Arithmetic functionIn number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function f(n) whose domain is the positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition the requirement that an arithmetical function "expresses some arithmetical property of n". An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n.
Average order of an arithmetic functionIn number theory, an average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average". Let be an arithmetic function. We say that an average order of is if as tends to infinity. It is conventional to choose an approximating function that is continuous and monotone. But even so an average order is of course not unique. In cases where the limit exists, it is said that has a mean value (average value) .
Oxygen-18Oxygen-18 (18O, Ω) is a natural, stable isotope of oxygen and one of the environmental isotopes. 18O is an important precursor for the production of fluorodeoxyglucose (FDG) used in positron emission tomography (PET). Generally, in the radiopharmaceutical industry, enriched water (H218O) is bombarded with hydrogen ions in either a cyclotron or linear accelerator, producing fluorine-18. This is then synthesized into FDG and injected into a patient. It can also be used to make an extremely heavy version of water when combined with tritium (hydrogen-3): 3H218O or T218O.
Kunlun MountainsThe Kunlun Mountains constitute one of the longest mountain chains in Asia, extending for more than . In the broadest sense, the chain forms the northern edge of the Tibetan Plateau south of the Tarim Basin. The exact definition of Kunlun Mountains varies over time. Older sources used Kunlun to mean the mountain belt that runs across the center of China, that is, Altyn Tagh along with the Qilian and Qin Mountains. Recent sources have the Kunlun range forming most of the south side of the Tarim Basin and then continuing east, south of the Altyn Tagh.
GroundwaterGroundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidated deposit is called an aquifer when it can yield a usable quantity of water. The depth at which soil pore spaces or fractures and voids in rock become completely saturated with water is called the water table.
Earliest known life formsThe earliest known life forms on Earth are believed to be fossilized microorganisms found in hydrothermal vent precipitates, considered to be about 3.42 billion years old. The earliest time for the origin of life on Earth is at least 3.77 billion years ago, possibly as early as 4.28 billion years ago—not long after the oceans formed 4.5 billion years ago, and after the formation of the Earth 4.54 billion years ago. The earliest direct evidence of life on Earth is from microfossils of microorganisms permineralized in 3.
Iron in folkloreIron has a long and varied tradition in the mythology and folklore of the world. While iron is now the name of a chemical element, the traditional meaning of the word "iron" is what is now called wrought iron. In East Asia, cast iron was also common after 500 BCE, and was called "cooked iron", with wrought iron being called "raw iron" (in Europe, cast iron remained very rare until it was used for cannonballs in the 14th century).
Hot springA hot spring, hydrothermal spring, or geothermal spring is a spring produced by the emergence of geothermally heated groundwater onto the surface of the Earth. The groundwater is heated either by shallow bodies of magma (molten rock) or by circulation through faults to hot rock deep in the Earth's crust. In either case, the ultimate source of the heat is the radioactive decay of naturally occurring radioactive elements in the Earth's mantle, the layer beneath the crust. Hot spring water often contains large amounts of dissolved minerals.
Kinetic isotope effectIn physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for the reactions involving the light (kL) and the heavy (kH) isotopically substituted reactants (isotopologues): This change in reaction rate is a quantum mechanical effect that primarily results from heavier isotopologues having lower vibrational frequencies compared to their lighter counterparts.
Lake ErieLake Erie (ˈɪəri ) is the fourth-largest lake by surface area of the five Great Lakes in North America and the eleventh-largest globally. It is the southernmost, shallowest, and smallest by volume of the Great Lakes and also has the shortest average water residence time. At its deepest point Lake Erie is deep. Situated on the International Boundary between Canada and the United States, Lake Erie's northern shore is the Canadian province of Ontario, specifically the Ontario Peninsula, with the U.S.
