vanish at infinity造句

• The proof also assumes that the density vanishes at infinity, making it valid only for finite systems.
• Since it is harmonic on ? " c " and vanishes at infinity, it must vanish identically.
• However, provided we require that the potentials vanish at infinity, they can be expressed neatly in terms of fields:
• As these symmetries vanish at infinity, they cannot be constrained by boundary conditions and so must be summed over in the path integral.
• vanishes at infinity, since f ( x ) \ rightarrow 0 as | x | \ rightarrow \ infty, but its support \ mathbb { R } is not compact.
• The set C 0 ( " X " ) of all continuous complex-valued functions that vanish at infinity is a dual; this is shown using the Gelfand representation.
• It is not too difficult to show that the Fourier transform of an L ^ 1 function on G is a bounded continuous function on \ widehat { G } which vanishes at infinity.
• In particular, every element of C _ 0 ( \ mathbb { R } ), the space of continuous functions on \ mathbb { R } that vanish at infinity, is uniformly continuous.
• In other words, a vector field can be constructed with both a specified divergence and a specified curl, and if it also vanishes at infinity, it is uniquely specified by its divergence and curl.
• However, if we are only interested in the subgroup of gauge transformations that vanish at infinity, we may consider the 3-sphere at infinity to be a single point, as the gauge transformations vanish there anyway.
• Of course if n is large the information become more relevant, but the fact that f vanishes at infinity never enters, unless what you want is an asymptotic information on the matrices A n as n ?!  ".
• In this calculation, two integrations by parts show that the first equality holds; the boundary terms are zero when " a " and " b " are finite, or when " f " vanishes at infinity.
• |2 = Further gauge transformations that retain the Coulomb gauge condition might be made with gauge functions that satisfy, but as the only solution to this equation that vanishes at infinity ( where all fields are required to vanish ) is, no gauge arbitrariness remains.
• The following theorem, also referred to as the " Riesz Markov theorem ", gives a concrete realisation of the topological dual space of " C " 0 ( " X " ), the set of continuous functions on " X " which vanish at infinity.
• :Not relevant to your problem since " f " vanishes at infinity and you're probably aware of this anyway, but if " f " is a polynomial then the determinant of the matrix will vanish if it has order 2 or more greater than the order of the polynomial . talk ) 09 : 30, 16 January 2010 ( UTC)