Eigendecomposition of a matrixIn linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. Eigenvalue, eigenvector and eigenspace A (nonzero) vector v of dimension N is an eigenvector of a square N × N matrix A if it satisfies a linear equation of the form for some scalar λ.
Distribution (mathematics)Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used in the theory of partial differential equations, where it may be easier to establish the existence of distributional solutions (weak solutions) than classical solutions, or where appropriate classical solutions may not exist.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
Finite difference methodIn numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
Eduard ZehnderEduard J. Zehnder is a Swiss mathematician, considered one of the founders of symplectic topology. Zehnder studied mathematics and physics at ETH Zurich from 1960 to 1965, where he also did his Ph.D. in theoretical physics, defending his thesis on the three-body problem in 1971 under the direction of Res Jost. He was a visiting professor at Courant Institute of Mathematical Sciences (invited by Jürgen Moser), visiting member of Institute for Advanced Study in Princeton from 1972 to 1974.
Adrian ConstantinAdrian Constantin (born 22 April 1970) is a Romanian-Austrian mathematician who does research in the field of nonlinear partial differential equations. He is a professor at the University of Vienna and has made groundbreaking contributions to the mathematics of wave propagation. He is listed as an ISI Highly Cited Researcher with more than 160 publications and 11000 citations. Adrian Constantin was born in Timișoara, Romania, where he studied at the Nikolaus Lenau High School.
Hee OhHee Oh (오희, born 1969) is a South Korean mathematician who works in dynamical systems. She has made contributions to dynamics and its connections to number theory. She is a student of homogeneous dynamics and has worked extensively on counting and equidistribution for Apollonian circle packings, Sierpinski carpets and Schottky dances. She is currently the Abraham Robinson Professor of Mathematics at Yale University. She graduated with a bachelor's degree from Seoul National University in 1992 and obtained her Ph.
Mark SternMark Stern is an American mathematician whose focus has been on geometric analysis, Yang–Mills theory, Hodge theory, and string theory. One of Stern's foremost accomplishments is his proof (joint with Leslie D. Saper) of the Zucker conjecture concerning locally symmetric spaces. Since about 2000, Stern has focused on geometric problems arising in physics, ranging from harmonic theory to string theory and supersymmetry. Stern has taught at Duke University since 1985, and was promoted to professor in 1992.
Sergei ChernikovSergei Nikolaevich Chernikov (11 May 1912 – 23 January 1987; Сергей Николаевич Черников) was a Russian mathematician who contributed significantly to the development of infinite group theory and linear inequalities. Chernikov was born on 11 May 1912 in Sergiyev Posad, in Moscow Oblast, Russia, to Nikolai Nikolaevich, a priest, and Anna Alekseevna, a housewife. After graduating from secondary school, he worked as a labourer, as a driver, as a book-keeper and as an accountant. Until November 1931 he taught mathematics in a school for workers.
Benjamin NagengastBenjamin Nagengast is a German educational psychologist. He has been Full Professor of Educational Psychology at the University of Tübingen, Germany, since November 2012. He has been vice-director of LEAD Graduate School & Research Network since 2012, and vice-director of Hector Research Institute of Education Sciences and Psychology at Tübingen University since 2014. Nagengast was born in Mainz and grew up near Frankfurt, Germany.
MapA map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although most commonly used to depict geography, maps may represent any space, real or fictional, without regard to context or scale, such as in brain mapping, DNA mapping, or computer network topology mapping.
Restriction enzymeA restriction enzyme, restriction endonuclease, REase, ENase or restrictase is an enzyme that cleaves DNA into fragments at or near specific recognition sites within molecules known as restriction sites. Restriction enzymes are one class of the broader endonuclease group of enzymes. Restriction enzymes are commonly classified into five types, which differ in their structure and whether they cut their DNA substrate at their recognition site, or if the recognition and cleavage sites are separate from one another.
