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The Gouy-Stodola theorem is often applied to refrigeration cycles. These are thermodynamic cycles or mechanical systems where external work can be used to move heat from low temperature sources to high temperature sinks, or vice versa. Specifically, the theorem is useful in analyzing vapor compression and vapor absorption refrigeration cycles.
Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines , circles or other points.
Desargues's theorem in geometry states that these two conditions are equivalent: if two triangles are in perspective centrally then they must also be in perspective axially, and vice versa. When this happens, the ten points and ten lines of the two perspectivities (the six triangle vertices, three crossing points, and center of perspectivity ...
The Poisson–Boltzmann equation describes a model proposed independently by Louis Georges Gouy and David Leonard Chapman in 1910 and 1913, respectively. [3] In the Gouy-Chapman model, a charged solid comes into contact with an ionic solution, creating a layer of surface charges and counter-ions or double layer. [4]
The point stabilizer is O(3, R), and the group G is the 6-dimensional Lie group R 3 × O(3, R), with 2 components. Examples are the 3-torus, and more generally the mapping torus of a finite-order automorphism of the 2-torus; see torus bundle. There are exactly 10 finite closed 3-manifolds with this geometry, 6 orientable and 4 non-orientable.
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory.
In mathematics, cylindrical algebraic decomposition (CAD) is a notion, along with an algorithm to compute it, that is fundamental for computer algebra and real algebraic geometry. Given a set S of polynomials in R n , a cylindrical algebraic decomposition is a decomposition of R n into connected semialgebraic sets called cells , on which each ...
The reason for defining the vector derivative and integral as above is that they allow a strong generalization of Stokes' theorem. Let L ( A ; x ) {\displaystyle {\mathsf {L}}(A;x)} be a multivector-valued function of r {\displaystyle r} -grade input A {\displaystyle A} and general position x {\displaystyle x} , linear in its first argument.