Spectrum (functional analysis)In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number is said to be in the spectrum of a bounded linear operator if either has no set-theoretic inverse; or the set-theoretic inverse is either unbounded or defined on a non-dense subset. Here, is the identity operator. By the closed graph theorem, is in the spectrum if and only if the bounded operator is non-bijective on .
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.
Monoclonal gammopathy of undetermined significanceMonoclonal gammopathy of undetermined significance (MGUS) is a plasma cell dyscrasia in which plasma cells or other types of antibody-producing cells secrete a myeloma protein, i.e. an abnormal antibody, into the blood; this abnormal protein is usually found during standard laboratory blood or urine tests. MGUS resembles multiple myeloma and similar diseases, but the levels of antibodies are lower, the number of plasma cells (white blood cells that secrete antibodies) in the bone marrow is lower, and it rarely has symptoms or major problems.
GlossematicsGlossematics is a structuralist linguistic theory proposed by Louis Hjelmslev and Hans Jørgen Uldall although the two ultimately went separate ways each with their own approach. Hjelmslev’s theory, most notably, is an early mathematical methodology for the analysis of language which was subsequently incorporated into the analytical foundation of current models of functional—structural grammar such as Danish Functional Grammar, Functional Discourse Grammar and Systemic Functional Linguistics.
