The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:^{[1]}
where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume,^{[2]} although this is scientifically inaccurate – this quantity is more specifically called specific weight.
For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser.
To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water.
The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid. This causes it to rise relative to more dense unheated material.
The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.
Density  

Common symbols  ρ D 
SI unit  kg/m^{3} 
In a wellknown but probably apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy.^{[3]} Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass; but the king did not approve of this. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!" (Εύρηκα! Greek "I have found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.
The story first appeared in written form in Vitruvius' books of architecture, two centuries after it supposedly took place.^{[4]} Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time.^{[5]}^{[6]}
From the equation for density (ρ = m/V), mass density has units of mass divided by volume. As there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per cubic metre (kg/m^{3}) and the cgs unit of gram per cubic centimetre (g/cm^{3}) are probably the most commonly used units for density. One g/cm^{3} is equal to one thousand kg/m^{3}. One cubic centimetre (abbreviation cc) is equal to one millilitre. In industry, other larger or smaller units of mass and or volume are often more practical and US customary units may be used. See below for a list of some of the most common units of density.
A number of techniques as well as standards exist for the measurement of density of materials. Such techniques include the use of a hydrometer (a buoyancy method for liquids), Hydrostatic balance (a buoyancy method for liquids and solids), immersed body method (a buoyancy method for liquids), pycnometer (liquids and solids), air comparison pycnometer (solids), oscillating densitometer (liquids), as well as pour and tap (solids).^{[7]} However, each individual method or technique measures different types of density (e.g. bulk density, skeletal density, etc.), and therefore it is necessary to have an understanding of the type of density being measured as well as the type of material in question.
The density at all points of a homogeneous object equals its total mass divided by its total volume. The mass is normally measured with a scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. To determine the density of a liquid or a gas, a hydrometer, a dasymeter or a Coriolis flow meter may be used, respectively. Similarly, hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object.
If the body is not homogeneous, then its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: , where is an elementary volume at position . The mass of the body then can be expressed as
In practice, bulk materials such as sugar, sand, or snow contain voids. Many materials exist in nature as flakes, pellets, or granules.
Voids are regions which contain something other than the considered material. Commonly the void is air, but it could also be vacuum, liquid, solid, or a different gas or gaseous mixture.
The bulk volume of a material—inclusive of the void fraction—is often obtained by a simple measurement (e.g. with a calibrated measuring cup) or geometrically from known dimensions.
Mass divided by bulk volume determines bulk density. This is not the same thing as volumetric mass density.
To determine volumetric mass density, one must first discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For the closepacking of equal spheres the nonvoid fraction can be at most about 74%. It can also be determined empirically. Some bulk materials, however, such as sand, have a variable void fraction which depends on how the material is agitated or poured. It might be loose or compact, with more or less air space depending on handling.
In practice, the void fraction is not necessarily air, or even gaseous. In the case of sand, it could be water, which can be advantageous for measurement as the void fraction for sand saturated in water—once any air bubbles are thoroughly driven out—is potentially more consistent than dry sand measured with an air void.
In the case of noncompact materials, one must also take care in determining the mass of the material sample. If the material is under pressure (commonly ambient air pressure at the earth's surface) the determination of mass from a measured sample weight might need to account for buoyancy effects due to the density of the void constituent, depending on how the measurement was conducted. In the case of dry sand, sand is so much denser than air that the buoyancy effect is commonly neglected (less than one part in one thousand).
Mass change upon displacing one void material with another while maintaining constant volume can be used to estimate the void fraction, if the difference in density of the two voids materials is reliably known.
In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures.
The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10^{−6} bar^{−1} (1 bar = 0.1 MPa) and a typical thermal expansivity is 10^{−5} K^{−1}. This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires a temperature increase on the order of thousands of degrees Celsius.
In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is
where M is the molar mass, P is the pressure, R is the universal gas constant, and T is the absolute temperature. This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature.
In the case of volumic thermal expansion at constant pressure and small intervals of temperature the temperature dependence of density is :
where is the density at a reference temperature, is the thermal expansion coefficient of the material at temperatures close to .
The density of a solution is the sum of mass (massic) concentrations of the components of that solution.
Mass (massic) concentration of each given component ρ_{i} in a solution sums to density of the solution.
Expressed as a function of the densities of pure components of the mixture and their volume participation, it allows the determination of excess molar volumes:
provided that there is no interaction between the components.
Knowing the relation between excess volumes and activity coefficients of the components, one can determine the activity coefficients.
Material  ρ (kg/m^{3})^{[note 1]}  Notes 

Hydrogen  0.0898  
Helium  0.179  
Aerographite  0.2  ^{[note 2]}^{[8]}^{[9]} 
Metallic microlattice  0.9  ^{[note 2]} 
Aerogel  1.0  ^{[note 2]} 
Air  1.2  At sea level 
Tungsten hexafluoride  12.4  One of the heaviest known gases at standard conditions 
Liquid hydrogen  70  At approx. −255 °C 
Styrofoam  75  Approx.^{[10]} 
Cork  240  Approx.^{[10]} 
Pine  373  ^{[11]} 
Lithium  535  
Wood  700  Seasoned, typical^{[12]}^{[13]} 
Oak  710  ^{[11]} 
Potassium  860  ^{[14]} 
Ice  916.7  At temperature < 0 °C 
Cooking oil  910–930  
Sodium  970  
Water (fresh)  1,000  At 4 °C, the temperature of its maximum density 
Water (salt)  1,030  3% 
Liquid oxygen  1,141  At approx. −219 °C 
Nylon  1,150  
Plastics  1,175  Approx.; for polypropylene and PETE/PVC 
Tetrachloroethene  1,622  
Magnesium  1,740  
Beryllium  1,850  
Glycerol  1,261  ^{[15]} 
Concrete  2,400  ^{[16]}^{[17]} 
Silicon  2,330  
Aluminium  2,700  
Diiodomethane  3,325  Liquid at room temperature 
Diamond  3,500  
Titanium  4,540  
Selenium  4,800  
Vanadium  6,100  
Antimony  6,690  
Zinc  7,000  
Chromium  7,200  
Tin  7,310  
Manganese  7,325  Approx. 
Iron  7,870  
Niobium  8,570  
Brass  8,600  ^{[17]} 
Cadmium  8,650  
Cobalt  8,900  
Nickel  8,900  
Copper  8,940  
Bismuth  9,750  
Molybdenum  10,220  
Silver  10,500  
Lead  11,340  
Thorium  11,700  
Rhodium  12,410  
Mercury  13,546  
Tantalum  16,600  
Uranium  18,800  
Tungsten  19,300  
Gold  19,320  
Plutonium  19,840  
Rhenium  21,020  
Platinum  21,450  
Iridium  22,420  
Osmium  22,570  
Notes: 
Entity  ρ (kg/m^{3})  Notes 

Interstellar medium  1×10^{−19}  Assuming 90% H, 10% He; variable T 
The Earth  5,515  Mean density.^{[18]} 
The inner core of the Earth  13,000  Approx., as listed in Earth.^{[19]} 
The core of the Sun  33,000–160,000  Approx.^{[20]} 
Supermassive black hole  9×10^{5}  Density of a 4.5millionsolarmass black hole Event horizon radius is 13.5 million km. 
White dwarf star  2.1×10^{9}  Approx.^{[21]} 
Atomic nuclei  2.3×10^{17}  Does not depend strongly on size of nucleus^{[22]} 
Neutron star  1×10^{18}  
Stellarmass black hole  1×10^{18}  Density of a 4solarmass black hole Event horizon radius is 12 km. 
Temp. (°C)^{[note 1]}  Density (kg/m^{3}) 

−30  983.854 
−20  993.547 
−10  998.117 
0  999.8395 
4  999.9720 
10  999.7026 
15  999.1026 
20  998.2071 
22  997.7735 
25  997.0479 
30  995.6502 
40  992.2 
60  983.2 
80  971.8 
100  958.4 
Notes:

T (°C)  ρ (kg/m^{3}) 

−25  1.423 
−20  1.395 
−15  1.368 
−10  1.342 
−5  1.316 
0  1.293 
5  1.269 
10  1.247 
15  1.225 
20  1.204 
25  1.184 
30  1.164 
35  1.146 
The SI unit for density is:
The litre and metric tons are not part of the SI, but are acceptable for use with it, leading to the following units:
Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m^{3}). Liquid water has a density of about 1 kg/dm^{3}, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm^{3}.
In US customary units density can be stated in:
Imperial units differing from the above (as the Imperial gallon and bushel differ from the US units) in practice are rarely used, though found in older documents. The Imperial gallon was based on the concept that an Imperial fluid ounce of water would have a mass of one Avoirdupois ounce, and indeed 1 g/cc ≈ 1.00224129 ounces per Imperial fluid ounce = 10.0224129 pounds per Imperial gallon. The density of precious metals could conceivably be based on Troy ounces and pounds, a possible cause of confusion.
The Big Bang theory is the prevailing cosmological model for the observable universe from the earliest known periods through its subsequent largescale evolution. The model describes how the universe expanded from a very highdensity and hightemperature state, and offers a comprehensive explanation for a broad range of phenomena, including the abundance of light elements, the cosmic microwave background (CMB), large scale structure and Hubble's law (the farther away galaxies are, the faster they are moving away from Earth). If the observed conditions are extrapolated backwards in time using the known laws of physics, the prediction is that just before a period of very high density there was a singularity which is typically associated with the Big Bang. Physicists are undecided whether this means the universe began from a singularity, or that current knowledge is insufficient to describe the universe at that time. Detailed measurements of the expansion rate of the universe place the Big Bang at around 13.8 billion years ago, which is thus considered the age of the universe. After its initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, and later simple atoms. Giant clouds of these primordial elements (mostly hydrogen, with some helium and lithium) later coalesced through gravity, eventually forming early stars and galaxies, the descendants of which are visible today. Astronomers also observe the gravitational effects of dark matter surrounding galaxies. Though most of the mass in the universe seems to be in the form of dark matter, Big Bang theory and various observations seem to indicate that it is not made out of conventional baryonic matter (protons, neutrons, and electrons) but it is unclear exactly what it is made out of.
Since Georges Lemaître first noted in 1927 that an expanding universe could be traced back in time to an originating single point, scientists have built on his idea of cosmic expansion. The scientific community was once divided between supporters of two different theories, the Big Bang and the Steady State theory, but a wide range of empirical evidence has strongly favored the Big Bang which is now universally accepted. In 1929, from analysis of galactic redshifts, Edwin Hubble concluded that galaxies are drifting apart; this is important observational evidence consistent with the hypothesis of an expanding universe. In 1964, the cosmic microwave background radiation was discovered, which was crucial evidence in favor of the Big Bang model, since that theory predicted the existence of background radiation throughout the universe before it was discovered. More recently, measurements of the redshifts of supernovae indicate that the expansion of the universe is accelerating, an observation attributed to dark energy's existence. The known physical laws of nature can be used to calculate the characteristics of the universe in detail back in time to an initial state of extreme density and temperature.
BuoyancyIn physics, buoyancy () or upthrust, is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained by Archimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the volume of the object, i.e. the displaced fluid.
For this reason, an object whose average density is greater than that of the fluid in which it is submerged tends to sink. If the object is less dense than the liquid, the force can keep the object afloat. This can occur only in a noninertial reference frame, which either has a gravitational field or is accelerating due to a force other than gravity defining a "downward" direction.The center of buoyancy of an object is the centroid of the displaced volume of fluid.
Electric currentAn electric current is a flow of electric charge. In electric circuits this charge is often carried by electrons moving through a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionized gas (plasma).The SI unit of electric current is the ampere, which is the flow of electric charge across a surface at the rate of one coulomb per second. Electric current is measured using a device called an ammeter.Electric currents cause Joule heating, which creates light in incandescent light bulbs. They also create magnetic fields, which are used in motors, inductors and generators.
The moving charged particles in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom, and can move freely about within the metal. These conduction electrons are the charge carriers in metal conductors.
Energy densityEnergy density is the amount of energy stored in a given system or region of space per unit volume. Colloquially it may also be used for energy per unit mass, though the accurate term for this is specific energy. Often only the useful or extractable energy is measured, which is to say that inaccessible energy (such as rest mass energy) is ignored. In cosmological and other general relativistic contexts, however, the energy densities considered are those that correspond to the elements of the stress–energy tensor and therefore do include mass energy as well as energy densities associated with the pressures described in the next paragraph.
Energy per unit volume has the same physical units as pressure, and in many circumstances is a synonym: for example, the energy density of a magnetic field may be expressed as (and behaves as) a physical pressure, and the energy required to compress a compressed gas a little more may be determined by multiplying the difference between the gas pressure and the external pressure by the change in volume. In short, pressure is a measure of the enthalpy per unit volume of a system. A pressure gradient has the potential to perform work on the surroundings by converting enthalpy to work until equilibrium is reached.
Floppy diskA floppy disk, also known as a floppy, diskette, or simply disk, is a type of disk storage composed of a disk of thin and flexible magnetic storage medium, sealed in a rectangular plastic enclosure lined with fabric that removes dust particles. Floppy disks are read and written by a floppy disk drive (FDD).
Floppy disks, initially as 8inch (203 mm) media and later in 5 1⁄4inch (133 mm) and 3 1⁄2 inch (90 mm) sizes, were a ubiquitous form of data storage and exchange from the mid1970s into the first years of the 21st century. By 2006 computers were rarely manufactured with installed floppy disk drives; 3 1⁄2inch floppy disks can be used with an external USB floppy disk drive, but USB drives for 5 1⁄4inch, 8inch, and nonstandard diskettes are rare to nonexistent. These formats are usually handled by older equipment.
The prevalence of floppy disks in latetwentieth century culture was such that many electronic and software programs still use the floppy disks as save icons. While floppy disk drives still have some limited uses, especially with legacy industrial computer equipment, they have been superseded by data storage methods with much greater capacity, such as USB flash sticks, flash storage cards, portable external hard disk drives, optical discs, cloud storage and storage available through computer networks.
HistogramA histogram is an accurate representation of the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable (quantitative variable) and was first introduced by Karl Pearson. It differs from a bar graph, in the sense that a bar graph relates two variables, but a histogram relates only one. To construct a histogram, the first step is to "bin" (or "bucket") the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, nonoverlapping intervals of a variable. The bins (intervals) must be adjacent, and are often (but are not required to be) of equal size.If the bins are of equal size, a rectangle is erected over the bin with height proportional to the frequency—the number of cases in each bin. A histogram may also be normalized to display "relative" frequencies. It then shows the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1.
However, bins need not be of equal width; in that case, the erected rectangle is defined to have its area proportional to the frequency of cases in the bin. The vertical axis is then not the frequency but frequency density—the number of cases per unit of the variable on the horizontal axis. Examples of variable bin width are displayed on Census bureau data below.
As the adjacent bins leave no gaps, the rectangles of a histogram touch each other to indicate that the original variable is continuous.Histograms give a rough sense of the density of the underlying distribution of the data, and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the xaxis are all 1, then a histogram is identical to a relative frequency plot.
A histogram can be thought of as a simplistic kernel density estimation, which uses a kernel to smooth frequencies over the bins. This yields a smoother probability density function, which will in general more accurately reflect distribution of the underlying variable. The density estimate could be plotted as an alternative to the histogram, and is usually drawn as a curve rather than a set of boxes. Histograms are nevertheless preferred in applications, when their statistical properties need to be modeled. The correlated variation of a kernel density estimate is very difficult to describe mathematically, while it is simple for a histogram where each bin varies independently.
An alternative to kernel density estimation is the average shifted histogram,
which is fast to compute and gives a smooth curve estimate of the density without using kernels.
The histogram is one of the seven basic tools of quality control.Histograms are sometimes confused with bar charts. A histogram is used for continuous data, where the bins represent ranges of data, while a bar chart is a plot of categorical variables. Some authors recommend that bar charts have gaps between the rectangles to clarify the distinction.
List of countries and dependencies by population densityThis is a list of countries and dependent territories ranked by population density, measured by the number of human inhabitants per square kilometer.
The list includes sovereign states and selfgoverning dependent territories based upon the ISO standard ISO 31661. The list also includes but does not rank unrecognized but de facto independent countries. The figures in the following table are based on areas including inland water bodies (lakes, reservoirs, rivers).
Figures used in this article are mainly based on the latest censuses and official estimates (or projections). Where there is not such updated national data available, figures are based on the online projections provided by the Population Division of the United Nations Department of Economic and Social Affairs.
Lowdensity lipoproteinLowdensity lipoprotein (LDL) is one of the five major groups of lipoprotein which transport all fat molecules around the body in the extracellular water. These groups, from least dense, compared to surrounding water (largest particles) to most dense (smallest particles), are chylomicrons (aka ULDL by the overall density naming convention), very lowdensity lipoprotein (VLDL), intermediatedensity lipoprotein (IDL), lowdensity lipoprotein and highdensity lipoprotein (HDL). LDL delivers fat molecules to the cells and can drive the progression of atherosclerosis if they become oxidized within the walls of arteries.
Magnetic fieldA magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials (such as iron) and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges (electric currents) such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.
The term 'magnetic field' is used for two distinct but closely related fields denoted by the symbols B and H. In the International System of Units, H, magnetic field strength, is measured in the SI base units of ampere per meter. B, magnetic flux density, is measured in tesla (in SI base units: kilogram per second^{2} per ampere), which is equivalent to newton per meter per ampere. H and B differ in how they account for magnetization. In a vacuum, B and H are the same aside from units; but in a magnetized material, B/ and H differ by the magnetization M of the material at that point in the material.
Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated, and are both components of the electromagnetic force, one of the four fundamental forces of nature.
Magnetic fields are widely used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.
Mediumdensity fibreboardMediumdensity fibreboard (MDF) is an engineered wood product made by breaking down hardwood or softwood residuals into wood fibres, often in a defibrator, combining it with wax and a resin binder, and forming panels by applying high temperature and pressure. MDF is generally denser than plywood. It is made up of separated fibres, but can be used as a building material similar in application to plywood. It is stronger and much denser than particle board.The name derives from the distinction in densities of fibreboard. Largescale production of MDF began in the 1980s, in both North America and Europe.
Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent realvalued random variables whose distributions are not known. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.
The normal distribution is useful because of the central limit theorem. In its most general form, under some conditions (which include finite variance), it states that averages of samples of observations of random variables independently drawn from independent distributions converge in distribution to the normal, that is, they become normally distributed when the number of observations is sufficiently large. Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal. Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.
The normal distribution is sometimes informally called the bell curve. However, many other distributions are bellshaped (such as the Cauchy, Student's t, and logistic distributions).
The probability density of the normal distribution is
where
PolyethylenePolyethylene or polythene (abbreviated PE; IUPAC name polyethene or poly(methylene)) is the most common plastic. As of 2017, over 100 million tonnes of polyethylene resins are produced annually, accounting for 34% of the total plastics market. Its primary use is in packaging (plastic bags, plastic films, geomembranes, containers including bottles, etc.). Many kinds of polyethylene are known, with most having the chemical formula (C2H4)n. PE is usually a mixture of similar polymers of ethylene with various values of n. Polyethylene is a thermoplastic; however, it can become a thermoset plastic when modified (such as crosslinked polyethylene).
Population densityPopulation density (in agriculture: standing stock and standing crop) is a measurement of population per unit area or unit volume; it is a quantity of type number density. It is frequently applied to living organisms, and most of the time to humans. It is a key geographical term. In simple terms population density refers to the number of people living in an area per kilometer square.
Probability density functionIn probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample. In other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there are an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would equal one sample compared to the other sample.
In a more precise sense, the PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.
The terms "probability distribution function" and "probability function" have also sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. In other sources, "probability distribution function" may be used when the probability distribution is defined as a function over general sets of values, or it may refer to the cumulative distribution function, or it may be a probability mass function (PMF) rather than the density. "Density function" itself is also used for the probability mass function, leading to further confusion. In general though, the PMF is used in the context of discrete random variables (random variables that take values on a discrete set), while PDF is used in the context of continuous random variables.
Properties of waterWater (H2O) is a polar inorganic compound that is at room temperature a tasteless and odorless liquid, which is nearly colorless apart from an inherent hint of blue. It is by far the most studied chemical compound and is described as the "universal solvent" and the "solvent of life". It is the most abundant substance on Earth and the only common substance to exist as a solid, liquid, and gas on Earth's surface. It is also the third most abundant molecule in the universe.Water molecules form hydrogen bonds with each other and are strongly polar. This polarity allows it to dissociate ions in salts and bond to other polar substances such as alcohols and acids, thus dissolving them. Its hydrogen bonding causes its many unique properties, such as having a solid form less dense than its liquid form, a relatively high boiling point of 100 °C for its molar mass, and a high heat capacity.
Water is amphoteric, meaning that it can exhibit properties of an acid or a base, depending on the pH of the solution that it is in; it readily produces both H+ and OH− ions. Related to its amphoteric character, it undergoes selfionization. The product of the activities, or approximately, the concentrations of H+ and OH− is a constant, so their respective concentrations are inversely proportional to each other.
Provinces of ChinaProvinciallevel administrative divisions (Chinese: 省级行政区; pinyin: shěngjí xíngzhèngqū) or firstlevel administrative divisions (一级行政区; yījí xíngzhèngqū), are the highestlevel Chinese administrative divisions. There are 34 such divisions, classified as 23 provinces (Chinese: 省; pinyin: shěng), four municipalities, five autonomous regions, and two Special Administrative Regions. All but Taiwan Province and a small fraction of Fujian Province (currently administered by the Republic of China) are controlled by the People's Republic of China.
Note that every province (except Hong Kong and Macau, the two special administrative regions) has a Communist Party of China provincial committee (Chinese: 省委; pinyin: shěngwěi), headed by a secretary (Chinese: 书记; pinyin: shūjì). The committee secretary is effectively in charge of the province, rather than the nominal governor of the provincial government.
Specific gravitySpecific gravity is the ratio of the density of a substance to the density of a reference substance; equivalently, it is the ratio of the mass of a substance to the mass of a reference substance for the same given volume. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance for liquids is nearly always water at its densest (at 4 °C or 39.2 °F); for gases it is air at room temperature (20 °C or 68 °F). Nonetheless, the temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 atm (101.325 kPa).
Temperatures for both sample and reference vary from industry to industry. In British beer brewing, the practice for specific gravity as specified above is to multiply it by 1,000. Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, hydrocarbons, antifreeze coolants, sugar solutions (syrups, juices, honeys, brewers wort, must, etc.) and acids.
Spectral density
The power spectrum of a time series describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum.
When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (or simply power spectrum), which applies to signals existing over all time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The power spectral density (PSD) then refers to the spectral energy distribution that would be found per unit time, since the total energy of such a signal over all time would generally be infinite. Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical process), identical to what would be obtained by integrating over the time domain, as dictated by Parseval's theorem.
The spectrum of a physical process often contains essential information about the nature of . For instance, the pitch and timbre of a musical instrument are immediately determined from a spectral analysis. The color of a light source is determined by the spectrum of the electromagnetic wave's electric field as it fluctuates at an extremely high frequency. Obtaining a spectrum from time series such as these involves the Fourier transform, and generalizations based on Fourier analysis. In many cases the time domain is not specifically employed in practice, such as when a dispersive prism is used to obtain a spectrum of light in a spectrograph, or when a sound is perceived through its effect on the auditory receptors of the inner ear, each of which is sensitive to a particular frequency.
However this article concentrates on situations in which the time series is known (at least in a statistical sense) or directly measured (such as by a microphone sampled by a computer). The power spectrum is important in statistical signal processing and in the statistical study of stochastic processes, as well as in many other branches of physics and engineering. Typically the process is a function of time, but one can similarly discuss data in the spatial domain being decomposed in terms of spatial frequency.
Uniform distribution (continuous)In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values. The distribution is often abbreviated U(a,b). It is the maximum entropy probability distribution for a random variable X under no constraint other than that it is contained in the distribution's support.
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