Orthogonal Sentence Examples

Such a determinant is of importance in the theory of orthogonal substitution.

We may therefore form an orthogonal transformation in association with every skew determinant which has its leading diagonal elements unity, for the Zn(n-I) quantities b are clearly arbitrary.

This is called the direct orthogonal substitution, because the sense of rotation from the axis of X i to the axis of X, is the same as that from that of x i to that of x 2.

In both cases the solution can be made orthogonal to any number of specified functions.

Orthogonal System.-In particular, if we consider the transformation from one pair of rectangular axes to another pair of rectangular axes we obtain an orthogonal system which we will now briefly inquire into.

Clerk Maxwell, who showed amongst other things that a reciprocal can always be drawn to any figure which is the orthogonal projection of a plane-faced polyhedron.

If we project both polyhedra orthogonally on a plane perpendicular to the axis of the paraboloid, we obtain two figures which are reciprocal, except that corresponding lines are orthogonal instead of parallel.

It may denote a simultaneous orthogonal invariant of forms of orders n i, n2, n3,...; degree 0 of the covariant in the coefficients.

The curves 0 = constant and 4, = constant form an orthogonal system; and the interchange of 0 and 4, will give a new state of uniplanar motion, in which the velocity at every point is turned through a right angle without alteration of magnitude.

Thus for m =2, the spheres are orthogonal, and it can be verified that a13 a2 3 aY3 i f /' = ZU (I - 13 - 7.2 3 + 3) ' (8) where a l, a2, a =a l a 2 /J (a 1 2 +a 2 2) is the radius of the spheres and their circle of intersection, and r 1, r 2, r the distances of a point from their centres.

The orthogonal projection of a section of this surface by a plane containing one of the perpendiculars and inclined to the axis is the quadratrix.

We may describe, through all the points in an electric field which have the same potential, surfaces called equipotential surfaces, and these will be everywhere perpendicular or orthogonal to the lines of electric force.

In the case of non-intersecting circles, it is seen that the minimum circles of the coaxal system are a pair of points I and I', where the orthogonal circle to the system intersects the line of centres; these points are named the " limiti,ng points."

In the first place, each of these figures may be conceived as an orthogonal projection of a closed plane-faced polyhedron.

Work.The work done by a force acting on a particle, in any infinitely small displacement, is defined as the product of the force into the orthogonal projection of the displacement on the direction of the force; i.e.

The area of the ellipse is 7rab, where a, b are the semi-axes; this result may be deduced by regarding the ellipse as the orthogonal projection of a circle, or by means of the calculus.

If the keyword FRACTIONAL is present, the translation is assumed to be in fractional coordinates, otherwise orthogonal angstroms.

Pass Point that lies on a local convexity that is orthogonal to a local concavity.

In all such cases, there is no component to plan convexity, any curvature being entirely orthogonal to the xy plane.

The only restriction is that the atomic coordinates are given in Angstroms on arbitrary orthogonal axes.

This quantity is equal to the width of the error ellipse orthogonal to the visibility vector.

The wavelength associated with the vector resultant of these three orthogonal propagation constants is just the free space wavelength lambda.

They note " Computational modeling has strengths orthogonal to the strengths of either traditional research discipline " (p. 7 ).

The columns T are constrained to be mutually orthogonal.

The flags are not orthogonal, in that more restrictive flags will often make less restrictive ones redundant.

Talking about Perl's multimethod dispatch, he pointed out that multi is " now completely orthogonal to scoping " .

The rings have an O 120 o bridge, and are almost orthogonal to each other.

This strongly suggests that the philosophy of intelligent tutoring is really orthogonal to the mindtool approach to learning.

At the design stage, a design should be chosen to be as nearly orthogonal as possible to the nuisance effects.

Here, orthogonal polynomials play an important role in the analysis.

These estimators function on the principle that the noise subspace eigenvectors should be orthogonal to the signal vectors.

This theorem has been generalized for any tetrahedron; a sphere can be drawn through the four feet of the perpendiculars, and consequently through the mid-points of the lines from the vertices to the centre of the hyperboloid having these perpendiculars as generators, and through the orthogonal projections of these points on the opposite faces.

Note the equivalence of orthogonal arrays with affine resolvable designs.

Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.

The corresponding expression for two orthogonal cylinders will be With a 2 = co, these reduce to / y /, = Uy (I ra 2 p22 +-C24)..

The problem was to find the orthogonal trajectories of a series of curves represented by a single equation.

The inconvenience of orthogonal illumination, which certainly gives better results, is avoided in the coaxial apparatus.