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Soliton

In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets. Its remarkable stability can be traced to a balanced cancellation of nonlinear and dispersive effects in the medium. (Dispersive effects are a property of certain systems where the speed of a wave depends on its frequency.) Solitons were subsequently found to provide stable solutions of a wide class of weakly nonlinear dispersive partial differential equations describing physical systems.

The soliton phenomenon was first described in 1834 by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation". The term soliton was coined by Zabusky and Kruskal to describe localized, strongly stable propagating solutions to the Korteweg–de Vries equation, which models waves of the type seen by Russell. The name was meant to characterize the solitary nature of the waves, with the 'on' suffix recalling the usage for particles such as electrons, baryons or hadrons, reflecting their observed particle-like behaviour.

Definition
A single, consensus definition of a soliton is difficult to find. ascribe three properties to solitons:
 * 1) They are of permanent form;
 * 2) They are localized within a region;
 * 3) They can interact with other solitons, and emerge from the collision unchanged, except for a phase shift.

More formal definitions exist, but they require substantial mathematics. Moreover, some scientists use the term soliton for phenomena that do not quite have these three properties (for instance, the 'light bullets' of nonlinear optics are often called solitons despite losing energy during interaction).

Explanation
Dispersion and nonlinearity can interact to produce permanent and localized wave forms. Consider a pulse of light traveling in glass. This pulse can be thought of as consisting of light of several different frequencies. Since glass shows dispersion, these different frequencies travel at different speeds and the shape of the pulse therefore changes over time. However, also the nonlinear Kerr effect occurs; the refractive index of a material at a given frequency depends on the light's amplitude or strength. If the pulse has just the right shape, the Kerr effect exactly cancels the dispersion effect and the pulse's shape does not change over time. Thus, the pulse is a soliton. See soliton (optics) for a more detailed description.

Many exactly solvable models have soliton solutions, including the Korteweg–de Vries equation, the nonlinear Schrödinger equation, the coupled nonlinear Schrödinger equation, and the sine-Gordon equation. The soliton solutions are typically obtained by means of the inverse scattering transform, and owe their stability to the integrability of the field equations. The mathematical theory of these equations is a broad and very active field of mathematical research.

Some types of tidal bore, a wave phenomenon of a few rivers including the River Severn, are 'undular': a wavefront followed by a train of solitons. Other solitons occur as the undersea internal waves, initiated by seabed topography, that propagate on the oceanic pycnocline. Atmospheric solitons also exist, such as the morning glory cloud of the Gulf of Carpentaria, where pressure solitons traveling in a temperature inversion layer produce vast linear roll clouds. The recent and not widely accepted soliton model in neuroscience proposes to explain the signal conduction within neurons as pressure solitons.

A topological soliton, also called a topological defect, is any solution of a set of partial differential equations that is stable against decay to the "trivial solution". Soliton stability is due to topological constraints, rather than integrability of the field equations. The constraints arise almost always because the differential equations must obey a set of boundary conditions, and the boundary has a nontrivial homotopy group, preserved by the differential equations. Thus, the differential equation solutions can be classified into homotopy classes.

No continuous transformation maps a solution in one homotopy class to another. The solutions are truly distinct, and maintain their integrity, even in the face of extremely powerful forces. Examples of topological solitons include the screw dislocation in a crystalline lattice, the Dirac string and the magnetic monopole in electromagnetism, the Skyrmion and the Wess–Zumino–Witten model in quantum field theory, the magnetic skyrmion in condensed matter physics, and cosmic strings and domain walls in cosmology.

History
In 1834, John Scott Russell describes his wave of translation. The discovery is described here in Scott Russell's own words:

"I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped – not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation."

Scott Russell spent some time making practical and theoretical investigations of these waves. He built wave tanks at his home and noticed some key properties:
 * The waves are stable, and can travel over very large distances (normal waves would tend to either flatten out, or steepen and topple over)
 * The speed depends on the size of the wave, and its width on the depth of water.
 * Unlike normal waves they will never merge – so a small wave is overtaken by a large one, rather than the two combining.
 * If a wave is too big for the depth of water, it splits into two, one big and one small.

Scott Russell's experimental work seemed at odds with Isaac Newton's and Daniel Bernoulli's theories of hydrodynamics. George Biddell Airy and George Gabriel Stokes had difficulty accepting Scott Russell's experimental observations because they could not be explained by the existing water wave theories. Additional observations were reported by Henry Bazin in 1862 after experiments carried out in the canal de Bourgogne in France. Their contemporaries spent some time attempting to extend the theory but it would take until the 1870s before Joseph Boussinesq and Lord Rayleigh published a theoretical treatment and solutions. In 1895 Diederik Korteweg and Gustav de Vries provided what is now known as the Korteweg–de Vries equation, including solitary wave and periodic cnoidal wave solutions.

In 1965 Norman Zabusky of Bell Labs and Martin Kruskal of Princeton University first demonstrated soliton behavior in media subject to the Korteweg–de Vries equation (KdV equation) in a computational investigation using a finite difference approach. They also showed how this behavior explained the puzzling earlier work of Fermi, Pasta, Ulam, and Tsingou.

In 1967, Gardner, Greene, Kruskal and Miura discovered an inverse scattering transform enabling analytical solution of the KdV equation. The work of Peter Lax on Lax pairs and the Lax equation has since extended this to solution of many related soliton-generating systems.

Solitons are, by definition, unaltered in shape and speed by a collision with other solitons. So solitary waves on a water surface are near-solitons, but not exactly – after the interaction of two (colliding or overtaking) solitary waves, they have changed a bit in amplitude and an oscillatory residual is left behind.

Solitons are also studied in quantum mechanics, thanks to the fact that they could provide a new foundation of it through de Broglie's unfinished program, known as "Double solution theory" or "Nonlinear wave mechanics". This theory, developed by de Broglie in 1927 and revived in the 1950s, is the natural continuation of his ideas developed between 1923 and 1926, which extended the wave–particle duality introduced by Albert Einstein for the light quanta, to all the particles of matter. The observation of accelerating surface gravity water wave soliton using an external hydrodynamic linear potential was demonstrated in 2019. This experiment also demonstrated the ability to excite and measure the phases of ballistic solitons.

In fiber optics
Much experimentation has been done using solitons in fiber optics applications. Solitons in a fiber optic system are described by the Manakov equations. Solitons' inherent stability make long-distance transmission possible without the use of repeaters, and could potentially double transmission capacity as well.

In biology
Solitons may occur in proteins and DNA. Solitons are related to the low-frequency collective motion in proteins and DNA.

A recently developed model in neuroscience proposes that signals, in the form of density waves, are conducted within neurons in the form of solitons. Solitons can be described as almost lossless energy transfer in biomolecular chains or lattices as wave-like propagations of coupled conformational and electronic disturbances.

In material physics
Solitons can occur in materials, such as ferroelectrics, in the form of domain walls. Ferroelectric materials exhibit spontaneous polarization, or electric dipoles, which are coupled to configurations of the material structure. Domains of oppositely poled polarizations can be present within a single material as the structural configurations corresponding to opposing polarizations are equally favorable with no presence of external forces. The domain boundaries, or “walls”, that separate these local structural configurations are regions of lattice dislocations. The domain walls can propagate as the polarizations, and thus, the local structural configurations can switch within a domain with applied forces such as electric bias or mechanical stress. Consequently, the domain walls can be described as solitons, discrete regions of dislocations that are able to slip or propagate and maintain their shape in width and length.

In recent literature, ferroelectricity has been observed in twisted bilayers of van der Waal materials such as molybdenum disulfide and graphene. The moiré superlattice that arises from the relative twist angle between the van der Waal monolayers generates regions of different stacking orders of the atoms within the layers. These regions exhibit inversion symmetry breaking structural configurations that enable ferroelectricity at the interface of these monolayers. The domain walls that separate these regions are composed of partial dislocations where different types of stresses, and thus, strains are experienced by the lattice. It has been observed that soliton or domain wall propagation across a moderate length of the sample (order of nanometers to micrometers) can be initiated with applied stress from an AFM tip on a fixed region. The soliton propagation carries the mechanical perturbation with little loss in energy across the material, which enables domain switching in a domino-like fashion.

It has also been observed that the type of dislocations found at the walls can affect propagation parameters such as direction. For instance, STM measurements showed four types of strains of varying degrees of shear, compression, and tension at domain walls depending on the type of localized stacking order in twisted bilayer graphene. Different slip directions of the walls are achieved with different types of strains found at the domains, influencing the direction of the soliton network propagation.

Nonidealities such as disruptions to the soliton network and surface impurities can influence soliton propagation as well. Domain walls can meet at nodes and get effectively pinned, forming triangular domains, which have been readily observed in various ferroelectric twisted bilayer systems. In addition, closed loops of domain walls enclosing multiple polarization domains can inhibit soliton propagation and thus, switching of polarizations across it. Also, domain walls can propagate and meet at wrinkles and surface inhomogeneities within the van der Waal layers, which can act as obstacles obstructing the propagation.

In magnets
In magnets, there also exist different types of solitons and other nonlinear waves. These magnetic solitons are an exact solution of classical nonlinear differential equations — magnetic equations, e.g. the Landau–Lifshitz equation, continuum Heisenberg model, Ishimori equation, nonlinear Schrödinger equation and others.

In nuclear physics
Atomic nuclei may exhibit solitonic behavior. Here the whole nuclear wave function is predicted to exist as a soliton under certain conditions of temperature and energy. Such conditions are suggested to exist in the cores of some stars in which the nuclei would not react but pass through each other unchanged, retaining their soliton waves through a collision between nuclei.

The Skyrme Model is a model of nuclei in which each nucleus is considered to be a topologically stable soliton solution of a field theory with conserved baryon number.

Bions
The bound state of two solitons is known as a bion,  or in systems where the bound state periodically oscillates, a breather. The interference-type forces between solitons could be used in making bions. However, these forces are very sensitive to their relative phases. Alternatively, the bound state of solitons could be formed by dressing atoms with highly excited Rydberg levels. The resulting self-generated potential profile features an inner attractive soft-core supporting the 3D self-trapped soliton, an intermediate repulsive shell (barrier) preventing solitons’ fusion, and an outer attractive layer (well) used for completing the bound state resulting in giant stable soliton molecules. In this scheme, the distance and size of the individual solitons in the molecule can be controlled dynamically with the laser adjustment.

In field theory bion usually refers to the solution of the Born–Infeld model. The name appears to have been coined by G. W. Gibbons in order to distinguish this solution from the conventional soliton, understood as a regular, finite-energy (and usually stable) solution of a differential equation describing some physical system. The word regular means a smooth solution carrying no sources at all. However, the solution of the Born–Infeld model still carries a source in the form of a Dirac-delta function at the origin. As a consequence it displays a singularity in this point (although the electric field is everywhere regular). In some physical contexts (for instance string theory) this feature can be important, which motivated the introduction of a special name for this class of solitons.

On the other hand, when gravity is added (i.e. when considering the coupling of the Born–Infeld model to general relativity) the corresponding solution is called EBIon, where "E" stands for Einstein.

Alcubierre drive
Erik Lentz, a physicist at the University of Göttingen, has theorized that solitons could allow for the generation of Alcubierre warp bubbles in spacetime without the need for exotic matter, i.e., matter with negative mass.

title: Soliton


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Severn bore

The Severn bore is a tidal bore seen on the tidal reaches of the River Severn in south western England. It is formed when the rising tide moves into the funnel-shaped Bristol Channel and Severn Estuary and the surging water forces its way upstream in a series of waves, as far as Gloucester and beyond. The bore behaves differently in different stretches of the river; in the lower, wider parts it is more noticeable in the deep channels as a slight roller, while the water creeps across the sand and mudflats. In the narrower, upper reaches, the river occupies the whole area between its banks and the bore advances in a series of waves that move upstream. Near Gloucester, the advancing water overcomes two weirs, and sometimes one in Tewkesbury, before finally petering out.

Bores are present on about 130 days in the year, concentrated on the days immediately following the new and full moon. The size and precise timing of the bore depend on such things as the time of high tide, the barometric pressure, the wind speed and direction, the amount of water coming down the river and how well scoured the main drainage channels are. There are a number of viewpoints from which the bore can be seen, or viewers can walk along the river bank or floodbanks. Historically, the bore has been of importance to shipping visiting the docks at Gloucester, but this was alleviated by the construction of an alternative route, the Gloucester and Sharpness Canal, which opened in 1827. Nowadays the bore is of interest to surfers and canoeists who attempt to ride the waves.

Formation
The Severn Estuary, which empties into the Bristol Channel, has one of the largest tidal ranges in the world – about 13 m. It is exceeded only by the Bay of Fundy, and possibly Ungava Bay, both in Canada.

The tidal wave starts far out in mid-ocean. It moves towards the continent of Europe at about 700 miles (1100 km) wide. When it reaches the continental shelf, its width decreases to about 200 miles (320 km) wide, and its amplitude increases. Approaching the Bristol Channel, a segment of the wave has to accommodate to the ever-decreasing width by raising its height. When it reaches the Severn proper, its width has decreased from a 100 mi or so to less than 5 mi, and its height is nearly 50 ft. As the bed of the estuary starts to rise and the sides continue to converge, the bore forms and begins to surge up the river in a tidal stream. The front edge of the wave is steep and the trailing edge flatter. The bore consists of three or four sizeable waves followed by a few of diminishing size. As with other waves, the wave tends to break in shallow places and near the bank, and flow smoothly in deep water. The wave travels upstream against the river current at a speed of 8 to 13 mph.

In the lower, broader part of the estuary near Avonmouth, the tidal surge advances as a slight roll in the deepwater channels and the water rapidly spreads across the sands and mudbanks. Often, the Severn Bore floods the lower village of Pill if flood defences are not closed. Past Sharpness, the bore begins to form and when it encounters the large left-handed bend at Hock Cliff, it crashes headlong into the rocks. Reforming, it runs up-river close to the Overton shore before crossing the estuary towards Box Cliff. As it rounds the Horseshoe Bend it keeps to the outside but it afterwards moves across to the eastern side of the river. Above Longney Sands, the river abruptly narrows to a hundred yards, the sands diminish and the channel occupies the whole of the river. Now the bore is recognisably the spectacular phenomenon that people expect rather than a swelling flood of water. From Minsterworth to Gloucester, the width of the river varies little and the bore continues unhindered, climbing the banks on the outer side of bends and breaking over shallow places. At Lower Parting, close to Gloucester, it splits in two to pass either side of Alney Island. Both branches encounter and overcome weirs and rejoin at Upper Parting, and the much diminished bore continues upstream. In particularly high tides the water may overtop the weir at Tewkesbury, and even the foot of the weir at Worcester may experience a rise in water level of a foot (30 cm) or so.

Timing
The largest bores occur around the times of the equinoxes but smaller ones can be seen throughout the year. There are about 260 bores in each year occurring twice a day on 130 days. Because the bores are associated with the phases of the moon, one occurs between 7 a.m. and noon on bore days, and the other between 7 p.m. and midnight GMT, with the largest bores occurring between 9 and 11 in both the morning and evening. Maximum bores occur between one and three days after new and full moons, and smaller ones on the days that precede and follow the maxima.

Timetables for the bore and predictions of bore heights are published each year; however, the heights and timings are subject to minor variations. The bore height is increased by a strong southwest or west wind, low barometric pressure, about 2 ft of fresh water below Gloucester and well-scoured channels in the estuary. The height is decreased by strong winds from the east or north, high barometric pressure and little fresh water below Gloucester or excessive fresh water. The bore is made earlier by strong southwest or west wind, low barometric pressure, between two and five feet of fresh water, and shorter and well-scoured channels in the estuary. Conversely, it is delayed by strong winds from the east or north, high barometric pressure, little fresh water and more meandering, poorly scoured channels. The wind direction out at sea is of more significance than the local air-flow.

Being the onset of the flood tide, the bore is accompanied by a rapid rise in water level which continues for about one and a half hours after the bore has passed. The Severn bore is not a self-reinforcing solitary wave or soliton but rather a shock wave which is formed because the wave is travelling faster than the wave speed in water above the bore (see tidal bore for more details). The passing of the bore causes a churning of the water, and the myriads of tiny bubbles popping contributes much of the roaring sound made by the bore. The largest recorded bore was on 15 October 1966, when it reached a height of 9.2 ft at Stonebench.

Viewpoints
There are a number of viewpoints from which the bore can be seen; viewers do not have to restrict themselves to these because most of the river banks and floodbanks are public footpaths. Crowds often assemble at popular viewing points and car parking may prove difficult. Related to the time of the high tide at Sharpness, the bore passes Newnham on Severn one hour before this, Framilode and Arlingham, twenty-five minutes before, Epney twenty minutes before, Minsterworth at the high tide, Stonebench, on the east bank, fifteen minutes after the high tide and Over Bridge thirty-five minutes afterwards.

One of the main viewpoints is at Minsterworth at the Severn Bore Inn on the A48. Another good place to see the spectacle is Over Bridge, but the view here is rather restricted by the adjacent railway bridge.

Transport and surfing
The River Severn is considered a navigable river and Gloucester used to be an important port, with shipping having to deal with the bore. Vessels can ride the tide up from Sharpness to Gloucester. The tide will outstrip the vessel but by timing the journey correctly, a barge can reach Gloucester at high water. Descending is more difficult, and barges often needed to start their descent with one tide, lay up before crossing Longney Sands, and finish the descent at the next tide. These inconveniences in accessing Gloucester were overcome when the Gloucester and Sharpness Canal was opened in 1827, bypassing the need for shipping to use the river to reach Gloucester.

River surfing enthusiasts attempt to surf along on the wave, which can be 7 ft high. The river was first surfed in 1955 by World War II veteran Jack Churchill, a Military Cross recipient renowned both for carrying a Scottish broadsword, and for being the only Allied soldier to kill an enemy with a longbow during the war. He became a surfing enthusiast in his later life and rode the bore on a board he designed himself.

In September 2005, several hundred surfers gathered in Newnham on Severn to celebrate 50 years since the first recorded attempt at surfing the Severn bore and to view the première of Longwave by Donny Wright, a historical film documenting the evolution of the sport since its inception in 1955. In March 2006, Steve King, a railway engineer from Gloucestershire, set a world record for the longest surfing ride on a river bore while riding the Severn bore; King surfed up the river for a distance of 7.6 mi, a Guinness World Record.

On days when a large bore is expected, hundreds of surfing enthusiasts may accumulate, waiting for the waves to arrive. Hazards in high water conditions can include floating trees, collapsing portions of river bank, overhanging branches and even dead farm animals. The Gloucester Harbour Trustees, as competent harbour authority for this part of the river, have issued safety guidance for surfers, canoeists, small craft and river bank users in relation to the bore.

Historical accounts
An eighteenth century account of the bore that has been attributed to Charles Blagden (died 1820), secretary of the Royal Society, is in the collection of the Gloucestershire Archives under reference Glos. R.O., D 1914. In the account, the author described it rising to eight feet and how he rode on horseback between bends in the river in order to "overtake" the bore as observers still attempt to do. The phenomenon is referred to as a "head of tide" with the author noting at the end that elsewhere such things are known as a "boar" or "bore".

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

title: Severn bore


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Talk:Closure (topology)

Clarity of Explanation
Keeping in mind that every mathematical article requires some background necessary to begin considering the relevant ideas - this article (and a great many others) could benefit considerably by further explanation and expansion of the concepts. This article, while clearly written by knowledgeable individuals, is too notation dense to be extremely useful - what I mean is that it lacks the critical element of sufficient, patient, explanations.

I may suggest that this article can be substantially improved by diagrammatic examples and other devices (together with discussion) to expand upon the terse, notation-dense list given here.

152.3.183.223 (talk) 17:02, 15 July 2010 (UTC)

Dense set
I phrased the bit about density as a fact relating it to closure (expressed with "iff") rather than as a definition in terms of closure (expressed with "if"), since there are alternative definitions of dense sets. (And someday I'll probably edit the article on dense sets to mention them.) -- Toby Bartels 2002/05/08

Closed set
A separate article is titled closed set. Should these two articles be merged? -- Michael Hardy, 2003 Aug 12

I don't think so; conceptually they are quite different, since one is a property of sets, while the other is an operation on them. To be sure, they are closely related and should be interlinked; but the concepts of open set, dense set, and the like are also closely related, yet separate. We can afford to have an article on each of these, eventually expanding them all like Open set is now. -- Toby Bartels 05:11, 25 Sep 2003 (UTC)

Alternative characterization
I have found this characterization of a closure useful. For any S in topological space X

1. Cl(S) is in topological space X

2. Cl(S) is closed

3. For any closed A in topological space X, A ⊇ Cl(S) iff A ⊇ S

The Interior can be defined similarly.

This seems to me a much less clumsy way of doing things than using the standard definition. Many results follow immediately by substituting various terms for A. Since CL(S) ⊇ CL(S) always holds, we also have CL(S) ⊇ S, CL(S) being closed by assumption. For closed S, we similarly have S ⊇ CL(S), hence S = CL(S). Jamie Oglethorpe 8 July 2004
 * Yes, this seems to be another way of saying that Cl(S) is the smallest closed set containing S.

Adherent point
Is an adherent point of a topological space the same thing as a closure point? Surely a neighbourhood gives you an open set, and vice versa? Xanthoxyl 14:11, 12 March 2007 (UTC)
 * Yes. Paul August ☎ 23:24, 9 July 2008 (UTC)

Point of Closure
Hi,

Regarding the present statement :

"For S a subset of a Euclidean space, x is a point of closure of S if every open ball centered at x contains a point of S (this point may be x itself)."

Would it be OK to clarify this in the following (or similar) way (OR would this be making the paragraph too long?):

"For S a subset of a Euclidean space, x is a point of closure of S if every open ball centered at x contains a point of S (this point may be x itself). Whether x is or is not a member of S depends on the space in which the closure is taken."

The motivation for this was the statement lower down that :

"The closure of a set also depends upon in which space we are taking the closure. For example, if X is the set of rational numbers, with the usual subspace topology induced by the Euclidean space R, and if S = {q in Q : q2 > 2}, then S is closed in Q, and the closure of S in Q is S; however, the closure of S in the Euclidean space R is the set of all real numbers greater than or equal to \sqrt2."

Please let me know your thoughts,

Thanks

Arjun r acharya (talk) 11:05, 22 January 2009 (UTC)

Closure vs Interior
It seems to me that the following sentence (copied from the article as at 2011-06-24) is worse than useless:

 * The notion of closure is in many ways dual to the notion of interior."

The sentence seems to refer to a simple case like an open disc in the Euclidean plane. But I think the statement is incorrect. The limit set of the open disc is a circle with the same center and radius. The closure of the open disc is the union of the open disc and the circle, namely the closed disc. The circle and the open disc are mutual complements with respect to the closure.But anyway, even if that were corrected, what does it mean in this context for something to be "dual to" something else -- or worse yet, "in many ways dual to" something else?

I could be wrong about this. That's why I'm stating my point here rather than just taking out the sentence I don't like.

Point of Closure
I have recently added a number of references for this article. I selected a fairly broad spectrum of general (point-set) topology texts to use. One thing that they have in common is that none of them use the term "point of closure". Older treatments use the term "adherent point", but more modern texts drop the concept entirely and only talk about limit points. I would like to find a reference that actually uses the term "point of closure". Bill Cherowitzo (talk) 18:53, 23 February 2014 (UTC)

“Locally closed subset”
In the last paragraph of part “Facts about closure”, it is mentioned that a certain notion of a “locally closed subset” coincides with the one of a closed set. However, there is already a different notion of a locally closed subset, which is different from the one discussed here.

I think this expression should be replaced, because it is misleading (even though there are quotation marks). But I don’t know if there is a name for this property (which is equivalent to being closed, though) that could replace this awkward formulation. I’m thinking maybe we should just remove it. Any thought? 37.167.91.168 (talk) 18:18, 16 January 2023 (UTC)

title: Talk:Closure (topology)


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Shoot (botany)

In botany, a plant shoot consists of any plant stem together with its appendages like leaves, lateral buds, flowering stems, and flower buds. The new growth from seed germination that grows upward is a shoot where leaves will develop. In the spring, perennial plant shoots are the new growth that grows from the ground in herbaceous plants or the new stem or flower growth that grows on woody plants.

In everyday speech, shoots are often synonymous with stems. Stems, which are an integral component of shoots, provide an axis for buds, fruits, and leaves.

Young shoots are often eaten by animals because the fibers in the new growth have not yet completed secondary cell wall development, making the young shoots softer and easier to chew and digest. As shoots grow and age, the cells develop secondary cell walls that have a hard and tough structure. Some plants (e.g. bracken) produce toxins that make their shoots inedible or less palatable.

Shoot types of woody plants
Many woody plants have distinct short shoots and long shoots. In some angiosperms, the short shoots, also called spur shoots or fruit spurs, produce the majority of flowers and fruit. A similar pattern occurs in some conifers and in Ginkgo, although the "short shoots" of some genera such as Picea are so small that they can be mistaken for part of the leaf that they have produced.

A related phenomenon is seasonal heterophylly, which involves visibly different leaves from spring growth and later lammas growth. Whereas spring growth mostly comes from buds formed the previous season, and often includes flowers, lammas growth often involves long shoots.

title: Shoot (botany)


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Aryan Nations

Aryan Nations is a North American antisemitic, neo-Nazi and white supremacist hate group that was originally based in Kootenai County, Idaho, about $2 3⁄4$ miles (4.4 km) north of the city of Hayden Lake. Richard Girnt Butler founded Aryan Nations in the 1970s.

In 2001, the Federal Bureau of Investigation (FBI) classified Aryan Nations as a "terrorist threat." In a review of terrorist organizations, the RAND Corporation called it the "first truly nationwide terrorist network" in the United States and Canada.

History
Aryan Nations beliefs are based on the teachings of Wesley A. Swift, a leading figure in the early Christian Identity movement. Swift was originally exposed to British Israelism while at the Angelus Temple through the teachings of visiting minister Gerald Burton Winrod. Swift was also exposed to Charles Parham's British Israel teachings at the Angelus Temple. Combining British Israelism, extreme antisemitism, and political militancy, Swift later founded his own church in California in the mid-1940s known as the Anglo-Saxon Christian Congregation. He hosted a daily radio broadcast in California during the 1950s and 1960s. In 1957, the name of his church was changed to the Church of Jesus Christ–Christian, a name which continues to be used by Aryan Nations churches.

William Potter Gale introduced Richard Girnt Butler to Swift in 1962. Swift quickly converted Butler, who was an admirer of Adolf Hitler and Wisconsin Senator Joseph McCarthy, to Christian Identity. When Swift died in 1971, Butler fought against Gale, James Warner, and Swift's widow for control of the Church of Jesus Christ–Christian. Butler eventually gained control of the organization and moved it from California to Idaho in 1973. After moving to Idaho, Butler founded Aryan Nations as a paramilitary wing of the church with an ideological mixture of Christian Identity and Nazism.

From 1974 until 2001, the Aryan Nations headquarters was located in a 20-acre (8.1 ha) compound 1.8 miles (3 km) north of Hayden, Idaho. Aryan Nations had a number of state chapters, but it was highly decentralized and the chapters' ties to the organization's headquarters were extremely loose. The group hosted an annual World Congress of Aryan Nations at Hayden Lake for Aryan Nations members and members of similar groups.

Until 1998, the leadership of Aryan Nations remained firmly in the hands of Richard Girnt Butler. By that time, he was over 80 years old and his health was poor. At the annual Aryan Nations World Congress in 2001, Neuman Britton was appointed to lead Aryan Nations as Butler's successor. Following Neuman's death in August 2001, Butler appointed Harold Ray Redfeairn of Ohio to lead Aryan Nations as his successor; he had been agitating for control of the organization since the mid-1990s. Redfeairn had brought in Dave Hall, an FBI informant who exposed the group's illegal activities. After this was discovered, Redfeairn was distrusted by some in the group. Redfeairn and August Kreis III, the propaganda minister for Aryan Nations, formed a splinter group, and Butler expelled them from Aryan Nations.

A few months later, Redfeairn returned to form an alliance with Butler. Butler's 2002 World Congress drew fewer than 100 people, and when he ran for mayor, he lost, garnering only 50 votes against more than 2,100 votes. Redfeairn died in October 2003, and Butler died of heart failure in September 2004. At the time of Butler's death, Aryan Nations had about 200 actively participating members.

Shooting, lawsuit and breakup
In September 2000, the Southern Poverty Law Center (SPLC) won a $6.3 million judgment against Aryan Nations from an Idaho jury, who awarded punitive and compensatory damages to plaintiffs Victoria Keenan and her son Jason. The two Native Americans had been beaten with rifles by Aryan Nations security guards in Coeur d'Alene, Idaho in July 1998. The woman and her son were driving near the Aryan Nations compound when their car backfired, which the guards claimed to misinterpret as gunfire. The guards fired at the car, striking it several times. The car crashed and one of the Nations guards held the Keenans at gunpoint, beating them. Two of the assailants, Aryan Nations security chief Edward Jessie Warfield and guard John Yeager, were prosecuted for the attack. Warfield pleaded guilty to aggravated assault and was sentenced to two to five years in prison. Yeager entered an Alford plea for assault and was sentenced to up 2.5 years in prison. A third attacker was never found.

The SPLC filed suit on behalf of the Keenans. A jury found that Butler and Aryan Nations were grossly negligent in selecting and supervising the guards, and awarded the Keenans $6.3 million. A local attorney from Keenan's legal team said that the large verdict was partly to compensate the Keenans, but largely to punish Butler and his followers, and serve to deter similar conduct in the future.

The $6.3 million verdict caused Butler to file for bankruptcy one month later. As part of the bankruptcy process, the group's property was put up for auction. SPLC loaned the Keenans $95,000 to bid on the 20-acre property. In February 2001, the group's Hayden Lake compound and intellectual property, including the names "Aryan Nations" and "Church of Jesus Christ Christian", were transferred to the Keenans. Idaho native and millionaire philanthropist Greg Carr purchased the property from the Keenans, donating it to the North Idaho College Foundation. It has been converted to a park dedicated to peace.

Local fire departments demolished some of the church's former buildings by burning them during training exercises. Edgar Steele, the attorney who had represented Butler, was later convicted of hiring a handyman to kill his own wife. In 2014, Steele died while serving a 50-year prison sentence.

Decline and legacy
The Aryan Nations were divided between three main factions. The largest group after Aryan Nations' bankruptcy was led by Charles John Juba, followed by August Kreis III until Kreis stepped down as leader and designated Drew Bostwick as his successor in 2012. In 2002, Juba's group was based on a 10 acre compound in the rural town of Ulysses in Potter County, north central Pennsylvania; it hosted the 2002 Aryan Nations World Congress. Juba resigned in March 2005, announcing that Kreis was the group's new leader.

Kreis established a new headquarters in Lexington, South Carolina, and he eventually moved it close to Union City, Tennessee. In 2005, Kreis received media attention because he attempted to form an Aryan Nations–al Qaeda alliance.

In 2005, the Holy Order of the Phineas Priesthood, previously in association with the faction which was led by Kreis, seceded and formed Aryan Nations Revival, based in New York City. The Holy Order was created in opposition to Kreis's acceptance of adherents of Wicca, Islam, and Odinism. It considered such groups to be a deviation from the core Christian Identity belief of Aryan Nations. This Revival rapidly became the largest faction.

In the Congressional Record, the leaders of Aryan Nations Revival were listed as domestic terrorists. The government concluded that the Holy Order of the Brotherhood of the Phineas Priesthood was the enforcement/terrorist wing of Aryan Nations. Aryan Nations Revival hosted a weekly radio broadcast which it titled The Aryan Nations Broadcast. Airing from 1979 to 2009, the radio program was authorized by Richard Butler. The program ended when host Hal Turner was arrested for threatening the lives of federal judges in Chicago. While incarcerated, Turner announced, through his attorney, that he was a federal informant, and that Aryan Nations was among those organizations which had been informed upon.

In 2009, Aryan Nations Revival, which was then based in Texas, merged with Pastor Jerald O'Brien's Aryan Nations, which was based in Coeur d'Alene, Idaho. Both parties ardently adhered to Christian Identity.

Symbols
The emblem (or shield) of Aryan Nations is designed to reflect aspects of British Israelism.

Associates
In 1983, Robert Jay Mathews, who had visited the Aryan Nations compound many times, formed The Order, along with Aryan Nations members Dan Bauer, Randy Duey, Denver Parmenter, and Bruce Pierce. The Order's mission was to overthrow the Zionist Occupational Government and establish the Northwest Territorial Imperative through an orchestrated plot to commit acts of domestic terrorism which would include murder, arson, armed robbery, theft, counterfeiting, and extortion between 1983 and 1984. Dennis McGiffen, who also had ties to Aryan Nations, formed a group called "The New Order", inspired by Mathews' group. The members were arrested before they could follow through with their violent plans.

Buford O. Furrow, Jr., who was convicted of the Los Angeles Jewish Community Center shooting and the murder of Filipino American postal worker Joseph Ileto, had previously worked as a security guard at the Aryan Nations compound for some time.

On April 4, 2004, intending to start a "Race War", Sean Michael Gillespie (a former member of Aryan Nations) threw a Molotov cocktail at B'nai Temple Israel in Oklahoma City, Oklahoma. There were no casualties, but the building sustained material damage. Gillespie was arrested in Little Rock, Arkansas, on April 16 of the same year, but it was not until August 2005 that he was sentenced to 39 years in prison for attacking the Jewish temple and trying to send a racist letter to the congregation. The defendant raised his hand in a Nazi salute with stiff arms as the judge left the courtroom.

title: Aryan Nations


text:
Quatorzain

A quatorzain (from Italian quattordici or French quatorze, fourteen) is a poem of fourteen lines. Historically the term has often been used interchangeably with the term "sonnet". Various writers have tried to draw distinctions between "true" sonnets and quatorzains. Nowadays the term is seldom used, and when it is, it usually is used to distinguish fourteen-line poems that do not follow the various rules that describe the sonnet.

title: Quatorzain


text:
Vacuous truth

In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement) that is true because the antecedent cannot be satisfied. It is sometimes said that a statement is vacuously true because it does not really say anything. For example, the statement "all cell phones in the room are turned off" will be true when no cell phones are present in the room. In this case, the statement "all cell phones in the room are turned on" would also be vacuously true, as would the conjunction of the two: "all cell phones in the room are turned on and turned off", which would otherwise be incoherent and false.

More formally, a relatively well-defined usage refers to a conditional statement (or a universal conditional statement) with a false antecedent. One example of such a statement is "if Tokyo is in Spain, then the Eiffel Tower is in Bolivia".

Such statements are considered vacuous truths because the fact that the antecedent is false prevents using the statement to infer anything about the truth value of the consequent. In essence, a conditional statement, that is based on the material conditional, is true when the antecedent ("Tokyo is in Spain" in the example) is false regardless of whether the conclusion or consequent ("the Eiffel Tower is in Bolivia" in the example) is true or false because the material conditional is defined in that way.

Examples common to everyday speech include conditional phrases used as idioms of improbability like "when hell freezes over ..." and "when pigs can fly ...", indicating that not before the given (impossible) condition is met will the speaker accept some respective (typically false or absurd) proposition.

In pure mathematics, vacuously true statements are not generally of interest by themselves, but they frequently arise as the base case of proofs by mathematical induction. This notion has relevance in pure mathematics, as well as in any other field that uses classical logic.

Outside of mathematics, statements in the form of a vacuous truth, while logically valid, can nevertheless be misleading. Such statements make reasonable assertions about qualified objects which do not actually exist. For example, a child might truthfully tell their parent "I ate every vegetable on my plate", when there were no vegetables on the child's plate to begin with. In this case, the parent can believe that the child has actually eaten some vegetables, even though that is not true.

Scope of the concept
A statement $$S$$ is "vacuously true" if it resembles a material conditional statement $$P \Rightarrow Q$$, where the antecedent $$P$$ is known to be false.

Vacuously true statements that can be reduced (with suitable transformations) to this basic form (material conditional) include the following universally quantified statements:
 * $$\forall x: P(x) \Rightarrow Q(x)$$, where it is the case that $$\forall x: \neg P(x)$$.
 * $$\forall x \in A: Q(x)$$, where the set $$A$$ is empty.
 * This logical form $$\forall x \in A: Q(x)$$ can be converted to the material conditional form in order to easily identify the antecedent. For the above example $$S$$ "all cell phones in the room are turned off", it can be formally written as $$\forall x \in A: Q(x)$$ where $$A$$ is the set of all cell phones in the room and $$Q(x)$$ is "$$x$$ is turned off". This can be written to a material conditional statement $$\forall x \in B: P(x) \Rightarrow Q(x)$$ where $$B$$ is the set of all things in the room (including cell phones if they exist in the room), the antecedent $$P(x)$$ is "$$x$$ is a cell phone", and the consequent $$Q(x)$$ is "$$x$$ is turned off".
 * $$\forall \xi: Q(\xi)$$, where the symbol $$\xi$$ is restricted to a type that has no representatives.

Vacuous truths most commonly appear in classical logic with two truth values. However, vacuous truths can also appear in, for example, intuitionistic logic, in the same situations as given above. Indeed, if $$P$$ is false, then $$P \Rightarrow Q$$ will yield a vacuous truth in any logic that uses the material conditional; if $$P$$ is a necessary falsehood, then it will also yield a vacuous truth under the strict conditional.

Other non-classical logics, such as relevance logic, may attempt to avoid vacuous truths by using alternative conditionals (such as the case of the counterfactual conditional).

In computer programming
Many programming environments have a mechanism for querying if every item in a collection of items satisfies some predicate. It is common for such a query to always evaluate as true for an empty collection. For example:

 * In JavaScript, the array method  executes a provided callback function once for each element present in the array, only stopping (if and when) it finds an element where the callback function returns false. Notably, calling the   method on an empty array will return true for any condition.
 * In Python, the  function returns   if all of the elements of the given iterable are  . The function also returns   when given an iterable of zero length.
 * In Rust, the  function accepts an iterator and a predicate and returns   only when the predicate returns   for all items produced by the iterator, or if the iterator produces no items.

Examples
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths:

 * "For any integer x, if x > 5 then x > 3." – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 then 2 > 3".
 * "All my children are goats" is a vacuous truth when spoken by someone without children. Similarly, "None of my children is a goat" would also be a vacuous truth when spoken by the same person.

title: Vacuous truth


text:
Moro Islamic Liberation Front

The Moro Islamic Liberation Front (MILF; Jabhat Taḥrīr Moro al-ʾIslāmiyyah) is an Islamist group based in Mindanao, Philippines, seeking an autonomous region of the Moro people from the central government. The group has a presence in the Bangsamoro region of Mindanao, the Sulu Archipelago, Palawan, Basilan, and other neighbouring islands. The armed wing of the group was the Bangsamoro Islamic Armed Forces (BIAF), although the name of its parent organization, the MILF, was often used to refer to the BIAF. In July, 2018, the Philippine government passed the Bangsamoro Organic Law, giving more autonomy to Muslims. In return, MILF announced that it would disarm its 30,000 fighters.

History
Following the Jabidah massacre in 1968, the Moro National Liberation Front (MNLF) was established clandestinely in 1969 by Moro students studying at the University of the Philippines, Egypt, and in the Middle East who sought to create an independent Muslim nation in southern Philippines. The MNLF gained foreign support from Muammar Gaddafi of Libya, which supplied arms and provided training for Moro youths. The MNLF took part in terrorist attacks and assassinations to achieve their goals. The government in Manila sent troops into the southern Philippines to control the insurgency. In 1976, Libyan leader Muammar Gaddafi brokered a negotiation between the Philippine government and MNLF Leader Nur Misuari which led to the signing of the MNLF-GRPH Tripoli Agreement of 1976 wherein the MNLF accepted the Philippine government's offer of semi-autonomy of the regions in dispute. There where some members based in the small Italian town of Portofino who helped to find the organizations footing during the early stages of their development.

The signing of this agreement brought about a serious rift in MNLF leadership, leading to the formation of a breakaway group in 1977 by Hashim Salamat and 57 MNLF officers. The group was initially known as "The New Leadership". Misuari expelled Salamat in December 1977, after which Salamat moved his new organization first to Cairo, Egypt, and then, in 1980, to Lahore, Pakistan, where it engaged in diplomatic activities. This organization was formally established in 1984 as the Moro Islamic Liberation Front (MILF). Muammar Gaddafi became a longstanding supporter of the MILF after its emergence.

In January 1987, the MNLF accepted the Philippine government's offer of semi-autonomy of the regions in dispute, subsequently leading to the establishment of the Autonomous Region in Muslim Mindanao on November 6, 1990. The MILF, however, refused to accept this offer and continued their insurgency operations. A general cessation of hostilities between the government in Manila and the MILF was signed in July 1997, but this agreement was abolished in 2000 by the Philippine Army under the administration of President Joseph Estrada. In response, the MILF declared a jihad against the government, its citizens and supporters. Under President Gloria Arroyo, the government entered into a cease-fire agreement with the MILF and resumed peace talks.

Despite peace negotiations and the cease-fire agreement, the MILF attacked government troops in Maguindanao, resulting in at least twenty-three deaths in January 2005. The combined armies of the MILF and Abu Sayyaf were involved in days of fighting, which necessitated government troops using heavy artillery to engage rebel forces.

The bombing incident in Davao Airport in 2003, which the Philippine government blamed on MILF members, raised speculation that the peace negotiations would be ineffectual in bringing peace to Mindanao if the MILF was unable to control its operatives. The MILF has denied ties with terrorist group Jemaah Islamiyah, although Jemaah Islamiyah is considered to have provided them with training facilities in areas they control. The MILF has also continued to deny connections with Al-Qaeda, though it has admitted to sending around 600 volunteers to Al-Qaeda training camps in Afghanistan and that Osama bin Laden sent money to the Philippines, though the group denies directly receiving any payment.

From June 28 to July 6, 2006, conflict between the MILF and armed civilian volunteers under Maguindanao provincial governor Andal Ampatuan who were supported by the Philippine Army had been reported. The fighting began after Ampatuan blamed the MILF for a June 23 bomb attack on his motorcade, which killed five in his entourage. The MILF denied responsibility, but Ampatuan sent police and civilian volunteers to arrest MILF members connected to the attack. Four thousand families were reported displaced by the fighting that followed, which was ended by a cease-fire agreement signed on July 10 and 11.

Talks between the MILF and the government collapsed in 2008 after a Supreme Court decision in Sema vs. COMELEC rejected a preliminary accord that would have expanded the Autonomous Region in Muslim Mindanao. In 2011, the MILF withdrew their demands for independence, instead saying that they would pursue substate status, likened to a U.S. state instead of independence from the Philippines.

Memorandum of Agreement on Ancestral Domain
On August 4, 2008, the Supreme Court of the Philippines issued a temporary restraining order, preventing the government and the MILF from officially signing the Memorandum of Agreement on Ancestral Domain (MOA-AD), which would conclude all dispute and begin formal talks that would lead to the drafting and eventual signing of a Final Comprehensive Compact between the two groups. The court accepted motions by the southern provincial governments that objected to the extended boundaries for the Autonomous Region in Muslim Mindanao envisioned in the peace deal. The MOA-AD would have allowed the Moro people to gain control of the region under the concept of human rights with the right to establish a police force and to control natural resources.

The MOA-AD was initialed by former governor and peace panel chair Rodolfo Garcia and Presidential Adviser on the Peace Process Hermogenes Esperon and MILF peace panel chair Mohagher Iqbal on July 27, 2008, in Malaysia. It was scheduled for formal signing on August 5, but the Supreme Court issued no negotiation preventing the executive department from signing the agreement. The MOA-AD was the last of several agenda items under the 2001 agreement of the GRP-MILF, after security and relief and rehabilitation, prior to the discussion on the political settlement.

The Young Moro Professionals Network (YMPN) appealed to the public not to be afraid of the MOA-AD and to "open your hearts to the Moro grievance". The YMPN said in a statement dated August 21, 2009: "In these times of hardship, we hold hands as one, with our Christian and Islamic neighbours, in the name of peace, acceptance and justice. We are committed to democratic and peaceful resolution of the conflict. Do not be afraid of the MOA-AD. To the national public, open your hearts to the Moro grievance."

Over the next month, several MILF commanders were tagged by government officials as having initiated an offensive campaign. The Armed Forces of the Philippines responded to the allegation by immediately deploying ten battalions composed of a total of 6,000 soldiers into Mindanao under the command of Lt. Gen. Cardozo Luna. The violence displaced over 600,000 people and left about 300 dead.

On October 14, 2008, the court conducted a series of divided votes declared "contrary to law and the Constitution" the MOA-AD of the Government of the Republic of the Philippines and Moro Islamic Liberation Front Tripoli Agreement of Peace on 2001. Conchita Carpio-Morales ruled: "In sum, the Presidential Adviser on the Peace Process committed grave abuse of discretion when he failed to carry out the pertinent consultation process. The furtive process by which the MOA-AD was designed and crafted runs contrary to and in excess of the legal authority and amounts to a whimsical, capricious, oppressive, arbitrary and despotic exercise thereof. It illustrates a gross evasion of positive duty and a virtual refusal to perform the duty enjoined."

Civil society organizations such as Consortium of Bangsamoro Civil Society submitted a motion for reconsideration. However, on November 21, 2008, the Supreme Court affirmed its October 14 ruling that declared unconstitutional the MOA-AD between the Philippine government and the MILF.

MILF soldiers offered to help free the Irish priest father Michael Sinott, who was kidnapped in the Philippines on October 14, 2009, and sought permission to deploy about 100 of its soldiers in the area where Sinnott is believed to be held. However, this was turned down by the Philippine government.

Modification of demands
On September 23, 2010, Mohagher Iqbal said that the MILF would pursue a substate, likened to a U.S. state, instead of independence from the Philippines. The Muslim substate would not exercise power over national defense, foreign affairs, currency and coinage, and postal services, which the central government would continue to exercise. Iqbal further added that the substate would not have its own armed forces but instead would have troops for internal security.

Peace talks
On October 7, 2012, President Benigno Aquino announced a peace deal with the MILF and that "This framework agreement paves the way for a final and enduring peace in Mindanao". MILF vice-chair Ghazali Jaafar said, "We are very happy. We thank the president for this." The deal was signed on October 15, 2012. Its aim is to pave the way to enduring peace between the two parties by officially envisaging an autonomous region in Mindanao. According to the framework, this semi-independent Muslim area would have a more just share of revenues from the extraction of its own plentiful resources, budgetary autonomy, its own police, and sharia law only for Muslims. In exchange for this, the MILF would be willing to stop armed movements against the government for autonomy and allow the national government to retain its control of national security and foreign policy. The autonomy agreement to be gradually implemented would also rename the region Bangsamoro, after the Moro people.

Chief peace negotiator Miriam Coronel-Ferrer said that the government was cautiously optimistic for a final agreement soon following six days of talks on July 13, 2013. She said: "This signing indicates that both sides are really committed to finish the peace negotiations. Nobody wants this not to reach its fruition." The agreement would see government allowances for the MILF to have a 75 percent share of earnings from natural resources and metallic minerals in a proposed autonomous region. For other energy resources, earnings would be split equally in accordance with Malaysia-brokered talks.

Peace agreement
On January 24, 2014, Philippine government chief negotiator Miriam Coronel Ferrer and MILF chief negotiator Mohagher Iqbal signed a peace agreement in Kuala Lumpur. The agreement would pave the way for the creation of the new Muslim autonomous entity called Bangsamoro under a law to be approved by the Philippine Congress. The government aimed to set up the region by 2016. The agreement called for Muslim self-rule in parts of the southern Philippines in exchange for a deactivation of rebel forces by the MILF. MILF forces would turn over their firearms to a third party selected by the MILF and the Philippine government. A regional police force would be established, and the Philippine military would reduce the presence of troops and help disband private armies in the area. President Rodrigo Duterte signed the law, a key step to ending a Muslim rebellion in the south of the mainly Catholic Philippines. In early January 2020, the Office of the Presidential Adviser on the Peace Process announced progress exceeding its target for the decommissioning of MILF fighters, noting that "8,879 out of the 12,000 MILF combatants were decommissioned from the last quarter of 2019". Some former rebel fighters have joined the police and military to protect certain areas of the Bangsamoro region until an elected government is established in 2022.

title: Moro Islamic Liberation Front


text:
Talk:Christadelphians

Comparisons to other groups
The theology comparisons are proselytizing and not informative. They should be deleted. (crazenate) — Preceding unsigned comment added by 70.28.9.135 (talk) 16:21, 31 July 2014 (UTC)

I agree with the above comment. The Comparisons section is essentially an apologetic work and contains numerous claims which are dubious or debatable, including: Clement of Rome's beliefs about the intermediate state, Jonathan ben Uzziel's beliefs about Satan, the Christology of the Nazarenes, etc. Tjfarrar1983 (talk) 09:26, 25 June 2015 (UTC)
 * I also agree. Anyone opposed to removing this section?Richardson mcphillips (talk) 01:49, 17 July 2018 (UTC)

Basing their beliefs solely on the Bible ... not
They are Millerites because they follow the Day-year principle. So the notion that they base their beliefs solely on the Bible is their own fiction. Rursus dixit. ( m bork3 !) 18:41, 9 July 2017 (UTC)

 * Of course. Nobody does straight Bible all by itself. What should we change in the article? Alephb (talk) 20:45, 9 July 2017 (UTC)

 * Nevermind. Found it! Alephb (talk) 20:48, 9 July 2017 (UTC)

An Apology to Anyone Watching This Article
After a fairly long editing spree, I just discovered the page WP:LINKROT and discovered that I may have removed some dead links from this page that I should not have removed. Any time I dedicate to Wikipedia will be focused on restoring any links I should not have removed from this article until I have restored them all. My apologies. I had it in my head that dead links could simply be removed, and it seems I was wrong. I'll work to make the problem right. After this I'll check John Thomas and see if I removed any links I shouldn't have. If you notice any other times I've violated WP:LINKROT, I'll work to fix those violations as well. In the future I intend to work through the processes recommended at WP:LINKROT first. Alephb (talk) 01:05, 10 July 2017 (UTC)
 * All right. I reverted my whole editing spree, the article is in the condition I found it in. Alephb (talk) 01:11, 10 July 2017 (UTC)

External links modified
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title: Talk:Christadelphians


text:
The Powerpuff Girls

The Powerpuff Girls is an American superhero animated television series created by animator Craig McCracken and produced by Hanna-Barbera (later Cartoon Network Studios) for Cartoon Network. The show centers on Blossom, Bubbles, and Buttercup, three kindergarten-aged girls with superpowers. They live in the fictional city of Townsville with their father and creator, a scientist named Professor Utonium, and are frequently called upon by the city's mayor to help fight nearby criminals and other enemies using their powers.

While attending his second year at CalArts in 1992, McCracken created a short film, Whoopass Stew!, about a trio of child superheroes known as the Whoopass Girls, which was only shown at festivals. Following the name change to The Powerpuff Girls, McCracken submitted his student film to Cartoon Network, who aired the series' refined pilot, "Meat Fuzzy Lumpkins", in its animation showcase program World Premiere Toons on February 20, 1995, along with its follow-up, "Crime 101", on January 28, 1996. Network executives gave McCracken the greenlight for a full series, which debuted as a Cartoon Cartoon on November 18, 1998.

The Powerpuff Girls aired on Cartoon Network for six seasons, three specials, and a feature film, with the final episode airing on March 25, 2005. A total of 78 episodes were produced, in addition to the two pilots, a Christmas special, the film, a tenth anniversary special, and a special episode in computer animation. Various spin-off media include an anime, three CD soundtracks, a home video collection, comic books, a series of video games, a 2016 reboot series, and an upcoming second reboot, as well as various licensed merchandise. The series has been nominated for six Emmy Awards, nine Annie Awards, and a Kids' Choice Award during its run.

Premise
The show revolves around the adventures of three kindergarten-aged girls with an array of various superpowers: Blossom (pink), Bubbles (blue), and Buttercup (green). The plot of an episode is usually some humorous variation of standard superhero and tokusatsu shows, with the girls using their powers to defend their town from villains and giant monsters. In addition, the girls have to deal with the normal issues that young children face, such as sibling rivalries, loose teeth, personal hygiene, going to school, bed wetting, or dependence on a security blanket. Episodes often contain hidden references to older pop culture (especially noticeable in the episode "Meet the Beat Alls", which is a homage to the Beatles). The cartoon always tries to keep different ideas within each episode with some small tributes and parodies thrown in.

The show is set mainly in the city of Townsville, USA. Townsville is depicted as a major American city, with a cityscape consisting of several major skyscrapers. In his review of The Powerpuff Girls Movie, movie critic Bob Longino of The Atlanta Journal-Constitution said, "the intricate drawings emanate 1950s futuristic pizzazz like a David Hockney scenescape," and that the show is "one of the few American creations that is both gleeful pop culture and exquisite high art."

Characters

As depicted in the opening sequence of each episode, the Powerpuff Girls Blossom, Bubbles, and Buttercup were created by Professor Utonium in an attempt to create the "perfect little girl" using a mixture of "sugar, spice, and everything nice". However, he accidentally spilled a mysterious substance called "Chemical X" into the mixture, creating three girls and granting them superpowers, including flight, superhuman strength, superhuman speed, superhuman senses, limited invulnerability, x-ray vision, red heat vision, energy projection, space survivability, and thermal resistance. In the original concept, the accidental substance was a can of "Whoopass", which was replaced by "Chemical X" in the television show.

The three girls all have abnormally large eyes inspired by Margaret Keane's art, and stubby arms and legs, and lack of noses, ears, fingers, flat feet, toes, and necks. McCracken preferred them to look more symbolic of actual children rather than going for a "realistic" look, meaning fewer body parts were needed. Blossom, Bubbles, and Buttercup normally wear dresses that match the colors of their eyes with black stripes, as well as white stockings and black Mary Janes. The closing theme to the cartoon offers a nutshell description of the three Powerpuff Girls' personalities: ''Blossom, commander and the leader. Bubbles, she is the joy and the laughter. Buttercup, she is the toughest fighter.'' They individually represent body, mind and spirit.

 * Blossom (voiced by Cathy Cavadini) is the self-appointed leader of the Powerpuff Girls. Her personality ingredient is "everything nice", her signature color is pink, and she has long red-orange hair with a red bow. She was named for having spoken freely and honestly to the Professor shortly after her creation as shown in The Powerpuff Girls Movie. She is often seen as the most level-headed, and composed member of the group and also strong and determined. Her unique abilities include ice breath, microscopic vision, lightning bolts, and advanced intelligence; she is also an exceptional leader, master strategist, and apt planner.
 * Bubbles (voiced by Tara Strong in the series, and by Kath Soucie in the What a Cartoon! episodes) is the "softest and sweetest" of the three. Her personality ingredient is "sugar", her signature color is blue, and she has blonde hair in pigtails. Bubbles is seen as kind and very sweet but she is also capable of extreme rage and can fight monsters just as well as her sisters can. Her best friend is a stuffed octopus doll she calls "Octi", and she also loves animals. She exhibits the ability to both understand multiple languages and communicate with various animals; her unique powers are projecting powerful sonic screams, and creating a shockwave of thunder with a single clap from her hands.
 * Buttercup (voiced by E. G. Daily) is described as a "tough hotheaded tomboy". Her personality ingredient is "spice", her signature color is green, and she has short black hair in a flip. She loves to get dirty, fights hard and plays rough; she does not plan and is all action. Her unique powers are curling her tongue, spinning into a tornado, and creating fireballs by rubbing her hands together until smoke comes out which forms a flaming ball that she throws at an opponent. McCracken originally wanted to name the character "Bud" until a friend suggested the name Buttercup.

Production

During Craig McCracken's first year in the character animation program of CalArts, he wanted to produce an animated short film based on a wrestler-type character he made named "El Fuego". In June 1991, he drew three girls with large eyes, visually inspired by the paintings of Margaret Keane, on a small sheet of orange construction paper as a birthday card design for his brother. Looking for some "diversity and balance" in the drawing, he had created a blonde, a redhead, and a brunette. He liked how "cute" they looked and turned them into superheroes, thus replacing the aforementioned wrestler. The following year, the girls starred on McCracken's animated short ''Whoopass Stew! The Whoopass Girls in: A Sticky Situation''. Initially, McCracken wanted to animate all four Whoopass Girls shorts, but only one was produced. McCracken's shorts were selected to be shown at Spike and Mike's Sick and Twisted Festival of Animation in 1994.

While he was working on 2 Stupid Dogs in 1992, McCracken's Whoopass Girls short was picked up for a series by Cartoon Network. The name Whoopass was dropped for inclusion as part of the What a Cartoon! animated shorts showcase. McCracken explained that Cartoon Network executives believed no one would make a children's show with the word "ass" in it, so the title changed to The Powerpuff Girls and the "can of whoopass" was renamed "Chemical X". McCracken's new short, titled "The Powerpuff Girls in: Meat Fuzzy Lumpkins", aired as part the network's World Premiere Toon-In on February 20, 1995. The short was not as popular as Dexter's Laboratory, a project McCracken and former classmate Genndy Tartakovsky (who also directed many episodes of The Powerpuff Girls) worked on together; being the most popular of the shorts, Dexter's Laboratory was the first to be greenlit by the network. Furthermore, McCracken's cartoon did not do well with a test audience composed by 11-year-old boys; "They were saying, 'This is stupid, little girls can't be heroes'", he recalled in 1999. They also found the girls' designs to be disturbing, which caused McCracken to panic and attempt to redesign them in a more realistic style. However, Cartoon Network executive Mike Lazzo convinced McCracken to stay true to his original vision, and allowed him to produce a second Powerpuff Girls short titled "Crime 101", which aired on What a Cartoon! in early 1996. Veteran ABC announcer Ernie Anderson, who narrated the pilot episodes and died of cancer in 1997, was replaced by Tom Kenny when it became a series.

Following the second short, Cartoon Network picked up The Powerpuff Girls for a regular animated series. McCracken said that the show did not go through a large development process, but he was advised to change the name of the three main characters to Pink, Blue and Green, since the network executives found it hard to differentiate them by Blossom, Bubbles and Buttercup. Instead, he put together a bible for the show, explaining the essential aspects of the characters. The Powerpuff Girls series debuted on November 18, 1998, and was the highest-rated premiere in Cartoon Network's history at the time. During its run, the series consistently scored the highest rating for an original series each week for the network across a wide range of demographics—from young children to adults. In October 2000, Cartoon Network credited the series for its Friday night prime time ratings win among cable networks. By the end of 2000, merchandising based on the series encompassed a whole variety of products, including T-shirts, toys, video games, lunchboxes, and dishware. Concerning the show's success, Craig McCracken has stated, "I thought it would get on Cartoon Network and college kids would watch it and there would be a few random T-shirts out there in the rave scene or in record shops. But I had no idea that it would take off to this extent." The cost per each episode was $500,000. A theatrical film based on the show, The Powerpuff Girls Movie, was also commissioned that year and was released July 3, 2002. The film received positive reviews from critics but was a commercial failure, earning $16 million worldwide against its $11 million budget. The production of the film also marked the series' switch from traditional cel animation to the digital ink and paint technique.

Following the series' fourth season, the closing of Hanna-Barbera Productions and the death of its executive William Hanna in 2001, along with the muted reception to The Powerpuff Girls Movie, McCracken left the series to focus on developing his next animated series for the network, Foster's Home for Imaginary Friends, leaving Chris Savino to take his place while production of The Powerpuff Girls was moved to Cartoon Network Studios. The show's last original run episode was on March 25, 2005; in all, six seasons were made. Cartoon Network had offered to give McCracken and Savino a seventh season of the series, but they believed six was enough, and that the series had run its course.

All of the original episodes were hand-drawn and produced at the Korean studio Rough Draft Studios, except the What a Cartoon! shorts, with the first one being animated at Animal House in Japan and the second being animated at Fil Cartoons in the Philippines. James L. Venable, Thomas Chase, & Steve Rucker composed the opening theme of the series, and Scottish band Bis performed the ending theme song, as played during the credits. The opening theme uses a sped-up drum break sample of "Funky Drummer" performed by Clyde Stubblefield.

Tenth anniversary special
In August 2008, McCracken revealed on his DeviantArt account, as had been announced in that year's Comic Con, that he was working with Cartoon Network on a new half-hour The Powerpuff Girls special to celebrate the series' tenth anniversary. Titled "The Powerpuff Girls Rule!!!", it aired on the Pan-Euro Cartoon Network on November 29, 2008, during the Powerpuff Girls Birthday Marathon, and in the United States on January 19, 2009, as part of its 10th anniversary marathon. Unlike previous episodes of the series, the special was animated using Adobe Flash at Cartoon Network Studios. It also provides a glimpse of Sara Bellum's face as an easter egg, which at the time could be captured with a TiVo digital video recorder. Originally an idea for season 4, the special was meant to be the final episode of the series, but Cartoon Network was against giving their series a definitive ending at the time.

2014 special

On January 28, 2013, a CGI special titled Powerpuff Girls: Dance Pantsed was announced to premiere that year, though it was later delayed to January 20, 2014. Former Beatle Ringo Starr promoted the special on Cartoon Network singing a new original song "I Wish I Was a Powerpuff Girl" with previews leading up to the airdate. Ringo also voiced a new character named Fibonacci Sequins in the episode. The special was directed by Dave Smith, who directed episodes for the series in the past, and featured the original cast members reprising their roles. This Powerpuff Girls special marked the first time that series creator Craig McCracken had no input. The episode's plot has Mojo Jojo kidnap Fibonacci along with an opera singer and a badger. The girls rescue all of them, and the Powerpuff Girls defeat Mojo yet again. Not deterred, he then goes on to invent an evil video game called "Dance Pants R-EVILution" (a parody of the video game Dance Dance Revolution) to take over Townsville. Common Sense Media gave the special 3/5 stars citing the "tasteful update of the original animation style" however recommends it for older kids around the age of 7. Geeked Out Nation gave the show a B rank and described it as "...a good special with the return of the characters that many of us grew up [with]", while they said that the special has few flaws. Den of Geek gave the special a 2.5 out 5 said "The Powerpuff reboot needs those paddles to jump-start it. I want more. But I want better."

Critical reception

In a 2000 Entertainment Weekly review, Marc Bernardin complimented the show on its "spot-on pop-culture acumen" and "unparalleled sense of fun", giving it a warm welcome from earlier "lame" superhero cartoons that he grew up with. Peter Marks of The New York Times noted the show's use of adult humor and pop culture references, declaring it "the sort of playful satire that can appeal as much to a viewer of 37 as 7." Joly Herman of Common Sense Media described the show as a "cute, highly stylized series [that] thrills the senses with its strange characters, funny situations, and lots of lowbrow humor". She went on to say, however, that the show does go from innocent to violent in no time and that there is not much protecting young viewers against the violent undertones. Robert Lloyd of the LA Times said that the series might be "transgressive" based on little violence, but "also cute." In another review, he had called it "perfectly drawn, perfectly written and perfectly voiced."

The show began airing at the height of the "Girl power" trend in entertainment media. The Powerpuff Girls were often compared to the likes of Sailor Moon, Lara Croft and Buffy the Vampire Slayer, who are also strong and heroic female leads. Craig McCracken argued that he did not create the show to fill a gap in the market encompassed by the "Girl Power" slogan, but that its true vehicle was "good, strong characters" that made for good storytelling. However, he did believe that it gained momentum from being considered a "girl power" cartoon, and that it became successful among boys and girls for the inclusion of action scenes. Terrence Briggs of Animation World Network noted that, "at the very least, Powerpuff Girls works as an interesting comic deviation from the more sexual presences" of other fictional heroines.

TV Guide chose The Powerpuff Girls as No. 13 in a list of the 50 Greatest cartoon characters of all time. IGN ranked the series 18th in its Top 25 Primetime Animated Series of All Time list in 2006. Delta Express promoted the series by having a Boeing 737-232 jet painted with a special livery featuring the characters Blossom, Bubbles, and Buttercup on its exterior. The plane's inaugural flight was held at Logan International Airport in Boston, Massachusetts, on July 17, 2000. In 2002 the aircraft was repainted with a different Powerpuff Girls theme to promote The Powerpuff Girls Movie. The Powerpuff Girls series has won two Primetime Emmys, two Annie Awards, and including those four wins, has been nominated a total of sixteen times for various awards.

Film
The Powerpuff Girls Movie was released in the United States on July 3, 2002, by Warner Bros. Pictures. The movie, a prequel to the series, tells the story of how the Powerpuff Girls were created, and how Mojo Jojo became a supervillain. The movie received a rating of 63% at review aggregator Rotten Tomatoes, as well as some criticism for the violence involved. In all, the movie grossed $16 million worldwide with an $11 million budget.

Anime adaptation
In April 2005, plans for a Japanese anime series based on the cartoon, ''Demashita! Powerpuff Girls Z'', were announced. The series premiered in Japan the following year with 52 half-hour episodes, airing each Saturday from July 1 to December 23, 2006, and from January 6 to June 30, 2007. Powerpuff Girls Z deviates from the original series in terms of genre and animation style. It features junior high school students Momoko Akatsutsumi (Hyper Blossom), Miyako Gotokuji (Rolling Bubbles), and Kaoru Matsubara (Powered Buttercup) as the three heroes. McCracken told NPR's Talk of the Nation that he had little involvement in this version: "I said, well, as long you keep that core foundation the same, feel free to reinterpret or re-imagine it in a way that you feel is going to better play in your marketplace [...] once we did the initial development on it, I kind of gave them my blessing and said, you guys can go off and make this show [...] I was really just there in the initial conception of it."

Cancelled live-action adaptation
On August 24, 2020, a live-action television series based on The Powerpuff Girls was announced to be in development at The CW. According to Variety, it would depict Blossom, Bubbles and Buttercup as "disillusioned twentysomethings" resentful at losing their childhood to fighting crime and faced with the choice of reuniting "when the world needs them more than ever." The project, produced by Warner Bros. Television Studios, was being written by Heather Regnier and Diablo Cody, who were also serving as executive producers with Greg Berlanti, Sarah Schechter and David Madden. Craig McCracken was not involved; however, he declared his liking of Berlanti's superhero shows and admitted he was "curious" to see what they would do with their adaptation. Genndy Tartakovsky, who directed and produced several episodes of the original show, also expressed a similar sentiment, suggesting that the idea was "strong" and could work if there's "good people attached to it".

A pilot was officially ordered on February 9, 2021, and Maggie Kiley was hired as the director. Variety later reported that Chloe Bennet, Dove Cameron and Yana Perrault were cast as Blossom, Bubbles, and Buttercup. On March 30, 2021, following the title change to Powerpuff, Donald Faison was cast in the role of Professor "Drake" Utonium. On April 1, Nicholas Podany was cast as Joseph "Jojo" Mondel Jr., the son of Mojo Jojo. On April 7, production on the pilot began. On April 9, Robyn Lively was cast as Sara Bellum and Tom Kenny was confirmed to be reprising his role as the Narrator from the original series. On May 24, The CW announced that the pilot would be reworked off-cycle, with the cast and crew remaining on board. The script was later leaked to overwhelmingly negative reviews on social media. Mark Pedowitz, the head of The CW, stated that the script would be largely rewritten. On August 11, Bennet dropped out of the project due to scheduling conflicts. In May 2022, it was said to be in "some stage" of redevelopment. However, on May 18, 2023, The CW announced that the series had been cancelled by its new majority owners, Nexstar Media Group, and that the rights had been returned to Warner Bros. On July 5, it was reported that the series was no longer in development at Warner Bros. Television.

Merchandise
In 2001, Warner Bros. Consumer Products deemed The Powerpuff Girls their flagship brand, given the success of the show's merchandise. The International Licensing Industry Merchandisers Association (LIMA) named it License of the Year at their 2001 awards ceremony. The array of products was so extensive in 2002 that, according to Janan Sheria of the Dayton Daily News, even people without cable television could recognize the Powerpuff Girls. The franchise made nearly $1 billion in retail sales by 2002, according to Cartoon Network.

Beginning in 1999, Trendmasters made Powerpuff Girls dolls, playsets, and action figures, aimed primarily at girls ages 6–11. Craig McCracken and Genndy Tartakovsky were initially involved in the conception of these toys. From August 21 to October 1, 2000, Subway promoted the series with four toys in their kids' meals. A set of six kids' meal toys was available as part of an April 2001 Dairy Queen promotion, which also included a sweepstakes offering the Powerpuff Girls VHS Boogie Frights. Jack in the Box released six Powerpuff Girls toys in July 2002 as a tie-in for The Powerpuff Girls Movie. On February 10, 2003, Burger King began a four-week promotion featuring The Powerpuff Girls and Dragon Ball Z toys as well as special codes to redeem online for Cartoon Network's Cartoon Orbit. In the United Kingdom the characters of Buttercup and Mojo Jojo were given away in Kellogg's cereal boxes as part of the Cartoon Network Wobble Heads in 2003.

From 2000 to 2006, DC published a series of seventy comics based on the television show. Golden Books also published a series of Powerpuff Girls-themed activity books and storybooks, including one written and illustrated by Craig McCracken, titled Big, Terrible Trouble?. Around 400,000 total units of these books had been sold by 2001. From 2013 to 2017, IDW Publishing published a range of comics based on the series. In 2014, that company published a variant cover which showed aged-up versions of Powerpuff Girls with breasts and dressed in latex. The cover was designed by an artist working for Cartoon Network who was "thinking of it more along the lines of 'female empowerment' than the kind of thing you guys are talking about". Cartoon Network said in a statement: "We recognise some fans' reaction to the cover and, as such, will no longer be releasing it at comic book shops."

On October 12, 2023, Dynamite announced a deal with Warner Bros. Discovery to create a new line of comics based on various properties, including The Powerpuff Girls. And it was released in July 17, 2024.

Music
Three CD soundtracks were officially released for the series. The first, titled Heroes & Villains, features original songs about the Powerpuff Girls characters by a number of artists, including the new wave group Devo, Bis, The Apples in Stereo and Frank Black. Mark Mothersbaugh, who originally sought out to be the series' composer, produced the album along with Bob Casale, his bandmate of Devo. The album did well, topping the Billboard's children's music chart for six weeks. Another album titled The City of Soundsville features electronica-style character themes and also did well with critics. The third album, titled Power Pop, features a more teen-oriented variety of pop songs. This third and final album was considered a "big disappointment" and was not received as well as the previous albums. The British girl group Sugababes also released a song called "Angels with Dirty Faces" to promote The Powerpuff Girls Movie. The song received generally positive reviews from critics and peaked at number seven on the UK Singles Chart. The music video hearkens to "Nano of the North", an episode from the fourth season of The Powerpuff Girls, in which each Sugababes member portrays a Powerpuff Girl.

Parodies
A crossover parody of The Powerpuff Girls and 2 Broke Girls was done in the second season of Cartoon Network's TV series MAD, known as "2 Broke Powerpuff Girls". The episode, which aired on January 30, 2012, is of Bubbles and Buttercup, who are broke and work for "Him" in a diner after the show got placed on permanent hiatus. Tara Strong (Bubbles) and Tom Kane ("Him") reprised their roles here. The MAD episode with the parody ranked #26/30 for the week with 1.903 million viewers.

Video games
Several video games were made for this show all being action in genre. The Powerpuff Girls: Bad Mojo Jojo, released on November 14, 2000, follows Blossom as she tries to beat Mojo Jojo. The game was called "simple and boring" by GameSpot and was a failure critically. The Powerpuff Girls: Paint the Townsville Green, another game released in November 2000, follows Buttercup as she fights crime. The Powerpuff Girls: Battle HIM follows Bubbles in her fight against HIM and was released in February 2001. The Powerpuff Girls: Chemical X-traction was released in October 2001, where the girls battle enemies in a variety of settings in order to reclaim Chemical X and track down Mojo Jojo, who fed the material to all the villains in Townsville. IGN gave the game a positive review while giving the PSone version a 2.0/10 bad review. The Powerpuff Girls: Relish Rampage was released in November 2002. All three girls are playable in a 3D world, and the game received mixed reviews. The Powerpuff Girls: Mojo Jojo A-Go-Go released in 2001 centers around the name of the Powerpuff Girls' mission to stop Mojo Jojo and his minions. The game received mixed reviews. The Powerpuff Girls: HIM and Seek was released in 2002 where the girls battle their variety of enemies through Townsville while on a scavenger hunt. The game received mostly positive reviews. PC games were also made for the series. These include: The Powerpuff Girls: Mojo Jojo Clone Zone, The Powerpuff Girls: Princess Snorebucks, The Powerpuff Girls: Mojo Jojo's Pet Project, and The Powerpuff Girls: Gamesville.

title: The Powerpuff Girls


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Paula Danziger

Paula Danziger (August 18, 1944 – July 8, 2004) was an American children's author. She wrote more than 30 books, including her 1974 debut The Cat Ate My Gymsuit, for children's and young adult audiences. At the time of her death, all her books were still in print; they had been published in 53 countries and translated into 14 languages.

Birth and family
Paula Danziger was born August 18, 1944, to Samuel and Carolyn Danziger. A younger brother, Barry, was born in 1947.

Education and early career
The Danziger family lived in Nutley, New Jersey, and Hollidaysburg, Pennsylvania, before settling in Metuchen, New Jersey, when Paula was in sixth grade. In an interview with BookPage, she said: "At age 12, I was put on tranquilizers when I should have gotten help. There was nothing major and awful. I just didn't feel [my family] was supportive and emotionally generous. My father was a very unhappy person, very sarcastic, and my mother [was] very nervous and worried about what people thought. They weren't monsters, but it wasn't a good childhood." She graduated from Metuchen High School.

She was encouraged to study nursing in college but instead studied to become a teacher at Montclair State University, where she was mentored by poet John Ciardi. After earning a bachelor's degree in education, Danziger taught junior high school English while pursuing a master's degree. After being injured in an automobile accident, she had trouble writing, as she was only able to write backwards. She was able to regain the ability to write normally, but she remained able to write backwards for the rest of her life. This sequence of events prompted her to do what she really want to do in life; she began writing.

Following the success of The Cat Ate My Gymsuit, Danziger left teaching to write full-time in 1978. She maintained homes in New York City and in Bearsville, New York. For several years, she had a flat in London, where she was known for presenting a regular item about children's literature on the BBC's Saturday-morning show Live & Kicking in the 1980s and 1990s.

Death
On June 9, 2004, she experienced chest pain while her niece, Carrie Danziger, was visiting. After trying to hide her discomfort and phoning a neighbor about her concern, she ultimately went to a hospital, where she was diagnosed as having suffered a heart attack. She remained in the hospital and died from complications of the heart attack at St. Luke's Hospital in Manhattan on July 8, 2004.

Following a memorial service at Riverside Memorial Chapel in New York City, Paula was buried in the Woodstock Artists Cemetery in Woodstock, New York. She was survived by her brother Barry, her niece Carrie, and three nephews.

Writing career
Danziger's debut novel was The Cat Ate My Gymsuit, whose characters were largely based on her childhood experiences. She continued writing books for teens through the 1980s, expanding to books for younger readers with the Amber Brown series, whose protagonist is based on Danziger's niece Carrie. She frequently gave lectures and speeches, wearing elaborate costumes and calling herself a children's Dame Edna Everage. She is quoted as saying that her alternative career choice would have been to be a comedian.

She collaborated with Ann M. Martin twice, with P.S. Longer Letter Later (1998) and Snail Mail No More (2000). The two would send correspondence to each other as if they were the main characters.

Paula Danziger and her fellow author Bruce Coville read their work to each other over the phone beginning in 1992, continuing for over a decade as a two-person writers' group and later including author Elizabeth Levy. Following Danziger's passing, Coville and Levy continued her Amber Brown series, beginning with Amber Brown is Tickled Pink (2012), which told the story of the remarriage of the title character's mother.

Awards
Paula Danziger's works were nominated for and won many US state-level children's book awards, including the Massachusetts Children's Book Award for The Cat Ate My Gymsuit in 1979 and the California Young Reader Medal for There's a Bat in Bunk Five in 1984. Four of her works were named IRA-CBC Children's Choices: The Pistachio Prescription in 1979, The Cat Ate My Gymsuit and Can You Sue Your Parents for Malpractice? in 1980, and There's a Bat in Bunk Five in 1981.

The Society of Children's Book Writers and Illustrators awards the Amber Brown Grant, which provides an all-expenses-paid, full-day visit by a well-respected children's author or illustrator, a stipend to assist in creating the event, and $250 worth of books by the visiting author, to one or two schools annually in her honor.

Amber Brown books

 * Amber Brown is Not a Crayon (1994)
 * You Can't Eat Your Chicken Pox, Amber Brown (1995)
 * Amber Brown Goes Fourth (1995)
 * Amber Brown Wants Extra Credit (1996)
 * Forever Amber Brown (1996)
 * Amber Brown Sees Red (1997)
 * Amber Brown is Feeling Blue (1998)
 * I, Amber Brown (1999)
 * Amber Brown is Green with Envy (2003)
 * Amber Brown is Tickled Pink (2012; in the style of, inspired by, dedicated to)

A is for Amber Brown series

 * What a Trip, Amber Brown (2001)
 * It's Justin Time, Amber Brown (2001)
 * Get Ready for Second Grade, Amber Brown (2002)
 * Orange You Glad It's Halloween, Amber Brown? (2002)
 * It's a Fair Day, Amber Brown (2003)

Others

 * Barfburger Baby, I Was Here First (2004)

Matthew Martin books

 * Everyone Else's Parents Said Yes (1989)
 * Make Like a Tree and Leave (1990)
 * Earth to Matthew (1991)
 * Not for a Billion Gazillion Dollars (1992)

Tara*Starr and Elizabeth books

 * P.S. Longer Letter Later (with Ann M. Martin) (1998)
 * Snail Mail No More (with Ann M. Martin) (2000)

Rosie and Phoebe books

 * The Divorce Express (1982)
 * It's an Aardvark-Eat-Turtle World (1985)

Marcy Lewis books

 * The Cat Ate My Gymsuit (1974)
 * There's a Bat in Bunk Five (1980)

Kendra Kaye books

 * Remember Me to Harold Square (1987)
 * Thames Doesn't Rhyme With James (1994)

Others

 * The Pistachio Prescription (1978)
 * Can You Sue Your Parents for Malpractice? (1979)
 * This Place Has No Atmosphere (1986)
 * United Tates of America (2002)

title: Paula Danziger