Taylor seriesIn mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century.
Entropy (classical thermodynamics)In classical thermodynamics, entropy () is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid-19th century to explain the relationship of the internal energy that is available or unavailable for transformations in form of heat and work. Entropy predicts that certain processes are irreversible or impossible, despite not violating the conservation of energy.
HapticityIn coordination chemistry, hapticity is the coordination of a ligand to a metal center via an uninterrupted and contiguous series of atoms. The hapticity of a ligand is described with the Greek letter η ('eta'). For example, η2 describes a ligand that coordinates through 2 contiguous atoms. In general the η-notation only applies when multiple atoms are coordinated (otherwise the κ-notation is used). In addition, if the ligand coordinates through multiple atoms that are contiguous then this is considered denticity (not hapticity), and the κ-notation is used once again.
Negative temperatureCertain systems can achieve negative thermodynamic temperature; that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This should be distinguished from temperatures expressed as negative numbers on non-thermodynamic Celsius or Fahrenheit scales, which are nevertheless higher than absolute zero. The absolute temperature (Kelvin) scale can be understood loosely as a measure of average kinetic energy. Usually, system temperatures are positive.
Entropy (statistical thermodynamics)The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of large ensembles of microstates that constitute thermodynamic systems.
ArsenicArsenic is a chemical element with the symbol As and atomic number 33. Arsenic occurs in many minerals, usually in combination with sulfur and metals, but also as a pure elemental crystal. Arsenic is a metalloid. It has various allotropes, but only the grey form, which has a metallic appearance, is important to industry. The primary use of arsenic is in alloys of lead (for example, in car batteries and ammunition). Arsenic is a common n-type dopant in semiconductor electronic devices.
Madhava seriesIn mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century Kerala by the mathematician and astronomer Madhava of Sangamagrama (c. 1350 – c. 1425) or his followers in the Kerala school of astronomy and mathematics. Using modern notation, these series are: All three series were later independently discovered in 17th century Europe.
Half sandwich compoundHalf sandwich compounds, also known as piano stool complexes, are organometallic complexes that feature a cyclic polyhapto ligand bound to an MLn center, where L is a unidentate ligand. Thousands of such complexes are known. Well-known examples include cyclobutadieneiron tricarbonyl and (C5H5)TiCl3. Commercially useful examples include (C5H5)Co(CO)2, which is used in the synthesis of substituted pyridines, and methylcyclopentadienyl manganese tricarbonyl, an antiknock agent in petrol. MMT-2D-skeletal.
Sandwich compoundIn organometallic chemistry, a sandwich compound is a chemical compound featuring a metal bound by haptic, covalent bonds to two arene (ring) ligands. The arenes have the formula , substituted derivatives (for example ) and heterocyclic derivatives (for example ). Because the metal is usually situated between the two rings, it is said to be "sandwiched". A special class of sandwich complexes are the metallocenes. The term sandwich compound was introduced in organometallic nomenclature in 1956 in a report by J.
Metal aquo complexIn chemistry, metal aquo complexes are coordination compounds containing metal ions with only water as a ligand. These complexes are the predominant species in aqueous solutions of many metal salts, such as metal nitrates, sulfates, and perchlorates. They have the general stoichiometry . Their behavior underpins many aspects of environmental, biological, and industrial chemistry. This article focuses on complexes where water is the only ligand ("homoleptic aquo complexes"), but of course many complexes are known to consist of a mix of aquo and other ligands.
Transition metalIn chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. The lanthanide and actinide elements (the f-block) are called inner transition metals and are sometimes considered to be transition metals as well. Since they are metals, they are lustrous and have good electrical and thermal conductivity.
Natural logarithmThe natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.
