query: which is a metric unit of amount of a pure substance

pos: Amount of substance Amount of substance Amount of substance is a standard-defined quantity that measures the size of an ensemble of particles, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units (SI) defines the amount of substance to be proportional to the number of entities present. The SI unit for amount of substance is the mole. It has the unit symbol mol. The proportionality constant is the inverse of the Avogadro constant. The mole is defined as the amount of substance that contains an equal number of elementary entities as there

pos: Avogadro constant of molecules in one gram-molecule of oxygen (exactly of oxygen, according to the definitions of the period), and this term is still widely used, especially in introductory works. The change in name to "Avogadro constant" ("N") came with the introduction of the mole as a base unit in the International System of Units (SI) in 1971, which regarded amount of substance as an independent dimension of measurement. With this recognition, the Avogadro constant was no longer a pure number, but had a unit of measurement, the reciprocal mole (mol). While it is rare to use units of amount of substance

pos: Mole (unit) The term "gram-molecule" was formerly used for essentially the same concept. The term "gram-atom" has been used for a related but distinct concept, namely a quantity of a substance that contains Avogadro's number of "atoms", whether isolated or combined in molecules. Thus, for example, 1 mole of MgBr is 1 gram-molecule of MgBr but 3 gram-atoms of MgBr. Amount of substance is a measure of the quantity of substance proportional to the number of its entities. , the mole is defined by International Bureau of Weights and Measures as: Thus, by definition, one mole of pure C has a mass

pos: Mole (unit) informal holiday in honor of the unit among chemists. The date is derived from the Avogadro number, which is approximately . It starts at 6:02 a.m. and ends at 6:02 p.m. Alternatively, some chemists celebrate June 2 or February 6, a reference to the 6.02 part of the constant. Mole (unit) The mole is the unit of measurement for amount of substance in the International System of Units (SI). Effective 20 May 2019, the mole is defined as the amount of a chemical substance that contains exactly (Avogadro's constant) constitutive particles, e.g., atoms, molecules, ions or electrons. This definition was

pos: Mole (unit) Mole (unit) The mole is the unit of measurement for amount of substance in the International System of Units (SI). Effective 20 May 2019, the mole is defined as the amount of a chemical substance that contains exactly (Avogadro's constant) constitutive particles, e.g., atoms, molecules, ions or electrons. This definition was adopted in November of 2018, revising its old definition based on the number of atoms in 12 grams of carbon-12 (C) (the isotope of carbon with standard atomic weight 12 by definition). The mole is an SI base unit, with the unit symbol mol. The mole is widely used

pos: Mole (unit) in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation can be interpreted to mean that 2 mol dihydrogen (H) and 1 mol dioxygen (O) react to form 2 mol water (HO). The mole may also be used to represent the number of atoms, ions, or other entities in a given sample of a substance. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is moles per litre (mol/l).

pos: Atomic mass The formation of elements with more than seven nucleons requires the fusion of three atoms of He-4 in the so-called triple alpha process, skipping over lithium, beryllium, and boron to produce carbon. Here are some values of the ratio of atomic mass to mass number: Direct comparison and measurement of the masses of atoms is achieved with mass spectrometry. The standard scientific unit used to quantify the amount of a substance in macroscopic quantities is the mole (symbol: mol), which is defined arbitrarily as the amount of a substance which has as many atoms or molecules as there are atoms

pos: Chemistry angular pyramidal etc.) the structure of polyatomic molecules, that are constituted of more than six atoms (of several elements) can be crucial for its chemical nature. A chemical substance is a kind of matter with a definite composition and set of properties. A collection of substances is called a mixture. Examples of mixtures are air and alloys. The mole is a unit of measurement that denotes an amount of substance (also called chemical amount). The mole is defined as the number of atoms found in exactly 0.012 kilogram (or 12 grams) of carbon-12, where the carbon-12 atoms are unbound, at

pos: Mole (unit) or theoretical space craft, the change is significant. The amount of substance remains the same regardless of temperature, pressure, speed or gravity, unless a (chemical or nuclear) reaction changes the number of particles. The history of the mole is intertwined with that of molecular mass, atomic mass unit, Avogadro number and related concepts. The first table of standard atomic weight (atomic mass) was published by John Dalton (1766–1844) in 1805, based on a system in which the relative atomic mass of hydrogen was defined as 1. These relative atomic masses were based on the stoichiometric proportions of chemical reaction and

neg: Heat capacity system. When expressing the same phenomenon as an intensive property, the heat capacity is divided by the amount of substance, mass, or volume, thus the quantity is independent of the size or extent of the sample. The molar heat capacity is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the specific heat capacity, often called simply specific heat, is the heat capacity per unit mass of a material. Nonetheless some authors use the term specific heat to refer to the ratio of the specific heat capacity of a substance at any given temperature to

neg: Heat The "molar heat capacity" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the "specific heat capacity", often called simply "specific heat", is the heat capacity per unit mass of a material. Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration. The specific heats of monatomic gases, such as helium, are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more. Before the development of the laws of

neg: Amount of substance are atoms in of the isotope carbon-12. This number is called the Avogadro number and has the value It is the numerical value of the Avogadro constant, which has the unit mol, and relates the molar mass of an amount of substance to its mass. Therefore, the amount of substance of a sample is calculated as the sample mass divided by the molar mass of the substance. Amount of substance appears in thermodynamic relations such as the ideal gas law, and in stoichiometric relations between reacting molecules as in the law of multiple proportions. Another unit of amount of substance

neg: Amount of substance the molar mass. Molar quantities are sometimes denoted by a subscript Latin "m" in the symbol, e.g. "C", molar heat capacity at constant pressure: the subscript may be omitted if there is no risk of ambiguity, as is often the case in pure chemistry. The main derived quantity in which amount of substance enters into the numerator is amount of substance concentration, "c". This name is often abbreviated to "amount concentration", except in clinical chemistry where "substance concentration" is the preferred term to avoid ambiguity with mass concentration. The term "molar concentration" is incorrect, but commonly used. The alchemists, and

neg: Wasserstein metric Wasserstein metric In mathematics, the Wasserstein or Kantorovich-Rubinstein metric or distance is a distance function defined between probability distributions on a given metric space formula_1. Intuitively, if each distribution is viewed as a unit amount of "dirt" piled on "formula_1", the metric is the minimum "cost" of turning one pile into the other, which is assumed to be the amount of dirt that needs to be moved times the mean distance it has to be moved. Because of this analogy, the metric is known in computer science as the earth mover's distance. The name "Wasserstein distance" was coined by R.

neg: International System of Units Another three base units (for temperature, amount of substance and luminous intensity) were added later. The early metric systems defined a unit of weight as a base unit, while the SI defines an analogous unit of mass. In everyday use, these are mostly interchangeable, but in scientific contexts the difference matters. Mass, strictly the inertial mass, represents a quantity of matter. It relates the acceleration of a body to the applied force via Newton's law, : force equals mass times acceleration. A force of 1 N (newton) applied to a mass of 1 kg will accelerate it at 1 m/s.

neg: Volumetric flow rate area through which the volume passes through, , and a unit vector normal to the area, . The relation is . The reason for the dot product is as follows. The only volume flowing "through" the cross-section is the amount normal to the area, that is, parallel to the unit normal. This amount is: where is the angle between the unit normal and the velocity vector of the substance elements. The amount passing through the cross-section is reduced by the factor . As increases less volume passes through. Substance which passes tangential to the area, that is perpendicular to the

neg: Epoxy the ratio of the amount of substance of epoxide groups, "n"(EP), and the mass "m"(B) of the material B, with the SI unit "mol/kg", or the so-called "epoxide equivalent weight", which is the ratio of the mass of a sample B of the resin and the amount of substance of epoxide groups present in that sample B, with the SI unit "kg/mol". The so-called "epoxide equivalent weight" is simply the inverse of the so-called "epoxide number". The specific amount of substance of epoxide groups is used to calculate the mass of co-reactant (hardener) to use when curing epoxy resins. Epoxies

neg: International unit that substance is officially abandoned in favor of a newly established mass. International unit In pharmacology, the international unit is a unit of measurement for the amount of a substance; the mass or volume that constitutes one international unit varies based on which substance is being measured, and the variance is based on the biological activity or effect, for the purpose of easier comparison across substances. International units are used to quantify vitamins, hormones, some medications, vaccines, blood products, and similar biologically active substances. The name international unit has often been capitalized (in English and other languages), although major English-language

neg: British thermal unit British thermal unit The British thermal unit (Btu or BTU) is a traditional unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is part of the United States customary units. Its counterpart in the metric system is the calorie, which is defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius. Heat is now known to be equivalent to energy, for which the SI unit is the joule; one BTU is about 1055

neg: Mole (unit) containing of hydrogen atoms in it, weighing exactly 1.008 grams (same as the Ar of one hydrogen atom). The molar mass of a substance is the mass of a sample divided by the amount of substance in that sample. This is a constant for any given substance. Since the unified atomic mass unit (symbol: u, or Da) is defined as 1/12 of the mass of the C atom, it follows that the molar mass of a substance, measured in grams per mole, is numerically equal to its mean atomic or molecular mass expressed in Da. One can determine the amount

neg: International unit International unit In pharmacology, the international unit is a unit of measurement for the amount of a substance; the mass or volume that constitutes one international unit varies based on which substance is being measured, and the variance is based on the biological activity or effect, for the purpose of easier comparison across substances. International units are used to quantify vitamins, hormones, some medications, vaccines, blood products, and similar biologically active substances. The name international unit has often been capitalized (in English and other languages), although major English-language dictionaries treat it as a common noun and thus use lower case.

neg: British thermal unit or 1899 joules. This unit was sometimes used in the United Kingdom as an alternative to BTU but is now obsolete. British thermal unit The British thermal unit (Btu or BTU) is a traditional unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is part of the United States customary units. Its counterpart in the metric system is the calorie, which is defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius. Heat

neg: Thermodynamic databases for pure substances slope of a plot of temperature vs. isobaric heat content (or the derivative of a temperature/heat content equation). The SI units for heat capacity are J/(mol·K). When heat is added to a condensed-phase substance, its temperature increases until a phase change temperature is reached. With further addition of heat, the temperature remains constant while the phase transition takes place. The amount of substance that transforms is a function of the amount of heat added. After the transition is complete, adding more heat increases the temperature. In other words, the enthalpy of a substance changes isothermally as it undergoes a physical

neg: Jensen–Shannon divergence it gives the upper bound for amount of classical information encoded by the quantum states formula_33 under the prior distribution formula_39 (see Holevo's theorem). Quantum Jensen–Shannon divergence for formula_40 and two density matrices is a symmetric function, everywhere defined, bounded and equal to zero only if two density matrices are the same. It is a square of a metric for pure states but it is unknown whether the metric property holds in general. The Bures metric is closely related to the quantum JS divergence; it is the quantum analog of the Fisher information metric. Nielsen introduced the skew K-divergence: formula_41

neg: Molality Molality Molality, also called molal concentration, is a measure of the concentration of a in a solution in terms of amount of substance in a specified amount of mass of the solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. A commonly used unit for molality in chemistry is mol/kg. A solution of concentration 1 mol/kg is also sometimes denoted as "1 molal". The molality ("b"), of a solution is defined as the amount of substance (in moles) of solute, "n", divided by the mass (in kg) of the solvent, "m": In

neg: Mole (unit) measure the amount of substance (although in practice it is usual). There are many physical relationships between amount of substance and other physical quantities, the most notable one being the ideal gas law (where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these colligative properties. Chemical engineers use the unit extensively, and decimal multiples may be more suitable for industrial use. For convenience in avoiding conversions in the imperial (or American customary units), some engineers adopted the "pound-mole" (notation "lb-mol" or "lbmol"), which is defined as the number of entities in

neg: Dobson unit squared. Dobson unit The Dobson unit (DU) is a unit of measurement of the amount of a trace gas in a vertical column through the Earth's atmosphere. It originated, and continues to be primarily used in respect to, atmospheric ozone, whose total column amount, usually termed "total ozone", and sometimes "column abundance", is dominated by the high concentrations of ozone in the stratospheric ozone layer. The Dobson Unit is defined as the thickness (in units of 10 µm) of that layer of pure gas which would be formed by the total column amount at standard conditions for temperature and pressure

neg: Dobson unit Dobson unit The Dobson unit (DU) is a unit of measurement of the amount of a trace gas in a vertical column through the Earth's atmosphere. It originated, and continues to be primarily used in respect to, atmospheric ozone, whose total column amount, usually termed "total ozone", and sometimes "column abundance", is dominated by the high concentrations of ozone in the stratospheric ozone layer. The Dobson Unit is defined as the thickness (in units of 10 µm) of that layer of pure gas which would be formed by the total column amount at standard conditions for temperature and pressure (STP).

neg: Entropy entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin (J K) in the International System of Units (or kg m s K in terms of base units). The entropy of a substance is usually given as an intensive property—either entropy per unit mass (SI unit: J K kg) or entropy per unit amount of substance (SI unit: J K mol). The French mathematician Lazare Carnot proposed in his 1803 paper "Fundamental Principles of Equilibrium and Movement" that in any machine the accelerations and shocks of the moving parts represent losses of "moment of

neg: Wasserstein metric bounded by some constant "C", then and so convergence in the Radon metric (identical to total variation convergence when "M" is a Polish space) implies convergence in the Wasserstein metric, but not vice versa. For any "p" ≥ 1, the metric space (P("M"), "W") is separable, and is complete if ("M", "d") is separable and complete. Wasserstein metric In mathematics, the Wasserstein or Kantorovich-Rubinstein metric or distance is a distance function defined between probability distributions on a given metric space formula_1. Intuitively, if each distribution is viewed as a unit amount of "dirt" piled on "formula_1", the metric is the

neg: Gram per litre Gram per litre A gram per litre or gram per liter (g/L or g/l) is a unit of measurement of mass concentration that shows how many grams of a certain substance are present in one litre of a (usually liquid or gaseous) mixture. It is not an SI unit – the SI unit of mass concentration is kilogram per cubic metre, which is equivalent. Metric prefixes are often applied, giving units like milligrams per litre (mg/L) or micrograms per decilitre (µg/dL). When measuring concentration in water, parts per million is an older expression of mg/L, since one litre of water

neg: Molar concentration Molar concentration Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per litre, having the unit symbol mol/L. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 "M". Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution. For

neg: Wood of wood as an indicator of wood quality is specific gravity (Timell 1986), as both pulp yield and lumber strength are determined by it. Specific gravity is the ratio of the mass of a substance to the mass of an equal volume of water; density is the ratio of a mass of a quantity of a substance to the volume of that quantity and is expressed in mass per unit substance, e.g., grams per milliliter (g/cm or g/ml). The terms are essentially equivalent as long as the metric system is used. Upon drying, wood shrinks and its density increases. Minimum

neg: Equivalent (chemistry) Equivalent (chemistry) An equivalent (symbol: equiv) is the amount of a substance that reacts with (or is "equivalent" to) an arbitrary amount of another substance in a given chemical reaction. It is an archaic unit of measurement that was used in chemistry and the biological sciences in the era before researchers knew how to determine the chemical formula for a compound. The mass of an equivalent is called its equivalent weight. In a more formal definition, the "equivalent" is the amount of a substance needed to do one of the following: By this definition, an "equivalent" is the number of

neg: Quaternionic manifold structure is called an almost quaternionic manifold. The quaternion structure bundle formula_26 naturally admits a bundle metric coming from the quaternionic algebra structure, and, with this metric, formula_26 splits into an orthogonal direct sum of vector bundles formula_33 where formula_34 is the trivial line bundle through the identity operator, and formula_35 is a rank-3 vector bundle corresponding to the purely imaginary quaternions. Neither the bundles formula_26 or formula_35 are necessarily trivial. The unit sphere bundle formula_38 inside formula_35 corresponds to the pure unit imaginary quaternions. These are endomorphisms of the tangent spaces that square to −1. The bundle formula_40 is

neg: Tonne Tonne The tonne () (Non-SI unit, symbol: t), commonly referred to as the metric ton in the United States, is a non-SI metric unit of mass equal to 1,000 kilograms; or one megagram (Mg); it is equivalent to approximately pounds, or 0.984 long tons (UK). Although not part of the SI, the tonne is accepted for use with SI units and prefixes by the International Committee for Weights and Measures. The tonne is derived from the weight of pure water; there are 1,000 litres in one tonne. The SI symbol for the tonne is "t", adopted at the same time

neg: Thermodynamic activity 1 atm (101.325 kPa) or 1 bar (100 kPa) depending on the source of data, and should always be quoted. The most convenient way of expressing the composition of a generic mixture is by using the amount fractions (written in the gas phase) of the different components, where The standard state of each component in the mixture is taken to be the pure substance, i.e. the pure substance has an activity of one. When activity coefficients are used, they are usually defined in terms of Raoult's law, where is the Raoult's law activity coefficient: an activity coefficient of one indicates

neg: Insulin (medication) by the mass of pure crystalline insulin required to obtain the USP unit. The unit of measurement used in insulin therapy is not part of the International System of Units (abbreviated SI) which is the modern form of the metric system. Instead the pharmacological international unit (IU) is defined by the WHO Expert Committee on Biological Standardization. The central problem for those requiring external insulin is picking the right dose of insulin and the right timing. Physiological regulation of blood glucose, as in the non-diabetic, would be best. Increased blood glucose levels after a meal is a stimulus for prompt

neg: Gram Gram The gram (alternative spelling: gramme; SI unit symbol: g) (Latin "", from Greek , "grámma") is a metric system unit of mass. Originally defined as "the absolute weight of a volume of pure water equal to the cube of the hundredth part of a metre [1 cm], and at the temperature of melting ice" (later at 4 °C, the temperature of maximum density of water). However, in a reversal of reference and defined units, a gram is now defined as one thousandth of the SI base unit, the kilogram, or 1×10 kg, which itself is "now defined" by the

neg: Enzyme unit many kinds of substance besides enzymes (for example, vitamins and hormones). Enzyme unit The enzyme unit (symbol U or sometimes EU) is a unit for the amount of a particular enzyme. One U is defined as the amount of the enzyme that produces a certain amount of enzymatic activity, that is, the amount that catalyzes the conversion of 1 micro-mole of substrate per minute. The conditions also have to be specified: one usually takes a temperature of 25°C and the pH value and substrate concentration that yield the maximal substrate conversion rate. The enzyme unit was adopted by the International

neg: Thermodynamic system It also leads to the idea of the chemical potential. A wall selectively permeable only to a pure substance can put the system in diffusive contact with a reservoir of that pure substance in the surroundings. Then a process is possible in which that pure substance is transferred between system and surroundings. Also, across that wall a contact equilibrium with respect to that substance is possible. By suitable thermodynamic operations, the pure substance reservoir can be dealt with as a closed system. Its internal energy and its entropy can be determined as functions of its temperature, pressure, and mole number.

neg: Overall equipment effectiveness Total Units, not Good Units. The Performance metric does not penalize for Quality. Time to Produce Parts = 242 Units * 1.5 Minutes/Unit = 363 Minutes Performance (Productivity) = 363 Minutes / 390 Minutes = 93.1% The Quality portion of the OEE Metric represents the Good Units produced as a percentage of the Total Units Started. The Quality Metric is a pure measurement of Process Yield that is designed to exclude the effects of Availability and Performance. The losses due to defects and rework are called "quality losses". Calculation: Quality = (Units produced - defective units) / (Units produced) "Example:"

neg: Equivalent (chemistry) univalent ions provides the same amount of equivalents while the same amount of divalent ions provides twice the amount of equivalents. For example, 1 mmol (0.001 mol) of Na is equal 1 meq, while 1 mmol of Ca is equal 2 meq. Equivalent (chemistry) An equivalent (symbol: equiv) is the amount of a substance that reacts with (or is "equivalent" to) an arbitrary amount of another substance in a given chemical reaction. It is an archaic unit of measurement that was used in chemistry and the biological sciences in the era before researchers knew how to determine the chemical formula

neg: Epoxy epoxy resins is the epoxide group content. This is correctly expressed as the specific amount of substance of epoxide groups in the material B under consideration, calculated as the ratio of the amount of substance of epoxide groups in this material B, "n"(EP), divided by the mass "m"(B) of the material B under consideration, in this case, the mass of the resin. The SI unit for this quantity is "mol/kg", or multiples thereof. Deprecated quantities which are still in use are the so-called "epoxide number" which is (not a number and should therefore not be referred to as such, but)

neg: Molar mass of the pure solvent, and the boiling-point elevation (Δ"T") is directly proportional to the amount concentration for dilute solutions. When the composition is expressed as a molality, the proportionality constant is known as the ebullioscopic constant ("K") and is characteristic for each solvent. If "w" represents the mass fraction of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by Molar mass In chemistry, the molar mass "M" is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The base

neg: Standard state concentration, to a specified condition (usually unit concentration or pressure) using an ideal extrapolating function, such as ideal solution or ideal gas behavior, or by empirical measurements. The standard state for a gas is the hypothetical state it would have as a pure substance obeying the ideal gas equation at standard pressure (10 Pa, or 1 bar). No real gas has perfectly ideal behavior, but this definition of the standard state allows corrections for non-ideality to be made consistently for all the different gases. The standard state for liquids and solids is simply the state of the pure substance subjected

neg: Poincaré metric the point on the unit disk that corresponds to the point "z" in the upper half plane. In this mapping, the constant "z" can be any point in the upper half plane; it will be mapped to the center of the disk. The real axis formula_41 maps to the edge of the unit disk formula_42 The constant real number formula_43 can be used to rotate the disk by an arbitrary fixed amount. The canonical mapping is which takes "i" to the center of the disk, and "0" to the bottom of the disk. The Poincaré metric tensor in the Poincaré

neg: History of the metric system which the bending or droop of the bar is minimised. The 9th CGPM met in 1948, fifteen years after the 8th CGPM. In response to formal requests made by the International Union of Pure and Applied Physics and by the French government to establish a practical system of units of measure, the CGPM requested the CIPM to prepare recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention. The CIPM's draft proposal, was an extensive revision and simplification of the metric unit definitions, symbols and terminology based on the

neg: ISO 31-8 S are listed in Definitions of pH scales, standard reference values, measurement of pH, and related terminology. Pure Appl. Chem. (1985), 57, pp 531–542, where further details can be found. pH has no fundamental meaning; its official definition is a practical one. However, in the restricted range of dilute aqueous solutions having amount-of-substance concentrations less than 0.1 mol/L, and being neither strongly alkaline nor strongly acidic (2 < pH < 12), the definition is such that where "c"(H) denotes the amount-of-substance concentration of hydrogen ion H and "y" denotes the activity coefficient of a typical uni-univalent electrolyte in the solution.

neg: Metric system of gravitation, and later, a more subtle one for the dimension of an "invisible substance" known as electricity or more generally, electromagnetism. One and only one unit in each of these dimensions was defined, unlike older systems where multiple perceptual quantities with the same dimension were prevalent, like inches, feet and yards or ounces, pounds and tons. Units for other quantities like area and volume, which are also spacial dimensional quantities, were derived from the fundamental ones by logical relationships, so that a unit of square area for example, was the unit of length squared. Many derived units were already

neg: Psychrometrics the vapor pressure of moisture in the sample to the saturation pressure at the dry bulb temperature of the sample. Analogous to the specific enthalpy of a pure substance. In psychrometrics, the term quantifies the total energy of both the dry air and water vapour per kilogram of dry air. Analogous to the specific volume of a pure substance. However, in psychrometrics, the term quantifies the total volume of both the dry air and water vapour per unit mass of dry air. The psychrometric ratio is the ratio of the heat transfer coefficient to the product of mass transfer coefficient

neg: Amount of substance replaces the term "number of moles" which should no longer be used according to IUPAC recommendation. However, confusion can arise due to the everyday usage of the term amount and the term "enplethy" has been suggested for international usage to replace amount of substance. When amount of substance enters into a derived quantity, it is usually as the denominator: such quantities are known as molar quantities. For example, the quantity which describes the volume occupied by a given amount of substance is called the molar volume, while the quantity which describes the mass of a given amount of substance is

neg: Molar mass Molar mass In chemistry, the molar mass "M" is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The base SI unit for molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol. In simple terms, molar mass of a substance is the total weight of that substance (in either kilogram or gram) for one mole of that substance. That is, the weight of a substance for 6.02214076×10^23 molecules or atoms of that substance. As an example, the molar mass of

neg: Uric acid rather low. All these salts exhibit greater solubility in hot water than cold, allowing for easy recrystallization. This low solubility is significant for the etiology of gout. The solubility of the acid and its salts in ethanol is very low or negligible. In ethanol/water mixtures, the solubilities are somewhere between the end values for pure ethanol and pure water. The figures given indicate what mass of water is required to dissolve a unit mass of compound indicated. The lower the number the more soluble the substance in the said solvent. Xanthine oxidase is an enzyme which catalyzes the formation of

neg: Climate Change Response (Emissions Trading) Amendment Act 2008 literature because it does not place a cap on New Zealand's emissions of greenhouse gases. The 2008 NZ ETS created a new emission unit, the New Zealand Unit (NZU), which the Ministry for the Environment described as being the 'primary domestic unit of trade'. The NZU is equivalent to one metric tonne of greenhouse gases in a one-year compliance period. The NZU is 'backed' by an assigned amount unit. It is the NZUs that will be allocated by 'grandfathering" to forestry, industry, energy, fishing and agriculture under an allocation plan. As noted in the previous paragraph, participants in the NZ

neg: Ge (unit) commercial purposes has been criminalized in South Korea, although it continues to be used in the North. The "gō" or cup is a traditional Japanese unit based on the "ge" which is equal to or . It was officially equated with liters in 1891. The "gō" is the traditional amount used for a serving of rice and a cup of sake in Japanese cuisine. Although the "gō" is no longer used as an official unit, 1-"gō" measuring cups or their 180mL metric equivalents are often included with Japanese rice cookers. In dining, a 1-"gō" serving is sometimes equated with 150g

neg: Measuring instrument energy—produces entropy (Example: Heat conduction in an isolated rod; "thermal friction"). Concerning a given sample, a proportionality factor relating temperature change and energy carried by heat. If the sample is a gas, then this coefficient depends significantly on being measured at constant volume or at constant pressure. (The terminiology preference in the heading indicates that the classical use of heat bars it from having substance-like properties.) The temperature coefficient of energy divided by a substance-like quantity (amount of substance, mass, volume) describing the sample. Usually calculated from measurements by a division or could be measured directly using a unit amount

neg: Assigned amount units Assigned amount units An Assigned Amount Unit (AAU) is a tradable 'Kyoto unit' or 'carbon credit' representing an allowance to emit greenhouse gases comprising one metric tonne of carbon dioxide equivalents calculated using their Global Warming Potential. The "assigned amounts" are the Kyoto Protocol Annex B emission targets (or "quantified emission limitation and reduction objectives") expressed as levels of allowed emissions over the 2008–2012 commitment period. Article 17 of the Kyoto Protocol allows emissions trading between Annex B Parties (countries). Parties that have "assigned amount units" to spare because of reductions in emissions below their Kyoto commitment set out in

neg: Assigned amount units Article 3 and Annex B may sell those units to countries that have emissions exceeding their targets. Article 17 also requires that any such emissions trading shall be supplemental to domestic action for the purpose of meeting quantified emission limitation and reduction commitments (QELRCs). Assigned amount units An Assigned Amount Unit (AAU) is a tradable 'Kyoto unit' or 'carbon credit' representing an allowance to emit greenhouse gases comprising one metric tonne of carbon dioxide equivalents calculated using their Global Warming Potential. The "assigned amounts" are the Kyoto Protocol Annex B emission targets (or "quantified emission limitation and reduction objectives") expressed

neg: Density 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. 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,

neg: Gram base units in 1960. The gram is today the most widely used unit of measurement for non-liquid ingredients in cooking and grocery shopping worldwide. Most standards and legal requirements for nutrition labels on food products require relative contents to be stated per 100 g of the product, such that the resulting figure can also be read as a percentage by weight. Gram The gram (alternative spelling: gramme; SI unit symbol: g) (Latin "", from Greek , "grámma") is a metric system unit of mass. Originally defined as "the absolute weight of a volume of pure water equal to the cube

neg: Bloch sphere sphere is also known as the Poincaré sphere and specifically represents different types of polarizations. Six common polarization types exist and are called Jones Vectors. Indeed Henri Poincaré was the first to suggest the use of this kind of geometrical representation at the end of 19th century, as a three-dimensional representation of Stokes parameters. The natural metric on the Bloch sphere is the Fubini–Study metric. The mapping from the unit 3-sphere in the two-dimensional state space ℂ to the Bloch sphere is the Hopf fibration. Given an orthonormal basis, any pure state formula_3 of a two-level quantum system can be

neg: 2006 Ontario terrorism plot area north of Toronto. The police stated that one of the arrested men ordered three metric tonnes (6,600 pounds) of ammonium nitrate fertilizer, a potentially powerful ingredient often used as quarry and mining explosives. This weight has widely been compared to the amount of ammonium nitrate used in the 1995 Oklahoma City bombing in the United States. The official account estimates the ammonium nitrate in the Oklahoma City bomb at 2,000 pounds, or about 0.9 metric tonnes. There was not any imminent danger to the public, as a harmless substance was substituted for the ordered ammonium nitrate and delivered to

neg: Heat capacity capacity may be assumed to be constant: Heat capacity is an extensive property, meaning it depends on the extent or size of the physical system studied. A sample containing twice the amount of substance as another sample requires the transfer of twice the amount of heat (formula_5) to achieve the same change in temperature (formula_6). For many purposes it is more convenient to report heat capacity as an intensive property, an intrinsic characteristic of a particular substance. In practice, this is most often an expression of the property in relation to a unit of mass; in science and engineering, such

neg: Dimitrie Cuclin and a purpose for the realising of which the will mobilises. The purpose of this great harmonic system is to acquire self-consciousness. Therefore, the essence degrades itself in an impure mode, the substance, which is the second fundamental category of Cuclin's metaphysics. The process of degradation that commences with the pure essence and ends with the pure substance is called by Cuclin “the separation of essence”. In this process of separation are generated diverse entities which are a mixture of substance and essence, where one of these aspects is prevalent. Actually, every extant thing is a mixture of essence and

neg: Bures metric Bures metric In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom) defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the Fubini–Study metric when restricted to the pure states alone. The metric may be defined as where formula_2 is Hermitian 1-form operator implicitly given by which is a special case of a continuous Lyapunov equation. Some of the applications of the Bures metric include that given a target error,

neg: Defining equation (physics) of measurements to be made when they might appear ambiguous and unclear otherwise. A basic example is mass density. It is not clear how compare how much matter constitutes a variety of substances given only their masses or only their volumes. Given both for each substance, the mass "m" per unit volume "V", or mass density "ρ" provides a meaningful comparison between the substances, since for each, a fixed amount of volume will correspond to an amount of mass depending on the substance. To illustrate this; if two substances A and B have masses "m" and "m" respectively, occupying volumes

neg: Solubility Insolubility is the inability to dissolve in a solid, liquid or gaseous solvent. Most often, the solvent is a liquid, which can be a pure substance or a mixture. One may also speak of solid solution, but rarely of solution in a gas (see vapor–liquid equilibrium instead). Under certain conditions, the equilibrium solubility can be exceeded to give a so-called supersaturated solution, which is metastable. Metastability of crystals can also lead to apparent differences in the amount of a chemical that dissolves depending on its crystalline form or particle size. A supersaturated solution generally crystallises when 'seed' crystals are introduced

neg: Arbitrary unit Arbitrary unit In science and technology, an arbitrary unit (abbreviated arb. unit, "see below") or procedure defined unit (p.d.u.) is a relative unit of measurement to show the ratio of amount of substance, intensity, or other quantities, to a predetermined reference measurement. The reference measurement is typically defined by the local laboratories or dependent on individual measurement apparatus. It is therefore impossible to compare "1 arb. unit" by one measurer and "1000 arb. unit" by another measurer without detailed prior knowledge on how the respective "arbitrary units" were defined; thus, the unit is sometimes called an unknown unit. The unit

neg: History of the metric system new, practical realisation would ultimately become the base unit of mass. On 7 April 1795, the "gramme", upon which the kilogram is based, was decreed to be equal to "the absolute weight of a volume of pure water equal to a cube of one hundredth of a metre, and at the temperature of the melting ice". Although the definition of the "kilogramme" specified water at 0 °C – a highly stable temperature point – it was replaced with the temperature at which water reaches maximum density, measured at the time as 4 °C. They concluded that one cubic decimetre of

neg: System of measurement include gravitational systems, the centimetre–gram–second systems (cgs) useful in science, the metre–tonne–second system (mts) once used in the USSR and the metre–kilogram–second system (mks). The current international standard metric system is the International System of Units ("Système international d'unités" or SI) It is an mks system based on the metre, kilogram and second as well as the kelvin, ampere, candela, and mole. The SI includes two classes of units which are defined and agreed internationally. The first of these classes includes the seven SI base units for length, mass, time, temperature, electric current, luminous intensity and amount of substance. The

neg: Arbitrary unit (such as "p.d.u./L"). Arbitrary unit In science and technology, an arbitrary unit (abbreviated arb. unit, "see below") or procedure defined unit (p.d.u.) is a relative unit of measurement to show the ratio of amount of substance, intensity, or other quantities, to a predetermined reference measurement. The reference measurement is typically defined by the local laboratories or dependent on individual measurement apparatus. It is therefore impossible to compare "1 arb. unit" by one measurer and "1000 arb. unit" by another measurer without detailed prior knowledge on how the respective "arbitrary units" were defined; thus, the unit is sometimes called an unknown

neg: Internal energy density called "specific internal energy" which is internal energy per unit of mass (kilogram) of the system in question. The SI unit of specific internal energy is J/kg. If the specific internal energy is expressed relative to units of amount of substance (mol), then it is referred to as "molar internal energy" and the unit is J/mol. From the standpoint of statistical mechanics, the internal energy is equal to the ensemble average of the sum of the microscopic kinetic and potential energies of the system. The internal energy, , expresses the thermodynamics of a system in the "energy-language", or in

neg: Cubic metre Cubic metre The cubic metre (in British English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the SI derived unit of volume. Its SI symbol is m. It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère, still sometimes used for dry measure (for instance, in reference to wood). Another alternative name, no longer widely used, was the kilolitre. A cubic metre of pure water at the temperature of maximum density

neg: Cubic metre Cubic metre The cubic metre (in British English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the SI derived unit of volume. Its SI symbol is m. It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère, still sometimes used for dry measure (for instance, in reference to wood). Another alternative name, no longer widely used, was the kilolitre. A cubic metre of pure water at the temperature of maximum density

neg: Standard state Standard state In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. In principle, the choice of standard state is arbitrary, although the International Union of Pure and Applied Chemistry (IUPAC) recommends a conventional set of standard states for general use. IUPAC recommends using a standard pressure "p" = 10 Pa. Strictly speaking, temperature is not part of the definition of a standard state. For example, as discussed below, the standard state of a gas is conventionally chosen to be unit pressure (usually in bar)

neg: Heat capacity properties are often prefixed with the term "specific". International standards now recommend that specific heat capacity always refer to division by mass. The units for the specific heat capacity are formula_7. In chemistry, heat capacity is often specified relative to one mole, the unit of amount of substance, and is called the molar heat capacity. It has the unit formula_8. For some considerations it is useful to specify the volume-specific heat capacity, commonly called volumetric heat capacity, which is the heat capacity per unit volume and has SI units formula_9. This is used almost exclusively for liquids and solids, since

neg: Thermodynamic databases for pure substances and thermodynamic properties may be described by an equation of state. It is very difficult to measure the absolute amount of any thermodynamic quantity involving the internal energy (e.g. enthalpy), since the internal energy of a substance can take many forms, each of which has its own typical temperature at which it begins to become important in thermodynamic reactions. It is therefore the "change" in these functions that is of most interest. The isobaric change in enthalpy "H" above the common reference temperature of 298.15 K (25 °C) is called the "high temperature heat content", the "sensible heat", or the

neg: Plane of immanence is a pure immanence, an unqualified immersion or embeddedness, an immanence which denies transcendence as a "real distinction", Cartesian or otherwise. Pure immanence is thus often referred to as a pure plane, an infinite field or smooth space without substantial or constitutive division. In his final essay entitled "Immanence: A Life", Deleuze writes: "It is only when immanence is no longer immanence to anything other than itself that we can speak of a plane of immanence." The plane of immanence is metaphysically consistent with Spinoza’s single substance (God or Nature) in the sense that immanence is not immanent "to" substance

neg: IUPAC polymer nomenclature IUPAC polymer nomenclature IUPAC Polymer Nomenclature are standardized naming conventions for polymers set by the International Union of Pure and Applied Chemistry (IUPAC) and described in their publication "Compendium of Polymer Terminology and Nomenclature", which is also known as the "Purple Book". Both the IUPAC and Chemical Abstracts Service (CAS) make similar naming recommendations for the naming of polymers. The terms polymer and macromolecule do not mean the same thing. A polymer is a substance composed of macromolecules. The latter usually have a range of molar masses (unit g mol), the distributions of which are indicated by dispersity ("Đ"). It

neg: Gas constant "V" is the volume of gas (SI unit cubic metres), "n" is the amount of gas (SI unit moles), "m" is the mass (SI unit kilograms) contained in "V", and "T" is the thermodynamic temperature (SI unit kelvins). "R" is the molar-weight-specific gas constant, discussed below. The gas constant is expressed in the same physical units as molar entropy and molar heat capacity. From the general equation "PV" = "nRT" we get: where "P" is pressure, "V" is volume, "n" is number of moles of a given substance, and "T" is temperature. As pressure is defined as force per unit

neg: Clearance (pharmacology) renal plasma clearance. Each substance has a specific clearance that depends on its filtration characteristics. Clearance is a function of glomerular filtration, secretion from the peritubular capillaries to the nephron, and re-absorption from the nephron back to the peritubular capillaries. Clearance is variable in zero-order kinetics because a constant amount of the drug is eliminated per unit time, but it is constant in first-order kinetics, because the amount of drug eliminated per unit time changes with the concentration of drug in the blood. The concept of clearance was described by Thomas Addis, a graduate of the University of Edinburgh Medical

neg: Chilling requirement Chilling requirement The chilling requirement of a fruit is the minimum period of cold weather after which a fruit-bearing tree will blossom. It is often expressed in chill hours, which can be calculated in different ways, all of which essentially involve adding up the total amount of time in a winter spent at certain temperatures. Some bulbs have chilling requirements to bloom, and some seeds have chilling requirements to sprout. Biologically, the chilling requirement is a way of ensuring that vernalization occurs. A "chilling unit" in agriculture is a metric of a plant's exposure to chilling temperatures. Chilling temperatures extend

neg: The Law in Her Hands of pure chivalry, we would have her protected from such amiable mediocrities as "The Law in Her Hands," which now occupies the screen at the Palace. Neither she nor the many other members of the Warner-First National stock company employed in the film can give substance to a narrative which, despite any amount of ingenious fabrication, could hardly aspire to be more than a congenial triviality." The Law in Her Hands The Law in Her Hands is a 1936 American drama film directed by William Clemens and written by George Bricker and Luci Ward. The film stars Margaret Lindsay and

neg: Gravitational metric system name for the unit of energy, “metre” is simply appended to “kilopond”, but usually the symbol of the kilopond-metre is written without the middle dot. In 19th-century France there was as a unit of power, the poncelet, which was defined as the power required to raise a mass of 1 quintal (1 q = 100 kg) at a velocity of 1 m/s. The German or metric horsepower (PS, "Pferdestärke") is arbitrarily selected to be three quarters thereof. Gravitational metric system The gravitational metric system (original French term ) is a non-standard system of units, which does not comply with the

neg: Molar concentration use in broader applications, it is defined as amount of substance of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase "c": Here, "n" is the amount of the solute in moles, "N" is the number of molecules present in volume "V" (in litres), the ratio "N"/"V" is the number concentration "C", and "N" is the Avogadro constant, approximately 6.022 mol. In thermodynamics the use of molar concentration is often not convenient because the volume of most solutions slightly depends on temperature due to thermal expansion. This problem is usually resolved by

neg: Ionization energy The sciences of physics and chemistry use different measures of ionization energy. In physics, the unit is the amount of energy required to remove a single electron from a single atom or molecule, expressed as electronvolts. In chemistry, the unit is the amount of energy required for all of the atoms in a mole of substance to lose one electron each: molar ionization energy or enthalpy, expressed as kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol). Comparison of "E" of elements in the periodic table reveals two periodic trends: The latter trend results from the outer electron shell being

neg: Siemens mercury unit small drop of mercury into one end of the tube, then measuring its length while sucking it along. The cross-sectional area at each end can then be measured by filling the tube with pure mercury at a fixed temperature, weighing it, and comparing that weight to the relative lengths of the mercury drop at each end. The tube can then be used for measurement by applying a formula obtained from these measurements that corrects for its conical shape. In 1881, a similar unit, the siemens, was formally defined by the metric system as the unit of electric conductivity, equal to

neg: Tonne a (now obsolete) force unit of the same name, the tonne-force, equivalent to about 9.8 kilonewtons: a unit also often called simply "tonne" or "metric ton" without identifying it as a unit of force. In contrast to the tonne as a mass unit, the tonne-force or metric ton-force is not acceptable for use with SI, partly because it is not an exact multiple of the SI unit of force, the newton. Tonne The tonne () (Non-SI unit, symbol: t), commonly referred to as the metric ton in the United States, is a non-SI metric unit of mass equal to 1,000

neg: Metric prefix Metric prefix A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in common use today are decadic, historically there have been a number of binary metric prefixes as well. Each prefix has a unique symbol that is prepended to the unit symbol. The prefix "kilo-", for example, may be added to "gram" to indicate "multiplication" by one thousand: one kilogram is equal to one thousand grams. The prefix "milli-", likewise, may be added to "metre" to indicate "division" by one thousand; one

neg: Megabit semiconductor chips are still marketed using the metric prefix names to designate binary multiples. Using the common byte size of eight bits and the standardized metric definition of megabit and kilobyte, 1 megabit is equal to 125 kilobytes (kB) or approximately 122 kibibytes (KiB). The megabit is widely used when referring to data transfer rates of computer networks or telecommunications systems. Network transfer rates and download speeds often use the megabit as the amount transferred per time unit, e.g., a 100 Mbit/s (megabit per second) Fast-Ethernet connection, or a 10 Mbit/s Internet access service, whereas the sizes of data units

neg: Critique of Pure Reason a different persisting identity to me. In the third paralogism, the "I" is a self-conscious person in a time continuum, which is the same as saying that personal identity is the result of an immaterial soul. The third paralogism mistakes the "I", as unit of apperception being the same all the time, with the everlasting soul. According to Kant, the thought of "I" accompanies every personal thought and it is this that gives the illusion of a permanent I. However, the permanence of "I" in the unity of apperception is not the permanence of substance. For Kant, permanence is a

neg: Metrication opposition metric 10 - {2, 3, 4, 6} and {2, 4, 8} vs. {2, 5}. However, easily divisible numbers can be selected for use with metric units, e.g. 300 mm and its multiples. The amount of times that these odd fractional numbers would come up has also been pointed out as a counterargument; in construction and engineering, for example, measurements would not only likely be in integers to begin with, but would also rarely be needed to convert to another unit. The main disadvantage cited by critics of customary measures is the proliferation of units, their (sometimes) non-unique definition and the

neg: Vaidya metric clear differences between the Schwarzschild and Vaidya metric: While the Vaidya metric is an extension of the Schwarzschild metric to include a pure radiation field, the Kinnersley metric constitutes a further extension of the Vaidya metric; it describes a massive object that accelerates in recoil as it emits massless radiation anisotropically. The Kinnersley metric is a special case of the Kerr-Schild metric, and in cartesian spacetime coordinates formula_45 it takes the following form: formula_46 formula_47 formula_48 where for the duration of this section all indices shall be raised and lowered using the "flat space" metric formula_49, the "mass" formula_50 is

neg: Chemical substance regard. A chemical substance may well be defined as "any material with a definite chemical composition" in an introductory general chemistry textbook. According to this definition a chemical substance can either be a pure chemical element or a pure chemical compound. But, there are exceptions to this definition; a pure substance can also be defined as a form of matter that has both definite composition and distinct properties. The chemical substance index published by CAS also includes several alloys of uncertain composition. Non-stoichiometric compounds are a special case (in inorganic chemistry) that violates the law of constant composition, and for

neg: Grain (unit) cod. gr. ss tablets" (using the medical abbreviations ASA for aspirin, c̄ for "with", and cod. for codeine). The apothecaries' system has gradually been replaced by the metric system, and the use of the grain in prescriptions is now rare. Particulate emission levels, used to monitor and regulate pollution, are commonly measured in grains per cubic foot. This is the same unit commonly used to measure the amount of moisture in the air, also known as the absolute humidity. The SI unit used to measure particulate emissions and absolute humidity is mg/m. One grain per cubic foot is approximately .

neg: International System of Quantities are included in Table 8 of non-SI units that are approved for use in "Chapter 4 – Units outside the SI". The ISQ recognizes another logarithmic quantity: information entropy, for which the coherent unit is the natural unit of information (symbol nat). International System of Quantities The International System of Quantities (ISQ) is a system based on seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Other quantities such as area, pressure, and electrical resistance are derived from these base quantities by clear, non-contradictory equations. The ISQ defines the quantities that are measured

neg: History of the metric system but physicists defined oxygen in terms of the O isotope whereas chemists assigned 16 amu to O, O and O isotopes mixed in the proportion that they occur in nature. Finally an agreement between the International Union of Pure and Applied Physics (IUPAP) and the International Union of Pure and Applied Chemistry (IUPAC) brought this duality to an end in 1959/60, both parties agreeing to define the atomic weight of C as being exactly 12 amu. This agreement was confirmed by ISO and in 1969 the CIPM recommended its inclusion in SI as a base unit. This was done in

neg: Carathéodory metric Carathéodory metric In mathematics, the Carathéodory metric is a metric defined on the open unit ball of a complex Banach space that has many similar properties to the Poincaré metric of hyperbolic geometry. It is named after the Greek mathematician Constantin Carathéodory. Let ("X", || ||) be a complex Banach space and let "B" be the open unit ball in "X". Let Δ denote the open unit disc in the complex plane C, thought of as the Poincaré disc model for 2-dimensional real/1-dimensional complex hyperbolic geometry. Let the Poincaré metric "ρ" on Δ be given by (thus fixing the curvature

neg: Metre (music) using time to bar how long it will take to play the bar (). Metric structure includes metre, tempo, and all rhythmic aspects that produce temporal regularity or structure, against which the foreground details or durational patterns of any piece of music are projected (). Metric levels may be distinguished: the beat level is the metric level at which pulses are heard as the basic time unit of the piece. Faster levels are division levels, and slower levels are multiple levels (). A rhythmic unit is a durational pattern which occupies a period of time equivalent to a pulse or