Twins of this kind are known as "mimetic-twins or pseudo-symmetric twins.
Many of the so-called "optical anomalies" of crystals may be explained by this pseudo-symmetric twinning.
Thus, for an equation of the fifth degree the various transitive subgroups of the symmetric group of degree five have to be considered.
These processes consist in forming resolvents of the equation corresponding to each distinct type of subgroup of the symmetric group whose degree is that of the equation.
In general, if the equation is given arbitrarily, the group will be the symmetric group.
It is known as the symmetric group of degree n, the only rational functions of the symbols which are unaltered by all possible permutations being the symmetric functions.
Suppose there is no rotation, that all the stars are in two planes at right angles, in such a way that their distribution is symmetric with regard to these two planes.
For a Latin, truth can be expressed only by equations; it must obey laws simple, logical, symmetric and fitted to satisfy minds in love with mathematical elegance.
That, as every conceivable right section of the cone discloses the circle, so in all which is fair and symmetric you will discover Deity, if you but analyse it in a right and symmetric direction?
With goodly shoulder-blade and proper leg, A portly make and a symmetric shape, And curls that clustered to the tonsure quite.
Two blots, you saw I knew how to extend into a line Symmetric on the sheet they blurred before-- Such little act sufficed, this time, such thought.
The criterion whether a pseudo-symmetric form is a true polymorph or not consists in the determination of the scalar properties (e.
When developmental, originating in childhood, the outgrowths may be found on any part of the skeleton, and upon many and generally symmetric parts at the same time, as is shown in Figure 248.
In the most extreme degree the parts are swollen, stiff, and livid, and the capillary circulation is almost stagnant; this is local or symmetric gangrene, the mildest form of which follows asphyxia.
Figure 251 shows an analogous condition, called by Hutchinson symmetric osteomata of the nasal processes of the maxilla.
Occasional symmetric patches appear on the limbs and trunk, and in extensive cases terminate in gangrene.
Congenital asymmetry and hemihypertrophy of the body are most peculiar anomalies and must not be confounded with acromegaly or myxedema, in both of which there is similar lack of symmetric development.
Erichsen mentions a young man of twenty-one with 15 groups of symmetric exostoses in various portions of the body; they were spongy or cancellous in nature.
In this way each part of the fan is aggraded and itssymmetric form is preserved.
Valleys aggraded with fine waste form well-nigh level plains over which streams wind from side to side of a direct course in symmetric bends known as meanders, from the name of a winding river of Asia Minor.
The normal profile is thus a symmetric cone with a flaring base.
Note the circular mouth not supplied with jaws, the lack of paired fins, and the symmetric tail fin, with the column of cartilaginous, ringlike vertebrae running through it to the end.
Here the tendency to grow in a horizontal direction is lacking, and with it the bilateral and symmetric structure of the branches has disappeared.
The delicate tracery of the basement is divided by slender pilasters and the frieze beneath the symmetriccornice is richly festooned, parrots nestling in the foliage among the flowers.
Of the three forms of symmetric objects that have, or haven't, fallen from the sky, it seems to me that the disk is the most striking.
In some fishes with vertebrated tail fins the fin is symmetric (Fig.
This extensive theorem of algebraic reciprocity includes many known theorems of symmetry in the theory of Symmetric Functions.
If the restriction be to the effect that an aggregate of similar parcels is not to contain more than one object of a kind, we have clearly to deal with the elementary symmetric functions a1, a2, a3, .
See "Symmetric Functions and the Theory of Distributions," Proc.
He introduced the method of symmetric functions and the method of differential operators, applying both methods to the two important subdivisions, the theory of composition and the theory of partition.
Previous to discussing these in detail, it is necessary to describe the method of symmetricfunctions which will be largely utilized.
The whole of the theory has been extended to include symmetric functions symbolized by partitions which contain as well zero and negative parts.
Observe that transposition of the diagrams furnishes a proof of the simplest of the laws of symmetry in the theory of symmetric functions.
To determine the nature of the symmetricfunction P a few definitions are necessary.
The vascular ramules which surround the intestine and the skin, run out from a main stem, and are directed in a symmetricmanner downwards and upwards (in the horizontal body of animals), or towards the belly and back.
The liver that was originally also symmetric in form has become wholly symmetric in the higher organized head and forms two glands.
The ovi-and seminal ducts are likewise symmetricand in pairs.
They are symmetric and well finished, vary more in size than those of the last group, being from 1¼ to 4¼ inches long, the others not reaching either of these limits.
The one shown in figure 215, from Kanawha valley, West Virginia, has the most symmetric outline of any specimen in the entire collection.
Texas usually shrubby, with numerous stems forming a symmetric round-topped bush only a few feet high.
These particles gradually increase in size, and we may watch their growth until eventually we have a symmetric figure, beautifully shaped, the primary form of which is a right rhomboidal prism.
Of the metallic and earthy minerals, nature furnishes us with an almost infinite variety of crystals, and, by a reduction of temperature, yet more simple bodies assume the most symmetric forms.
The great Epicurus speculated on the “plastic nature” of atoms, and attributed to this nature the power they possess of arranging themselves into symmetric forms.
Keratosis palmaris et plantaris (symmetric keratodermia), as regards the local condition, is a somewhat similar affection.
