This expression gives the work done by a given wrench when the body receives a given infinitely small twist; it must of course be an absolute invariant for all transformations of rectangular axes.
In such a diagram invariant systems will be represented by points; univariant systems by lines, and bivariant systems by areas.
B represents the temperature and pressure at which the invariant system ice--hydrate--solution II.
Passing to higher temperatures, FG is the solubility curve of potassium iodide in sulphur dioxide; at G two liquid phases are formed, and the system therefore becomesinvariant (cf.
This, of course, will constitute an invariant system, and the point will correspond to the point C in Fig.
Lastly, the ternary eutectic point, K, represents an invariant system; three solid phases can exist in equilibrium with a ternary solution, only when the latter has one fixed composition and when the temperature has a definite value.
With this restriction, therefore, four phases will constitute an invariant system, three phases an univariant, and two phases a bivariant system.
Again, addition of heat to the invariant system at F will cause the disappearance of the solid phase, and there will be formed the univariant system solution I.
O is the quadruple point at which the invariantsystem exists, and may be regarded as the point of intersection of the solubility curve with the freezing-point curve.
K is also an invariant point at which potassium iodide is in equilibrium with two liquid phases and vapour.
Since a linear complex has an invariantof the second degree in its coefficients, it follows that two linear complexes have a lineo-linear invariant.
This number, now denoted by pa, is then a second invariant of birational transformation.
Nevertheless this number for m = n - 4 is also found to beinvariant for birational transformation.
The invariant laws are the relations between the crude facts, while the relations between the 'scientific facts' remain always dependent on certain conventions.
So we see what should be understood by conditions too simple; they are those which conserve something, which leave an invariant remaining.
What now is the nature of this invariant it is easy to understand, and a word will suffice us.
Will it thus shrink in convergence toward zero, or will there remain an irreducible residue which will then be the universal invariant sought?
The main reason is connected to the dynamism associated with the European spirit, which cannot accept an invariant model (religion).
PSM, that model becomes invariant (it cannot be changed by any information from the external reality).
A model, which belongs to PSM, cannot be changed regardless of the information received from external reality (the PSM contains only invariant models).
Political discussions are associated with short-range models compared to the masonic goals, and the religious discussion are nonsense, as religion is based on invariant shielding models.
An invariant model is a model, which cannot be changed by direct interaction with the external reality.
When there is an OMPSM, all the models contained in the brain have to be in harmony with this invariant model as well.
The spirit of adventure is associated closely with the desire of knowledge, the search for new ways of evolution, and the need to analyze everything, and never accept an invariant situation.
A dream is a model, which is developed, based on an invariant QER.
They are artificial models (they are not generated by direct interaction with the external reality) and they are also invariant (they cannot be changed by direct interaction with the external reality).
Of course, an invariant ideology could be useful only on short-range.
ZAM-models: they are artificial and invariant models.
The structure of models, including PSM, is almost invariant and, as a consequence, the brain has not the flexibility required by a fast evolution of the society.
It takes the camera to fix you, so that you are an iconic invariant in the Mantram.
She is the invariant of each of her iconic Mantrams and her surroundings are the variables that enter and leave the screen.
The collineation is a special one in that the general one has an invariant triangle instead of an invariant point and line.
This is the group already mentioned which underlies the theory of the elliptic modular functions; a modular function being a function of z which is invariant for some subgroup of finite index of the group in question.
If a differential invariant of a continuous group of the plane be equated to zero, the resulting differential equation remains unaltered when the variables undergo any transformation of the group.
G contained in the preceding, may be shown to have the same invariant properties as the subgroups of a composition series.
The curvature and torsion of a curve, which are invariant for all transformations by the group of motions, are special instances of what are known as differential invariants.
For such curves the ordinary theory of curvature has no meaning, but they nevertheless have invariant properties in regard to the group of motions.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "invariant" in a variety of sentences. We hope that you will now be able to make sentences using this word.
