nonvanishing
non-vanishing

Nonetheless, its nonvanishing components look familiar: .

Second class constraints are constraints that have nonvanishing Poisson bracket with at least one other constraint.

A smooth path has differentiable an appropriate number of times (typically ), and a regular path has nonvanishing derivative.

Interestingly, this example has a nonvanishing commutator between and , which means this structure specifies a noncommutative geometry.

The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on even dimensional n-spheres.

In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold.

(Proof idea: the existence of a Lorentzian metric is shown to be equivalent to the existence of a nonvanishing vector field.)

(This extra term is actually physically significant, since it accounts for the nonvanishing angular momentum of the ground-state Bohr orbit in the hydrogen atom, cf. ).

Both metrics are of Petrov-type D with being the only nonvanishing Weyl-NP scalar (as calculated in Boxes A and B).

This fact is immediately convincing to most people, even though they might not recognize the more formal statement of the theorem, that there is no nonvanishing continuous tangent vector field on the sphere.

Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well).

Jürgen Schmidhuber argues that "Although Tegmark suggests that '... all mathematical structures are a priori given equal statistical weight', there is no way of assigning equal nonvanishing probability to all (infinitely many) mathematical structures".

In fact the first nonvanishing term in the Taylor series is cubic in L and the next nonvanishing term is to the fifth power of L. Thus a series expansion for is reasonable.

For example, the Wigner map of the quantum angular-momentum-squared operator L is not just the classical angular momentum squared, but it further contains an offset term 3ħ/2, which accounts for the nonvanishing angular momentum of the ground-state Bohr orbit.

A bit later, in 1985, Shokurov published a paper titled The nonvanishing theorem, which became a cornerstone for the whole MMP as it was used in the proofs of such fundamental theorems as the Cone theorem and the Semi-ampleness theorem.

(Planets' gravitational fields, as of 2011, are well-described by linearized gravity except for Mercury's perihelion precession; so strong-field effects-any effects of gravity beyond lowest nonvanishing order in φ/c-have not been observed even in the gravitational fields of planets and main sequence stars).

In the case of only exclusion restrictions, it must "be possible to form at least one nonvanishing determinant of order M from the columns of A corresponding to the variables excluded a priori from that equation" (Fisher 1966, p. 40), where A is the matrix of coefficients of the equations.

In physical applications, the presence of a nonvanishing sectional curvature does not necessarily indicate the presence of any mass locally; if an initially circular cross-section of a cone of world-lines later becomes elliptical, without changing its volume, then this is due to tidal effects from a mass at some other location.

The support of a, i.e., the set of indices of the nonvanishing coefficients must be a left-finite set, i.e., for any member of , there are only finitely many members of the set less than it; this restriction is necessary in order to make multiplication and division well defined and unique.

Complementary to the definition of degeneracy is that of rank: for a square matrix, the sum of the degeneracy and rank is the order of the matrix; thus The rank is in fact the order of the largest nonvanishing minor of, so that rank 0 implies a null matrix.

He may have even found a way to express Calabi-Yau manifolds in a way that goes beyond a nonvanishing harmonic spinor and, independent of Charlie, published a work of genius entitled Zero Point Energy and Quantum Cosmology, which could provide insight into the cosmological constant problem (episode 3x4,The Mole).

Equivalently, we can find a Newman-Penrose complex null tetrad such that the Ricci-NP scalars (describing any matter or nongravitational fields which may be present in a spacetime) and the Weyl-NP scalars (describing any gravitational field which may be present) each have only one nonvanishing component.