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Drum (container)

A drum (also called a barrel) is a cylindrical shipping container used for shipping bulk cargo. Drums can be made of steel, dense paperboard (commonly called a fiber drum), or plastic, and are generally used for the transportation and storage of liquids and powders. Drums are often stackable, and have dimensions designed for efficient warehouse and logistics use. This type of packaging is frequently certified for transporting dangerous goods. Proper shipment requires the drum to comply with all applicable regulations.

Steel drums

Steel drums are ubiquitous industrial shipping containers. They are manufactured from sheets of cold rolled steel formed into a tube and welded along the side seam. Stainless steel, nickel, and special alloys are occasionally used. The bottom head is permanently attached by the manufacturer. Two primary options are available for the top head:
 * Open head drum, removable head drum:  Top head is attached after filling with a closing ring and bolted lock.  Liquids, granular solids and waste are commonly shipped in these.
 * Tight head drum, closed head drum, non-removable head drum: The top head is permanently attached by the manufacturer. It is usually made with one or two threaded access fittings, closed by threaded bungs after filling. Liquids are suited to these drums.

History
Henry Wehrhahn, employee of Nellie Bly's Iron Clad Manufacturing Company of New York, received two patents in December 1905 that would lead to the modern 55-gallon steel drum Use of 200-litre drums became widespread in World War II, the first war in which trucks, cold rolled steel, stamp or pattern forging machinery and welding were widely available. They were first utilized by the Axis powers (Germany and Italy), but were quickly adopted by Allies. The drums helped win the Guadalcanal Campaign in the first U.S. offensive in the South Pacific Theater. The U.S. Navy could not maintain command of the sea long enough to offload aviation gasoline for aircraft ashore, so the drums were often transported to the island on fast ships, such as destroyers, and shoved over the sides (or, time permitting, lowered in cargo nets). Because gasoline's density is much less than that of water, the drums floated. Navy Seabees in small craft corralled the drums.

Constructions
A wide variety of constructions and sizes are available. When the intended use is for shipment of dangerous goods (hazardous materials), strict regulatory requirements are applicable. Coordinated by the UN, countries and regional authorities require drum construction and the demonstrated performance of severe testing. The Industrial Steel Drum Institute has also provided guidance for conducting the tests. Drums have embossed symbols to identify certification for shipment of certain types of products.

Many drums nominally measure just under 880 mm tall with a diameter just under 610 mm, and have a common nominal volume of 208 L whereas the barrel volume of crude oil is 42 usgal. In the United States, 25 USgal drums are also in common use and have the same height. This allows easy stacking of mixed pallets. Barrels can be constructed of plastic, laminated paperboard or steel.

Drums have top and (usually) bottom chimes or rims: sometimes called chines. Most steel drums have reinforcing rolling hoops or rings of thickened metal or plastic. This sufficiently strengthens them so that they can readily be turned on their sides and rolled when filled with heavy materials, like liquids. Over short to medium distances, drums can be tipped and rolled on the bottom rim while being held at an angle, balanced, and rotated with a two-handed top grip that also supplies the torque (rotational or rolling force).

The open-top sub-type is sealed by a mechanical ring clamp (concave inwards) that exerts sufficient pressure to hold many non-volatile liquids and make an airtight seal against a gasket, as it exerts force inward and downward when tightened by a normal three-quarter inch wrench or ratchet wrench. Tops exist with bung holes as above, and these hybrid drums with lid can be used to ship many non-volatile liquids as well as industrial powders. Many drums are used to ship and store powdered products as well as liquids, such as plastic beads for injection moulding, extrusion, and purified industrial grade powders like cleansers (e.g., fertilizers, and powdered aluminum). If used to transport dangerous goods across international boundaries, they may need to have UN certification. In general, drum usage is limited to wholesale distribution of bulk products, which are then further processed or sub-divided in a factory.

These metal drums have two openings with flanges, often 2 inch NPS and 0.75 inch NPS in diameter. Once the drums are filled, the plugs (bungs) are screwed in the flanges using pneumatic or hand-operated bung tightener (plug wrench). To secure the contents of the drums against theft and adulteration during shipment, cap-seals made of metal and other types like metal-plastic laminates are used. These cap-seals sit on top of the flanges and are crimped, using a drum cap-seal crimping tool, also called a drum cap sealer. Once cap-seals are crimped, the plugs can be unscrewed only by breaking these cap-seals. Pneumatic and hand-operated cap-seal crimping tools are available. Pneumatic ones are used in production lines for high production.

International standard size

A 200-litre drum (known as a 55-gallon drum in the United States and a 44-gallon drum in the United Kingdom and the rest of the world) is a cylindrical container with a nominal capacity of 200 litres (55 US or 44 imp gal). The exact capacity varies by manufacturer, purpose, or other factors. Standard drums have inside dimensions of 22.5 in diameter and 33.5 in height. These dimensions yield a volume of about 218.7 L, but they are commonly filled to about 200 litres. The outside dimensions of a 200-litre drum are typically 23 in diameter at the top or bottom rim, 23.5 in diameter at the chines (ridges around drum), and 34.5 in height. Exact dimensions are specified in ANSI MH2.

The drums are typically made of steel with a ribbed outer wall to improve rigidity and for rolling. The lids can be welded or secured with a head gasket and bolt ring. They are commonly used for transporting oils, fuels, chemicals, and dry goods.

Drums are frequently transported on pallets for ease of handling by a fork truck and for shipping. The drum's size, shape, and weight distribution lends itself to being moved about readily on the loading dock or factory floor with a two-wheeled hand truck. They can be turned on side and rolled. They can also be moved by hand short distances on firm surfaces by tilting and then rolling along the base, or by using a drum handler, which is designed especially for that purpose.

Closed-head steel barrels and drums used for shipment of chemicals and petroleum products have a standardised bunghole arrangement, with one 2 in (DN50) NPT and one 3/4 in (DN20) NPT threaded bunghole on opposite sides of the top head. Drums can also be made of durable plastic or paperboard and this arrangement is echoed in many plastic drums. Various components can be mounted to the drum, such as drum pumps and bung mixers.

In the past, hazardous waste was often placed in drums of this size and stored in open fields or buried. Over time, some drums would corrode and leak. As a result, these drums have become iconic of pollution problems, even though they have numerous uses and are ubiquitous in commerce. Tests have shown that a leaking 55-gallon drum can disperse its contents over a 1,200 square-foot area of level surface. Drums are often cleaned or re-conditioned and then used for storing or shipping various liquids or materials.

Although crude oil is sometimes shipped in 55-US-gallon drums, the measurement standard of oil in barrels is based on the whiskey containers of the 1870s that measured 42 usgal. The measure of 42 US or wine gallons corresponds to a wine tierce (third-pipe). A wine barrel, or $1/8$ tun, measures 31.5 usgal.

Applicable standards include:
 * ISO 15750-1:2002. Packaging — Steel drums — Part 1: Removable head (open head) drums with a minimum total capacity of 208 L, 210 L, and 216.5 L
 * ISO 15750-2:2002. Packaging — Steel drums — Part 2: Non-removable head (tight head) drums with a minimum total capacity of 212 L, 216.5 L, and 230 L
 * ISO 15750-3:2022. Packaging — Steel drums — Part 3: Inserted flange-type closure systems

Reconditioning
Steel drums are commonly reconditioned for further use. Life cycle studies of reconditioning and reuse have been quite favorable. Clean drums go to a qualified reconditioner: hazardous residue can be a concern to regulators. Reconditioning usually consists of inspection, removal of labels, cleaning (mechanical, heat, or caustic cleaner), straightening of dents and chimes, replace gaskets, painting, testing, marking and labeling. Steel drums can often go through many use - reconditioning - reuse cycles before they are recycled or landfilled.

Fibre drums
Fibre drums (occasionally: fiber drums) are shipping containers with paperboard : laminated paperboard; plastics, foils, and other protective layers. The heads can be of fibreboard, metal, plywood, plastic or other suitable material. Drums typically have a circular cross section but square drums are also available: these can be packed closer during shipment and storage.

Fibre drums are available in a variety of constructions and sizes. They are used for shipping various granular materials, coiled wire and cable, long Fluorescent light bulbs, and (when certified) for dangerous goods. Compatibility with the contents is important; drum liners are commonly used.

Steel, fibre, and plastic covers are available with steel lever lock ring closures.

Plastic Drums
Plastic drums are typically made of blow molded high density polyethylene. They are available in a variety of sizes and constructions designed for specific purposes and markets. Plastic drums are used for liquids, granular solids, and inner packages. When designed, tested, and labeled, plastic drums can be used with dangerous goods or hazardous materials. The plastic drum, inner coating, or drum liner should be compatible with the intended contents. Foods and pharmaceuticals can be particularly sensitive. Some liquid chemicals can permeate through plastics or can cause embrittlement.

The compression stability of plastic drums can be sensitive to heat. The Plastic Drum Institute does not recommend stacking when temperatures are above about 32 C. Some methods of reinforcing the sidewalls are available.

Plastic drums are used for more than shipping containers. They can be used for water collection and storage. Also, plastic drums are used along highways to mark construction zones.

Applicable standards include:
 * ISO 20848-2:2006. Packaging — Plastics drums — Part 1. Removable head (open head) drums with a nominal capacity of 113,6 l to 220 l
 * ISO 20848-2:2006. Packaging — Plastics drums — Part 2: Non-removable head (tight head) drums with a nominal capacity of 208,2 l and 220 l
 * ISO 20848-3:2018. Packaging — Plastics drums — Part 3: Plug bung closure systems for plastics drums with a nominal capacity of 113,6 l to 220 l

title: Drum (container)


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Talk:Francois Gautier

Sorry. There is no license to reproduce what I had done. I will try to create a stub in the temporary location. Kartheeque 05:55, 28 May 2004 (UTC)

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

title: Talk:Francois Gautier


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Talk:Lysias

Comments
Why are there so many random-letter strings littering this article? Can someone replace them with the correct Greek or whatever should be there?

e.g. "iirirthr". These are apparently mistransliterations of Greek. The original article would be needed. --Erauch 23:50, 20 Nov 2004 (UTC)

 * I think they're not transliterations, but rather something meant to be displayed in an old, badly coded Greek font, a relic from before Unicode. It is certainly difficult to figure out the coding without having the font. Is there anyone who has experience with these old fonts? (I have used one, but not this one, I think; I'll check anyway). – Krun 23:37, 11 November 2005 (UTC)

---I don't agree with a lot of the "dates" by Lysias' speeches, most shouldn't be there at all or at least should have a more vague set of dates. Can someone do this because I'm waaay too busy... Sorry... -ALEXXXTH 11:27:31GMT 3rd May 2007

This article makes a major factual error in claiming that Lysias was in any way involved in the events detailed in "Against Simon". As the article correctly states, Lysias was a logographer, a writer of speeches for others, and further, Lysias couldn't be the speaker, because he was not an Athenian citizen (the speaker states that he was involved in an antidosis, a process only a citizen could have had a part in). This must be remedied. —Preceding unsigned comment added by 141.211.120.160 (talk) 03:23, 14 July 2008 (UTC)

 * A lot of the stuff about the speeches looks like its from Jebb, which is 135 years old. Not that being old, in this context, is necessarily a problem, but more recent scholarship has probably corrected some of these problems. The stuff in the table like "forensic, in public causes," is verbatim from Jebb. 65.25.46.236 (talk) 23:33, 22 December 2008 (UTC)

I've put all the speech information from the "Works" section into a table. I believe it's much more readable, but I've done nothing to check the veracity of the information. Please correct date and other kinds of errors as you see them. —Preceding unsigned comment added by Jlg4104 (talk • contribs) 17:33, 21 December 2008 (UTC)

 * I should add that it really needs a better "notes" system than the cumbersome "A" and "B" thing I've got. Jlg4104 (talk) 21:20, 21 December 2008 (UTC)

title: Talk:Lysias


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East Mountain

East Mountain may refer to:

Elevations

 * East Mountain (Massachusetts), in Hampden County
 * East Mountain, a summit of the Brodie Mountain ridgeline, in Berkshire County, Massachusetts
 * East Mountains (Bernalillo County, New Mexico), in Bernalillo County, New Mexico
 * East Mountain (Ulster County, New York)
 * East Mountain (Utah), one of Utah's mountains
 * East Mountain (Essex County, Vermont)

Settlements

 * East Mountain, Texas, a city in Upshur County
 * East Mountain (Waterbury), a section of Waterbury, Connecticut

title: East Mountain


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Helicoid

The helicoid, also known as helical surface, is a smooth surface embedded in three-dimensional space. It is the surface traced by an infinite line that is simultaneously being rotated and lifted along its fixed axis of rotation. It is the third minimal surface to be known, after the plane and the catenoid.

Description
It was described by Euler in 1774 and by Jean Baptiste Meusnier in 1776. Its name derives from its similarity to the helix: for every point on the helicoid, there is a helix contained in the helicoid which passes through that point. Since it is considered that the planar range extends through negative and positive infinity, close observation shows the appearance of two parallel or mirror planes in the sense that if the slope of one plane is traced, the co-plane can be seen to be bypassed or skipped, though in actuality the co-plane is also traced from the opposite perspective.

The helicoid is also a ruled surface (and a right conoid), meaning that it is a trace of a line. Alternatively, for any point on the surface, there is a line on the surface passing through it. Indeed, Catalan proved in 1842 that the helicoid and the plane were the only ruled minimal surfaces.

A helicoid is also a translation surface in the sense of differential geometry.

The helicoid and the catenoid are parts of a family of helicoid-catenoid minimal surfaces.

The helicoid is shaped like Archimedes screw, but extends infinitely in all directions. It can be described by the following parametric equations in Cartesian coordinates:
 * $$ x = \rho \cos (\alpha \theta), \ $$
 * $$ y = \rho \sin (\alpha \theta), \ $$
 * $$ z = \theta, \ $$

where $ρ$ and $θ$ range from negative infinity to positive infinity, while $α$ is a constant. If $α$ is positive, then the helicoid is right-handed as shown in the figure; if negative then left-handed.

The helicoid has principal curvatures $$\pm \alpha /(1+ \alpha^2 \rho ^2) \ $$. The sum of these quantities gives the mean curvature (zero since the helicoid is a minimal surface) and the product gives the Gaussian curvature.

The helicoid is homeomorphic to the plane $$ \mathbb{R}^2 $$. To see this, let $α$ decrease continuously from its given value down to zero. Each intermediate value of $α$ will describe a different helicoid, until $α = 0$ is reached and the helicoid becomes a vertical plane.

Conversely, a plane can be turned into a helicoid by choosing a line, or axis, on the plane, then twisting the plane around that axis.

If a helicoid of radius $R$ revolves by an angle of $θ$ around its axis while rising by a height $h$, the area of the surface is given by

 * $$\frac{\theta}{2} \left[R \sqrt{R^2+c^2}+c^2 \ln \left(\frac{R + \sqrt{R^2+c^2}} c\right) \right],

\ c = \frac{h}{\theta}.$$

Helicoid and catenoid
The helicoid and the catenoid are locally isometric surfaces; see Catenoid.

title: Helicoid


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Staten Island Advance

The Staten Island Advance is a daily newspaper published in Staten Island, one of the five boroughs of New York City. It is the only daily newspaper published in Staten Island and the only major daily newspaper focused on covering it exclusively. Staten Island Advance covers news of local and community interest, including Staten Island politics. Staten Island Advance is the namesake and nominal flagship publication of Advance Publications.

As of April 25, 2007, the newspaper's weekday circulation was down 3.9% from 2006, to 59,461, and its Sunday circulation dropped 4.6% from 2006, to 73,203.

19th century
The Advance was founded in 1886 by printer John J. Crawford and businessman James C. Kennedy and initially known as the Richmond County Advance. The name was later changed to the Daily Advance and then to its current name. When The Advance was founded in 1886, there were nine competing daily newspapers in Staten Island. The circulation of The Advance quickly surpassed these early competitors, growing from 4,500 in 1910 to over 80,000 by the mid-1990s.

20th century
In 1908, Samuel Irving Newhouse Sr. began working as an office assistant to Hyman Lazarus, an attorney, owner of the Bayonne Times, and a leader of New Jersey's Democratic Party machine. By 1916, when Newhouse was 21, Lazarus rewarded him with a salary of around $30,000 per year, and 25 percent ownership of the Bayonne Times, for loyal service.

In 1922, Newhouse and Lazarus purchased the Staten Island Advance in one of the first in a series of newspapers Lazarus acquired. When Lazarus died in 1924, Newhouse bought his family's share of Staten Island Advance stock.

Throughout the 1920s, the Newhouse family loaned money to Henry Garfinkle, which enabled him to open newsstands that increased sales of the newspaper at St. George Ferry Terminal on Staten Island, and later opened newsstands throughout Manhattan and at LaGuardia Airport in Queens, Newark Airport in Newark, New Jersey, and Port Authority Bus Terminal; the newsstand at Port Authority was, at the time, the world's largest and most lucrative newsstand.

Even during the Great Depression in the 1930s, the Newhouse family had enough money to buy the Long Island Press in Jamaica, Queens and several of its competitors, including the Long Island Star, North Shore Journal, Nassau Journal, Newark Ledger, the Newark Star, and newspapers in Syracuse, New York. Throughout the 1930s, the Newhouse family paid its non-unionized newsroom employees at the Long Island Press a third less than the unionized employees at The New York Times and New York Daily Newss. Newhouse, in turn, paid himself a salary greater than the total of all the salaries paid to the 65 Staten Island Advance newsroom employees combined.

Throughout the 1940s, the Newhouse family continued aggressively acquiring purchasing newspapers in Syracuse, Jersey City, New Jersey, and Harrisburg, Pennsylvania. In the 1950s, they acquired newspapers in St. Louis, Oregon, and Alabama. The Newhouse family's wealth approached $200 million in the late 1950s, enabling it to purchase Vogue and other Conde Nast magazines. Author Richard Meeker describes the mounting suspicions about the Newhouse family's source of wealth in Newspaperman: S.I. Newhouse and the Business Of News:

"Newspaper analysts were so suspicious of the source of Newhouse's funds that they discussed openly the possibility that he was laundering money...Some went so far as to suggest that his newspaper operations had been used as a front for the notorious Reinfeld mob, a group of booze-peddling hoodlums whose boss had made millions during prohibition."

One way the Newhouse family was able to accumulate so much money so rapidly was by hiring accountants and lawyers who figured out unique ways for the Newhouse dynasty to avoid paying taxes. As Newspaperman reported:

"'They played every tax game there was', recalled one man who once served as publisher for several Newhouse newspapers. That meant that every cost that could conceivably be written off as a business deduction was, that assets were depreciated as rapidly as possible, and that new acquisitions were 'written up' as high as the law allowed ... Where Newhouse developed a special advantage was in the way he avoided paying taxes for the profits that remained to him after the payment of corporate taxes ... Thanks to an ingenious device created by his accountant, Louis Glickman, and implemented by his attorney, Charles Goldman, Newhouse was able to avoid paying taxes on accumulated earnings and, thus, to multiply the value of his earnings several times. Doing so involved the creation of a special corporate structure for the various newspapers ... Because the Goldman–Glickman construct kept the various enterprises separate—for tax purposes at least—each could claim the right to its own surplus. Taken together, the accumulation that resulted was many times what the IRS would have allowed had Newhouse simply treated all of his operations as a single corporation."

Meeker characterized the Samuel I. Newhouse Foundation as "a charity his Samuel Irving Newhouse Sr.'s lawyers had created as an additional tax dodge", and charged that Newhouse Foundation funds were used by the Newhouse family to finance its $18 million purchase of Alabama's Birmingham News in 1955.

After Newhouse died in 1979, his two sons, Samuel Irving Newhouse Jr. and Donald Newhouse, were accused of tax evasion by the IRS in 1983. While the IRS dropped tax fraud charges against them in the 1980s, it increased the Newhouse family tax delinquency bill to $1.2 billion, asserting that the Newhouse estate was actually worth $2.2 billion, not $1.2 billion when Samuel Newhouse Sr. died in 1979, according to the March 13, 1989, issue of The Nation.

One year after Newhouse's death in 1979, the Advance Group purchased Random House, and then sold it to Bertelsmann eleven years later, in 1998.

The original Staten Island Advance office was located on Castleton Avenue in the West Brighton neighborhood of Staten Island. In 1960, the paper moved to its current office on West Fingerboard Road in the Grasmere neighborhood of Staten Island. For many years, the Advance was listed as the nominal headquarters for the Newhouse chain; it did not have a formal headquarters until moving to One World Trade Center in the 2020s.

title: Staten Island Advance


text:
Mean curvature

In mathematics, the mean curvature $$H$$ of a surface $$ S$$ is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space.

The concept was used by Sophie Germain in her work on elasticity theory. Jean Baptiste Marie Meusnier used it in 1776, in his studies of minimal surfaces. It is important in the analysis of minimal surfaces, which have mean curvature zero, and in the analysis of physical interfaces between fluids (such as soap films) which, for example, have constant mean curvature in static flows, by the Young–Laplace equation.

Definition
Let $$p$$ be a point on the surface $$S$$ inside the three dimensional Euclidean space $R^{3}$. Each plane through $$p$$ containing the normal line to $$S$$ cuts $$S$$ in a (plane) curve. Fixing a choice of unit normal gives a signed curvature to that curve. As the plane is rotated by an angle $$\theta$$ (always containing the normal line) that curvature can vary. The maximal curvature $$\kappa_1$$ and minimal curvature $$\kappa_2$$ are known as the principal curvatures of $$S$$.

The mean curvature at $$p\in S$$ is then the average of the signed curvature over all angles $$\theta$$:
 * $$H = \frac{1}{2\pi}\int_0^{2\pi} \kappa(\theta) \;d\theta$$.

By applying Euler's theorem, this is equal to the average of the principal curvatures :
 * $$H = {1 \over 2} (\kappa_1 + \kappa_2).$$

More generally, for a hypersurface $$T$$ the mean curvature is given as
 * $$H=\frac{1}{n}\sum_{i=1}^{n} \kappa_{i}.$$

More abstractly, the mean curvature is the trace of the second fundamental form divided by n (or equivalently, the shape operator).

Additionally, the mean curvature $$H$$ may be written in terms of the covariant derivative $$\nabla$$ as
 * $$H\vec{n} = g^{ij}\nabla_i\nabla_j X,$$

using the Gauss-Weingarten relations, where $$ X(x) $$ is a smoothly embedded hypersurface, $$\vec{n}$$ a unit normal vector, and $$g_{ij}$$ the metric tensor.

A surface is a minimal surface if and only if the mean curvature is zero. Furthermore, a surface which evolves under the mean curvature of the surface $$ S$$, is said to obey a heat-type equation called the mean curvature flow equation.

The sphere is the only embedded surface of constant positive mean curvature without boundary or singularities. However, the result is not true when the condition "embedded surface" is weakened to "immersed surface".

Surfaces in 3D space
For a surface defined in 3D space, the mean curvature is related to a unit normal of the surface:
 * $$2 H = -\nabla \cdot \hat n$$

where the normal chosen affects the sign of the curvature. The sign of the curvature depends on the choice of normal: the curvature is positive if the surface curves "towards" the normal. The formula above holds for surfaces in 3D space defined in any manner, as long as the divergence of the unit normal may be calculated. Mean Curvature may also be calculated
 * $$ 2 H = \text{Trace}((\mathrm{II})(\mathrm{I}^{-1}))$$

where I and II denote first and second quadratic form matrices, respectively.

If $$S(x,y)$$ is a parametrization of the surface and $$u, v$$ are two linearly independent vectors in parameter space then the mean curvature can be written in terms of the first and second fundamental forms as $$\frac{l G-2 m F + n E}{2 ( E G - F^2)}$$ where $$E = \mathrm{I}(u,u)$$, $$F = \mathrm{I}(u,v)$$, $$G = \mathrm{I}(v,v)$$, $$l = \mathrm{II}(u,u)$$, $$m = \mathrm{II}(u,v)$$, $$n = \mathrm{II}(v,v)$$.

For the special case of a surface defined as a function of two coordinates, e.g. $$z = S(x, y)$$, and using the upward pointing normal the (doubled) mean curvature expression is

 * $$\begin{align}

2 H & = -\nabla \cdot \left(\frac{\nabla(z-S)}{|\nabla(z - S)|}\right) \\ & = \nabla \cdot \left(\frac{\nabla S-\nabla z} {\sqrt{1 + |\nabla S|^2}}\right) \\ & = \frac{ \left(1 + \left(\frac{\partial S}{\partial x}\right)^2\right) \frac{\partial^2 S}{\partial y^2} - 2 \frac{\partial S}{\partial x} \frac{\partial S}{\partial y} \frac{\partial^2 S}{\partial x \partial y} + \left(1 + \left(\frac{\partial S}{\partial y}\right)^2\right) \frac{\partial^2 S}{\partial x^2} }{\left(1 + \left(\frac{\partial S}{\partial x}\right)^2 + \left(\frac{\partial S}{\partial y}\right)^2\right)^{3/2}}. \end{align} $$

In particular at a point where $$\nabla S=0$$, the mean curvature is half the trace of the Hessian matrix of $$S$$.

If the surface is additionally known to be axisymmetric with $$z = S(r)$$,

 * $$2 H = \frac{\frac{\partial^2 S}{\partial r^2}}{\left(1 + \left(\frac{\partial S}{\partial r}\right)^2\right)^{3/2}} + {\frac{\partial S}{\partial r}}\frac{1}{r \left(1 + \left(\frac{\partial S}{\partial r}\right)^2\right)^{1/2}},$$

where $${\frac{\partial S}{\partial r}} \frac{1}{r}$$ comes from the derivative of $z = S(r) = S\left(\sqrt{x^2 + y^2} \right)$.

Implicit form of mean curvature
The mean curvature of a surface specified by an equation $$F(x,y,z)=0$$ can be calculated by using the gradient $$\nabla F=\left( \frac{\partial F}{\partial x}, \frac{\partial F}{\partial y}, \frac{\partial F}{\partial z} \right)$$ and the Hessian matrix
 * $$\textstyle \mbox{Hess}(F)=

\begin{pmatrix} \frac{\partial^2 F}{\partial x^2} & \frac{\partial^2 F}{\partial x\partial y} & \frac{\partial^2 F}{\partial x\partial z} \\ \frac{\partial^2 F}{\partial y\partial x} & \frac{\partial^2 F}{\partial y^2} & \frac{\partial^2 F}{\partial y\partial z} \\ \frac{\partial^2 F}{\partial z\partial x} & \frac{\partial^2 F}{\partial z\partial y} & \frac{\partial^2 F}{\partial z^2} \end{pmatrix} . $$ The mean curvature is given by:

 * $$H = \frac{ \nabla F\ \mbox{Hess}(F) \ \nabla F^{\mathsf {T}} - |\nabla F|^2\, \text{Trace}(\mbox{Hess}(F)) } { 2|\nabla F|^3 }$$

Another form is as the divergence of the unit normal. A unit normal is given by $$\frac{\nabla F}{|\nabla F|}$$ and the mean curvature is
 * $$H = -{\frac{1}{2}}\nabla\cdot \left(\frac{\nabla F}{|\nabla F|}\right).$$

Mean curvature in fluid mechanics
An alternate definition is occasionally used in fluid mechanics to avoid factors of two:
 * $$H_f = (\kappa_1 + \kappa_2) \,$$.

This results in the pressure according to the Young–Laplace equation inside an equilibrium spherical droplet being surface tension times $$H_f$$; the two curvatures are equal to the reciprocal of the droplet's radius
 * $$\kappa_1 = \kappa_2 = r^{-1} \,$$.

Minimal surfaces

A minimal surface is a surface which has zero mean curvature at all points. Classic examples include the catenoid, helicoid and Enneper surface. Recent discoveries include Costa's minimal surface and the Gyroid.

CMC surfaces
An extension of the idea of a minimal surface are surfaces of constant mean curvature. The surfaces of unit constant mean curvature in hyperbolic space are called Bryant surfaces.

title: Mean curvature


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Ameridelphia

Ameridelphia is traditionally a superorder that includes all marsupials living in the Americas except for the Monito del monte (Dromiciops). It is now regarded as a paraphyletic group.

Orders
The orders within this group are listed below:

 * Order Didelphimorphia (108 species)
 * Family Didelphidae: opossums
 * Order Paucituberculata (7 species)
 * Family Caenolestidae: shrew opossums

Evolution and phylogenetics
Modern marsupials are now understood to be an originally South American lineage that later reached Australia and diversified there in a massive adaptive radiation. Molecular data, including analysis of retrotransposon insertion sites in the nuclear DNA of a variety of marsupials, and the fossil evidence indicate that Ameridelphia might best be understood as an evolutionary grade. Since Didelphimorphia appears to be the basal marsupial group, it and Paucituberculata do not seem to be closest relatives. Meanwhile, the unranked clade Euaustralidelphia has been proposed as the name for the Australian marsupials (Australidelphia minus Microbiotheria, of which Dromiciops is the only survivor), which in all probability derive from a single colonization out of South America via Antarctica.

title: Ameridelphia


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Nihoa

Nihoa (Nīhoa or Nihoa ), also known as Bird Island or Moku Manu, is the  tallest of ten islands and atolls in the uninhabited Northwestern Hawaiian Islands (NWHI). The island is located at the southern end of the NWHI chain, 296 km southeast of Necker Island. Nihoa is the closest NWHI in proximity to the eight main windward Hawaiian Islands at approximately 240 km northwest of the island of Kauai. The island has two peaks, 272 m Miller's Peak in the west, and 259 m Tanager Peak in the east. Nihoa's area is about 171 acres and is surrounded by a 142000 acre coral reef. Its jagged outline gives the island its name, Nīhoa, which is Hawaiian for "toothed, serrated".

The island is home to 25 species of plants and several animals, making it the most diverse island in the entire NWHI. Endemic birds like the Nihoa finch and Nihoa millerbird, and endemic plants like Pritchardia remota and Schiedea verticillata are found only on Nihoa. Amaranthus brownii was considered the rarest plant on Nihoa and has not been directly observed on the island since 1983, and is now considered to be extinct. The plant communities and rocky outcrops provide nesting and perching areas for 18 species of seabirds, such as red-footed boobies and brown noddies, terns, shearwaters, and petrels. Prehistoric evidence indicates Native Hawaiians lived on or visited the island around AD 1000, but over time the location of Nihoa was mostly forgotten, with only an oral legend preserving its name. Captain James Colnett rediscovered the island in 1788, and Queen Kaʻahumanu visited it in 1822. It was made part of the Kingdom of Hawaii by King Kamehameha IV.

In 1909, Nihoa became part of the Hawaiian Islands Reservation, a federal wildlife refuge established by U.S. President Theodore Roosevelt. The Tanager Expedition surveyed the island in 1923, taking a comprehensive biological inventory of its many species. In 1940, it became part of the Northwestern Hawaiian Islands Wildlife Refuge and in 1988, it was listed on the National Register of Historic Places due to its culturally significant archaeological sites. In 2006, it became part of the Papahānaumokuākea Marine National Monument. Efforts are underway to ensure that endangered plant species are propagated beyond their limited range and represented in ex situ collections. Persons intending to visit Nihoa for cultural and scientific research purposes require a USFWS-issued special-use permit to land on the island so as to reduce the risk of introducing alien species to Nihoa's already fragile ecosystem.

Geology and geography

Nihoa is part of the Hawaiian – Emperor seamount chain of volcanic islands, atolls, and seamounts starting from the island of Hawaii in the southeast to the Aleutian Islands in the northwest. It is the youngest of ten islands in the uninhabited Northwestern Hawaiian Islands (NWHI), having formed 7.2 million years ago; the oldest, Kure Atoll, formed 30 million years ago. Over the millennia, Nihoa has experienced significant erosion; along with Necker, French Frigate Shoals, and Gardner Pinnacles, Nihoa is one of only four islands in the NWHI that still has an exposed basalt rock substrate. Six valleys slant down from north to south, meeting at the south side of the island: West Valley, West Palm Valley, Miller Valley, Middle Valley, East Palm Valley, and East Valley.

The valleys slant towards Adam's bay on the south side, which also has sea cave.

Among features on Nihoa are Dog's Head Peak (358 ft), named for its likeness, and  Pinnacle Peak (626 ft), a volcanic dike created when less resilient rock was eroded away and harder rock was open to the elements. The only flat area on the island is Albatross Plateau, just below Miller's Peak. The Devil's Slide is a narrow cleft descending 700 ft irrespective of the surrounding elevation. Extending northward from Albatross Plateau, it ends at the vertical cliffs with a 190 ft drop straight down to the ocean below. In this chasm, rare ferns grow, along with several endemic species, including a giant cricket.

The island is about 1371 meters long going from east to west, and 274–914 meters wide. The overall shape is that of half saddle, with one side having sheer cliffs and the other sloping towards the ocean.

Ecology
Nihoa's inaccessibility and lack of major guano deposits made the island unattractive to humans, helping to preserve its endemic species from extinction. Because of Nihoa's small size, most of its endemic organisms are endangered, as one single disaster, such as an island-wide fire or an introduction of invasive species, could wipe out the whole population. One such invasive species is the gray bird grasshopper, Schistocerca nitens; from the period between 1999 and 2003, grasshoppers devastated much of the vegetation on the island and posed a real threat to the continued health of plants on Nihoa. The following year, the numbers decreased and the vegetation became lush again. The grasshoppers probably came to Nihoa by way of wind from Kauai.

The north side of the island's cliffs are mostly bare, but the sloping valleys are covered with a variety of grasses and shrubs. The two most common grasses on these slopes are Eragrosis Varabilis and Panicum torridum.

There is also a variety of scrubs and bushes on the island slopes, such as Chenopodium sandwicheum and ilima bushes (Sida fallax).

Unique species include:

 * Pritchardia remota fan palm, the only tree on the island
 * Nihoa millerbird
 * Nihoa finch
 * Nihoa conehead katydid
 * Nihoa carnation
 * Sesbania tomentosa
 * the amaranth Amaranthus brownii
 * the trapdoor spider Nihoa mahina
 * Thaumatogryllus conanti, a giant cricket found in the Devil's Slide area
 * Plagithmysus nihoae, a longhorned beetle
 * Eupelmus nihoaensis, a wasp
 * Hylaeus perkinsianus, Perkin's yellow-faced bee

Important Bird Area
The island forms part of the Northwest Hawaiian Islands Important Bird Area (IBA), designated as such by BirdLife International because of its seabirds and endemic landbirds.

Ancient history
Nihoa was well known to the early Hawaiians. Archaeological expeditions found extensive prehistoric agricultural terraces and house sites. At least one site has been dated to around the 1st millennium AD, sometime between 867 and 1037. There is some doubt as to the number of people that lived on Nihoa, because while the large terraces suggest a considerable number, there is scant fresh water to be found. Archaeologists Kenneth Emory and Paul Cleghorn estimate that water could support as many as 100 people, although if the island were previously forested, this would have increased fresh water supplies relative to its current state. Because of the island's importance, the island was added to the National Register of Historic Places in 1988, and subsequently became part of Papahānaumokuākea Marine National Monument in June 2006.

Nihoa, along with Necker Island to the northwest, is among the most northern, isolated, smallest and driest of the high volcanic Hawaiian islands, and receives the lowest dust and tephra input. All of these features were found to strongly predict deforestation among the Pacific Islands. The abandonment of Nihoa may be tied to deforestation although this has not been proven and small groves of trees were noted in the major drainage valleys during survey work conducted in 1928.

Artifacts recorded on the island represent a unique material culture demonstrating restraint in the utilization of wood. A number of artifact types such as bowls and human figures called ki'i that elsewhere in the Hawaiian chain would have been made out of wood were instead carved from stone, a lengthy and labor-intensive process. Archaeological sites on the island are similar to other site types within the Hawaiian islands and include both packed dirt and stone terraces likely for habitation and agricultural uses on the steep slopes of the island, cave shelters, and heiau. Some scholars consider Nihoa to be a matched pair with Necker Island although the latter appears not to have had a permanent population.

The heiau on Nihoa and Necker Islands are unique in the Hawaiian chain representing a raised pavement of basalt stones with upright stones placed across this pavement often near the edges as opposed to the form common to other islands in the chain represented by a high stacked stone wall enclosing a central space. This difference in form represents an earlier iteration of Hawaiian monumental architecture that offers a unique perspective on cultural norms prior to the abandonment of Nihoa. Thanks to this difference in form, scholars often use the term 'marae' as opposed to 'heiau' in reference to these structures and some scholars argue that the shift in form represents a shift in ritual practice in Hawaii.

Early exploration
The first Westerner to discover Nihoa was Captain James Colnett of the Prince of Wales, on March 21, 1788. Due to Colnett's lengthy absence from England, including his imprisonment by the Spanish for his part in the Nootka Sound Incident, the discovery was once widely accredited to Captain William Douglas of the Iphigenia, who sighted Nihoa almost a year later.

The abandoned settlements seen by the early explorers caused Nihoa and Necker islands, to be called the 'mystery islands'. However, this term is used more generally to refer to any island in the Pacific that was similarly abandoned prior to European contact.

By the end of the 18th century, Nihoa had been forgotten by most Hawaiians. In 1822, Queen Kaahumanu and her husband King Kaumualii traveled with Captain William Sumner to find Nihoa, as her generation had only known the island through songs and myths. Later, King Kamehameha IV sailed there to officially annex the island as part of the Kingdom of Hawaii. Finally, in 1885, Princess Liliuokalani made a pilgrimage to Nihoa with her escorts, but their luncheon was cut short when one of the party ignited a wildfire by accident. The group tried to flee the island, but the rising tides made it difficult and several boats were flooded, destroying some of the photographs taken. On this visit a carved basalt bowl was found and taken back to the main islands by the Queen.

In 1859 the position of Nihoa island was determined by the survey schooner, USS Fenimore Cooper.

Tanager expedition
During 1923-4 the Tanager expedition was a noted scientific exploration of Nihoa island. This resulted in various biological and archeological discoveries. The Tanager expedition conducted the first archeological survey of the island. Evidence of an ancient settlement on Nihoa was discovered, along with platforms, terraces, and human remains.

Noted events include finding a specimen of Amaranthus brownii and the discovery of the Nihoa millerbird which was formally named  Acrocephalus familiaris kingi,

On this expedition, several hundred Loulu fan palms were counted on the island. Twenty other flowering plants were also noted at this time.

Examples of exploration work:
 * Survey map of island
 * Bird life
 * Plants
 * Insects
 * Marine life
 * Geology

On the Tanager expedition they also found the remnants of a modern Fishing camp in a cave near the landing, with some leftover coats and bags of rice.

title: Nihoa


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New Brighton, Staten Island

New Brighton is a neighborhood located on the North Shore of Staten Island in New York City. The neighborhood comprises an older industrial and residential harbor front area along the Kill Van Kull west of St. George. New Brighton is bounded by Kill Van Kull on the north, Jersey Street on the east, Brighton and Castleton Avenues to the south, and Lafayette Avenue and Snug Harbor Cultural Center to the west. It is adjacent to St. George to the east, Tompkinsville to the south, and West New Brighton to the west.

The village of New Brighton was incorporated in 1866 out of six wards of the town of Castleton. It originally stretched four miles (6.4 km) long and was two miles (3.2 km) wide, encompassing the entire northeast tip of the island from Tompkinsville to Snug Harbor, and included what is now St. George. The current neighborhood includes Hamilton Park, an enclave of Victorian homes built before the American Civil War. The surrounding area includes several older churches such as St. Peter's Church, the oldest Roman Catholic church on Staten Island. The original New Brighton Village Hall, constructed in 1871 on present Fillmore Street, was demolished in 2004. New Brighton public housing includes the Cassidy-Laffayette Houses and the Richmond Terrace Houses on Jersey Street.

New Brighton is part of Staten Island Community District 1 and its ZIP Codes are 10304 and 10301. New Brighton is patrolled by the 120th Precinct of the New York City Police Department.

Precolonial and colonial period
Originally, Staten Island was inhabited by the Munsee-speaking Lenape Native Americans. The Lenape relocated during different seasons, moving toward the shore to fish during the summers, and moving inland to hunt and grow crops during the fall and winter. The present-day area of New York City was inhabited in 1624 by Dutch settlers as part of New Netherland. In 1664, the Dutch gave New Netherland to the British, and six years later the British finalized a purchase agreement with the Lenape.

At the time of British handover, several British, Dutch, and French settlers occupied the area, but did not have an established title to the land. A series of surveys were conducted through 1677, and several parcels were distributed to different landowners. Among them were the 340 acre "Duxbury Glebe", given to Ellis Duxbury in 1708, bequeathed to the Protestant Episcopal Church of St. Andrew's ten years later, and then leased for 54 years by John Bard in 1765. Another tract was granted to Lambert Jansen Dorlant in 1680, whose western boundary was a brook on present-day Jersey Street. By 1748 it had been purchased by Salmon Comes, who ran a ferry to Manhattan. By 1765, part of the Dorlant tract was owned by John Wandel, a molasses distiller who operated a plant at the Kill Van Kull near Richmond Terrace and Westervelt Avenue, taking advantage of the Jersey Street brook. Two Native American roads intersected near the distiller: Shore Road (today's Richmond Terrace) on the North Shore, and a road that winded southward on St. Marks Place and then Hamilton and Westervelt Avenues.

Fort Hill, one of the hills overlooking the harbor, was the location on Duxbury's Point or Ducksberry Point, fortified by the British during the American Revolutionary War. Hessian troops, contracted by the British, were stationed near the Jersey Street brook, which then became known as Hessian Springs. After the end of the war, the area remained primarily rural through the early 19th century. The area became part of the town of Castleton upon the town's incorporation in 1788.

Early ownership
Among the first people to promote the widespread development of Staten Island was former U.S. vice president Daniel D. Tompkins, who purchased land in the northern part of Staten Island in the early 1810s. Tompkins purchased Abraham Crocheron's farm, located on present-day Jersey Street south of Richmond Terrace, in 1814. The next year, he acquired 700 acre from St. Andrew's Church, and two years after that, he bought Philip Van Buskirk's land claim, located between the two disconnected pieces of land. Tompkins also incorporated the Richmond Turnpike Company to build present-day Victory Boulevard in 1816, started operating a ferry to Manhattan in 1817, and laid out the adjacent village of Tompkinsville for development between 1819 and 1821. Tompkins then expanded the Van Buskirks' old farmhouse, using it as his primary residence. He died in 1825.

Tompkins's property on the North Shore was sold in April 1834 to Manhattan developer Thomas E. Davis, who continued to buy land through the following year. Davis came to own all the land on Staten Island's northeastern shore, bounded to the south by Victory Boulevard, to the west by Sailors' Snug Harbor, and to the north and east by the waterfront. He planned to develop the area into a summer retreat called New Brighton, renaming Shore Road to Richmond Terrace, and the first five Greek Revival summer bungalows were erected in 1835. Davis sold the development to a five-person syndicate for $600,000 in 1836, and the New Brighton Association was incorporated that April. The area on the northeast shore thus came to be called New Brighton.

Increasing development
Development on the New Brighton street grid proceeded according to a plan that surveyor James Lyons had created in 1835. Streets were arranged around existing topography. When the New Brighton Association laid out streets in northeastern Staten Island, many of these roads were named after notable politicians, with such names as Hamilton Avenue, Jay Street, and Madison Street. Other streets were named after people or places that were associated with the development of the area, including Tompkins, Davis, or the Stuyvesant family (who were early investors). For instance, St. Marks Place was named after Davis's developments on St. Marks Place in Manhattan, while Westervelt Avenue was named after Tompkins's son-in-law. Several of these street names replaced preexisting appellations. Work on the street grid and development of the land continued, but in March 1837, one major investor declared bankruptcy following the Panic of 1837. The same year, the Pavilion Hotel opened in a mansion along the shore, being converted from a residence. The association continued to lay out streets. However, in 1840, four of the five original New Brighton Association investors' properties were foreclosed upon. The foreclosed lots were thus repurchased by Thomas E. Davis in 1844. According to a survey conducted the following year, several streets had been laid out in New Brighton, including Carroll Place, Hamilton Avenue, St. Marks Place, Richmond Terrace, and numerous smaller streets. Most development was on the waterfront, where there were mansions with carriage buildings, as well as smaller homes and the Pavilion Hotel. St. Peter's Church on Carroll Street, dedicated in 1844, was the island's first Roman Catholic house of worship; it remains one of Staten Island's most historically important churches, with more than half of the island's Catholic churches having been derived from St. Peter's parish. Two Greek Revival houses remain on the waterfront, at 404 and 272 Richmond Terrace.

By the 1840s and 1850s, New Brighton including modern-day St. George began to develop into a summer resort area. In addition to the existing Pavilion, hotels in modern-day St. George/New Brighton included the Peteler (later St. Marks) Hotel, as well as the Belmont Hotel. Additionally, new houses such as Italianate villas were built, while existing Richmond Terrace mansions were expanded or received new annexes and gardens. Several greenhouses were also built in the neighborhood, particularly on the land of the merchant John C. Green, whose estate is now the site of Curtis High School. The silk printer John Crabtree established a printing plant for his company, Crabtree and Wilkinson, on the eastern bank of the Jersey Street brook in 1844. The factory had over 180 workers and a small residential and commercial community by 1853, and the establishment of similar factories led to the population of New Brighton doubling between 1840 and 1860.

In 1861, the onset of the American Civil War resulted in large changes to the neighborhood's land use. Initially, the local economy suffered due to cessation of trade with the Southern United States, but because of the Union Army's demand for material, many entrepreneurs and workers moved to New York City, including to Staten Island's North Shore. According to a 1865 article from the Richmond County Gazette, "the demand for dwelling houses upon the island has never before been equalled." During this time, many new houses were designed in the Second Empire style and/or as duplexes, particularly on as-yet-undeveloped plots along Westervelt Avenue or St. Marks Place. The end of the Civil War, cheaper building materials, and technological improvements resulted in an increase in real estate prices on the North Shore, and by the early 1870s, the area was described as being prosperous, with real estate in high demand.

Late 19th century
The New Brighton Village Hall was built in 1871 and was one of the few Village Halls to remain from the old village system that existed before it was merged with New York City. A passage from an anonymous author in the Illustrated Sketch Book of Staten Island, NY: Its industries and commerce, from 1886, describes New Brighton as follows: The village of New Brighton is unique in its attractiveness. Its public buildings, churches, hotels and institutions are all handsome and substantial, its residences the perfection of refined taste; it has fifteen miles (24 km) of streets, the principal of which are wide, well paved, and generally well shaded with ornamental trees. A complete system of sewerage has been adopted. The inhabitants are filled with a sense of local pride which is in itself most commendable and leads to the happiest results, the most noticeable of which perhaps is the great care bestowed upon their private residences. The neighbors seem to vie with each other in friendly emulation as to who shall keep the smoothest lawn, the neatest fence or the most graceful fountain.

As a whole, the effect is most pleasing, but when the eye wanders beyond the artificial beauty of its immediate surroundings and rests upon the sparkling waters of the incomparable Bay of New York, with stretches of cultivated landscape in the distance, the picture is singularly lovely and complete.

The Panic of 1873 resulted in a near-cessation of building activity on the North Shore. By the late 1870s, industries had started to move to the area again, such as J. B. King and Company, whose plaster mill opened in 1877. A water system was established upon the Staten Island Water Supply Company's 1879 incorporation, and a sewage system was added between 1884 and 1890. In the 1880s, the area closest to the ferry terminals on the northeastern shore became known as "St. George", after developer George Law, who acquired rights to the New Brighton waterfront at bargain prices. According to island historians Charles Leng and William T. Davis, the businessman Erastus Wiman, who was expanding the Staten Island Railway to New Brighton, promised to "canonize" Law if the latter agreed to relinquish the land rights for a new railroad–ferry terminal there. The St. George Terminal opened in early 1886, bringing more development to the neighborhood.

The completion of new transportation options also resulted in further real estate development, especially around the areas close to New Brighton and St. George stations. Developers such as John M. Pendleton and Anson Phelps Stokes constructed cottages and houses in the northern part of St. George, while existing property owners expanded their properties. Many newer houses, meanwhile, were designed in the Queen Anne, Shingle, and Colonial Revival styles. Although Staten Island as a whole remained largely residential and less densely populated and developed than the surrounding region, the inhabitants of the region favored consolidation with the greater metropolis. In 1898, Staten Island was consolidated with New York City, and this move accelerated development of the region. At this time immigrant groups settled in New Brighton in greater numbers; Italians and African-Americans along the Kill Van Kull, and Jewish communities on the eastern boundary of the village near St. George and Tompkinsville.

20th century
In the years after unification, the North Shore became quickly urbanized, and the political and economic center of Staten Island shifted to the region. The area's first secondary school, Curtis High School, opened in 1904. The ferry service to Whitehall Terminal was transferred to municipal operation the following year. Other city services were also brought to Staten Island following unification, such as schools, emergency facilities, new roads, and utilities including an underground water supply. Neighboring St. George became the civic center of Staten Island, with a new Staten Island Borough Hall built in 1906 and the Richmond County Courthouse in 1919. This provided the impetus for improvements in infrastructure, including road construction, police and fire protection, and two commuter airports on Staten Island that were established in the 20th century. Navy and Coast Guard outposts could be found on the north shore of Staten Island, each employing local residents in military and civilian capacities.

Staten Island and New Brighton thrived economically. Larger manufacturers employed many local residents; Procter & Gamble, US Gypsum, and several other factories provided jobs for thousands of residents. The Procter & Gamble factory, opened in October 1907, operated for more than 80 years. At the end of the 1920s, some of the borough's first apartment buildings and four-family dwellings were concentrated in New Brighton. One such apartment building collapsed in a storm in 1937, killing nineteen people.

The 1964 opening of the Verrazzano-Narrows Bridge, connecting Brooklyn and Staten Island, allowed for a massive population and development boom that continues to this day. This, combined with the closing of many area factories, the construction of housing projects along Richmond Terrace and the surrounding area, and an increase in area poverty, caused large changes to New Brighton.

Demographics
For census purposes, the New York City government classifies New Brighton as part of a larger neighborhood tabulation area called West New Brighton-New Brighton-St. George. Based on data from the 2010 United States Census, the population of West New Brighton-New Brighton-St. George was 33,551, a change of 1,397 (4.2%) from the 32,154 counted in 2000. Covering an area of 1403.06 acres, the neighborhood had a population density of 23.9 PD/acre. The racial makeup of the neighborhood was 26.4% (8,859) White, 31.7% (10,630) African American, 0.3% (100) Native American, 5% (1,691) Asian, 0% (10) Pacific Islander, 0.4% (123) from other races, and 2.5% (835) from two or more races. Hispanic or Latino of any race were 33.7% (11,303) of the population.

The entirety of Community District 1, which comprises New Brighton and other neighborhoods on the North Shore, had 181,484 inhabitants as of NYC Health's 2018 Community Health Profile, with an average life expectancy of 79.0 years. This is lower than the median life expectancy of 81.2 for all New York City neighborhoods. Most inhabitants are youth and middle-aged adults: 24% are between the ages of between 0–17, 27% between 25 and 44, and 26% between 45 and 64. The ratio of college-aged and elderly residents was lower, at 10% and 13% respectively.

As of 2017, the median household income in Community District 1 was $48,018, though the median income in New Brighton individually was $49,807. In 2018, an estimated 21% of New Brighton and the North Shore residents lived in poverty, compared to 17% in all of Staten Island and 20% in all of New York City. One in fourteen residents (7%) were unemployed, compared to 6% in Staten Island and 9% in New York City. Rent burden, or the percentage of residents who have difficulty paying their rent, is 51% in New Brighton and the North Shore, compared to the boroughwide and citywide rates of 49% and 51% respectively. Based on this calculation,, New Brighton and the North Shore are considered high-income relative to the rest of the city and not gentrifying.

Attractions
One Pendleton Place, the Christ Church New Brighton (Episcopal), Hamilton Park Community Houses, and Neville House are listed on the National Register of Historic Places.

Snug Harbor
Sailors' Snug Harbor was built in 1833 by a wealthy New Yorker named Robert Richard Randall. Designed as a place for retired sailors, Snug Harbor was the first establishment of its kind in the United States. The 83 acre park-like setting is located on the North Shore of Staten Island along the Kill Van Kull. Sailors' Snug Harbor includes 26 Greek Revival, Beaux Arts, Italianate and Victorian style buildings. At its peak, 1,000 sailors made their home at Snug Harbor, but due to a decline in funding caused by the founding of the Social Security program, the site closed in the 1960s.

The site is considered Staten Island's "crown jewel" and "an incomparable remnant of New York's 19th-century seafaring past." It is a National Historic Landmark District and is also designated by the New York City Landmarks Preservation Commission. The site is now called Snug Harbor Cultural Center and Botanical Gardens and has gardens, museums, theaters, educational spaces, and special events.

St. Peter's Church
The first weekly Mass of St. Peter's Roman Catholic Church was held in 1839 in a gun factory in New Brighton. The New Brighton Association later donated land for the church, which opened in 1844 near its current location on St. Mark's Place. After a fire destroyed the original church in the 1890s, George Edward Harding & Gooch designed a new church building that was completed in 1903. The interior of the church has influence from the French-Gothic style, visible in its vaulted ceilings that are curved and end in a point at the top. It be seen from almost anywhere in New Brighton, and one that stands out while approaching from the Staten Island Ferry.

W.S. Pendleton Houses
The W.S. Pendleton Houses at 1 & 22 Pendleton Place are designated landmarks of New York City, and 1 Pendleton Place was additionally listed on the National Register of Historic Places in 2014. Both houses were once owned by W.S. Pendleton, a prominent local businessman who worked in real estate and owned a local ferry boat company. Pendleton, born in New York City in 1795, later became a pioneer lithographer in Boston.

Built in 1861, 1 Pendleton Place was designed by Charles Duggin in the Stick style. 22 Pendleton Place, a Gothic Revival style house built in 1855, possesses a distinctive individuality, with its square, spire-topped tower, steeply pitched gables, pendant scrollwork, asymmetrically placed dormers, bay windows and oriel window.

Atlantic Salt Company
The Atlantic Salt Company is located along Richmond Terrace and stores salt that is used to remove ice from roads in New York, New Jersey, and Connecticut. Walking along Richmond Terrace, the many hills of white salt can be glimpsed along the side of the road. During the winter, over 350,000 tons of salt are stored at this New Brighton location. The Atlantic Salt Co. purchased its current location in 1976, a gypsum corporation plant owned and used the property. The Atlantic Salt Co. is family-run and operated by the Mahoney family; the first generation, headed by founder and former president Leo Mahoney, started the business in 1955.

September 11 Memorial

This large mural, painted by a local artist who paints under the name FWID, adorns the side of the warehouse on Richmond Terrace where Gerardi's Farmer Market is located. The three firefighters raising the American Flag in the center of the image strike a pose that is reminiscent of the historic photograph Raising the Flag on Iwo Jima by Joe Rosenthal.

Farmer's market

Gerardi's Farmer Market, a local market on Richmond Terrace. The Farmer's Market carries fresh and local produce nearly year-round for the residents of New Brighton.

Hamilton Park subsection
Hamilton Park (sometimes known as Cottage Hill ), laid out circa 1851-52 was probably the earliest suburban residential park on Staten Island and one of the first self-contained, limited access suburban subdivisions in the United States. Unconnected to the grid of surrounding streets until 1886, it is a large, elevated tract bounded by today's East Buchanan, Franklin, Prospect and York. Traces of the original carriage roads which wound through the wooded terrain are still visible. Hamilton Park is an old tight-knit community nestled in a sea of developments and low income housing projects. It sits on top of a hill known as "Brighton Heights" and ranks with Todt Hill as one of the highest points on the eastern seaboard below Maine.

The hilly streets of the Hamilton Park neighborhood feature rows of gingerbread-trimmed Victorian mansions and shingle-style homes erected during the Civil War era. A number of suburban country dwellings of 12 to 14 rooms, originally dubbed as "cottages", survive. 66 Harvard Avenue, also known as the C.K. Hamilton House, was built c.1853 as part of Hamilton Park Community Houses and is believed to be the first speculatively built "cottage" and is the only intact survivor of Hamilton Park's original suburban residences. Among German architect Carl Pfeiffer's first American commissions in the early 1860s were 12 houses built for Hamilton, many of which survive today. Although somewhat simpler and less picturesque than the earlier Harvard Avenue house, the brick, Italianate "cottage" at 105 Franklin Avenue boasts a magnificent arcaded loggia.

Police and crime
New Brighton and the North Shore are patrolled by the 120th Precinct of the NYPD, located at 78 Richmond Terrace. The 120th Precinct ranked 12th safest out of 69 patrol areas for per-capita crime in 2010. , with a non-fatal assault rate of 94 per 100,000 people, New Brighton and the North Shore's rate of violent crimes per capita is more than that of the city as a whole. The incarceration rate of 719 per 100,000 people is higher than that of the city as a whole.

The 120th Precinct has a lower crime rate than in the 1990s, with crimes across all categories having decreased by 83.3% between 1990 and 2022. The precinct reported seven murders, 14 rapes, 118 robberies, 384 felony assaults, 124 burglaries, 338 grand larcenies, and 136 grand larcenies auto in 2022.

Fire safety
New Brighton is served by the New York City Fire Department (FDNY)'s Engine Co. 155/Ladder Co. 78, located at 14 Brighton Avenue.

Health
, preterm births and births to teenage mothers are more common in New Brighton and the North Shore than in other places citywide. In New Brighton and the North Shore, there were 96 preterm births per 1,000 live births (compared to 87 per 1,000 citywide), and 22.6 births to teenage mothers per 1,000 live births (compared to 19.3 per 1,000 citywide). New Brighton and the North Shore have a relatively average population of residents who are uninsured. In 2018, this population of uninsured residents was estimated to be 12%, the same as the citywide rate of 12%.

The concentration of fine particulate matter, the deadliest type of air pollutant, in New Brighton and the North Shore is 0.0071 mg/m3, less than the city average. Sixteen percent of New Brighton and the North Shore residents are smokers, which is higher than the city average of 14% of residents being smokers. In New Brighton and the North Shore, 24% of residents are obese, 9% are diabetic, and 26% have high blood pressure—compared to the citywide averages of 24%, 11%, and 28% respectively. In addition, 21% of children are obese, compared to the citywide average of 20%.

Eighty-seven percent of residents eat some fruits and vegetables every day, which is the same as the city's average of 87%. In 2018, 77% of residents described their health as "good", "very good", or "excellent", equal to the city's average of 78%. For every supermarket in New Brighton and the North Shore, there are 28 bodegas.

The nearest major hospital is Richmond University Medical Center in West New Brighton.

Post offices and ZIP Code
New Brighton is located within the ZIP Code 10301. The United States Postal Service operates the Saint George Station at 45 Bay Street and the West New Brighton Station at 1015 Castleton Avenue.

Education
New Brighton and the North Shore generally have a lower rate of college-educated residents than the rest of the city. While 37% of residents age 25 and older have a college education or higher, 15% have less than a high school education and 48% are high school graduates or have some college education. By contrast, 39% of Staten Island residents and 43% of city residents have a college education or higher. The percentage of New Brighton and the North Shore students excelling in math rose from 49% in 2000 to 65% in 2011, though reading achievement declined from 55% to 51% during the same time period.

New Brighton and the North Shore's rate of elementary school student absenteeism is slightly higher than the rest of New York City. In New Brighton and the North Shore, 25% of elementary school students missed twenty or more days per school year, more than the citywide average of 20%. Additionally, 73% of high school students in New Brighton and the North Shore graduate on time, about the same as the citywide average of 75%.

Schools
The New York City Department of Education operates the following public schools near New Brighton:
 * PS 31 William T Davis (grades PK-5)
 * IS 61 William A Morris (grades 6–8)
 * PS 373 (grades PK-7)

The Roman Catholic Archdiocese of New York operates Staten Island Catholic schools. St. Peter-St. Paul Parish School is in New Brighton. In 2011 St. Peter moved from the former building in New Brighton to the former Saint Paul Elementary School in New Brighton, which had closed in 2006. The school changed its name after the move.

Libraries
The nearest library is the New York Public Library (NYPL)'s West New Brighton branch at 976 Castleton Avenue in West New Brighton. The NYPL also operates the St. George Library Center at 5 Central Avenue in St. George.

Transportation
New Brighton was served by the Staten Island Railway's New Brighton station until March 31, 1953, when the entire North Shore Branch was shut down. , it is served by the local bus routes.

Religion
The Roman Catholic Archdiocese of New York operates Catholic churches on Staten Island. In 2015 it announced that St. Paul's Chapel in New Brighton will close.

Notable residents
Additionally, the movie Vox Lux has notable elements from New Brighton.
 * Walter Davis Lambert (1879–1968), geodesist, born in New Brighton
 * Mabel Normand (1892–1930), silent film actress, born in New Brighton
 * Adolfas Ramanauskas (1918–1957), head of Lithuanian anti-Soviet resistance fighters.
 * William Greenough Thayer (1863–1934), educator, born in New Brighton

title: New Brighton, Staten Island


text:
Australidelphia

Australidelphia is the superorder that contains roughly three-quarters of all marsupials, including all those native to Australasia and a single species – the monito del monte – from South America. All other American marsupials are members of the Ameridelphia. Analysis of retrotransposon insertion sites in the nuclear DNA of a variety of marsupials has shown that the South American monito del monte's lineage is the most basal of the superorder.

The Australian australidelphians form a clade, for which the name Euaustralidelphia ("true Australidelphia") has been proposed (the branching order within this group is yet to be determined). The study also showed that the most basal of all marsupial orders are the other two South American groups (Didelphimorphia and Paucituberculata, with the former probably branching first). This indicates that Australidelphia arose in South America along with the other major divisions of extant marsupials, and likely reached Australia via Antarctica in a single dispersal event after Microbiotheria split off.

Phylogeny
Phylogeny of living Australidelphia based on the work of May-Collado, Kilpatrick & Agnarsson 2015 with extinct clades from Black et al. 2012

(*)This clade has been called Agreodontia by other authors since 2014.

Taxonomy
The orders within this group are listed below:

 * Genera †Djarthia Godthelp, Wroe & Archer 1999
 * Order †Yalkaparidontia Archer, Hand & Godthelp 1988
 * Family †Yalkaparidontidae Archer, Hand & Godthelp 1988
 * ?Order Microbiotheria (1 species)
 * ?Family Microbiotheriidae: monito del monte
 * Order Dasyuromorphia (71 species)
 * Family †Thylacinidae: thylacine
 * Family Dasyuridae: antechinuses, quolls, dunnarts, Tasmanian devil, and allies
 * Family Myrmecobiidae: numbat
 * Order Peramelemorphia (21 species)
 * Family Thylacomyidae: bilbies
 * Family †Chaeropodidae: pig-footed bandicoots
 * Family Peramelidae: bandicoots and allies
 * Order Notoryctemorphia (2 species)
 * Family Notoryctidae: marsupial moles
 * Order Diprotodontia (117 species)
 * Family Phascolarctidae: koala
 * Family Vombatidae: wombats
 * Family Phalangeridae: brushtail possums and cuscuses
 * Family Burramyidae: pygmy possums
 * Family Tarsipedidae: honey possum
 * Family Petauridae: striped possum, Leadbeater's possum, yellow-bellied glider, sugar glider, mahogany glider, squirrel glider
 * Family Pseudocheiridae: ringtailed possums and allies
 * Family Potoridae: potoroos, rat kangaroos, bettongs
 * Family Acrobatidae: feathertail glider and feather-tailed possum
 * Family Hypsiprymnodontidae: musky rat-kangaroo
 * Family Macropodidae: kangaroos, wallabies, and allies
 * Family †Thylacoleonidae: marsupial lions
 * Family †Palorchestidae: marsupial tapirs
 * Family †Diprotodontidae: giant wombats
 * Family †Diprotodontidae: giant wombats
 * Family †Diprotodontidae: giant wombats
 * Family †Diprotodontidae: giant wombats
 * Family †Diprotodontidae: giant wombats

title: Australidelphia


text:
East Rochester

East Rochester is the name of the following places in the United States:

 * East Rochester, New Hampshire, a village in the city of Rochester

 * East Rochester, New York, a coterminous town and village
 * East Rochester, Ohio, an unincorporated community and census-designated place
 * East Rochester, Pennsylvania, a borough

title: East Rochester


text:
East Rockingham

East Rockingham may refer to:

 * East Rockingham, North Carolina, U.S.
 * East Rockingham, Western Australia
 * East Rockingham High School, Elkton, Virginia, U.S.

title: East Rockingham