Because of this property, the collapsed stars were called " frozen stars ," because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius.

* Stability radius, a property of continuous polynomial functions

One reason that the radius of gyration is an interesting property is that it can be determined experimentally with static light scattering as well as with small angle neutron-and x-ray scattering.

The size of particles has a major influence on their properties and the aerosol particle radius or diameter ( d < sub > p </ sub >) is a key property used to characterise aerosols.

One reported original settlement, " The Torry Lot ", was located approximately within a one mile radius of the Hill on Hotaling's property ( The first owner of a piece of the Boston Purchase ).

Another distinctive property is the amount of space covered by the n-ball in hyperbolic n-space: it increases exponentially with respect to the radius of the ball, rather than polynomially.

The money would be collected from all commercial property owners within radius of the proposed station by being charged special tax assessments.

In cellular automata defined over tessellations of the hyperbolic plane, or of higher dimensional hyperbolic spaces, the counting argument in the proof of the Garden of Eden theorem does not work, because it depends implicitly on the property of Euclidean spaces that the boundary of a region grows less quickly than its volume as a function of the radius.

This property can also be used to easily derive the formula for the area of a circle, because as the number of sides approaches infinity, the regular polygon's area approaches the area of the inscribed circle of radius r

From this being come new movement ideas that utilize dancer and property as a single unit.

This is being done both by the revaluation of real property and by seeking out forms of personal property hitherto neglected or ignored.

Although a similar situs for tangible property is mentioned in the statute, this is cancelled out by the provision that definite kinds of property `` and all other tangible property '' situated or being in any town is taxable where the property is situated.

The Smithfield tax assessor, in turn, claims the tax under the provision of law `` and all other tangible personal property situated or being in any town, in or upon any place of storage shall be taxed to such person in the town where said property is situated ''.

There was one vote for location being the place where the property is situated for the greater portion of the twelve months preceding the assessment date.

They were reluctant to appoint sheriffs to protect the property, thus running the risk of creating disturbances such as that on the Vermejo, and yet the cowboys protested that they got no salary for arresting cattle thieves and running the risk of being shot.

Anisotropy () is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions.

Similarly, intuitionists object to the existence property for classical logic, where one can prove, without being able to produce any term of which holds.

Pearl was the relative who prodded Jed to move to California, after being told his modest property could yield $ 25 million.

Heidegger coined the term " dasein " for this property of being in his influential work Being and Time (" this entity which each of us is himself … we shall denote by the term ' dasein.

French Academy member Étienne Gilson summarized this long-known characteristic of the experienced world as follows :"... the word being is a noun ... it signifies either a being ( that is, the substance, nature, and essence of anything existent ), or being itself, a property common to all that which can rightly be said to be.

As an example, the former camp considers surjectivity — or being onto — as a property of functions, while the latter sees it as a relationship that functions may bear to sets.

Then the same mapping property assures that continuous-time filters that are minimum-phase are converted to discrete-time filters that preserve that property of being minimum-phase.

All but one of the provinces of Canada use a common law system ( the exception being Quebec, which uses a civil law system for issues arising within provincial jurisdiction, such as property ownership and contracts ).

These physical properties are then represented by tensors, which are mathematical objects that have the required property of being independent of coordinate system.

Generalizations of compactness include H-closed and the property of being an H-set in a parent space.

The word chromosome comes from the Greek ( chroma, colour ) and ( soma, body ) due to their property of being very strongly stained by particular dyes.

An important property of the Legendre polynomials is that they are orthogonal with respect to the L < sup > 2 </ sup > inner product on the interval − 1 ≤ x ≤ 1:

For the special case of orthogonal isotropy, there are three different material property constants for each of Young's Modulus, Shear Modulus and Poisson's ratio — a total of 9 constants to describe the relationship between forces / moments and strains / curvatures.

Matrices for which this property holds are called orthogonal matrices.

Assume that there exists a basis for such that and are all approximately orthogonal to a good degree if i is not j and the same thing for and and also and for any i and j ( the decoherence property ).

An important property of the exponential map is the following lemma of Gauss ( yet another Gauss's lemma ): given any tangent vector v in the domain of definition of exp < sub > p </ sub >, and another vector w based at the tip of v ( hence w is actually in the double-tangent space T < sub > v </ sub >( T < sub > p </ sub > M )) and orthogonal to v, remains orthogonal to v when pushed forward via the exponential map.

Recall that an orthogonal matrix has the property

The prime mechanism then appeared to be this: Given a space X carrying a vector bundle, that implied in the homotopy category a mapping from X to a classifying space BG, for the relevant linear group G. For the homotopy theory the relevant information is carried by compact subgroups such as the orthogonal groups and unitary groups of G. Once the cohomology H *( BG ) was calculated, once and for all, the contravariance property of cohomology meant that characteristic classes for the bundle would be defined in H *( X ) in the same dimensions.

The key property of the Galerkin approach is that the error is orthogonal to the chosen subspaces.

It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis.

He defines the fundamental conic property as the equivalent of the Cartesian equation applied to oblique axes — i. e., axes consisting of a diameter and the tangent at its extremity — that are obtained by cutting an oblique circular cone.

He shows that the oblique axes are only a particular case after demonstrating that the basic conic property can be expressed in the same form with reference to any new diameter and the tangent at its extremity.

If ƒ is differentiable, then ƒ < sup >∗</ sup >( p ) can be interpreted as the negative of the y-intercept of the tangent line to the graph of ƒ that has slope p. In particular, the value of x that attains the maximum has the property that

One speaks also of curves and geometric objects having k-th order contact at a point: this is also called osculation ( i. e. kissing ), generalising the property of being tangent.

The term really has its origins in the identification of tangent spaces in Euclidean space by translation: this property means that Euclidean n-space is an affine space.

The essential property of the tractrix is constancy of the distance between a point P on the curve and the intersection of the tangent line at P with the asymptote of the curve.

* Due to the geometrical way it was defined, the tractrix has the property that the segment of its tangent, between the asymptote and the point of tangency, has constant length.

Apollonius discovered that there are two other non-intersecting circles, C < sub > 4 </ sub > and C < sub > 5 </ sub >, which have the property that they are tangent to all three of the original circles – these are called Apollonian circles ( see Descartes ' theorem ).

An ideal hyperbolic triangle has an angle sum of 0 °, a property it has in common with the triangular area in the Euclidean plane bounded by three tangent circles.

Further, any smooth algebraic variety with the property that every length four subscheme spans P < sup > 3 </ sup > has the property that the tangent and secant lines are pairwise disjoint, except at points of the variety itself.