These range from simplified forms of the first-principles equations that are easier or faster to solve, to approximations limiting the size of the system ( for example, periodic boundary conditions ), to fundamental approximations to the underlying equations that are required to achieve any solution to them at all.

These definitions lack precision: in particular the boundary between the classical objects and the scattered disk remains blurred.

These extinctions, occurring near the Pleistocene – Holocene boundary, are sometimes referred to as the Quaternary extinction event or Ice Age extinction.

These mountains are recognised by biogeographers as the boundary between two of the Earth's great ecozones: the temperate Palearctic that covers most of Eurasia and the tropical and subtropical Indomalaya ecozone which includes the Indian subcontinent, Southeast Asia and Indonesia.

These are the Rainy River, the Pigeon River, Lake Superior, the St. Mary's River, Lake Huron, the St. Clair River, Lake St. Clair, the Detroit River, Lake Erie, the Niagara River, Lake Ontario, and along the St. Lawrence River from Kingston, Ontario to the Quebec boundary just east of Cornwall, Ontario.

These points are: the boundary with Poland on a long Vistula Spit separating the Gdańsk Bay from the Vistula Lagoon ; and the farthest southeast of the Kuril Islands.

These are the North Anatolian Fault Zone, which forms the present day plate boundary of Eurasia near the Black Sea coast, and the East Anatolian Fault Zone, which forms part of the boundary of the North Arabian Plate in the southeast.

These errors include back-row or libero players spiking the ball or blocking ( back-row players may spike the ball if they jump from behind the attack line ), players not being in the correct position when the ball is served, attacking the serve in the front court and above the height of the net, using another player as a source of support to reach the ball, stepping over the back boundary line when serving, taking more than 8 seconds to serve, or playing the ball when it is above the opponent's court.

These so-called " hotspots ", for example Hawaii, are postulated to arise from upwelling diapirs with magma from the core – mantle boundary, 3, 000 km deep in the Earth.

These are postulated to comprise columns of hot material that rise from the core-mantle boundary.

These two layers have poor differentiated boundary but are increasingly stiffer than SLLPs.

These areas would have been strictly " free territory " by the Missouri Compromise, which allowed slavery in the State of Missouri but disallowed it everywhere north of the latitude 36 degrees, 30 minutes, which forms most of the southern boundary of Missouri.

These boundary conditions eliminate an infinite number of solutions to the wave equation, and the ones that remain are the possible solutions to the wave equation inside the waveguide.

These angles are measured with respect to the normal line, represented perpendicular to the boundary.

These predictions were confirmed by the experiments of Chang and Jones on commercial glasses and glass ceramics, where mean free paths were limited by " internal boundary scattering " to length scales of 10 < sup >− 2 </ sup > cm to 10 < sup >− 3 </ sup > cm.

These different boundary conditions strongly affect the applications of the transform and lead to uniquely useful properties for the various DCT types.

These Amorites, described in the Bible as being ruled by King Sihon, confined the Moabites to the country south of the river Arnon, which formed their northern boundary.

These routes provide a variety of links to locations within the Royal Borough of Greenwich, nearby and neighbouring boroughs including Bexley, Lewisham and Bromley, plus links into Central London and to Bluewater which is across the London boundary in the Dartford borough of Kent.

These meanings of open and closed, and the mathematical meanings, give rise to ambiguity because the terms can also refer to a closed manifold i. e. compact without boundary, not to be confused with a closed set.

These different boundary conditions strongly affect the applications of the transform, and lead to uniquely useful properties for the various DCT types.

These vesicles contain lipids, proteins and carbohydrates needed for the formation of a new cell boundary.

These wind changes force wind shear between the boundary layer and the wind aloft, and is most emphasized at night.

These treaties had awarded France territorial gains, but because of the vagaries of the language ( as with most treaties of the period ) they were notoriously imprecise and self-contradictory, and never specified exact boundary lines.

These conditions are unobtainable -- are not even approachable in the qualified sense I have indicated -- without the prior defeat of world Communism.

These conditions man did not keep, and thus he became mortal ; ;

These officials urged the President to use his leverage to insist on conditions assuring the rights of freedmen.

These conditions can be used to handle unusual situations.

These antigens should, under normal conditions, not be the target of the immune system, but, due to mainly genetic and environmental factors, the normal immunological tolerance for such an antigen has been lost in these patients.

These stress conditions have a negative impact on rice production.

These conditions played an important role in the development of the structure theory of commutative rings in the works of David Hilbert, Emmy Noether, and Emil Artin.

These tests were performed under wet exposure conditions.

These may be " natural alloys " manufactured by smelting zinc rich copper ores in reducing conditions.

These organisms are associated with certain predisposing conditions:

These center on the capabilities and limitations of doctors and other health-service providers, people identified with genetic conditions, and the general public in dealing with genetic information.

These disorders range from bipolar I disorder, featuring full-blown manic episodes, to cyclothymia, featuring less prominent hypomanic episodes, to " subsyndromal " conditions where only some of the criteria for mania or hypomania are met.

These conditions apparently had little effect in the deep tropics, where lush coal swamps flourished within 30 degrees of the northernmost glaciers.

These are provided by various independent shipping companies and their conditions and seaworthiness vary considerably.

These consisting of glacial periods where conditions are colder than normal, separated by interglacial periods.

These processes differ in the means by which chemical reactions are initiated ( e. g., activation process ) and process conditions.

These enzymes increase the rates of biochemical reactions, so that metabolic syntheses and decompositions impossible under ordinary conditions may be performed at the temperatures and concentrations present within a cell.

These two conditions comprise the cosmological principle.

These conditions can be achieved through improvements in macroeconomic and fiscal framework, public administration, and labour market flexibility.

These conditions are met in two places on Earth ; in the lithospheric mantle below relatively stable continental plates, and at the site of a meteorite strike.

These rights were subject to the following conditions: only good quality goods were to be supplied by the Faroese and were to be made in numbers proportionate to the rest of the market ; the goods were to be brought at their market value ; and the traders were to deal fairly and honestly with the Faroese.

These wounds, even when they are microscopic, increase the chances of contracting STDs that can be transmitted orally under these conditions.

These all require special conditions and considerations.

These granites are formed by melting of the lower crust under conditions that are usually extremely dry.