly (with refs).

DCwom (talk) 00:48, 28 August 2010 (UTC)

Decisions
It's still not clear who decided of the sea lanes, neither when nor where.--Laurentleap (talk) 12:21, 6 May 2012 (UTC)

"Sea route" listed at Redirects for discussion
A discussion is taking place to address the redirect Sea route. The discussion will occur at Redirects for discussion/Log/2021 May 26 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. -- Tamzin (she/they, no pref.) | o toki tawa mi. 22:47, 26 May 2021 (UTC)

title: Talk:Sea lane


text:
Passion (Buffy the Vampire Slayer)

"Passion" is the seventeenth episode of the second season of the fantasy-horror television series Buffy the Vampire Slayer (1997-2003). The episode was written by Ty King and directed by Michael Gershman, who served as the show's cinematographer. It originally aired on The WB in the United States on February 24, 1998.

The premise of Buffy the Vampire Slayer is that an adolescent girl, Buffy Summers, is chosen by mystical forces and given superhuman powers to kill vampires, demons, and other evil creatures in the fictional town of Sunnydale. She is supported by a close circle of friends, nicknamed the Scooby Gang. In "Passion", Buffy attempts to protect herself and her close ones from Angelus and his murderous intent as Jenny Calendar continues to search for a spell to restore his soul.

In 2014, British singer Ed Sheeran sampled the episode's background theme "Remembering Jenny" for his song "Afire Love".

Plot
Buffy wakes to find an envelope on her pillow containing a charcoal drawing of herself sleeping. Buffy asks Giles if there is a spell to reverse Angel's invitation into her house.

Buffy explains to her mother that she has been having problems with Angel, whom she describes as an abusive ex-boyfriend. Later that night, Willow discovers that Angelus has been in her room too, leaving behind a sick gift of her dead goldfish hanging from a fishing line. Drusilla has a vision showing someone attempting to break up the newly reunited vampire family. Jenny goes to a Gypsy novelty shop to buy an Orb of Thesulah.

Buffy confronts Jenny and explains that Giles misses her. Giles tells Buffy that he has found a ritual to revoke a vampire's invitation. Joyce finds Angelus waiting for her in the front yard. He starts to follow her into the house, but is unable to cross the threshold. Willow is shown reciting the ritual, and Buffy shuts the door in his face.

When Giles finds Jenny working late at the school, he invites her to call at his house when she has finished. Jenny completes her translation of a ritual's text that, along with the Orb of Thesulah, will restore Angelus' soul. She jumps when she notices Angelus sitting in the dark at the back of the room. He smashes the Orb of Thesulah and snaps Jenny's neck.

Giles returns home to find the place decorated in a romantic setting with candles, wine and rose petals. As Giles follows the trail he finds Jenny's lifeless body. Angelus lurks outside Buffy's house and watches with glee as a devastated Buffy and Willow are informed of Jenny's death over the phone. Giles returns to his apartment to arm for battle.

At the factory, there is an explosive crash as the long dining table erupts in flame. Angelus, Drusilla, and Spike recoil and move to escape. Giles attacks Angelus with a flaming baseball bat. Angelus grabs him by the throat and lifts him clear off the floor as Buffy enters the fray. She breaks Giles free of Angelus' grasp and fights Angelus, but is distracted by the unconscious Giles, now completely surrounded by flames. As Angelus makes his escape, Buffy jumps down and half-carries Giles from the building.

Later that night, Buffy apologizes for not being able to kill Angelus when she had the chance. The next day at the school, as Willow sets her books on the desk, the backup disk containing the translated ritual slides and falls into the narrow space between the desk and a filing cabinet.

Writing
Alyson Hannigan said in an interview that the cast knew Angelus "had to kill somebody we loved - we were all warned about that. Actually, I think it was supposed to be Oz that was killed, then they decided they'd keep Oz around and they killed Ms. Calendar."

Themes
According to Noel Murray from The A.V. Club, a recurring theme in "Passion" is "the common feeling of being left out".

Continuity
The Orb Of Thesulah is the key to translating the Transliteration Annals for the Rituals of the Undead. These texts contain the spell to restore a soul to the undead, but were lost. The owner of the Occult shop tells Jenny that he sold an Orb to someone who was going to use it as a paperweight. In "Becoming Part 1," Giles says to Willow that he has an Orb Of Thesulah, which he uses as a paperweight.

After the lair at the factory burns down, Angelus lives in a mansion on Crawford Street when he returns from Hell in Season 3's "Faith, Hope & Trick," until he moves to L.A. in "Graduation Day (Part 2)."

Reception
Vox ranked it at #12 on their "Every Episode Ranked From Worst to Best" list, calling it "the episode that makes it clear the transformation that occurred in "Innocence" is permanent: Angel really did go evil, and bad things really are going to happen on this show, and they won’t always be reversible. But they will lead to beautiful, heartbreaking moments of catharsis, like Buffy and Giles breaking down together in front of the burned-out factory while Buffy sobs, 'I can't do this without you.'"

Myles McNutt writes, "The episode is interested in what is to this point the most substantial death in the series, certainly, but it’s also interested in explaining how it is that Angel perceives this death, and how he sadistically uses it just to torment Buffy and to cause suffering. It’s a unique structure that make the episode something more than just another stop on the season’s arc, and really encapsulates how the demonic is colliding with humanity in a more substantial fashion at this stage in the season."

title: Passion (Buffy the Vampire Slayer)


text:
Huntsville Botanical Garden

The Huntsville Botanical Garden is a 118 acres botanical garden located at 4747 Bob Wallace Avenue, Huntsville, Alabama, near the U.S. Space & Rocket Center. It is open year-round for a fee. The garden is ranked third on the list of Alabama's top paid tourist attractions, receiving 353,841 visitors in 2018.

Gardens
The gardens include a seasonal butterfly house, and aquatic, annual, daylily, fern, herb, perennial, rose, and wildflower gardens, as well as a nature path and collection of Flowering Dogwood trees. Specific sections of the garden are as follows:

 * Nature center - overlooks Little Smith Lake, houses the open-aired butterfly house, open May through September
 * Biblical garden, featuring plants mentioned in the Bible
 * Central Corridor - with perennial garden, aquatic garden, and bulb and annual garden.
 * Daylily Garden - over 675 cultivars of daylilies.
 * Dogwood Trail - numerous Flowering Dogwood (Cornus florida) trees, including a hundred-year-old dogwood transplanted to the site, along a forest path.
 * Fern Glade - almost 150 species of ferns, including Christmas Fern (Polystichum acrostichoides), Northern Maidenhair Fern (Adiantum pedatum), Southern Maidenhair Fern (Adiantum capillus-veneris), Sensitive Fern (Onoclea sensibilis), Royal Fern (Osmunda spectabilis), and Cinnamon Fern (Osmundastrum cinnamomeum).
 * Herb Garden - 14 theme gardens and a cottage.
 * Nature Trail - paths through an indigenous southeastern lowland forest, with Black Tupelo (Nyssa sylvatica), Red Maple (Acer rubrum), Sycamore (Platanus occidentalis), and Sweetgum (Liquidambar styraciflua) trees, and undergrowth including Sweet William (Phlox divaricata), Wild Columbine (Aquilegia canadensis), Foamflower (Tiarella cordifolia), Scarlet Sage (Salvia coccinea), Bellflower (Campanula americana), and Black-eyed Susan (Rudbeckia hirta).
 * Azalea Trail - over 3000 azaleas native to the southeast U.S., and some native to Asia.
 * Vegetable Garden - four model gardens for the home gardener.

History
The idea for the creation of a botanical garden in Huntsville was first proposed by fourteen people in December 1979. In January 1980, the Huntsville-Madison County Botanical Garden Society was founded and held its first official meeting. The members of the new society persistently attended City Council meetings and politely asked for funding until they were offered 35 acres and three years to raise $200,000, which the city said that it would match. The funding goal was met in just six months.

In January 1983, it was decided that the gardens would be built on property leased to the city from the Alabama Space Science Commission. In late 1984, a volunteer crew began to clear the land. In October 1985, a Southern Magnolia was planted to dedicate the new botanical garden. The Huntsville Botanical Garden officially opened in 1988.

When the Huntsville Botanical Garden first opened, there were no buildings or restrooms; visitors only drove through. The first master plan for the garden was adopted in 1991. The children's garden and butterfly center opened in 2006. In 2017, the Huntsville Botanical Garden formally unveiled its new $16 million, 30,000 square-foot guest center.

The Huntsville Botanical Garden has twenty Classical Doric columns from the 1914 Madison County Courthouse that was demolished in 1964. Five of these limestone columns are arranged in a circle at the entrance to the garden, and four more were used as part of the entrance gate.

title: Huntsville Botanical Garden


text:
Z-matrix

Z-matrix may mean: It may also refer to:
 * Z-matrix (chemistry), a table of the locations of atoms comprising a molecule
 * Z-matrix (mathematics), a matrix whose off-diagonal entries are less than or equal to zero
 * The matrix of Z-parameters, a matrix characterizing an electrical network

title: Z-matrix


text:
File:Jacksons-destiny.jpg

Summary
Destiny by The Jacksons.

title: File:Jacksons-destiny.jpg


text:
Talk:Hao Wang (academic)

Academic Geneologies
This appears to be an academic geneology rather than a profile of a notable mathematician. Is this truly encyclopedic? Tobycat 18:23, 11 Jun 2005 (UTC)
 * It has probably been added to since then, but your view may also have been distorted by many appropriate links not showing up in What links here because they went to disambiguation page (haen't checked to see if this involved cut and paste move). Gene Nygaard (talk) 18:51, 16 January 2008 (UTC)

Not An Wang
He is differend person than An Wang, the guy behing Wang VS minicomputers. —Preceding unsigned comment added by 193.184.83.234 (talk) 11:33, 8 November 2010 (UTC)

AEA case
Should be some discussion of David Hilbert's Entscheidungsproblem, and in particular the AEA case that Kahr Moore and Wang settled; this was the reason Wang invented his celebrated tiles in the first place. I do not know enough about this to write it myself at this time--C Goodman-Strauss 23:39, 7 October 2007 (UTC)

Link to IBM web shop
The alleged PDF link is in fact a link to an IBM web shop. This is against Wikipedia policy.--217.232.236.86 (talk) 16:11, 4 September 2009 (UTC)

title: Talk:Hao Wang (academic)


text:
Talk:Electric displacement field

No article is complete without history
The history of the Electric Displacement Field must be available, including the date it was first used, and for what purpose. I find that Gauss's law was formulated in 1835, but not published until 1867. Hence, Gauss's law, which can be written using both Electric Intensity E and Electric Displacement Field D, must have been written not prior to the year. But exact period and purpose of its introduction must be established. Bkpsusmitaa (talk) 14:44, 25 May 2014 (UTC)

Dimension of the quantity
What is the dimension of electric displacement.Is it Similar to the displacement of electric dipole moment? Sea Of Enlightenment (talk) 23:35, 16 September 2018 (UTC)

Delete, and change to a redirect
There already exists a good page Displacement current which contains a good description of D that is consistent with standard texts such as Ashcroft and Mermin, Griffiths and others. Currently this page contains a lot of errors; for instance it omits to include and define polarization. Rather than attempting to repair this I think it should simply be deleted, and a minor sentence or so added to the Displacement current page to consider that is also includes D. Ldm1954 (talk) 19:22, 2 July 2023 (UTC)

 * I'm always happy to discuss changes. I agree, there are a lot of errors.  What is it that you want to delete? Constant314 (talk) 21:35, 2 July 2023 (UTC)
 * This page contains material that is already in displacement current, which is both much better and more rigorous. Therefore the whole page (Electrical displacement) should be deleted and replaced by a redirect to displacement current. Ldm1954 (talk) 21:43, 2 July 2023 (UTC)
 * I disagree with that entirely. Wikipedia does have a lot of duplication.  It can be frustrating when the duplications use different symbols and when they even contradict each other.  Still, people will ask, "what is the D field?" and it is more than just the progenitor of displacement current. I am in favor of fixing whatever is wrong here.  There are only a few sentences about displacement current.  I think it is necessary to tie the D field to displacement current, but yes, let the displacement current article do the heavy lifting.  I don't follow your point about polarization; polarization definitely appears in this article. Constant314 (talk) 22:04, 2 July 2023 (UTC)
 * If you can revise this page so it is textbook physics, then I will consider retracting the deletion. However, currently it is not. Some specifics:
 * The comment about the aether have nothing to do with Maxwells equation, they are a digression. It is also wrong to connect this as "this displacement appears as the term \epsE "
 * You have incorrectly stated the charge equivalence of polarization. You have both bound charge and the dot product of the surface normal and polarization vector.
 * The third paragraph is completely wrong. The polarization has to be included.
 * The Definition section is OK, although the polarization part is not well spelt out. Polarization is not easy.
 * The proof is messy. The standard textbook form is needed, with the conventional definitions.
 * The statement with Lorentz force is wrong, that is for moving charge.
 * The Definition section has zero sources, which is unacceptable
 * Please check better history sources. It is generally accepted that D comes from Maxwell, not Gauss (although his original equations needed to be simplified).
 * The Example using a capacitor needs to include the Polarization to be consistent with standard Physics undergrad texts.
 * For such a vital article this level of error and lack of sources is not appropriate. Ldm1954 (talk)
 * Let's take your points one at a time. First, regarding the proof: lets delete it.  Also, please sign your comments. Constant314 (talk) 23:19, 2 July 2023 (UTC)
 * The non signature was a WP editor glitch. I am OK to remove the Proof, but that is only a start. Ldm1954 (talk) 01:56, 3 July 2023 (UTC)
 * The statement about the Lorentz force doesn't seem to add anything. I am good with deleting that. Constant314 (talk) 03:54, 3 July 2023 (UTC)
 * Delete Ldm1954 (talk) 09:14, 3 July 2023 (UTC)
 * With regard to the history section, I have no sources and no opinion. Feel free to do anything you want with that.  As to not having enough sources in the definition and overall, feel free to tag the sections and the article or to add sources.
 * I think next, we should focus on the meaning of polarization and how you think what I said was wrong or incomplete. I have access to Griffiths, Jackson, and the Feynman Lectures, should you want to refer to those.  It is a busy day for me, so my responses may be slow in coming. Constant314 (talk) 13:14, 3 July 2023 (UTC)

title: Talk:Electric displacement field


text:
Hickory, Kentucky

Hickory (also, Hickory Grove) is a census-designated place in Graves County, Kentucky, United States., which is located north of Mayfield and 18 mi south of Paducah in far western Kentucky.

Hickory was laid out in 1856 along the tracks of Illinois Central Gulf railroad, and named for the large hickory trees dotting the landscape. A post office called Hickory Grove was established in 1858, and the name of the post office was designated Hickory in 1914.

Demographics
A total of 256 people lived in Hickory, Kentucky in 2020, with a median age of 28.3 and a typical household income of $18,600. Hickory, Kentucky's population decreased from 277 to 256 between 2019 and 2020, a loss of 7.58%, while its median household income increased from N/A to $18,600, a N/A% N/A.

White (non-Hispanic) (78.9%), Black or African American (non-Hispanic) (9.77%), Asian (non-Hispanic) (7.03%), Other (Hispanic) (2.34%), and Two+ (Hispanic) (1.95%) are the 5 major ethnic groups in Hickory, Kentucky.

title: Hickory, Kentucky


text:
Boom Boom Satellites

Boom Boom Satellites (ブンブンサテライツ) were a Japanese electronic music duo consisting of guitarist and vocalist Michiyuki Kawashima and bassist and programmer Masayuki Nakano. They were signed to Sony Music Entertainment Japan, with whom they had released all of their albums in Japan.

History
Kawashima and Nakano formed the band in 1990, having met at university and debuted in Europe as a rock unit in 1997. According to an interview, the name originated from a song by Sigue Sigue Sputnik.

In 1995, the group's music debuted in Japan on a compilation album released by Torema Records, also affiliated with Untitled Records. Belgian record company R&S Records released their first single in Europe later that year. Kawashima and Nakano also appeared in the European magazine Melody Maker, where they were lauded as the combination of The Chemical Brothers and The Prodigy. R&S Records released their first album, 7 Ignitions/Auto Re-Birth, on April 1, 1998, and the group performed at a large music festival the following June. The group then returned to Japan. Boom Boom Satellites toured with Moby for three months in the United States some time afterward, and artists such as Garbage also requested remixes from the group.

The group has contributed numerous songs to various films, commercials, and television programs: In 2004, a number of tracks from the group's album, Full of Elevating Pleasures, contributed to the soundtrack of the CGI anime film Appleseed. In 2005, the song "What Goes Around Comes Around" from the album Exposed, was featured in a commercial for Dodge, and "Easy Action" was included on the soundtrack of the 2007 anime film Vexille. The same year, they played in the UK at the prestigious In The City music industry showcase festival. In 2008, the track "Scatterin' Monkey" from their 1998 album Out Loud, was featured in the film The Dark Knight and "Shut Up and Explode" became the opening theme song for the PlayStation Store exclusive and later anime television series Xam'd: Lost Memories (亡念のザムド). In 2009, the single "Back on My Feet" is an additional opening theme song for the television broadcast of the series (the TV broadcast switches between "Shut Up and Explode" and "Back on My Feet").

In 2009, the band collaborated with Tahj Mowry and Flo Rida on a new envisioning of their track "Kick It Out". The track predominantly featured the lyrics of Tahj Mowry and Flo Rida in the verses, while the chorus remained the same as in the original release. Boom Boom Satellites added a new verse of their own not present on the original release. A music video was created for the song's release. That same year, Boom Boom Satellites released a remix for Fact's song "A Fact of Life" on the eponymous album.

In January 2010, Boom Boom Satellites released their first compilation album 19972007. The band released a new studio album in Japan, To the Loveless, on May 26, 2010, which featured many tracks from the Back on My Feet EP. A limited-edition version with a bonus DVD was also released. In late 2010, the Boom Boom Satellites kicked off a North American tour, beginning with a performance at New York Comic Con. They also released Over and Over (an abbreviated version of 19972007) in the United States to coincide with the tour.

In 2012, Boom Boom Satellites announced that they would be performing the theme song for the fifth episode of Mobile Suit Gundam Unicorn, titled "Broken Mirror", to begin the commemoration of their 15th anniversary since their debut. They also began a remix contest hosted by Nico Nico Douga, with the grand prize winner's remix of "Broken Mirror" included on their first remix album Remixed. This followed by the release of the song "Another Perfect Day" was used as the theme song of the Starship Troopers: Invasion animated movie. With the delay of the release of Remixed, the Boom Boom Satellites revealed that they were releasing their recent Japan-only singles internationally. Preceding the release of Remixed, Boom Boom Satellites announced that their entire back catalog had been added to the Japan iTunes Store.

To celebrate their 15th anniversary together, Boom Boom Satellites released their eighth studio album Embrace on January 9, 2013. For their first promotional single for the album, the duo recorded a cover of the Beatles' "Helter Skelter" as their first ever cover of any other artist. The Embrace 2013 tour had been planned to support the album as well as the group's 15th anniversary. However, in late December 2012 Kawashima was discovered to have symptoms of the early stages of a brain tumor, and the band cancelled all 23 shows scheduled from January to March 2013 to set aside for treatment and surgery; Nakano later revealed that Kawashima had a history of brain tumor issues, but this was the first time that they have had to cancel shows. The band decided that they would perform last few shows of December 2012, but had no plans to cancel the shows set for April and May 2013; the show in May was planned to be the band's first one-man live at the Nippon Budokan. On February 11, 2013, Nakano posted an update to the band's Facebook revealing that Kawashima had been discharged from the hospital and the two were writing and recording new songs. Following his recovery, the band announced that they were cancelling all but their Nippon Budokan show. This concert was later streamed live with 360 degree views on YouTube as part of YouTube Japan's Music Week as well as on Nico Nico Douga's live feature. In August 2013, they announced the concert would be released on an album due in November of that year, while also revealing that they were releasing Embrace internationally in September.

In 2014, Boom Boom Satellites created a new song, "Only Blood", for a special trailer for the film Monsterz. Boom Boom Satellites performed at the Ex Theater Roppongi with Acidman on July 2, 2014. On July 4, 2014, the band announced that they would be composing the main theme, "Back In Black", for the anime adaptation of Ninja Slayer. In late November 2014, the band announced that they would be releasing their new album Shine Like a Billion Suns in February 2015, supporting the album with a concert at the Tokyo EX Theater Roppongi in March 2015. On December 31, 2014, Nakano revealed in a blog post on their official website that Kawashima's brain tumor issue had once again relapsed at the conclusion of their March 2014 tour, making it the fourth time he had suffered a relapse, and after diagnosis had only been given two more years to live. However, after they had read about boron neutron capture therapy, Kawashima underwent the procedure, all the while writing the new album. Kawashima was informed that the spread of the tumors had been successfully stopped, and the band decided to share the information with their fans. Nakano mentioned how proud he was for Kawashima to be able to go through the procedures, continue to tour, and write the album.

In 2016, Boom Boom Satellites were announced to be performing the theme song for Kiznaiver titled "Lay Your Hands on Me". The version used for the anime was released as a single on April 17. A short music video was released on May 23, and it was announced that the full-size version of the song would be released digitally on June 1, followed by a physical/digital EP on June 22 featuring 3 other tracks. On the day of the release, Nakano posted on the official website and social media that the EP for "Lay Your Hands on Me" would be Boom Boom Satellites' final release, as Kawashima's tumors had relapsed for the fourth time and Kawashima was partially paralyzed. Nakano said that the "Lay Your Hands on Me" EP should be a suitable end to their career. On October 9, 2016, four months after the group stopped its activities, Kawashima died of his illness.

The next year, Nakano started to work with singer Toru Kitajima on intermittent songs in a project called Pandas, along with a remake of a theme song for Psycho-Pass: Sinners of the System. He ultimately ended up forming a new band in 2021 called The Spellbound with The Novembers frontman Yusuke Kobayashi, releasing five singles from January to May at the same year and releasing their debut album in 2022. In October 2022, The Spellbound released "Subete ga Soko ni Arimasu you ni.", the ending theme for season four of the TV anime Golden Kamuy.

Members

 * Michiyuki Kawashima (川島 道行) - guitar, vocals
 * Born August 24, 1969, Iwate Prefecture ( died October 9, 2016, aged 47 )
 * Kawashima was married to actress Risa Sudou; they have two daughters.
 * Masayuki Nakano (中野 雅之) - bass, programming
 * Born December 27, 1971, Kanagawa Prefecture

Touring members

 * Yoko Fukuda (福田 洋子) - drums (2009–2016)
 * Born July 29, 1977, Kanagawa Prefecture
 * Naoki Hirai (平井 直樹) - drums (1995–2009)

Discography

 * Studio albums
 * Out Loud (1998)
 * Umbra (2001)
 * Photon (2002)
 * Full of Elevating Pleasures (2005)
 * On (2006)
 * Exposed (2007)
 * To the Loveless (2010)
 * Embrace (2013)
 * Shine Like a Billion Suns (2015)

 * EP's
 * Boom Boom Satellites (1997) (Demo album)
 * Joyride (1997)
 * 7 Ignitions/Auto Re-Birth (1998)
 * Lay Your Hands on Me (2016)

 * Live albums
 * Experienced (2011)
 * Experienced II: Embrace Tour 2013 Budokan (2013)

 * Compilation albums
 * 19972007 (2010)
 * Over and Over (2010)
 * Remixed (2012)
 * Remix Festival 2013 - Winners - (2013)

 * Singles
 * "4 A Moment of Silence" (1997)
 * "Dub Me Crazy (Ver. 02)" (1997)
 * "Push Eject" (1998)
 * "On The Painted Desert - Rampant Colors" (1999)
 * "Fogbound" (2000)
 * "Sloughin' Blue" (2001)
 * "Soliloquy" (2001)
 * "Blink" (2002)
 * "Light My Fire" (2003)
 * "Spine/Dive for You" (2004)
 * "Easy Action" (2005)
 * "Back on My Feet" (2009)
 * "Kick It Out (feat. Tahj Mowry and Flo Rida)" (2009)
 * "Broken Mirror" (2012)
 * "Another Perfect Day" (2012)
 * "Drifter" (2013)
 * "Nine" (2013)
 * "Only Blood" (2014)
 * "A Hundred Suns" (2015)
 * "Lay Your Hands on Me" (2016)

 * DVDs
 * Epk (Promo) (2005)
 * Fuji Rock Festival '05 Live Cuts (2006)
 * Boom Boom Satellites Japan Tour '06 at Studio Coast (2007)
 * Boom Boom Satellites Japan Tour 2008 (2009)
 * Metamorphose 08 Live Cuts (2009)
 * Front Chapter - The Final Session - Lay Your Hands On Me Special Live (2018)

title: Boom Boom Satellites


text:
Prairie dress

A prairie dress or prairie skirt is a modest American style of skirt, an article of women's and girls' clothing.

Prairie dresses may be straight to slightly flared to very full, and may have one or more flounces (deep ruffles) or tiers; prairie dresses may be worn over a ruffled eyelet or lace-trimmed petticoat. Traditionally, prairie dresses have long sleeves. In keeping with their design inspiration, traditional prairie skirts are usually made of "country" fabrics such as denim and flowered calico, though they can be of a solid colour too. Prairie skirts are a staple of women's western wear, and very full prairie skirts are worn for square dancing. Prairie dresses are often worn by women who attend Christian churches that emphasize the practice of plain dress (as with the Bruderhof Communities) or the doctrine of outward holiness (as with the Allegheny Wesleyan Methodist Connection). They are seen as fashionable, especially in cold weather.

Prairie dresses earned their name for people travelling to the Western parts of the United States, though they were once "worn by women of all classes all over the country."

Origins in the 19th century
Prairie skirts are so-called after their resemblance to the home-sewn skirts worn by pioneer women in the mid-19th century, which in turn are a simplified version of the flared, ruffled skirts characteristic of high-fashion dresses of the 1820s. The style originated as an adaptation of high fashion to the practicalities of rural life in the Western United States. Deep colors and prints were used as they did not show dirt, while decorations were used to update clothing to changing fashions.

Revival in the 1960s and 1970s
Counterculture Hippies rejecting mainstream fashion looking instead to historical and non-Western styles. While 19th century prairie clothing was usually homemade, new companies such as Gunne Sax in San Francisco began manufacturing ready to wear prairie clothing. The style grew in popularity in the 1970s with the approach of the United States Bicentennial and was introduced to high fashion by Ralph Lauren in his fall 1978 Western-themed collection.

Mid-calf length, button-front denim prairie skirts with a single flounce, worn with a 1950s-style petticoat that was slightly longer than the skirt, became a mainstream fashion in the 1970s and early 1980s following Lauren's introduction.

21st century
Short, many-tiered prairie skirts of voile, chiffon or other lightweight fabrics were a fashion trend in 2005. Some wear longer-length prairie skirts with a slip or underskirt to preserve their modesty. Prairie dresses were again a fashion trend in the late 2010s, and were part of the cottagecore trend in 2020.

Prairie dresses are often worn by women who attend Christian churches that emphasize the practice of plain dress (as with the Bruderhof Communities, an Anabaptist denomination) or the doctrine of outward holiness (as with the Evangelical Wesleyan Church, a Methodist connexion in the holiness movement).

title: Prairie dress


text:
Hyperbolic secant distribution

In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function. The hyperbolic secant function is equivalent to the reciprocal hyperbolic cosine, and thus this distribution is also called the inverse-cosh distribution.

Generalisation of the distribution gives rise to the Meixner distribution, also known as the Natural Exponential Family - Generalised Hyperbolic Secant or NEF-GHS distribution.

Probability density function
A random variable follows a hyperbolic secant distribution if its probability density function can be related to the following standard form of density function by a location and shift transformation:

 * $$f(x) = \frac12 \operatorname{sech}\frac{\pi x}{2},$$

where "sech" denotes the hyperbolic secant function.

Cumulative distribution function
The cumulative distribution function (cdf) of the standard distribution is a scaled and shifted version of the Gudermannian function,

 * $$\begin{align}

F(x) &= \frac12 + {\frac{1}{\pi} \arctan} \Bigl({\operatorname{sinh}\frac{\pi x}2}\Bigr) \\[8mu] &= {\frac{2}{\pi} \arctan}\Bigl({\exp\frac{\pi x}2} \Bigr). \end{align}$$

where "arctan" is the inverse (circular) tangent function.

Johnson et al. (1995) places this distribution in the context of a class of generalized forms of the logistic distribution, but use a different parameterisation of the standard distribution compared to that here. Ding (2014) shows three occurrences of the Hyperbolic secant distribution in statistical modeling and inference.

Properties
The hyperbolic secant distribution shares many properties with the standard normal distribution: it is symmetric with unit variance and zero mean, median and mode, and its probability density function is proportional to its characteristic function. However, the hyperbolic secant distribution is leptokurtic; that is, it has a more acute peak near its mean, and heavier tails, compared with the standard normal distribution. Both the hyperbolic secant distribution and the logistic distribution are special cases of the Champernowne distribution, which has exponential tails.

The inverse cdf (or quantile function) for a uniform variate 0 ≤ p < 1 is

 * $$F^{-1}(p) = -\frac{2}{\pi}\, \operatorname{arsinh}\!\left[\cot(\pi\,p)\right] \! ,$$
 * $$ = \frac{2}{\pi}\, \ln\!\left[\tan\left(\frac{\pi}{2}\,p\right)\right] \! .$$

where "arsinh" is the inverse hyperbolic sine function and "cot" is the (circular) cotangent function.

Convolution
Considering the (scaled) sum of $$r$$ independent and identically distributed hyperbolic secant random variables:
 * $$X = \frac{1}{\sqrt{r}}\; (X_1 + X_2 + \;...\; + X_r)$$

then in the limit $$r\to\infty$$ the distribution of $$X$$ will tend to the normal distribution $$N(0,1)$$, in accordance with the central limit theorem.

This allows a convenient family of distributions to be defined with properties intermediate between the hyperbolic secant and the normal distribution, controlled by the shape parameter $$r$$, which can be extended to non-integer values via the characteristic function
 * $$\varphi(t) = \big(\operatorname{sech}(t /\sqrt{r})\big)^r$$

Moments can be readily calculated from the characteristic function. The excess kurtosis is found to be $$2/r$$.

Location and scale
The distribution (and its generalisations) can also trivially be shifted and scaled in the usual way to give a corresponding location-scale family:

 * $$f(x) = \frac{1}{2 \sigma} \operatorname{sech} \left(\frac{\pi}{2}\frac{x-\mu}{\sigma}\right)$$

Skew
A skewed form of the distribution can be obtained by multiplying by the exponential $$e^{\theta x}, |{\theta}|<{\pi}/2 $$ and normalising, to give the distribution
 * $$f(x) = \cos \theta \; \frac{e^{\theta x}}{2 \operatorname{cosh}(\frac{\pi x}{2})} $$

where the parameter value $$\theta = 0$$ corresponds to the original distribution.

Kurtosis
The Champernowne distribution has an additional parameter to shape the core or wings.

Meixner distribution
Allowing all four of the adjustments above gives distribution with four parameters, controlling shape, skew, location, and scale respectively, called either the Meixner distribution after Josef Meixner who first investigated the family, or the NEF-GHS distribution (Natural exponential family - Generalised Hyperbolic Secant distribution).

In financial mathematics the Meixner distribution has been used to model non-Gaussian movement of stock-prices, with applications including the pricing of options.

Related distribution
Losev (1989) has studied independently the asymmetric (skewed) curve $h(x)=\frac{1}{\exp(-a x) + \exp(b x)}$, which uses just two parameters $$a, b$$. In it, $$a$$ is a measure of left skew and $$b$$ a measure of right skew, in case the parameters are both positive. They have to be both positive or negative, with $$a = b$$ being the hyperbolic secant - and therefore symmetric - and $$h(x)^r$$ being its further reshaped form.

The normalising constant is as follows:
 * $$\frac{a+b}{\pi}\sin\left(\frac{b \pi}{a+b}\right)$$

which reduces to $$\frac{2a}{\pi}$$ for the symmetric version.

Furthermore, for the symmetric version, $$a$$ can be estimated as $$a=\frac{\pi}{2\sigma}$$.

title: Hyperbolic secant distribution


text:
Dean Friedman

Dean Friedman (born May 23, 1955) is an American singer-songwriter who plays piano, keyboard, guitar, and harmonica.

Although considered a one-hit wonder in the US, he has had multiple singles chart in other territories and continues to write, record, and tour.

Music
Born and raised in Paramus, New Jersey, United States, Friedman purchased his first guitar from Manny's Music with a bag of quarters he had saved, at age nine in 1964, and started writing songs. When he was a teenager, he played weddings and bar mitzvahs as part of Marsha and the Self-Portraits, sent out demos and majored in music at City College of New York where one of his teachers was guitarist David Bromberg. By the time he was 20, in 1975, he had a manager and a recording contract with Cashman and West's Lifesong label.

In the United States he is described as a one-hit wonder, following his 1977 hit song "Ariel", which reached number 26 on the Billboard Hot 100 chart and stayed in the chart for five months. American Top 40 ranked it as the 87th biggest hit of 1977. On the Cash Box Top 100, it reached number 17. In Canada, the song reached number 19.

"Ariel" has been described as a "quirkily irresistible and uncategorizable pop song about a free spirited, music loving, vegetarian Jewish girl," from Paramus, New Jersey, where he grew up. It is the only Billboard Top 40 song to contain the word Paramus. It describes the girl Ariel, "standing by the [since dismantled] waterfall at Paramus Park," one of the many shopping malls in Paramus. The quarters she was collecting for "friends of BAI" refers to the New York radio station WBAI, and their listener association; the song also makes reference to "channel 2", the local CBS flagship station WCBS-TV.

Although "Ariel" did not make the UK Singles Chart, "Lucky Stars", a duet with Denise Marsa taken from his second album Well Well Said the Rocking Chair, made No. 3 in the UK in late 1978, and both "Woman of Mine" and "Lydia" were lesser chart hits there.

Friedman also provided vocals for a series of television commercials in the 1970s in the New York City metro area. However, while he did re-record and perform one version for an employee event, Friedman is falsely credited with creating and singing on the jingle for electronics chain Crazy Eddie's "When you think you're ready, come down to Crazy Eddie", which was actually created, performed, produced and recorded in its various versions (doo-wop, disco and other versions) by Larry Weiss (Crazy Eddie's VP Advertising) along with Jeff Gottschalk and John Russo.

Friedman's single "McDonald's Girl" was officially banned by the BBC because the chorus mentioned the name of the fast food restaurant. In 2011, thirty years after the song was banned by the BBC, the McDonald's Corporation licensed "McDonald's Girl" for a national TV/Radio campaign, which aired in the US, featuring a vocal performance of the song by The Blenders.

During 2005, as part of a tie-in to one of his tour sponsors, Friedman's tour of the United Kingdom was almost canceled after it was revealed he intended to distribute cannabis seeds to purchasers of his new album. Although it is not illegal to own or distribute cannabis seeds in this manner "unless they get wet", the suggestion caused friction with a number of venues on the tour, so the intended distribution was not carried out.

Influence
The songs of Dean Friedman have been covered by several contemporary bands, including The Barenaked Ladies, Ben Folds Five, Ariel Pink, The Tone Rangers, and The Blenders. The lead singer of Barenaked Ladies, Steve Page, sang background vocals on Friedman's album Songs For Grownups (1998).

TV and films
Friedman has written, performed, and produced the theme music to several TV series including Boon (for which he did all of the music apart from the theme song which was performed by Jim Diamond), starring Michael Elphick. Other TV credits include Nick Arcade (Nickelodeon) and Eerie, Indiana (NBC). He also composed, performed, and produced the soundtrack to the 1990 cult horror film, I Bought a Vampire Motorcycle, in which he performs the track "She Runs on Blood, Not Gasoline".

Other (non-musical) work
In 1985, Friedman produced a seminal work on the newly emerging synthesizer industry called Complete Guide to Synthesizers, Sequencers, and Drum Machines. Whilst dated, this tome published by New York Amsco is still of use in evaluating devices that crop up on the second-hand market. Friedman also set up the New York School of Synthesis and provided a series of videos entitled Intro to Synthesis. Friedman presents the rudiments of this topic in an audio-visual format, whilst incorporating a unique sense of humor.

In 1986, Friedman saw a demo of a powerful virtual reality program that put the user right inside a video game using a video camera (similar to the technology used by the EyeToy). Friedman was impressed by the technology and wrote an article for Electronic Musician magazine. In 1989, he designed a game called Eat-A-Bug which was licensed to Nickelodeon, used on the series Total Panic and served as a prototype for the series Nick Arcade, for which Friedman produced a dozen games. He is now the President and Creative Director of InVideo games.

Revival
Friedman's 2002 album The Treehouse Journals was financed entirely by his fans via his website. Friedman invited people to finance the cost of the as-yet unrecorded album by making an advance purchase and by making limited edition signed copies available. This tactic has been adopted by other bands, including Marillion. He continued to tour, playing small venues.

He copied this tactic again in 2005 with the album Squirrels in the Attic and once more, in 2017, with 12 Songs.

Family
His sister, Racelle Rosett Schaefer, is a noted television writer who was executive producer of the show Blossom, starring Mayim Bialik.

He has lived in New York since 2007 with his wife, Alison, and two children: Hannah Friedman (born 1986), and Sam Friedman (born 1990), both of whom have appeared as a backing singer or musician on his later works.

Dean Friedman and Half Man Half Biscuit
The British band Half Man Half Biscuit recorded (in 1987, on the album Back Again in the DHSS) a song entitled "The Bastard Son of Dean Friedman", a claim Friedman considered improbable, as he was only seven years old when lyricist Nigel Blackwell was conceived. At the Edinburgh Festival in 2003, The Scotsman newspaper arranged a get together between Friedman and the band, in which he acknowledged that Blackwell had at least surmised right the underlying story in the song "Lucky Stars": "That guy Nigel was hip to the fact [song character] Lisa and I didn't just do lunch. You can't interpret a song that way unless you understand what it's about." It also transpired that Blackwell had a copy of a rare vinyl version of Well Well Said the Rocking Chair.

In 2009, Friedman wrote a "reply" called "A Baker's Tale", in which he firmly placed Blackwell's parentage as being that of the local baker, posting it on Half Man Half Biscuit's MySpace site. The band mentioned it on their own website as "Dean Friedman's Revenge/Dean Friedman strikes back". On September 15, 2010, Dean Friedman appeared at a Half Man Half Biscuit gig at the Robin 2 venue in Bilston, West Midlands (UK) and performed "A Baker's Tale". Half Man Half Biscuit's riposte was "The Bastard Son of Dean Friedman". Friedman's song is included on his 2010 album Submarine Races.

Albums

 * Deano's Demos Vol. 1 (1976)
 * Dean Friedman (1977)
 * "Well, Well" Said the Rocking Chair (1978) – UK #21, AUS #70
 * Rumpled Romeo (1981)
 * Live! At The Duke of York (1985)
 * Music From "Boon" (TV soundtrack) (1986)
 * I Bought a Vampire Motorcycle (Movie soundtrack) (1990)
 * The Very Best of Dean Friedman (1991)
 * Bloomsbury Live! (1995)
 * Dean Friedman in Concert – Shepherds Bush Empire (1998)
 * Songs for Grownups (1998)
 * The Treehouse Journals (2002)
 * A Million Matzoh Balls (2003)
 * Squirrels in the Attic (2005)
 * Dean's "Kids Songs" (2007)
 * Submarine Races (2010)
 * Words & Music (2014)
 * 12 Songs (2017)
 * American Lullaby (2021)

DVDs

 * Dean Friedman Live on the Isle of Wight (2009)

title: Dean Friedman


text:
Cedar, Michigan

Cedar is an unincorporated community and census-designated place in Leelanau County in the U.S. State of Michigan. The CDP had a population of 102 at the 2020 census. Cedar is located within Solon Township, and lies about 10 mi northwest of Traverse City. The town is known for its Polish heritage, and is home to an annual polka festival.

As an unincorporated community, Cedar has no legal autonomy of its own. However, it does have its own post office with the 49621 ZIP Code.

Geography
According to the U.S. Census Bureau, the CDP has a total area of 0.18 sqmi, all land. The village of Cedar is intersected by Victoria Creek, which passes under Kasson Street, through the Leelanau Conservancy's Cedar River Preserve, and into South Lake Leelanau.

Demographics
With 95 residents and a typical age of 27.1 in 2020, Cedar, Michigan had a median family income of $43,750. The population of Cedar, Michigan decreased from 106 to 95 between 2019 and 2020, a 10.4% decrease, and its median household income increased from $43,750 to $57,500, a 31.4% increase between 2020 and 2021.

White (Non-Hispanic) (87.4%), White (Hispanic) (12.6%), Black or African American (Non-Hispanic) (0%), Black or African American (Hispanic) (0%), and American Indian & Alaska Native (Non-Hispanic) (0%) make up Cedar, Michigan's top 5 ethnic groupings.

Economy
The village of Cedar sports a small number of brick and mortar stores. Notable among these is Bunting's Cedar Market, which is the sole general food-goods store within the community, and has been operating since the mid-1990s. Additional staples within the community include the Cedar Tavern, the Cedar Hardware Store, the Blue Moon Ice Cream Shop, and the Polish Art Center. Beyond the village but within the same zip code, industry is largely agricultural, ranging from cattle-rearing to fruit growing.

Controversies
In 2022, conflict arose as the proprietors (Northgate Resorts) of the Leelanau Pines Campground intended to double the campground's size, construct additional facilities, and increase access and use of Lake Leelanau. Many residents of Cedar and surrounding communities expressed their concerns that these developments will attract more individuals and traffic to the area than is desired, and in turn impede the rural character of the community. This controversy culminated with over 200 people filling the township hall to voice their concerns regarding the development. The planning commission unanimously voted to deny the expansion, but Northgate Resorts responded with a lawsuit towards the township. A settlement was reached which included moderate cutbacks in the development plans for the Leelanau Pines Campground. Concern still exists surrounding Northgate Resorts' intentions regarding increasing lake access through the issuance of more boat slips, but the matter must first be handled by the Michigan Department of Environment, Great Lakes, and Energy (EGLE) before the township can address the question. The issue is ongoing as of January 2024.

History
Cedar was founded in approximately 1885 by lumberman Benjamin Boughey. He named it Cedar City due to its location in a cedar forest. The depot on the Manistee and North-Eastern Railroad continued to be known as Cedar City, long after the post office named simply Cedar was established on August 15, 1893.

title: Cedar, Michigan


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Bighorn Lake

Bighorn Lake is a reservoir behind Yellowtail Dam within the Bighorn Canyon National Recreation Area, located in northern Wyoming and extending into southern Montana.

Geography
The reservoir is 40 mi (64 km) south of Billings, Montana. It stretches the entire 72 mi (115 km) length of the Bighorn Canyon at full pool. The Lake was created by the 1965 construction of Yellowtail Dam on the Bighorn River, near Fort Smith, Montana.

Fishing
Bighorn Lake has a surface area of 5574 acres, because of the dam, streamflow in the river is relatively stable with little daily fluctuation. Bighorn Lake supports a warmwater fishery.

title: Bighorn Lake


text: Category:Songs written by Al Hoffman

title: Category:Songs written by Al Hoffman