PennsylvaniaPennsylvania (ˌpɛnsɪlˈveɪniə ; Pennsilfaani), officially the Commonwealth of Pennsylvania, is a state spanning the Mid-Atlantic, Northeastern, Appalachian, and Great Lakes regions of the United States. Pennsylvania borders Delaware to its southeast, Maryland to its south, West Virginia to its southwest, Ohio to its west, Lake Erie and the Canadian province of Ontario to its northwest, New York to its north, and the Delaware River and New Jersey to its east.
New York (state)New York, often called New York State, is a state in the Northeastern United States. A Mid-Atlantic state, New York borders New England, and has an international border with Canada. With almost 19.7 million residents, it is the fourth-most populous state in the United States and seventh-most densely populated as of 2022. New York is the 27th-largest U.S. state by area, with a total area of . New York has a varied geography.
State (polity)A state is a centralized political organization that imposes and enforces rules over a population within a territory. Definitions of a state are disputed. One widely used definition comes from the sociologist Max Weber: a "state" is a polity that maintains a monopoly on the legitimate use of violence, although other definitions are common. Absence of a state does not preclude the existence of a society, such as stateless societies like the Haudenosaunee Confederacy that "do not have either purely or even primarily political institutions or roles".
Heat equationIn mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. As the prototypical parabolic partial differential equation, the heat equation is among the most widely studied topics in pure mathematics, and its analysis is regarded as fundamental to the broader field of partial differential equations.
Relations of productionRelations of production (Produktionsverhältnisse) is a concept frequently used by Karl Marx and Friedrich Engels in their theory of historical materialism and in Das Kapital. It is first explicitly used in Marx's published book The Poverty of Philosophy, although Marx and Engels had already defined the term in The German Ideology. Some social relations are voluntary or freely chosen (a person chooses to associate with another person or a group). But other social relations are involuntary, i.e.
AlaskaAlaska (əˈlæskə ) is a U.S. state on the northwest extremity of North America. A semi-exclave of the U.S., it borders British Columbia and Yukon in Canada to the east, and it shares a western maritime border in the Bering Strait with Russia's Chukotka Autonomous Okrug. To the north are the Chukchi and Beaufort Seas of the Arctic Ocean, and the Pacific Ocean lies to the south and southwest. Alaska is the largest U.S. state by area, comprising more total area than the next three largest states of Texas, California, and Montana combined, and is the seventh-largest subnational division in the world.
Linear equationIn mathematics, a linear equation is an equation that may be put in the form where are the variables (or unknowns), and are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients are required to not all be zero. Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.
HawaiiHawaii (həˈwaɪi ; Hawaii həˈvɐjʔi, həˈwɐjʔi) is an island state in the Western United States, about from the U.S. mainland in the Pacific Ocean. It is the only U.S. state outside North America, the only state that is an archipelago, and the only state in the tropics. Hawaii consists of 137 volcanic islands that comprise almost the entire Hawaiian archipelago; spanning , the state is physiographically and ethnologically part of the Polynesian subregion of Oceania. Hawaii's ocean coastline is consequently the fourth-longest in the U.
Ideal gas lawThe ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form: where , and are the pressure, volume and temperature respectively; is the amount of substance; and is the ideal gas constant.
State of PalestinePalestine (Filasṭīn, fɪ.lɪs.tʕiː.n), officially the State of Palestine (Dawlat Filasṭīn), is a state located in the Southern Levant region of West Asia. Officially governed by the Palestine Liberation Organization (PLO), it claims the West Bank (including East Jerusalem) and the Gaza Strip as its territory, though the entirety of that territory has been under Israeli occupation since the 1967 Six-Day War.
Wave equationThe (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields - as they occur in classical physics - such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics. Single mechanical or electromagnetic waves propagating in a pre-defined direction can also be described with the first-order one-way wave equation, which is much easier to solve and also valid for inhomogeneous media.
Ideal gasAn ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.
