The J-integral represents a way to calculate the strain energy release rate, or work (energy) per unit fracture surface area, in a material. The theoretical...

In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process...

calculated using the J-integral, i.e. G = J {\displaystyle G=J} , using J = ∫ Γ ( W n 1 − t i ∂ u i ∂ x 1 ) d Γ , {\displaystyle J=\int _{\Gamma }\left(Wn_{1}-t_{i}\...

In politics, integralism, integrationism or integrism (French: intégrisme) is an interpretation of Catholic social teaching that argues the principle...

The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}}...

elastic-plastic fracture mechanics can be used with parameters such as the J-integral or the crack tip opening displacement. The characterising parameter describes...

Henstock–Kurzweil integral or generalized Riemann integral or gauge integral – also known as the (narrow) Denjoy integral (pronounced [dɑ̃ʒwa]), Luzin integral or Perron...

as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. It...

central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators...

Integral theory as developed by Ken Wilber is a synthetic metatheory aiming to unify a broad spectrum of Western theories and models and Eastern meditative...

The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces...

mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may...

The INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) is a space telescope for observing gamma rays of energies up to 8 MeV. It was launched by...

Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function...

mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an...

The Fresnel integrals S(x) and C(x) are two transcendental functions named after Augustin-Jean Fresnel that are used in optics and are closely related...

mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations...

the J-integral for plane stress and plane strain in Mode I are the same: J = μ π a 2 4 . {\displaystyle J={\frac {\mu \pi a^{2}}{4}}.} The J-integral can...

the stress intensity factor K {\displaystyle K} and the elastic-plastic J-integral. For plane stress conditions, the CTOD can be written as: δ t = ( 8 σ...

In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that...

In mathematics, an abelian integral, named after the Norwegian mathematician Niels Henrik Abel, is an integral in the complex plane of the form ∫ z 0...

In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied...

In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration...

mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions are Si...

said to be integral over a subring A of B if b is a root of some monic polynomial over A. If A, B are fields, then the notions of "integral over" and of...

In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number...

Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was...

closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein...

In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and...

An integral, or intrinsic, membrane protein (IMP) is a type of membrane protein that is permanently attached to the biological membrane. All transmembrane...