The subgroup of orientation-preserving isometries ( i. e. translations, rotations, and compositions of these ) which leave the figure invariant is called its proper symmetry group.

The proper symmetry group is a subgroup of the special orthogonal group SO ( n ) then, and therefore also called rotation group of the figure.

It is the proper symmetry group of a circle and the continuous equivalent of C < sub > n </ sub >.

This caused not only " precedence wars " at provincial events ( where the governor general usurped the lieutenant governor's proper spot as most senior official in attendance ) and an occasion where the Govenror General accorded herself precedence before the Queen, but also constitutional issues by " unbalancing [...] the federalist symmetry.

A rigid body is called chiral if its mirror image is different in that sense, i. e., if it has either no symmetry or its symmetry group contains only proper rotations.

The symmetry group of x consists of all g for which x ( v ) = h ( g, x ) for all v. In this case the symmetry group of a constant function may be a proper subgroup of G: a constant vector has only rotational symmetry with respect to rotation about an axis if that axis is in the direction of the vector, and only inversion symmetry if it is zero.

This choice is unique up to the signs and switchings of the two vectors, and allows these two vectors to have proper symmetry when the molecular geometry is symmetric.

It is a special case of the configuration interaction method in which all Slater determinants ( or configuration state functions, CSFs ) of the proper symmetry are included in the variational procedure ( i. e. all Slater determinants obtained by exciting all possible electrons to all possible virtual orbitals, orbitals which are unoccupied in the electronic ground state configuration ).

" It is necessary to leave it clearly established [...] that it is unacceptable to attempt to justify State terrorism as a sort of game of counteracting violences, as if it were possible to look for a justifying symmetry in the action of individuals faced with the Nation and the State's estrangement from their proper goals.

The symmetry group of an object is sometimes also called full symmetry group, as opposed to its rotation group or proper symmetry group, the intersection of its full symmetry group and the rotation group SO ( 3 ) of the 3D space itself.

For example, a sphere has proper rotational symmetry.

) Thus, the symmetry group of the sphere with proper rotations is.

During the 1920's the Abstractionists, the German Bauhaus group of industrial designers, and the new architects all had the dream of some well ordered utopia, or welfare state, in which their neat and logical constructions might find their proper place.

If the automorphisms of an object X form a set ( instead of a proper class ), then they form a group under composition of morphisms.

The Holy See accepts as valid the ordinations of the Old Catholics in communion with Utrecht, as well as the Polish National Catholic Church ( which received its orders directly from Utrecht, and was — until recently — part of that communion ); but Roman Catholicism does not recognise the orders of any group whose teaching is at variance with what they consider the core tenets of Christianity ; this is the case even though the clergy of the Independent Catholic groups may use the proper ordination ritual.

The Beja language, or North Cushitic, is sometimes placed outside Cushitic proper, though there is no evidence that the rest of Cushitic forms a valid group.

He called the decomposition of a group into its left and right cosets a proper decomposition if the left and right cosets coincide, which is what today is known as a normal subgroup.

As some kind of orienting force is needed to place the amide group in the proper position for catalysis.

For example, a non-identity finite group is simple if and only if it is isomorphic to all of its non-identity homomorphic images, a finite group is perfect if and only if it has no normal subgroups of prime index, and a group is imperfect if and only if the derived subgroup is not supplemented by any proper normal subgroup.

Just as every finite p-group has a nontrivial center so that the inner automorphism group is a proper quotient of the group, every finite p-group has a nontrivial outer automorphism group

The functions of a shaman may include either guiding to their proper abode the souls of the dead ( which may be guided either one-at-a-time or in a cumulative group, depending on culture ), and / or curing ( healing ) of ailments.

A proper subgroup of a group G is a subgroup H which is a proper subset of G ( i. e. H ≠ G ).

Z-modules are the same as abelian groups, so a simple Z-module is an abelian group which has no non-zero proper subgroups.

Tau Ceti is considered to be a high-proper-motion star, although it only has an annual traverse of just under two arc seconds .< ref group =" nb "> The net proper motion is given by:

The vertebrates are the only chordate group to exhibit a proper brain.

the language, however, is a proper object of scrutiny, and the effects of the language are palpable even if sometimes inevitable.

Many fundamental questions of craftsmanship versus mass production, the relationship of usefulness and beauty, the practical purpose of formal beauty in a commonplace object, and whether or not a single proper form could exist, were argued out among its 1, 870 members ( by 1914 ).

According to the direct-reference view, an early version of which was originally proposed by Bertrand Russell, and perhaps earlier by Gottlob Frege, a proper name strictly has no meaning when there is no object to which it refers.

This view relies on the argument that the semantic function of a proper name is to tell us which object bears the name, and thus to identify some object.

In other words, you can have a proper presentation of an object if it is actually present, and an improper ( or symbolic as he also calls it ) if you only can indicate that object through signs, symbols, etc.

Frege, however, did not conceive of objects as forming parts of senses: If a proper name denotes a non-existent object, it does not have a reference, hence concepts with no objects have no truth value in arguments.

Though he valued first-hand experience as part of a proper education, he did not intend to found a professional school, but advocated instruction in useful knowledge that combined elements of both professional and liberal education, writing that " The true and only practicable object of a polytechnic school is, as I conceive, the teaching, not of the minute details and manipulations of the arts, which can be done only in the workshop, but the inculcation of those scientific principles which form the basis and explanation of them, and along with this, a full and methodical review of all their leading processes and operations in connection with physical laws.

His first clarification on the matter is that of a postulate, in which he states " ANY required change may be effected by the application of the proper kind and degree of Force in the proper manner, through the proper medium to the proper object.

The descriptive theory of proper names is the view that the meaning of a given use of a proper name is a set of properties that can be expressed as a description that picks out an object that satisfies the description.

The object is to drive on time, arriving at checkpoints with the proper amount of elapsed time from the previous checkpoint.

If C is a locally small category ( i. e. the hom-sets are actual sets and not proper classes ), then each object A of C gives rise to a natural functor to Set called a hom-functor.

If all factory objects are stored globally in a singleton object, and all client code goes through the singleton to access the proper factory for object creation, then changing factories is as easy as changing the singleton object.

He represented the anti-Franco-Prussian portion of her council, and his object was to bring about an Anglo-Austro-Russian alliance which, at that time, was undoubtedly Russia's proper system.

According to descriptivist theories, proper names either are synonymous with descriptions, or have their reference determined by virtue of the name's being associated with a description or cluster of descriptions that an object uniquely satisfies.

It is possible that international organization will ultimately supplant the multi-state system, but its proper function for the immediate future is to reform and supplement that system in order to render pluralism more compatible with an interdependent world.

Our proper objective, then, is the development of a new spirit, the realization of a potential community.

Now the park is filled with marble busts and all the streets in the immediate area have the full and proper names of the men who fell.

And then there is St. Louis county, where the Democratic leadership has shown little appreciation of the need for sound zoning, of the important relationship between proper land use and economic growth.

Either it is lack of training, lack of proper screening when hiring, lack of management or possibly lack of interest on the part of the telephone company, which does have a Government-blessed monopoly.

The cost of developing a major weapon system is now so enormous that the greatest care must be exercised in selecting new systems for development, in determining the most satisfactory rate of development, and in deciding the proper time at which either to place a system into production or to abandon it.

While clay is still pressed in mold, press three equally spaced holes 1/4'' '' deep, using pencil eraser, in bottom of clay to allow for proper drying and firing.

A stem jig is next cut to the proper shape and temporarily fastened to frame one.

Consultation with architects, clients, real estate men, fabric houses and furniture companies is essential to the proper development of class problems just as in actual work.

There is plenty of opportunity for proper education today.

The proper correlation of the art with the academic can be achieved only if this standard is observed.

For proper accreditation of schools, teachers in any course must have a degree at least one level above that for which the student is a candidate.

The thermostat is important to get your engine up to operating temperature quickly, and to keep it running at its most efficient temperature through the proper circulation of the coolant.

It is, obviously, a proper goal of research to improve on this property.

Private international law ( which Americans call the `` conflict of laws '' ) was thus segregated from international law proper, or, as it is often called, public international law.

He has advised me that the narrower interpretation is the proper one ; ;

Moreover, it is too readily forgotten that in the Republic what gave the initial impetus to Plato's excursus into the construction of an imaginary commonwealth with its ruling-class communism of goods, wives, and children, was his quest for a canon for the proper ordering of the individual human psyche ; ;

But it soon became clear that the search for eighteenth-century furniture ( which Mrs. Kennedy feels is the proper period for the White House ) must be pursued in places other than government storage rooms.

International Atomic Time ( TAI, from the French name Temps atomique international ) is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid.

In hindsight it is possible to discover errors in TAI, and to make better estimates of the true proper time scale.

Socio-cultural anthropology is considered anthropology proper in most of Europe, and in the parts of the world that were influenced by the European tradition.

This might be the proper standard of review, for example, if the lower court resolved the case by granting a pre-trial motion to dismiss or motion for summary judgment which is usually based only upon written submissions to the trial court and not on any trial testimony.

The satirical element of the pamphlet is often only understood after the reader notes the allusions made by Swift to the attitudes of landlords, such as the following: " I grant this food may be somewhat dear, and therefore very proper for Landlords, who as they have already devoured most of the Parents, seem to have the best Title to the Children.