orthogonal system

orthogonal system

[ȯr′thäg·ən·əl ′sis·təm]
(mathematics)
A system made up of n families of curves on an n-dimensional manifold in an n + l dimensional euclidean space, such that exactly one curve from each family passes through every point in the manifold, and, at each point, the tangents to the n curves that pass through that point are mutually perpendicular.
A set of real-valued functions, the inner products of any two of which vanish. Also known as orthogonal family.
References in periodicals archive ?
The problem of nonlinear bending of a strip of polystyrene is analyzed using the orthogonal system of coordinates.
Here physically nonlinear behaviour of a strip of polystyrene is analyzed using the model of a straight beam in the status of equilibrium coinciding with the x axis of the orthogonal system of coordinates.
The device used for this, the "CARDIOLOGIC EXPLORER", works with five electrodes in an orthogonal system which orients itself along the axis of the heart.
Just as the convexity of the hall plays against the orthogonal system dominating the building, so the sloping plane of the ground floor (which extends the sloping paving of Schubert-Platz), plays against the strong horizontals of the building's section.
Hilbert space with reproducing kernel, restriction operator, doubly orthogonal system, min-max principle
k], k [greater than or equal to] 0, form a doubly orthogonal system of functions, in the spaces H([OMEGA]) and the closed range RanR of R, endowed with the norm of [L.
The villa's parti of an orthogonal system defined not by the horizontal floor, but by the gently sloping roof, invariably recalls Frank Lloyd Wright's Taliesin West, which sought to connect with the surrounding Arizona desert.
For the proofs, we have to study the monic orthogonal system [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] obtained by inserting the polynomial w(x) := [[product].
2, we shall employ another orthogonal system which reveals why the determinants [V.
He covers Volterra integral equations, Fredholm integral equations, nonlinear integral equations, the singular integral equation, integro-differential equations, symmetric kernals and orthogonal systems of functions, and a range of applications.
Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations.
Early on he discovered the potential of the switch in territories between differently orientated orthogonal systems, and by 1953 he could exploit it with great refinement.

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