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.
Coordination geometryThe term coordination geometry is used in a number of related fields of chemistry and solid state chemistry/physics. Molecular geometry The coordination geometry of an atom is the geometrical pattern formed by atoms around the central atom. In the field of inorganic coordination complexes it is the geometrical pattern formed by the atoms in the ligands that are bonded to the central atom in a molecule or a coordination complex.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
Absolute zeroAbsolute zero is the lowest limit of the thermodynamic temperature scale; a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.
Correlation coefficientA correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible agreement and 0 the strongest possible disagreement.
Cross-correlationIn signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions.
Correlation does not imply causationThe phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase cum hoc ergo propter hoc ('with this, therefore because of this').
Order theoryOrder theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary. Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.
Metal ions in aqueous solutionA metal ion in aqueous solution or aqua ion is a cation, dissolved in water, of chemical formula [M(H2O)n]z+. The solvation number, n, determined by a variety of experimental methods is 4 for Li+ and Be2+ and 6 for most elements in periods 3 and 4 of the periodic table. Lanthanide and actinide aqua ions have higher solvation numbers (often 8 to 9), with the highest known being 11 for Ac3+. The strength of the bonds between the metal ion and water molecules in the primary solvation shell increases with the electrical charge, z, on the metal ion and decreases as its ionic radius, r, increases.
Thermodynamic limitIn statistical mechanics, the thermodynamic limit or macroscopic limit, of a system is the limit for a large number N of particles (e.g., atoms or molecules) where the volume is taken to grow in proportion with the number of particles. The thermodynamic limit is defined as the limit of a system with a large volume, with the particle density held fixed. In this limit, macroscopic thermodynamics is valid.
