Direct method in the calculus of variationsIn mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of a solution, direct methods may be used to compute the solution to desired accuracy. The calculus of variations deals with functionals , where is some function space and .
Harmonic functionIn mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function where U is an open subset of \mathbb R^n, that satisfies Laplace's equation, that is, everywhere on U. This is usually written as or The descriptor "harmonic" in the name harmonic function originates from a point on a taut string which is undergoing harmonic motion. The solution to the differential equation for this type of motion can be written in terms of sines and cosines, functions which are thus referred to as harmonics.
Alfred S. PosamentierAlfred S. Posamentier (born October 18, 1942) is an American educator and a lead commentator on American math and science education, regularly contributing to The New York Times and other news publications. He has created original math and science curricula, emphasized the need for increased math and science funding, promulgated criteria by which to select math and science educators, advocated the importance of involving parents in K-12 math and science education, and provided myriad curricular solutions for teaching critical thinking in math.
Java version historyThe Java language has undergone several changes since JDK 1.0 as well as numerous additions of classes and packages to the standard library. Since J2SE 1.4, the evolution of the Java language has been governed by the Java Community Process (JCP), which uses Java Specification Requests (JSRs) to propose and specify additions and changes to the Java platform. The language is specified by the Java Language Specification (JLS); changes to the JLS are managed under JSR 901.
Bounded operatorIn functional analysis and operator theory, a bounded linear operator is a linear transformation between topological vector spaces (TVSs) and that maps bounded subsets of to bounded subsets of If and are normed vector spaces (a special type of TVS), then is bounded if and only if there exists some such that for all The smallest such is called the operator norm of and denoted by A bounded operator between normed spaces is continuous and vice versa. The concept of a bounded linear operator has been extended from normed spaces to all topological vector spaces.
Bounded set (topological vector space)In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called unbounded. Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935.
FK Austria WienFußballklub Austria Wien AG (ˈaʊstri̯aː ˈviːn; known in English as Austria Vienna, and usually shortened to Austria (German: Österreich) in German-speaking countries, is an Austrian professional association football club from the capital city of Vienna. It has won the most trophies of any Austrian club from the top flight, with 24 Austrian Bundesliga titles and 27 cup titles, although its rival SK Rapid Wien holds the record for most national championships with 32.
Girsanov theoremIn probability theory, the Girsanov theorem tells how stochastic processes change under changes in measure. The theorem is especially important in the theory of financial mathematics as it tells how to convert from the physical measure which describes the probability that an underlying instrument (such as a share price or interest rate) will take a particular value or values to the risk-neutral measure which is a very useful tool for evaluating the value of derivatives on the underlying.
Pierre JohannsPierre Johanns (1 April 1882, Heinerscheid, Luxembourg – 8 February 1955, Arlon, Belgium) was a Luxemburger Jesuit priest, missionary in India and Indologist. Johanns was ordained priest on 1 August 1914 at Louvain, three days before World War I broke out and Germany invaded Belgium. He had studied philosophy under the prestigious metaphysician and mystic, Pierre Scheuer. Johanns' superior intelligence, nearing genius, had been recognized and he was destined to further studies while awaiting a still impeded passage to India.
