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In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory.
Over time, this became a separate branch of analytical chemistry called instrumental analysis. Because of the high volume of wet chemistry that must be done in today's society and new quality control requirements, many wet chemistry methods have been automated and computerized for streamlined analysis. The manual performance of wet chemistry ...
As shown in the section on correction formulas, as the length of test specimens is increased and their aspect ratio approaches zero (/), the compressive stresses (σ) approach the true value (σ′). However, conducting tests with excessively long specimens is impractical, as they would fail by buckling before reaching the material's true ...
STM image of a quinacridone adsorbate.The self-assembled supramolecular chains of the organic semiconductor are adsorbed on a graphite surface.. Surface science is the study of physical and chemical phenomena that occur at the interface of two phases, including solid–liquid interfaces, solid–gas interfaces, solid–vacuum interfaces, and liquid–gas interfaces.
In mathematics, Itô's lemma or Itô's formula (also called the Itô–Doeblin formula, especially in the French literature) is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule.
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
The uncertainty value is determined through a combination of statistical analysis of the calibration and uncertainty contribution from other errors in measurement process, which can be evaluated from sources such as the instrument history, manufacturer's specifications, or published information.