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.
AnalysisAnalysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development. The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.
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.
Quasi-projective varietyIn mathematics, a quasi-projective variety in algebraic geometry is a locally closed subset of a projective variety, i.e., the intersection inside some projective space of a Zariski-open and a Zariski-closed subset. A similar definition is used in scheme theory, where a quasi-projective scheme is a locally closed subscheme of some projective space. An affine space is a Zariski-open subset of a projective space, and since any closed affine subset can be expressed as an intersection of the projective completion and the affine space embedded in the projective space, this implies that any affine variety is quasiprojective.
DoctorateA doctorate (from Latin doctor, meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism licentia docendi ("licence to teach"). In most countries, a research degree qualifies the holder to teach at university level in the degree's field or work in a specific profession. There are a number of doctoral degrees; the most common is the Doctor of Philosophy (PhD), awarded in many different fields, ranging from the humanities to scientific disciplines.
Population healthPopulation health has been defined as "the health outcomes of a group of individuals, including the distribution of such outcomes within the group". It is an approach to health that aims to improve the health of an entire human population. It has been described as consisting of three components. These are "health outcomes, patterns of health determinants, and policies and interventions". A priority considered important in achieving the aim of population health is to reduce health inequities or disparities among different population groups due to, among other factors, the social determinants of health (SDOH).
Systems analysisSystems analysis is "the process of studying a procedure or business to identify its goal and purposes and create systems and procedures that will efficiently achieve them". Another view sees system analysis as a problem-solving technique that breaks down a system into its component pieces, and how well those parts work and interact to accomplish their purpose. The field of system analysis relates closely to requirements analysis or to operations research.
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.
Philosophy of social scienceThe philosophy of social science is the study of the logic, methods, and foundations of social sciences (psychology, cultural anthropology, sociology, etc...). Philosophers of social science are concerned with the differences and similarities between the social and the natural sciences, causal relationships between social phenomena, the possible existence of social laws, and the ontological significance of structure and agency.
Mathematical analysisAnalysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).
Word orderIn linguistics, word order (also known as linear order) is the order of the syntactic constituents of a language. Word order typology studies it from a cross-linguistic perspective, and examines how different languages employ different orders. Correlations between orders found in different syntactic sub-domains are also of interest. The primary word orders that are of interest are the constituent order of a clause, namely the relative order of subject, object, and verb; the order of modifiers (adjectives, numerals, demonstratives, possessives, and adjuncts) in a noun phrase; the order of adverbials.
Architecture description languageArchitecture description languages (ADLs) are used in several disciplines: system engineering, software engineering, and enterprise modelling and engineering. The system engineering community uses an architecture description language as a language and/or a conceptual model to describe and represent system architectures. The software engineering community uses an architecture description language as a computer language to create a description of a software architecture.
