Breath gas analysis is a method for gaining information on the clinical state of an individual by monitoring volatile organic compounds (VOCs) present in the exhaled breath.Exhaled breath is naturally produced by the human body through expiration and therefore can be collected in non-invasively and in an unlimited way. VOCs in exhaled breath can represent biomarkers for …

Absolute continuity of functions. A continuous function fails to be absolutely continuous if it fails to be uniformly continuous, which can happen if the domain of the function is not compact – examples are tan(x) over [0, π/2), x 2 over the entire real line, and sin(1/x) over (0, 1].But a continuous function f can fail to be absolutely continuous even on a compact interval.

イソプレン（isoprene）は構造式CH 2 =C(CH 3)CH=CH 2 の、二重結合を2つ持つ炭化水素。 ジエンの一種。 IUPAC命名法では 2-メチル-1,3-ブタジエン (2-Methyl-1,3-butadiene) と表される。 分子量 68.12、融点 −145.95 ℃、沸点 34.067 ℃。室温では揮発性の高い無色の液体で、ゴムもしくは都市ガス様の臭気を持つ。

In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system. More precisely, one considers a periodic orbit …

Radon–Nikodym derivative. The function satisfying the above equality is uniquely defined up to a -null set, that is, if is another function which satisfies the same property, then =-almost everywhere.The function is commonly written and is called the Radon–Nikodym derivative.The choice of notation and the name of the function reflects the fact that the function is analogous …

1) for given coefficient functions p (x) , q (x) , and w (x) and an unknown function y of the free variable x . The function w (x) , sometimes denoted r (x) , is called the weight or density function. All homogeneous (i.e. with the right-hand side equal to zero) second-order linear ordinary differential equations can be reduced to this form. In the simplest case where all coefficients …

Definition and illustration Motivating example: Euclidean vector space. One of the most familiar examples of a Hilbert space is the Euclidean vector space consisting of three-dimensional vectors, denoted by R 3, and equipped with the dot product.The dot product takes two vectors x and y, and produces a real number x ⋅ y.If x and y are represented in Cartesian coordinates, …

En matemáticas, una ecuación diferencial ordinaria (comúnmente abreviada "EDO") es la ecuación diferencial que relaciona una función desconocida de una variable independiente con sus derivadas. Es decir, una sola variable independiente (a diferencia de las ecuaciones diferenciales parciales que involucran derivadas parciales de varias variables), y una o más de …

Eine Adjazenzmatrix (manchmal auch Nachbarschaftsmatrix) eines Graphen ist eine Matrix, die speichert, welche Knoten des Graphen durch eine Kante verbunden sind. Sie besitzt für jeden Knoten eine Zeile und eine Spalte, woraus sich für n Knoten eine -Matrix ergibt.Ein Eintrag in der i-ten Zeile und j-ten Spalte gibt hierbei an, ob eine Kante von dem i-ten zu dem j-ten Knoten führt.

The Mathematics Genealogy Project – Database for the academic genealogy of mathematicians; List of mathematical artists; External links. The MacTutor History of Mathematics archive – Extensive list of detailed biographies; The Oberwolfach Photo Collection – Photographs of mathematicians from all over the world; Photos of mathematicians – Collection of photos of …