Vector measureIn mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization of the concept of finite measure, which takes nonnegative real values only.
Radon measureIn mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These conditions guarantee that the measure is "compatible" with the topology of the space, and most measures used in mathematical analysis and in number theory are indeed Radon measures.
Eating disorderAn eating disorder is a mental disorder defined by abnormal eating behaviors that negatively affect a person's physical or mental health. Types of eating disorders include binge eating disorder, where the patient eats a large amount in a short period of time; anorexia nervosa, where the person has an intense fear of gaining weight and restricts food or overexercises to manage this fear; bulimia nervosa, where individuals eat a large quantity (binging) then try to rid themselves of the food (purging); pica, where the patient eats non-food items; rumination syndrome, where the patient regurgitates undigested or minimally digested food; avoidant/restrictive food intake disorder (ARFID), where people have a reduced or selective food intake due to some psychological reasons; and a group of other specified feeding or eating disorders.
Unique identifierA unique identifier (UID) is an identifier that is guaranteed to be unique among all identifiers used for those objects and for a specific purpose. The concept was formalized early in the development of computer science and information systems. In general, it was associated with an atomic data type. In relational databases, certain attributes of an entity that serve as unique identifiers are called primary keys. In mathematics, set theory uses the concept of element indices as unique identifiers.
Σ-finite measureIn mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞), and a set A in Σ is of finite measure if μ(A) < ∞. The measure μ is called σ-finite if X is a countable union of measurable sets each with finite measure. A set in a measure space is said to have σ-finite measure if it is a countable union of measurable sets with finite measure. A measure being σ-finite is a weaker condition than being finite, i.
Child abuseChild abuse (also called child endangerment or child maltreatment) is physical, sexual, and/or psychological maltreatment or neglect of a child or children, especially by a parent or a caregiver. Child abuse may include any act or failure to act by a parent or a caregiver that results in actual or potential harm to a child and can occur in a child's home, or in the organizations, schools, or communities the child interacts with.
GasGas is one of the four fundamental states of matter. The others are solid, liquid, and plasma. A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture, such as air, contains a variety of pure gases. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles.
Binge eating disorderBinge eating disorder (BED) is an eating disorder characterized by frequent and recurrent binge eating episodes with associated negative psychological and social problems, but without the compensatory behaviors common to bulimia nervosa, OSFED, or the binge-purge subtype of anorexia nervosa. BED is a recently described condition, which was required to distinguish binge eating similar to that seen in bulimia nervosa but without characteristic purging.
Ideal gas lawThe ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form: where , and are the pressure, volume and temperature respectively; is the amount of substance; and is the ideal gas constant.
Boltzmann's entropy formulaIn statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy , also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the number of real microstates corresponding to the gas's macrostate: where is the Boltzmann constant (also written as simply ) and equal to 1.380649 × 10−23 J/K, and is the natural logarithm function (also written as , as in the image above).
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.
Obsessive–compulsive disorderObsessive–compulsive disorder (OCD) is a mental and behavioral disorder in which an individual has intrusive thoughts (an obsession) and feels the need to perform certain routines (compulsions) repeatedly to relieve the distress caused by the obsession, to the extent where it impairs general function. Obsessions are persistent unwanted thoughts, mental images, or urges that generate feelings of anxiety, disgust, or discomfort.
