Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
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.
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.
ManufacturingManufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of the secondary sector of the economy. The term may refer to a range of human activity, from handicraft to high-tech, but it is most commonly applied to industrial design, in which raw materials from the primary sector are transformed into finished goods on a large scale.
GunA gun is a device or ranged weapon designed to propel a projectile using pressure or explosive force. The projectiles are typically solid, but can also be pressurized liquid (e.g. in water guns/cannons), or gas (e.g. light-gas gun). Solid projectiles may be free-flying (as with bullets and artillery shells) or tethered (as with Tasers, spearguns and harpoon guns). A large-caliber gun is also called a cannon.
PresentThe present is the period of time that is occurring now. The present is contrasted with the past, the period of time that has already occurred, and the future, the period of time that has yet to occur. It is sometimes represented as a hyperplane in space-time, typically called "now", although modern physics demonstrates that such a hyperplane cannot be defined uniquely for observers in relative motion. The present may also be viewed as a duration.
Manufacturing engineeringManufacturing engineering or production engineering is a branch of professional engineering that shares many common concepts and ideas with other fields of engineering such as mechanical, chemical, electrical, and industrial engineering. Manufacturing engineering requires the ability to plan the practices of manufacturing; to research and to develop tools, processes, machines and equipment; and to integrate the facilities and systems for producing quality products with the optimum expenditure of capital.
Cross-validation (statistics)Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set. Cross-validation is a resampling method that uses different portions of the data to test and train a model on different iterations. It is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice.
Social statusSocial status is the relative level of social value a person is considered to possess. Such social value includes respect, honor, assumed competence, and deference. On one hand, social scientists view status as a "reward" for group members who treat others well and take initiative. This is one explanation for its apparent cross-cultural universality. On the other hand, while people with higher status experience a litany of benefits--such as greater health, admiration, resources, influence, and freedom--those with lower status experience poorer outcomes across all of those metrics.
Statistical model validationIn statistics, model validation is the task of evaluating whether a chosen statistical model is appropriate or not. Oftentimes in statistical inference, inferences from models that appear to fit their data may be flukes, resulting in a misunderstanding by researchers of the actual relevance of their model. To combat this, model validation is used to test whether a statistical model can hold up to permutations in the data.
Philosophical presentismPhilosophical presentism is the view that only present entities exist (or, equivalently, that everything is present). According to presentism, there are no past or future entities. In a sense, the past and the future do not exist for presentists—past events have happened (have existed) and future events will happen (will exist), but neither exist at all since they do not exist now.
Submachine gunA submachine gun (SMG) is a magazine-fed automatic carbine designed to fire handgun cartridges. The term "submachine gun" was coined by John T. Thompson, the inventor of the Thompson submachine gun, to describe its design concept as an automatic firearm with notably less firepower than a machine gun (hence the prefix "sub-"). As a machine gun must fire rifle cartridges to be classified as such, submachine guns are not considered machine guns. The submachine gun was developed during World War I (1914–1918) as a close quarter offensive weapon, mainly for trench raiding.
Socioeconomic statusSocioeconomic status (SES) is an economic and sociological combined total measure of a person's work experience and of an individual's or family's economic access to resources and social position in relation to others. When analyzing a family's SES, the household income, earners' education, and occupation are examined, as well as combined income, whereas for an individual's SES only their own attributes are assessed. Recently, research has revealed a lesser recognized attribute of SES as perceived financial stress, as it defines the "balance between income and necessary expenses".
