text:
Cauchy–Euler equation

In mathematics, an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation is a linear homogeneous ordinary differential equation with variable coefficients. It is sometimes referred to as an equidimensional equation. Because of its particularly simple equidimensional structure, the differential equation can be solved explicitly.

The equation
Let $y(x)$ be the nth derivative of the unknown function $y(x)$. Then a Cauchy–Euler equation of order n has the form $$a_{n} x^n y^{(n)}(x) + a_{n-1} x^{n-1} y^{(n-1)}(x) + \dots + a_0 y(x) = 0.$$

The substitution $$x = e^u$$ (that is, $$u = \ln(x)$$; for $$x < 0$$, one might replace all instances of $$x$$ by $$|x|$$, which extends the solution's domain to $$\reals \setminus \{0\}$$) may be used to reduce this equation to a linear differential equation with constant coefficients. Alternatively, the trial solution $$y = x^m$$ may be used to directly solve for the basic solutions.

Second order – solving through trial solution
The most common Cauchy–Euler equation is the second-order equation, appearing in a number of physics and engineering applications, such as when solving Laplace's equation in polar coordinates. The second order Cauchy–Euler equation is

$$x^2\frac{d^2y}{dx^2} + ax\frac{dy}{dx} + by = 0.$$

We assume a trial solution $$y = x^m.$$

Differentiating gives $$\frac{dy}{dx} = mx^{m-1} $$ and $$\frac{d^2y}{dx^2} = m\left(m-1\right)x^{m-2}. $$

Substituting into the original equation leads to requiring $$x^2\left( m\left(m-1 \right)x^{m-2} \right) + ax\left( mx^{m-1} \right) + b\left( x^m \right) = 0$$

Rearranging and factoring gives the indicial equation $$m^2 + \left(a-1\right)m + b = 0.$$

We then solve for m. There are three particular cases of interest:

 * Case 1 of two distinct roots, $m_{1}$ and $m_{2}$;
 * Case 2 of one real repeated root, $m$;
 * Case 3 of complex roots, $α ± βi$.

In case 1, the solution is $$y = c_1 x^{m_1} + c_2 x^{m_2}$$

In case 2, the solution is $$y = c_1 x^m \ln(x) + c_2 x^m $$

To get to this solution, the method of reduction of order must be applied after having found one solution $y = x$.

In case 3, the solution is $$y = c_1 x^\alpha \cos(\beta \ln(x)) + c_2 x^\alpha \sin(\beta \ln(x)) $$ $$\alpha = \operatorname{Re}(m)$$ $$\beta = \operatorname{Im}(m)$$

For $$c_1, c_2 \isin \R$$.

This form of the solution is derived by setting $x = e$ and using Euler's formula

Second order – solution through change of variables
$$x^2\frac{d^2y}{dx^2} +ax\frac{dy}{dx} + by = 0 $$

We operate the variable substitution defined by

$$t = \ln(x). $$ $$y(x) = \varphi(\ln(x)) = \varphi(t). $$ Differentiating gives $$\frac{dy}{dx}=\frac{1}{x}\frac{d\varphi}{dt}$$ $$\frac{d^2y}{dx^2}=\frac{1}{x^2}\left(\frac{d^2\varphi}{dt^2}-\frac{d\varphi}{dt}\right).$$

Substituting $$\varphi(t)$$ the differential equation becomes $$\frac{d^2\varphi}{dt^2} + (a-1)\frac{d\varphi}{dt} + b\varphi = 0.$$

This equation in $$\varphi(t)$$ is solved via its characteristic polynomial $$\lambda^2 + (a-1)\lambda + b = 0.$$

Now let $$\lambda_1$$ and $$\lambda_2$$ denote the two roots of this polynomial. We analyze the case where there are distinct roots and the case where there is a repeated root:

If the roots are distinct, the general solution is $$\varphi(t)=c_1 e^{\lambda_1 t} + c_2 e^{\lambda_2 t},$$ where the exponentials may be complex.

If the roots are equal, the general solution is $$\varphi(t)=c_1 e^{\lambda_1 t} + c_2 t e^{\lambda_1 t}.$$

In both cases, the solution $$y(x)$$ may be found by setting $$t = \ln(x)$$.

Hence, in the first case, $$y(x) = c_1 x^{\lambda_1} + c_2 x^{\lambda_2},$$ and in the second case, $$y(x) = c_1 x^{\lambda_1} + c_2 \ln(x) x^{\lambda_1}.$$

Second order - solution using differential operators
Observe that we can write the second-order Cauchy-Euler equation in terms of a linear differential operator $$ L $$ as $$Ly = (x^2 D^2 + axD + bI)y = 0,$$ where $$ D = \frac{d}{dx} $$ and $$ I $$ is the identity operator.

We express the above operator as a polynomial in $$ xD $$ rather than $$ D $$. By the product rule, $$ (x D)^2 = x D(x D) = x(D + x D^2) = x^2D^2 + x D.$$ So, $$ L = (xD)^2 + (a-1)(xD) + bI.$$

We can then use the quadratic formula to factor this operator into linear terms. More specifically, let $$ \lambda_1, \lambda_2 $$ denote the (possibly equal) values of $$-\frac{a-1}{2} \pm \frac{1}{2}\sqrt{(a-1)^2 - 4b}. $$ Then, $$L = (xD - \lambda_1 I)(xD - \lambda_2 I).$$

It can be seen that these factors commute, that is, $$(xD - \lambda_1 I)(xD - \lambda_2 I) = (xD - \lambda_2 I)(xD - \lambda_1 I)$$. Hence, if $$ \lambda_1 \neq \lambda_2 $$, the solution to $$ Ly = 0 $$ is a linear combination of the solutions to each of $$ (xD - \lambda_1 I)y = 0 $$ and $$ (xD - \lambda_2 I)y = 0 $$, which can be solved by separation of variables.

Indeed, with $$ i \in \{1,2\} $$, we have $$ (xD - \lambda_i I)y = x\frac{dy}{dx} - \lambda_i y = 0 $$. So, $$\begin{align} x\frac{dy}{dx} &= \lambda_i y\\ \int \frac{1}{y}\, dy &= \lambda_i \int \frac{1}{x}\, dx\\ \ln y &= \lambda_i \ln x + C\\ y &= c_i e^{\lambda_i \ln x} = c_i x^{\lambda_i}.\end{align}$$ Thus the general solution is $$ y = c_1 x^{\lambda_1} + c_2 x^{\lambda_2} $$.

If $$ \lambda = \lambda_1 = \lambda_2 $$, then we instead need to consider the solution of $$(xD - \lambda I)^2y = 0 $$. Let $$ z = (xD-\lambda I)y $$, so that we can write $$ (xD - \lambda I)^2y = (xD - \lambda I)z = 0.$$ As before, the solution of $$ (xD- \lambda I)z = 0 $$ is of the form $$ z = c_1x^\lambda $$. So, we are left to solve $$ (xD - \lambda I)y = x\frac{dy}{dx} - \lambda y = c_1x^\lambda.$$ We then rewrite the equation as $$ \frac{dy}{dx} - \frac{\lambda}{x} y = c_1x^{\lambda-1},$$ which one can recognize as being amenable to solution via an integrating factor.

Choose $$ M(x) = x^{-\lambda} $$ as our integrating factor. Multiplying our equation through by $$ M(x) $$ and recognizing the left-hand side as the derivative of a product, we then obtain $$\begin{align} \frac{d}{dx}(x^{-\lambda} y) &= c_1x^{-1}\\ x^{-\lambda} y &= \int c_1x^{-1}\, dx\\ y &= x^\lambda (c_1\ln(x) + c_2)\\ &= c_1\ln(x)x^\lambda +c_2 x^\lambda.\end{align}$$

Example
Given $$x^2 u'' - 3xu' + 3u = 0\,,$$ we substitute the simple solution $x$: $$x^2\left(m\left(m-1\right)x^{m-2}\right)-3x\left(m x^{m-1}\right) + 3x^m = m\left(m-1\right)x^m - 3m x^m+3x^m = \left(m^2 - 4m + 3\right)x^m = 0\,.$$

For $x$ to be a solution, either $x = 0$, which gives the trivial solution, or the coefficient of $x$ is zero. Solving the quadratic equation, we get $m = 1, 3$. The general solution is therefore

 * $$u=c_1 x+c_2 x^3\,.$$

Difference equation analogue
There is a difference equation analogue to the Cauchy–Euler equation. For a fixed $m > 0$, define the sequence $f_{m}(n)$ as $$f_m(n) := n (n+1) \cdots (n+m-1).$$

Applying the difference operator to $$f_m$$, we find that $$\begin{align} Df_m(n) & = f_{m}(n+1) - f_m(n) \\ & = m(n+1)(n+2) \cdots (n+m-1) = \frac{m}{n} f_m(n). \end{align}$$

If we do this $k$ times, we find that $$\begin{align} f_m^{(k)}(n) & = \frac{m(m-1)\cdots(m-k+1)}{n(n+1)\cdots(n+k-1)} f_m(n) \\ & = m(m-1)\cdots(m-k+1) \frac{f_m(n)}{f_k(n)}, \end{align}$$

where the superscript $^{(k)}$ denotes applying the difference operator $k$ times. Comparing this to the fact that the $k$-th derivative of $x$ equals $$m(m-1) \cdots (m-k+1)\frac{x^m}{x^k}$$ suggests that we can solve the N-th order difference equation $$f_N(n) y^{(N)}(n) + a_{N-1} f_{N-1}(n) y^{(N-1)}(n) + \cdots + a_0 y(n) = 0,$$ in a similar manner to the differential equation case. Indeed, substituting the trial solution $$y(n) = f_m(n) $$ brings us to the same situation as the differential equation case, $$m(m-1)\cdots(m-N+1) + a_{N-1} m(m-1) \cdots (m-N+2) + \dots + a_1 m + a_0 = 0.$$

One may now proceed as in the differential equation case, since the general solution of an $N$-th order linear difference equation is also the linear combination of $N$ linearly independent solutions. Applying reduction of order in case of a multiple root $m_{1}$ will yield expressions involving a discrete version of $ln$, $$\varphi(n) = \sum_{k=1}^n \frac{1}{k - m_1}.$$

(Compare with: $\ln (x - m_1) = \int_{1+m_1}^x \frac{dt}{t - m_1} .$ )

In cases where fractions become involved, one may use $$f_m(n) := \frac{\Gamma(n+m)}{\Gamma(n)}$$ instead (or simply use it in all cases), which coincides with the definition before for integer $m$.

title: Cauchy–Euler equation


text:
Cycles (The Doobie Brothers album)

Cycles is the tenth studio album by American rock band The Doobie Brothers. The album was released on May 17, 1989, by Capitol Records.

It marked the band's reunion after breaking up in 1982. Instead of the later configurations with Michael McDonald at the helm, the band reverted to their 1972-4 lineup although Bobby LaKind who had played percussion with later configurations also rejoined. Tom Johnston, John Hartman and Michael Hossack returned to the lineup for the first time since 1977, 1979 and 1974 respectively.

The album was largely co-written with producers and sidesmen. Bobby LaKind collaborated with former Doobie members John McFee and Keith Knudsen on "Time is Here and Gone" and Michael McDonald on "Tonight I'm Coming Through (The Border)". Two cover versions were included in the form of the Four Tops' "One Chain (Don't Make No Prison)" and The Isley Brothers' "Need a Little Taste of Love."

The title of the album was taken from an unused song written by Tiran Porter. Porter later recorded the song for his 1995 solo album Playing To An Empty House.

Lead track "The Doctor" was released as a single and stormed to No. 9 on Billboard's Hot 100 and No. 1 on the Mainstream Rock Chart. After this album, Bobby Lakind retired from the band because of terminal colorectal cancer, which claimed his life in 1992.

The album was reissued in 2002 by One Way Records with two bonus tracks. The first was "Anything for Love", written by Bobby LaKind with Eddie Schwartz and Zeke Zirngiebel, which originally appeared on a CD single of "The Doctor". The second was an extended remix of "Need A Little Taste of Love," which had appeared on a CD single of "One Chain".

Personnel
The Doobie Brothers
 * Tom Johnston – guitar, vocals (lead vocals on 1, 2, 4–6, 8, 9)
 * Patrick Simmons – guitar, vocals (lead vocals on 3, 7, 10)
 * Tiran Porter – bass, backing vocals
 * John Hartman – drums, backing vocals
 * Michael Hossack – drums, percussion
 * Bobby LaKind – percussion, backing vocals

Additional personnel
 * Bill Payne – keyboards
 * Dave Tyson – keyboards
 * Kim Bullard – keyboards
 * Dale Ockerman – keyboards
 * Phil Aaberg – keyboards
 * Don Frank – electronic drums
 * The Memphis Horns – horns
 * Wayne Jackson
 * Andrew Love
 * Rem Smiers – keytar
 * Shannon Eigsti – keyboards (3) (uncredited)

Technical personnel

 * Producers: Eddie Schwartz, Charlie Midnight, Rodney Mills
 * Production Assistant: Rodney Mills
 * Engineers: Tom Sadzeck, Devon Bernadoni, Jim Gaines, Rodney Mills, Jeffrey Norman
 * Mastering: Bob Ludwig
 * Remixing: Brian Wayy
 * Programming: Brian Wayy
 * Conductor: Bobby LaKind
 * Design: Jeffery Fey
 * Cover Photo: Tom Keller
 * Logo Design: Tom Nikosey
 * Art Direction: Tommy Steele

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

title: Cycles (The Doobie Brothers album)


text:
User talk:Warling

Hello and welcome to Wikipedia!

Here are some tips to help you get started:

 * Try the Tutorial, and feel free to experiment in the test area.
 * If you need help, post a question at the Help Desk
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Remember Neutral point of view
 * Explore, be bold in editing pages, and, most importantly, have fun!

Good luck!

[[User:Meelar|Meelar (talk)]]

P.S. One last helpful hint. To sign your posts like I did above (on talk pages, for example) use the '~' symbol. To insert just your name, type ~~~ (3 tildes), or, to insert your name and timestamp, use ~~~~ (4 tildes).

Praha, Texas
Hi, thank a lot for you editting the Praha article. I could speak english somehow and also understand but when I have to wrote something i fell like 3 years old. (In fact every three years old have a better gramer than I have.) I feel really stupid. :-) --Aida 05:41, 20 April 2006 (UTC)
 * Yes this is true. Thank for nice welcome. --Aida 19:31, 20 April 2006 (UTC)

title: User talk:Warling


text:
Sugar Bear

Sugar Bear is the advertising cartoon mascot of Post Super Sugar Crisp (later Golden Crisp) cereal.

History
Sugar Bear originally appeared in the 1940s as the mascot of Sugar Crisp (later known as Golden Crisp), a cereal produced by General Foods Corporation under the Post brand. The original bear was designed by Robert "Bob" Irwin, a graphic designer for Post Cereal and voiced, in animated commercials, for 40 years by Gerry Matthews in emulation of a Bing Crosby or Dean Martin persona – a shallow-eyed, easy going character who crooned his cereal's praises to the tune of "Joshua Fit the Battle of Jericho".

He was made a character in the 1964 Saturday morning cartoon Linus the Lionhearted. Most of the characters in the series, sponsored by General Foods, were mascots for Post cereal products (permitted at that time, later banned by the American Federal Trade Commission (FTC)).

Sugar Bear normally wore a blue turtleneck sweater with his name on the front, and in the 1980s a bite of Super Sugar Crisp would turn him into the muscular "Super Bear" (this alter ego was used to fight monsters who would steal the cereal). Several commercials in the mid 1980s had him using mere casual gestures to outsmart the aggressive tendencies of other animals. Examples include 1987 spots featuring Sugar Bear riding an elephant into a jungle of feisty tigers, playing matador to a raging bull, and sparring with irate sharks of the ocean.

His consistent nemesis was an elderly woman called Granny Goodwitch, with whom he engaged in elaborate contests, often involving trickery, magic, and high technology to decide who got a box of the cereal. In the end, Granny Goodwitch was never angry with Sugar Bear. Other nemeses included Blob, whose breakfast included pickles and soda; and Sugar Fox, who always tried and failed to keep Sugar Bear from getting his box of Super Sugar Crisp.

The Sugar Bear character was popular enough to have occasional premium toys. A yo-yo and padlock were produced in the 1960s, and even in 1993, a Christmas ornament saw him dressed as Santa Claus. Miniature talking plush dolls were also released in the early 1990s. Most recently, a Wacky Wobbler was released by Funko Inc.

Presently, Sugar Bear is being illustrated for the box covers by commercial illustrator Seymour Schachter.

Musical group
In 1971, producer Jimmy Bowen, singers Kim Carnes and Mike Settle, songwriter Baker Knight and others created a bubblegum pop studio group named the Sugar Bears. A cardboard cut-out record was produced and printed on the back of thousands of Super Sugar Crisp cereal boxes. The illustrated record identified four members: Sugar Bear, Honey Bear, Shoobee Bear, and Doobee Bear. Five different versions of the record were printed, each with one of five songs shown on the label. A commercial album, Presenting the Sugar Bears, and three singles were released by Big Tree Records with one song, "You Are the One", reaching No. 51 on the Billboard charts.

title: Sugar Bear


text:
Mabo

Mabo may refer to:

Places

 * Mabo, Togo, a village in Togo
 * Mabo Arrondissement, an area in Kaffrine Region, Senegal

People and related topics

 * Eddie Mabo (1936–1992), the Torres Strait Islander man who instigated the 1992 test case for native title over his people's land
 * Mabo (film), a 2012 Australian telemovie about Eddie Mabo's battle for Aboriginal land title rights
 * Mabo v Queensland (No 1) (1988), court case striking down the Coast Islands Act under the Racial Discrimination Act 1975
 * Mabo v Queensland (No 2) (1992), court case recognising native title in Australia for the first time
 * Mabo: Life of an Island Man, a 1997 documentary film produced and co-directed by Trevor Graham
 * Bonita Mabo (c. 1943–2018), Australian educator and activist, wife of Eddie
 * Gail Mabo (born 1965), daughter of Eddie and Bonita Mabo

title: Mabo


text: File:The Doobie Brothers - Brotherhood.jpg


text:
Gerber Baby

The Gerber Baby is the trademark logo of the Gerber Products Company, an American purveyor of baby food and baby products. Drawn by artist Dorothy Hope Smith, the Gerber Baby was modeled after Ann Turner Cook (1926–2022).

History
Fremont Canning Company, owned and operated by Dan Gerber, was looking for a baby face for its new baby food campaign, which was to start in the later part of 1928. To find a baby face that it believed would best represent the new baby food, the Fremont Canning Company conducted a contest in the summer of 1928. Many drawings and paintings were submitted. Some were elaborate baby portraits in oil paint, while others were simple sketches.

Dorothy Hope Smith of Westport, Connecticut, an artist specialising in children's drawings, submitted an unfinished charcoal drawing, that was closer to a simple sketch than a professional drawing. Smith told the judges that, if the sketch were selected as the winner, she would finish it professionally. The drawing won but, to her surprise, the judges wanted no changes to it.

In 1928, the “Gerber Baby” symbol was introduced to help identify the new product. It was first used in a baby food advertisement in the magazine Good Housekeeping. Within sixty days, Gerber Strained Foods, using the “Gerber Baby” symbol, had gained national recognition, being distributed to various places throughout the United States. It became internationally recognized.

The campaign encouraged mothers of newborns to participate directly in a coupon redemption program. The introductory offer gave each consumer six cans of the canning company's soup and strained vegetables for a dollar in exchange for the name of a favorite grocer.

The idea was to stress the nutritional value of Gerber's baby foods and the time and money saving advantages over buying by prescription. The sketch was so popular that it became the Fremont Canning Company's official trademark in 1931. The Gerber Baby has since appeared on all Gerber packaging and in every Gerber advertisement. The Fremont Canning Company changed its name to Gerber Products Company in 1941.

The model for Smith's original sketch, Ann Turner Cook (1926–2022) grew up to be a mystery novelist and English teacher. Although she avoided publicity for many years, Cook more recently granted interviews to several Florida newspapers. In the beginning of 2011, the company was in the process of looking for the next Gerber Baby. It eventually chose a toddler named Mercy Townsend.

Earlier, one poll conducted in the United States showed that many people thought that the Gerber Baby became someone famous, such as Humphrey Bogart, Elizabeth Taylor, or Ernest Borgnine. The trademark of the Gerber Baby has been shown by the United States public to be associated with the highest consumer loyalty, according to one survey in 1998.

Of note, in the beginning of February 2018, Gerber selected a baby affected by Down Syndrome for its advertising campaign, and received praise and appreciation from many sources. In 2020, for the first time, Gerber chose an adopted baby as the face of their campaign. In 2022, Gerber chose a baby born with a limb difference, and matched the $25,000 cash prize with a donation to March of Dimes.

title: Gerber Baby


text:
Planetary engineering

Planetary engineering is the development and application of technology for the purpose of influencing the environment of a planet. Planetary engineering encompasses a variety of methods such as terraforming, seeding, and geoengineering.

Widely discussed in the scientific community, terraforming refers to the alteration of other planets to create a habitable environment for terrestrial life. Seeding refers to the introduction of life from Earth to habitable planets. Geoengineering refers to the engineering of a planet's climate, and has already been applied on Earth. Each of these methods are composed of varying approaches and possess differing levels of feasibility and ethical concern.

Terraforming
Terraforming is the process of modifying the atmosphere, temperature, surface topography or ecology of a planet, moon, or other body in order to replicate the environment of Earth.

Technologies
A common object of discussion on potential terraforming is the planet Mars. To terraform Mars, humans would need to create a new atmosphere, due to the planet's high carbon dioxide concentration and low atmospheric pressure. This would be possible by introducing more greenhouse gases to below "freezing point from indigenous materials". To terraform Venus, carbon dioxide would need to be converted to graphite since Venus receives twice as much sunlight as Earth. This process is only possible if the greenhouse effect is removed with the use of "high-altitude absorbing fine particles" or a sun shield, creating a more habitable Venus.

NASA has defined categories of habitability systems and technologies for terraforming to be feasible. These topics include creating power-efficient systems for preserving and packaging  food for crews, preparing and cooking foods, dispensing water, and developing facilities for rest, trash and recycling, and areas for crew hygiene and rest.

Feasibility
A variety of planetary engineering challenges stand in the way of terraforming efforts. The atmospheric terraforming of Mars, for example, would require "significant quantities of gas" to be added to the Martian atmosphere. This gas has been thought to be stored in solid and liquid form within Mars' polar ice caps and underground reservoirs. It is unlikely, however, that enough for sufficient atmospheric change is present within Mars' polar deposits, and liquid  could only be present at warmer temperatures "deep within the crust". Furthermore, sublimating the entire volume of Mars' polar caps would increase its current atmospheric pressure to 15 millibar, where an increase to around 1000 millibar would be required for habitability. For reference, Earth's average sea-level pressure is 1013.25 mbar.

First formally proposed by astrophysicist Carl Sagan, the terraforming of Venus has since been discussed through methods such as organic molecule-induced carbon conversion, sun reflection, increasing planetary spin, and various chemical means. Due to the high presence of sulfuric acid and solar wind on Venus, which are harmful to organic environments, organic methods of carbon conversion have been found unfeasible. Other methods, such as solar shading, hydrogen bombardment, and magnesium-calcium bombardment are theoretically sound but would require large-scale resources and space technologies not yet available to humans.

Ethical considerations
While successful terraforming would allow life to prosper on other planets, philosophers have debated whether this practice is morally sound. Certain ethics experts suggest that planets like Mars hold an intrinsic value independent of their utility to humanity and should therefore be free from human interference. Also, some argue that through the steps that are necessary to make Mars habitable - such as fusion reactors, space-based solar-powered lasers, or spreading a thin layer of soot on Mars' polar ice caps - would deteriorate the current aesthetic value that Mars possesses. This calls into question humanity's intrinsic ethical and moral values, as it raises the question of whether humanity is willing to eradicate the current ecosystem of another planet for their benefit. Through this ethical framework, terraforming attempts on these planets could be seen to threaten their intrinsically valuable environments, rendering these efforts unethical.

Environmental considerations
Mars is the primary subject of discussion for seeding. Locations for seeding are chosen based on atmospheric temperature, air pressure, existence of harmful radiation, and availability of natural resources, such as water and other compounds essential to terrestrial life.

Developing microorganisms for seeding
Natural or engineered microorganisms must be created or discovered that can withstand the harsh environments of Mars. The first organisms used must be able to survive exposure to ionizing radiation and the high concentration of present in the Martian atmosphere. Later organisms such as multicellular plants must be able to withstand the freezing temperatures, withstand high levels, and produce significant amounts of O2.

Microorganisms provide significant advantages over non-biological mechanisms. They are self-replicating, negating the needs to either transport or manufacture large machinery to the surface of Mars. They can also perform complicated chemical reactions with little maintenance to realize planet-scale terraforming.

Geoengineering
Geoengineering, or climate engineering, is a form of planetary engineering which involves the process of deliberate and large-scale alteration of the Earth's climate system to combat climate change. Examples of geoengineering are carbon dioxide removal (CDR), which removes carbon dioxide from the atmosphere, and the use of space mirrors to reflect solar energy to space. Carbon dioxide removal (CDR) has multiple practices, the simplest being reforestation, to more complex processes such as direct air capture. The latter is rather difficult to deploy on an industrial scale, for high costs and substantial energy usage would be some aspects to address.

Another geoengineering discipline is solar radiation management (SRM), which is the process of rapidly cooling down the Earth's temperature. Examples of this process include stimulating the cooling effect of volcanoes and enhancing the reflectivity of marine clouds. When a volcano erupts, small particles known as aerosols proliferate throughout the atmosphere, reflecting the sun's energy back into space. This results in a cooling effect, and humanity could conceivably inject these aerosols into the stratosphere, spurring large-scale cooling.

Marine cloud brightening (MCB) is a solar radiation management theory that is designed to make marine clouds brighter, reflecting light back into deep space. By reflecting light from the sun, this process could help offset anthropogenic global warming, which threatens the lives of all human beings and life on Earth. One proposal involves spraying a vapor into low-laying sea clouds, creating more cloud condensation nuclei. This would in theory result in the cloud becoming whiter, and reflecting light more efficiently.

title: Planetary engineering


text: Category:Court Jews

title: Category:Court Jews


text:
Wassailing

The tradition of wassailing (also spelled wasselling) falls into two distinct categories: the house-visiting wassail and the orchard-visiting wassail. The house-visiting wassail is the practice of people going door-to-door, singing and offering a drink from the wassail bowl in exchange for gifts; this practice still exists, but has largely been displaced by carol singing. The orchard-visiting wassail refers to the ancient custom of visiting orchards in cider-producing regions of England, reciting incantations and singing to the trees to promote a good harvest for the coming year. Notable traditional wassailing songs include "Here We Come a-Wassailing", "Gloucestershire Wassail", and "Gower Wassail".

Etymology
According to the Oxford English Dictionary, the word "wassail" originated as a borrowing from the Old Norse salutation ves heill, corresponding to Old English hál wes þú or wes hál; literally meaning 'be in good health' or 'be fortunate'. It was initially used in the sense of 'hail' or 'farewell'. Later it developed into the first part of a drinking formula "wassail...drinkhail". By c. 1300, the sense had extended to the drink itself, especially to the spiced ale used in Twelfth-night and Christmas Eve celebrations, and by 1598 it was being applied to the custom of drinking healths on those nights.

Wassailing during Christmastide
Traditionally, the wassail is celebrated on Twelfth Night (variously on either 5 or 6 January). Some people still wassail on "Old Twelvey Night", 17 January, as it would have been before the introduction of the Gregorian Calendar in 1752.

In the Middle Ages, the wassail was a reciprocal exchange between the feudal lords and their peasants as a form of recipient-initiated charitable giving, to be distinguished from begging. This point is made in the song "Here We Come A-wassailing", when the wassailers inform the lord of the house that

"we are not daily beggars that beg from door to door But we are friendly neighbours whom you have seen before."

The lord of the manor would give food and drink to the peasants in exchange for their blessing and goodwill, i.e.

"Love and joy come to you, And to you your wassail too; And God bless you and send you a Happy New Year"

This would be given in the form of the song being sung. Wassailing is the background practice against which an English carol such as "We Wish You a Merry Christmas" can be made sense of. The carol lies in the English tradition where wealthy people of the community gave Christmas treats to the carol singers on Christmas Eve such as 'figgy puddings'.

Although wassailing is often described in innocuous and sometimes nostalgic terms—still practised in some parts of Scotland and Northern England on New Years Day as "first-footing"—the practice in England has not always been considered so innocent. Similar traditions have also been traced to Greece and the country of Georgia. Wassailing was associated with rowdy bands of young men who would enter the homes of wealthy neighbours and demand free food and drink (in a manner similar to the modern children's Halloween practice of trick-or-treating). If the householder refused, he was usually cursed, and occasionally his house was vandalized. The example of the exchange is seen in their demand for "figgy pudding" and "good cheer", i.e., the wassail beverage, without which the wassailers in the song will not leave; "We won't go until we get some, so bring some out here". Such complaints were also common in the early days of the United States, where the practice (and its negative connotations) had taken root by the early 1800s; it led to efforts from the American merchant class to promote a more sanitized Christmas.

The Orchard-visiting Wassail
In the cider-producing West of England (primarily the counties of Devon, Somerset, Dorset, Gloucestershire and Herefordshire) wassailing also refers to drinking (and singing) the health of trees in the hopes that they might better thrive. Wassailing is also a traditional event in Jersey, Channel Islands where cider (cidre) made up the bulk of the economy before the 20th century. The format is much the same as that in England but with terms and songs often in Jèrriais.

17th-century English lyric poet Robert Herrick writes in his poem "The Wassail":

"Wassail the trees, that they may bear You many a plum and many a pear: For more or less fruits they will bring, As you do give them wassailing."

The purpose of wassailing is to awake the cider apple trees and to scare away evil spirits to ensure a good harvest of fruit in autumn. The ceremonies of each wassail vary from village to village but they generally all have the same core elements. A wassail King and Queen lead the song and/or a processional tune played or sung from one orchard to the next. The wassail Queen will then be lifted up into the boughs of the tree where she will place toast soaked in Wassail from the Clayen Cup as a gift to the tree spirits (and to show the fruits created the previous year). Then an incantation is usually recited, such as:

"Here's to thee, old apple tree, That blooms well, bears well. Hats full, caps full, Three bushel bags full, An' all under one tree. Hurrah! Hurrah!"

This incantation is followed by noise-making from the assembled crowd until the gunsmen give a final volley through the branches. The crowd then moves onto the next orchard.

As the largest cider producing region of the country, the West Country hosts historic wassails annually, such as Whimple in Devon and Carhampton in Somerset, both on 17 January, or old Twelfth Night. Many new, commercial or "revival" wassails have also been introduced throughout the West Country, such as those in Stoke Gabriel and Sandford, Devon. Clevedon in North Somerset holds an annual wassailing event at the Clevedon Community Orchard, combining the traditional elements of the festival with the entertainment and music of the Bristol Morris Men.

Nineteenth-century wassailers of Somerset would sing the following lyrics after drinking the cider until they were "merry and gay":

"Apple tree, apple tree, we all come to wassail thee, Bear this year and next year to bloom and to blow, Hat fulls, cap fulls, three cornered sack fills, Hip, Hip, Hip, hurrah, Holler biys, holler hurrah."

A folktale from Somerset reflecting this custom tells of the Apple Tree Man, the spirit of the oldest apple tree in an orchard, and in whom the fertility of the orchard is thought to reside. In the tale a man offers his last mug of mulled cider to the trees in his orchard and is rewarded by the Apple Tree Man who reveals to him the location of buried gold.

Wassail bowls
Wassail bowls, generally in the shape of goblets, have been preserved. The Worshipful Company of Grocers made a very elaborate one in the seventeenth century, decorated with silver. It is so large that it must have passed around as a "loving cup" so that many members of the guild could drink from it.

In the English Christmas carol "Gloucestershire Wassail", the singers tell that their "bowl is made of the white maple tree, with a wassailing bowl we'll drink to thee". As white maple does not grow natively in Europe, the lyric may be a reference to sycamore maple or field maple, both of which do,  and both of which have white-looking wood. This is reinforced by an 1890s written account from a man describing the wassailing bowl of his friend from Gloucestershire: "The bowl was one of those wooden sycamore or maple ones used to hold boiled potatoes on a farm kitchen table."

Alternatively however, many formal publications from the 1800s list the lyric simply as saying "maplin tree", without mentioning "white". Additionally, the lyric appears to have varied significantly depending on location and other factors, calling into question how literal the term was and/or how varied the construction of wassail bowls was. For example, a 1913 publication by Ralph Vaughan Williams, who had recorded the lyric in 1909 by a wassailer in Herefordshire, recorded it as "green maple". Another version from Brockweir listed the bowl as being made from mulberry.

There are surviving examples of "puzzle wassail bowls", with many spouts. As you attempt to drink from one of the spouts, you are drenched from another spout. The drink was either punch, mulled wine or spicy ale.

title: Wassailing


text:
Climate engineering

Climate engineering (or geoengineering) is an umbrella term for both carbon dioxide removal and solar radiation modification, when applied at a planetary scale. However, these two processes have very different characteristics. For this reason, the Intergovernmental Panel on Climate Change no longer uses this overarching term. Carbon dioxide removal approaches are part of climate change mitigation. Solar radiation modification is reflecting some sunlight (solar radiation) back to space. Some publications place passive radiative cooling into the climate engineering category. This technology increases the Earth's thermal emittance. The media tends to use climate engineering also for other technologies such as glacier stabilization, ocean liming, and iron fertilization of oceans. The latter would modify carbon sequestration processes that take place in oceans.

Some types of climate engineering are highly controversial due to the large uncertainties around effectiveness, side effects and unforeseen consequences. Interventions at large scale run a greater risk of unintended disruptions of natural systems, resulting in a dilemma that such disruptions might be more damaging than the climate damage that they offset. However, the risks of such interventions must be seen in the context of the trajectory of climate change without them.

The Union of Concerned Scientists points to the danger that the use of climate engineering technology will become an excuse not to address the root causes of climate change, slow our emissions reductions and start moving toward a low-carbon economy.

Terminology
Climate engineering (or geoengineering) has been used as an umbrella term for both carbon dioxide removal and solar radiation management, when applied at a planetary scale. However, these two methods have very different geophysical characteristics, which is why the Intergovernmental Panel on Climate Change no longer uses this term. This decision was communicated in around 2018, see for example the "Special Report on Global Warming of 1.5 °C".

According to climate economist Gernot Wagner the term geoengineering is "largely an artefact and a result of the term's frequent use in popular discourse" and "so vague and all-encompassing as to have lost much meaning".

Specific technologies that fall into the "climate engineering" umbrella term include:

The following methods are not termed climate engineering in the latest IPCC assessment report in 2022 but are included under this umbrella term by other publications on this topic:
 * Carbon dioxide removal
 * Biochar: Biochar is a high-carbon, fine-grained residue that is produced via pyrolysis
 * Bioenergy with carbon capture and storage (BECCS): the process of extracting bioenergy from biomass and capturing and storing the carbon, thereby removing it from the atmosphere.
 * Direct air capture and carbon storage: a process of capturing carbon dioxide directly from the ambient air (as opposed to capturing from point sources, such as a cement factory or biomass power plant) and generating a concentrated stream of for sequestration or utilization or production of carbon-neutral fuel and windgas.
 * Enhanced weathering: a process that aims to accelerate the natural weathering by spreading finely ground silicate rock, such as basalt, onto surfaces which speeds up chemical reactions between rocks, water, and air. It also removes carbon dioxide from the atmosphere, permanently storing it in solid carbonate minerals or ocean alkalinity. The latter also slows ocean acidification.
 * Solar Radiation Management
 * Marine cloud brightening: a proposed technique that would make clouds brighter, reflecting a small fraction of incoming sunlight back into space in order to offset anthropogenic global warming.
 * Mirrors in space (MIS): satellites that are designed to change the amount of solar radiation that impacts the Earth as a form of climate engineering. Since the conception of the idea in 1923, 1929, 1957 and 1978 (Hermann Oberth) and also in the 1980s, space mirrors have mainly been theorized as a way to deflect sunlight to counter global warming and were seriously considered in the 2000s.
 * Stratospheric aerosol injection (SAI): a proposed method to introduce aerosols into the stratosphere to create a cooling effect via global dimming and increased albedo, which occurs naturally from volcanic eruptions.
 * Passive daytime radiative cooling
 * Ground-level albedo modification: a process of increasing Earth's albedo through the means of altering things on the Earth's surface. Examples include planting light-colored plants to help with reflecting sunlight back into space.
 * Glacier stabilization: proposals aiming to slow down or prevent sea level rise caused by the collapse of notable marine-terminating glaciers, such as Jakobshavn Glacier in Greenland or Thwaites Glacier and Pine Island Glacier in Antarctica. It may be possible to bolster some glaciers directly, but blocking the flow of ever-warming ocean water at a distance, allowing it more time to mix with the cooler water around the glacier, is likely to be far more effective.
 * Ocean geoengineering (adding material such as lime or iron to the ocean to affect its ability to sequester carbon dioxide)

Passive daytime radiative cooling
Enhancing the thermal emissivity of Earth through passive daytime radiative cooling has been proposed as an alternative or "third approach" to climate engineering that is "less intrusive" and more predictable or reversible than stratospheric aerosol injection.

Ocean geoengineering
Ocean geoengineering involves modifying the ocean to reduce the impacts of rising temperature. One approach is to add material such as lime or iron to the ocean to increase its ability to support marine life and/or sequester. In 2021 the US National Academies of Sciences, Engineering, and Medicine (NASEM) requested $2.5 billion funds for research in the following decade, specifically including field tests.

Another idea is to reduce sea level rise by installing underwater ‘curtains' to protect Antarctic glaciers from warming waters, or by drilling holes in ice to pump out water and heat.

Ocean liming
Enriching seawater with calcium hydroxide (lime) has been reported to lower ocean acidity, which reduces pressure on marine life such as oysters and absorb. The added lime raised the water's pH, capturing in the form of calcium bicarbonate or as carbonate deposited in mollusk shells. Lime is produced in volume for the cement industry. This was assessed in 2022 in an experiment in Apalachicola, Florida in an attempt to halt declining oyster populations. pH levels increased modestly, as was reduced by 70 ppm.

A 2014 experiment added sodium hydroxide (lye) to part of Australia's Great Barrier Reef. It raised pH levels to nearly preindustrial levels.

However, producing alkaline materials typically releases large amounts of, partially offsetting the sequestration. Alkaline additives become diluted and dispersed in one month, without durable effects, such that if necessary, the program could be ended without leaving long-term effects.

Submarine forest
Another 2022 experiment attempted to sequester carbon using giant kelp planted off the Namibian coast. Whilst this approach has been called ocean geoengineering by the researchers it is just another form of carbon dioxide removal via sequestration. Another term that is used to describe this process is blue carbon management and also marine geoengineering.

Problems
Interventions at large scale run a greater risk of unintended disruptions of natural systems, resulting in a dilemma that such disruptions might be more damaging than the climate damage that they offset.

Ethical aspects
Climate engineering may reduce the urgency of reducing carbon emissions, a form of moral hazard. Also, most efforts have only temporary effects, which implies rapid rebound if they are not sustained. The Union of Concerned Scientists points to the danger that the use of climate engineering technology will become an excuse not to address the root causes of climate change, slow our emissions reductions and start moving toward a low-carbon economy. However, several public opinion surveys and focus groups reported either a desire to increase emission cuts in the presence of climate engineering, or no effect. Other modelling work suggests that the prospect of climate engineering may in fact increase the likelihood of emissions reduction.

If climate engineering can alter the climate, then this raises questions whether humans have the right to deliberately change the climate, and under what conditions. For example, using climate engineering to stabilize temperatures is not the same as doing so to optimize the climate for some other purpose. Some religious traditions express views on the relationship between humans and their surroundings that encourage (to conduct responsible stewardship) or discourage (to avoid hubris) explicit actions to affect climate.

Public perception
A large 2018 study used an online survey to investigate public perceptions of six climate engineering methods in the United States, United Kingdom, Australia, and New Zealand. Public awareness of climate engineering was low; less than a fifth of respondents reported prior knowledge. Perceptions of the six climate engineering methods proposed (three from the carbon dioxide removal group and three from the solar radiation modification group) were largely negative and frequently associated with attributes like 'risky', 'artificial' and 'unknown effects'. Carbon dioxide removal methods were preferred over solar radiation modification. Public perceptions were remarkably stable with only minor differences between the different countries in the surveys.

Some environmental organizations (such as Friends of the Earth and Greenpeace) have been reluctant to endorse or oppose solar radiation modification, but are often more supportive of nature-based carbon dioxide removal projects, such as afforestation and peatland restoration.

Research and projects
Several organizations have investigated climate engineering with a view to evaluating its potential, including the US Congress, the US National Academy of Sciences, Engineering, and Medicine, the Royal Society, the UK Parliament, the Institution of Mechanical Engineers, and the Intergovernmental Panel on Climate Change.

In 2009, the Royal Society in the UK reviewed a wide range of proposed climate engineering methods and evaluated them in terms of effectiveness, affordability, timeliness, and safety (assigning qualitative estimates in each assessment). The key recommendations reports were that "Parties to the UNFCCC should make increased efforts towards mitigating and adapting to climate change, and in particular to agreeing to global emissions reductions", and that "[nothing] now known about geoengineering options gives any reason to diminish these efforts". Nonetheless, the report also recommended that "research and development of climate engineering options should be undertaken to investigate whether low-risk methods can be made available if it becomes necessary to reduce the rate of warming this century".

In 2009, a review examined the scientific plausibility of proposed methods rather than the practical considerations such as engineering feasibility or economic cost. The authors found that "[air] capture and storage shows the greatest potential, combined with afforestation, reforestation and bio-char production", and noted that "other suggestions that have received considerable media attention, in particular, "ocean pipes" appear to be ineffective". They concluded that "[climate] geoengineering is best considered as a potential complement to the mitigation of emissions, rather than as an alternative to it".

The IMechE report examined a small subset of proposed methods (air capture, urban albedo and algal-based capture techniques), and its main conclusions in 2011 were that climate engineering should be researched and trialed at the small scale alongside a wider decarbonization of the economy.

In 2015, the US National Academy of Sciences, Engineering, and Medicine concluded a 21-month project to study the potential impacts, benefits, and costs of climate engineering. The differences between these two classes of climate engineering "led the committee to evaluate the two types of approaches separately in companion reports, a distinction it hopes carries over to future scientific and policy discussions." The resulting study titled Climate Intervention was released in February 2015 and consists of two volumes: Reflecting Sunlight to Cool Earth and Carbon Dioxide Removal and Reliable Sequestration.

In June 2023 the US government released a report that recommended conducting research on stratospheric aerosol injection and marine cloud brightening.

As of 2024 the Coastal Atmospheric Aerosol Research and Engagement (CAARE) project was launching sea salt into the marine sky in an effort to increase cloud "brightness" (reflective capacity). The sea salt is launched from the USS Hornet Sea, Air & Space Museum (based on the project's regulatory filings).

title: Climate engineering


text:
User talk:Shiyoushi

Hey Shiyoushi, just wanted to say great edit on Boags! -- Chuq 03:35, 4 Oct 2004 (UTC)

Survey
Hi Erin!

I have put together a survey for female editors of Wikipedia (and related projects) in order to explore, in greater detail, women's experiences and roles within the Wikimedia movement. It'd be wonderful if you could participate!

It's an independent survey, done by me, as a fellow volunteer Wikimedian. It is not being done on behalf of the Wikimedia Foundation. I hope you'll participate!

Just click this link to participate in this survey, via Google!

Any questions or concerns, feel free to email me or stop by my user talk page. Also, feel free to share this any other female Wikimedians you may know. It is in English, but any language Wikimedia participants are encouraged to participate. I appreciate your contributions - to the survey and to Wikipedia! Thank you! SarahStierch (talk) 02:32, 28 September 2011 (UTC)

Brisbane workshop and meetup invitation
Hi there! You are cordially invited to a series of Paralympic History workshops and a meetup next Saturday (26 May) and Sunday. In attendance will be University of Queensland faculty and Australian Paralympic Committee staff. Details and an attendee list are at Meetup/Brisbane/5. Hope to see you there! John Vandenberg 07:03, 16 May 2012 (UTC)

(this automated message was delivered using replace.py to all users in Category:Wikipedians in Brisbane)

Brisbane meetup invitation
Hi there! You are cordially invited to a meetup this Friday evening (3 August). Details and an attendee list are at Meetup/Brisbane/6. Hope to see you there! John Vandenberg 01:20, 1 August 2012 (UTC)

(this automated message was delivered using replace.py to all users in Brisbane)

Brisbane meetup with Sue Gardner invitation
Hi there! You are cordially invited to a meetup on 11 Febrary 2013 with Sue Gardner.

Details at Meetup/Brisbane/7. Hope to see you there! John Vandenberg 10:42, 30 January 2013 (UTC)

(this automated message was delivered using replace.py to all users in SEQ)

WWI WiR
Hi! Wikimedia Australia is initiating a World War I program with a call for a group of Wikimedians in Residence at GLAMs across Australia.

Please see wmau:Proposal:WWI WiR and signup before the end of this month to help us gauge numbers.

(this automated message was delivered using replace.py to all users in Wikipedians in Australia and Female Wikipedians)

Hobart meetup
Hello! This is a message to inform you of a Wikipedia Hobart meetup which will be held on 10 January. New and experienced editors are welcome! Please check the meetup page for more information. This message has been sent to members of Category:Wikipedians in Tasmania by Chuq (talk) using MediaWiki message delivery (talk) 22:19, 29 December 2014 (UTC)

Hobart area articles
Hello, in advance of a possible project in the Hobart area, we're looking to identify and improve a specific range of articles, mainly those associated with locations in the Hobart City Council region. If you'd like to find out more, please join in the discussion at WikiProject Tasmania, or check out the list of articles at QR list. If you'd prefer to not receive these notifications in the future, please let me know.

This message has been sent to members of Category:Wikipedians in Tasmania, Category:Wikipedians in Hobart, and WikiProject Tasmania participants by Chuq (talk) using MediaWiki message delivery (talk) 12:05, 14 February 2015 (UTC)

Brisbane Meetup
Hi there! I'm dropping you this notice as you've indicated on your userpage that you're a Wikipedian in the Brisbane area. Assuming significant interest, I'm organising an event for August 22 at the SLQ Café in South Brisbane, and we'd love for you to come along. A list of people interested in coming, and a discussion space has been created at Meetup/Brisbane/8. Hope to see you there! MediaWiki message delivery (talk) 10:39, 7 August 2015 (UTC)

This message has been automatically sent to all users in Category:Wikipedians in Brisbane. If you do not wish to receive further messages like this, please either remove your user page from this category, or add yourself to Category:Opted-out of message delivery

Brisbane Meetup in January 2016
Hi there! I'm dropping you this notice as you've indicated on your userpage that you're a Wikipedian in the Brisbane area. To celebrate fifteen years of Wikipedia, we are holding a celebration in Brisbane on the 16th of January and you are invited! For further information, and to register your interest, please see our meetup page. Hope to see you there!

This message has been automatically sent to all users in Category:Wikipedians in Brisbane. If you do not wish to receive further messages like this, please either remove your user page from this category, or add yourself to Category:Opted-out of message delivery.

Brisbane meetup - Sunday 10 December 2017 at The Edge, State Library of Queensland
If you are in or near Brisbane, please join us on Sunday 10 December 2017 any time from noon to 4pm at The Edge at the State Library of Queensland. For more details and to sign up, please go to the meetup page. See you there! Kerry (talk) 22:39, 27 November 2017 (UTC)

Brisbane meetup: Saturday 13 January 2018 at The Edge, State Library of Queensland
If you are in or near Brisbane, please join us on Saturday 13 January 2018 any time from noon to 4pm at The Edge at the State Library of Queensland. For more details and to sign up, please go to the meetup page. See you there!

title: User talk:Shiyoushi


text: User talk:67.168.40.150

title: User talk:67.168.40.150


text:
User talk:Cecil (usurped)

Hello and welcome to Wikipedia!

Here are some tips to help you get started:

 * Try the Tutorial, and feel free to experiment in the test area.
 * If you need help, post a question at the Help Desk
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Remember Neutral point of view
 * Explore, be bold in editing pages, and, most importantly, have fun!

Good luck!

[[User:Meelar|Meelar (talk)]]

P.S. One last helpful hint. To sign your posts like I did above (on talk pages, for example) use the '~' symbol. To insert just your name, type ~~~ (3 tildes), or, to insert your name and timestamp, use ~~~~ (4 tildes).

title: User talk:Cecil (usurped)


text:
User:Jengod/List of U.S. Presidents by time in office

 * Franklin Delano Roosevelt: 4422 days
 * James Madison: 2922 days
 * Thomas Jefferson: 2922 days
 * James Monroe: 2922 days
 * Andrew Jackson: 2922 days
 * Ulysses S. Grant: 2922 days
 * Grover Cleveland: 2922 days
 * Woodrow Wilson: 2922 days
 * Dwight Eisenhower: 2922 days
 * Ronald Reagan: 2922 days
 * Bill Clinton: 2922 days
 * George Washington: 2865 days
 * Harry S. Truman: 2840 days
 * Theodore Roosevelt: 2728 days
 * Calvin Coolidge: 2040 days
 * Richard Nixon: 2027 days
 * Lyndon B. Johnson: 1886 days
 * William McKinley: 1654 days
 * Abraham Lincoln: 1503 days
 * John Quincy Adams: 1461 days
 * Martin Van Buren: 1461 days
 * Franklin Pierce: 1461 days
 * James Buchanan: 1461 days
 * Rutherford B. Hayes: 1461 days
 * Benjamin Harrison: 1461 days
 * William Howard Taft: 1461 days
 * Herbert Hoover: 1461 days
 * Jimmy Carter: 1461 days
 * George H. W. Bush: 1461 days
 * John Adams: 1460 days
 * James Knox Polk: 1460 days
 * John Tyler: 1430 days
 * Andrew Johnson: 1419 days
 * John F. Kennedy: 1036 days
 * Millard Fillmore: 969 days
 * Gerald Ford: 895 days
 * Warren G. Harding: 881 days
 * Zachary Taylor: 491 days
 * Chester A. Arthur: 200 days
 * James A. Garfield: 199 days
 * William Henry Harrison: 31 days


text:
Brotherhood (The Doobie Brothers album)

Brotherhood is the eleventh studio album by American rock band The Doobie Brothers. The album was released on April 15, 1991, by Capitol Records. It was their second and final album for Capitol. It also marked the final appearances on a Doobie Brothers album by bassist Tiran Porter and original drummer John Hartman.

Four of the ten tracks were written entirely by outside musicians, though two of these, songwriter Jerry Lynn Williams and Jim Peterik of Survivor, also collaborated with Tom Johnston and Patrick Simmons on some of their compositions.

The album contained no major hit singles, but "Dangerous", Simmons' anthem to his passion for Harley-Davidson motorcycles, peaked at #2 on the Hot Mainstream Rock Tracks chart and is still performed live by the band. Johnston's "Rollin' On" charted at #12 on the same listing.

Aftermath
The album was a critical and commercial failure, stalling at #82. Shortly after the album's release, the band was dropped by Capitol. There was also a shift in personnel as Tiran Porter left to pursue a brief solo career, frustrated that his own compositions were deemed unsuitable for the band, while John Hartman quit music altogether. Two other former members, drummer Keith Knudsen and guitarist John McFee, were recruited, but for the next nine years, the band concentrated entirely on live work, frustrated by the lack of support they had received from Capitol. The Doobie Brothers would not release another studio album until Sibling Rivalry in 2000, a period of time that was three years longer than the gap between the Doobies' "Farewell Tour" album and Cycles, their reunion album with Tom Johnston.

Personnel

 * The Doobie Brothers
 * Tom Johnston – guitars, vocals
 * Patrick Simmons – guitars, vocals
 * Tiran Porter – bass, vocals
 * John Hartman – drums
 * Michael Hossack – drums, percussion

 * Additional players
 * Steve Canali – slide guitar
 * Jimi Fox – percussion
 * Dale Ockerman – keyboards
 * Richard Bryant – background vocals
 * Vicki Randle – background vocals
 * Rem Smiers – background vocals

Production

 * Producer and Engineer – Rodney Mills
 * Assistant Producer – Kathy Nelson
 * Co-Engineer – Devon Rietveld
 * Mixing – Rodney Mills and Chris Lord-Alge
 * Recorded and Mixed at The Record Plant (Sausalito, California); Track 4 recorded and mixed at Image Recording Studios (Hollywood).
 * Mastered by Bob Ludwig at Masterdisk (New York).
 * Design – John Kehe
 * Photography – Peter Darley Miller
 * Front Cover Photo – Robert Doisneau
 * Art Direction – Tommy Steele
 * Management – Bruce Cohn
 * Tour Manager – Tim McCormick

title: Brotherhood (The Doobie Brothers album)