Ternary sentence example
The idea_can be generalized so as to have regard to ternary and higher forms each of the same order and of the same number of variables.
Thus the ternary quartic is not, in general, expressible as a sum of five 4th powers as the counting of constants might have led one to expect, a theorem due to Sylvester.
For instance, those of a ternary form involve two classes which may be geometrically interpreted as point and line co-ordinates in a plane; those of a quaternary form involve three classes which may be geometrically interpreted as point, line and plane coordinates in space.
This paper will discuss methods for making ternary sequence diffusers.
It was verified very exactly by Stas's experiments, in which he removed the oxygen from the ternary compound silver iodate and found that the whole of the silver and the iodine remained in combination with each other as silver iodide; his results prove, to one part in ten millions, that the combining ratio of the silver and the iodine is unaltered by the removal of the oxygen.Advertisement
With mercury it forms amalgams. Bismuth is a component of many ternary alloys characterized by their low fusibility and expansion in solidification; many of them are used in the arts (see Fusible Metal).
The ternary graph includes an optional legend that shows the data input.
The amount of γ ' depends on the chemical composition and temperature, as illustrated in the ternary phase diagrams below.
Can handle a distorted page, ternary plots, polar plots.
So be sure to ponder your reasons when choosing the ternary operator.Advertisement
Ternary and Higher Forms.-The ternary form of order n is represented symbolically by (aixl+a2x2+a3x3)' =a'; and, as usual, b, c, d,...
For example, take the ternary quadratic (aixl+a2x2+a3x3) 2 =a2x, or in real form axi +bx2+cx3+2fx 2 x 3+ 2gx 3 x 1 +2hx i x 2.
The ternary cubic has been investigated by Cayley, Aronhold, Hermite, Brioschi and Gordan.
Hesse showed independently that the general ternary cubic can be reduced, by linear transformation, to the form x3+y3+z3+ 6mxyz, a form which involves 9 independent constants, as should be the case; it must, however, be remarked that the counting of constants is not a sure guide to the existence of a conjectured canonical form.
This is of degree 8 in the coefficients, and degree 6 in the variables, and, for the canonical form, has the expression -9m 6 (x 3 +y 3 +z 3) 2 - (2m +5m 4 +20m 7) (x3 +y3+z3)xyz - (15m 2 +78m 5 -12m 8) Passing on to the ternary quartic we find that the number of ground forms is apparently very great.Advertisement
For the unipartite ternary quantic of order n he finds that the fundamental system contains a (n+4) (n -1) individuals.
He successfully considers the systems of two and three simultaneous ternary quadratics.
The alloy of the point e is the ternary eutectic; it deposits the three metals simultaneously during the whole period of its solidfication and solidifies at a constant temperature.
It is evident that any other property can be represented by similar diagrams. For example, we can construct the curve of conductivity of alloys of two metals or the surface of conductivity of ternary alloys, and so on for any measurable property.
This subject is far from being exhausted, and it is not improbable that the alloy-producing capacity of aluminium may eventually prove its most valuable characteristic. In the meantime, ternary light alloys appear the most satisfactory, and tungsten and copper, or tungsten and nickel, seem to be the best substances to add.Advertisement
We have in the Hessian the first instance of a covariant of a ternary form.
The theory of the invariants and covariants of a ternary cubic function u has been studied in detail, and brought into connexion with the cubic curve u = o; but the theory of the invariants and covariants for the next succeeding case, the ternary quartic function, is still very incomplete.